| Name | Category | Theorems |
|---|
cauchy π | CompOp | 14 mathmath: cauchy_sub, cauchy_inv, cauchy_nnratCast, cauchy_natCast, cauchy_neg, cauchy_intCast, cauchy_add, cauchy_zero, cauchy_one, cauchy_ratCast, cauchy_mul, ringEquivCauchy_apply, ext_cauchy_iff, ringEquivCauchy_symm_apply_cauchy
|
commRing π | CompOp | 459 mathmath: Polynomial.Chebyshev.isExtrOn_T_real_iff, Orientation.kahler_map_complex, SchwartzMap.lineDerivOpCLM_eq, ModularGroup.SLOnGLPos_smul_apply, Complex.coe_realPart, SchwartzMap.instLineDerivLeftSMulReal, taylorWithin_succ, MeasureTheory.Measure.addHaar_image_continuousLinearMap, MeasureTheory.charFun_eq_fourierIntegral', Complex.linearEquiv_det_conjLIE, Affine.Simplex.sSameSide_excenter_singleton_point, ZSpan.volume_real_fundamentalDomain, realPart_idem, Complex.kahler, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, SimpleGraph.det_lapMatrix_eq_zero, CliffordAlgebraComplex.ofComplex_conj, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, ModularForm.mul_slash, Polynomial.Chebyshev.complex_ofReal_eval_S, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Complex.real_smul, Polynomial.card_rootSet_le_derivative, realPart_ofReal, Orientation.linearEquiv_det_rotation, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, Orientation.kahler_comp_rightAngleRotation', QuadraticForm.posDef_toMatrix', ZLattice.covolume_eq_det_inv, instTrivialStarReal, instStarOrderedRing, Orientation.volumeForm_robust_neg, imaginaryPart_I_smul, Quaternion.coeComplex_mul, det_fderivPolarCoordSymm, CongruenceSubgroup.exists_Gamma_le_conj', NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, Orientation.volumeForm_neg_orientation, ModularForm.SL_slash, CongruenceSubgroup.conjGL_coe, UpperHalfPlane.im_smul_eq_div_normSq, NumberField.Units.regOfFamily_eq_det, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, MeasureTheory.charFun_eq_fourierIntegral, OrthonormalBasis.det_eq_neg_det_of_opposite_orientation, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, Polynomial.Chebyshev.eval_T_real_node, Polynomial.Chebyshev.complex_ofReal_eval_T, Polynomial.Chebyshev.sumNodes_le_sumNodes_T, UpperHalfPlane.moebius_im, ModularForm.prod_slash, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, vector_fourierIntegral_eq_integral_exp_smul, CongruenceSubgroup.strictPeriods_Gamma0, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, SchwartzMap.fderivCLM_apply, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, smul_map_diagonal_volume_pi, CliffordAlgebraComplex.ofComplex_toComplex, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, CliffordAlgebraComplex.toComplex_comp_ofComplex, OrthonormalBasis.toBasis_adjustToOrientation, ModularForm.prod_slash_sum_weights, Matrix.IsHermitian.rank_eq_rank_diagonal, Polynomial.Chebyshev.eval_T_real_mem_Icc, ModularGroup.coe_apply_complex, instStarModuleNNRealReal, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ModularForm.levelOne_neg_weight_rank_zero, Subgroup.IsArithmetic.is_commensurable, Polynomial.Chebyshev.isLocalMin_T_real, ModularGroup.sl_moeb, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, Affine.Simplex.sSameSide_incenter_point, Quaternion.instCStarRingReal, MeasureTheory.L1.setToL1_smul_left, Quaternion.linearIsometryEquivTuple_symm_apply, Polynomial.card_roots_le_derivative, Convex.closure_subset_interior_image_homothety_of_one_lt, Subgroup.instIsArithmeticRangeSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGL, AffineSubspace.isConnected_setOf_wOppSide, Polynomial.Chebyshev.complex_ofReal_eval_C, Orientation.areaForm_neg_orientation, SchwartzMap.smulLeftCLM_real_smul, Orientation.kahler_eq_zero_iff, Polynomial.Chebyshev.T_real_cos, Subgroup.instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex, Orientation.kahler_swap, Orientation.det_rotation, map_matrix_volume_pi_eq_smul_volume_pi, Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z, Orientation.volumeForm_def, VectorFourier.hasFDerivAt_fourierIntegral, isCusp_SL2Z_iff', VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, Polynomial.Chebyshev.coeff_eq_iff_of_forall_abs_le_one, ModularGroup.denom_apply, Orientation.kahler_comp_rightAngleRotation, selfAdjoint.imaginaryPart_coe, SchwartzMap.laplacianCLM_eq', Quaternion.nnnorm_star, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, InnerProductGeometry.norm_toLp_symm_crossProduct, ZSpan.measureReal_fundamentalDomain, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, NumberField.Units.regulator_eq_det, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, Quaternion.coeComplex_add, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, NumberField.Units.finrank_mul_regOfFamily_eq_det, Subgroup.strictWidthInfty_eq_one_of_T_mem, realPart.norm_le, ZSpan.volume_fundamentalDomain, VectorFourier.differentiable_fourierIntegral, Polynomial.Chebyshev.isLocalMax_T_real, ZSpan.measure_fundamentalDomain, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, Polynomial.Chebyshev.S_two_mul_real_cos, Quaternion.expSeries_odd_of_imaginary, ModularGroup.SL_to_GL_tower, ContDiffMapSupportedIn.uniformSpace_eq_iInf, ModularFormClass.one_mem_strictPeriods_SL2Z, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, VectorFourier.iteratedFDeriv_fourierIntegral, realPart_add_I_smul_imaginaryPart, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin, Quaternion.coeComplex_zero, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, ModularForm.levelOne_weight_zero_rank_one, CongruenceSubgroup.strictWidthInfty_Gamma0, CongruenceSubgroup.IsArithmetic.conj, CliffordAlgebraComplex.ofComplex_I, ModularGroup.lcRow0Extend_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, instIsTopologicalRingReal, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, Quaternion.norm_coe, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, Subgroup.IsArithmetic.isFiniteRelIndexSL, Polynomial.Chebyshev.abs_eval_T_real_le_one, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, orthogonalBilin_innerβ, Polynomial.Chebyshev.sumNodes_eq_sumNodes_T_iff, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, Complex.det_conjAe, Orientation.kahler_neg_orientation, SchwartzMap.smulRightCLM_apply_apply, MeasureTheory.setToFun_smul_left, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, CongruenceSubgroup.isArithmetic_conj_SL2Z, EisensteinSeries.q_expansion_riemannZeta, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, AffineSubspace.isConnected_setOf_wSameSide, Quaternion.exp_of_re_eq_zero, ModularGroup.denom_S, AffineSubspace.isPreconnected_setOf_wOppSide, MeasureTheory.Measure.toSignedMeasure_smul, MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux2, Quaternion.re_exp, MeasureTheory.Measure.addHaar_parallelepiped, LineDeriv.laplacianCLM_eq_sum, Polynomial.Chebyshev.S_two_mul_real_cosh, Polynomial.Chebyshev.one_lt_abs_eval_T_real, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, Orientation.rotation_neg_orientation_eq_neg, Complex.selfAdjointEquiv_apply, Distribution.mapCLM_apply, Quaternion.normSq_eq_norm_mul_self, CStarAlgebra.linear_combination_nonneg, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, star_mul_self_add_self_mul_star, imaginaryPart.norm_le, VectorFourier.fderiv_fourierIntegral, Algebra.norm_complex_eq, realPart_comp_subtype_selfAdjoint, InnerProductGeometry.norm_ofLp_crossProduct, MeasureTheory.integral_posConvolution, Quaternion.expSeries_even_of_imaginary, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, ContDiffMapSupportedIn.locallyConvexSpace, CuspForm.coe_translate, InnerProductSpace.instIsContPerfPairRealInnerβOfCompleteSpace, skewAdjoint.negISMul_apply_coe, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior_faceOpposite, Polynomial.Chebyshev.integral_eval_T_real_measureT_zero, imaginaryPart_realPart, SchwartzMap.fourier_evalCLM_eq, Subgroup.isArithmetic_iff_finiteIndex, imaginaryPart_eq_neg_I_smul_skewAdjointPart, SchwartzMap.evalCLM_apply_apply, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, Polynomial.Chebyshev.rootMultiplicity_T_real, isCusp_SL2Z_iff, realPart_I_smul, MeasureTheory.Measure.toSignedMeasure_add, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, selfAdjoint.realPart_unitarySelfAddISMul, surjective_cosetToCuspOrbit, Polynomial.Chebyshev.U_real_cos, MeasureTheory.Measure.addHaar_image_linearMap, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, Affine.Simplex.sOppSide_excenter_singleton_point, CongruenceSubgroup.strictWidthInfty_Gamma1, OrthonormalBasis.det_adjustToOrientation, Subgroup.instHasDetPlusMinusOneFinOfNatNatRealOfIsArithmetic, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, EuclideanGeometry.oangle_homothety, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, imaginaryPart_apply_coe, EisensteinSeries.eisensteinSeries_SIF_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Quaternion.normSq_exp, UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, imaginaryPart_comp_subtype_selfAdjoint, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Polynomial.Chebyshev.isMinOn_T_real, CongruenceSubgroup.finiteIndex_conjGL, CliffordAlgebraComplex.equiv_symm_apply, Polynomial.Chebyshev.isLocalExtr_T_real_iff, Quaternion.im_exp, SchwartzMap.integral_bilinear_laplacian_right_eq_left, ZLattice.covolume_eq_det_mul_measureReal, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', realPart_surjective, Orientation.kahler_apply_self, Quaternion.coeComplex_coe, Orientation.kahler_rotation_left', CliffordAlgebraComplex.toComplex_ΞΉ, ContDiff.fourierPowSMulRight, Complex.linearEquiv_det_conjAe, EuclideanGeometry.angle_homothety, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, ModularForm.SL_slash_def, Matrix.PosDef.toQuadraticForm', Quaternion.summable_coe, Complex.instStarModuleReal, Orientation.normSq_kahler, VectorFourier.contDiff_fourierIntegral, imaginaryPart_surjective, NumberField.Units.abs_det_eq_abs_det, CongruenceSubgroup.strictPeriods_Gamma1, Algebra.norm_complex_apply, selfAdjoint.realPart_coe, Polynomial.Chebyshev.isMaxOn_T_real, ProperCone.dual_flip_dual, EuclideanGeometry.inversion_mul, Polynomial.Chebyshev.rootMultiplicity_U_real, Quaternion.tsum_coe, map_linearMap_volume_pi_eq_smul_volume_pi, Affine.Simplex.sOppSide_point_excenter_singleton, Quaternion.continuous_im, AffineSubspace.isPreconnected_setOf_wSameSide, Orientation.kahler_rightAngleRotation_left, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, SlashInvariantForm.slash_action_eqn_SL'', CongruenceSubgroup.strictWidthInfty_Gamma, SchwartzMap.tsupport_fderivCLM_subset, bilinFormOfRealInner_orthogonal, Orientation.kahler_rotation_left, OrthonormalBasis.orthonormal_adjustToOrientation, EisensteinSeries.q_expansion_bernoulli, Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zero, StarModule.complexToReal, Quaternion.inner_def, linearEquiv_det_rotation, Complex.coe_selfAdjointEquiv, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, imaginaryPart_ofReal, ModularGroup.im_smul_eq_div_normSq, CliffordAlgebraComplex.equiv_apply, Polynomial.Chebyshev.T_real_cosh, CongruenceSubgroup.mem_conjGL, MeasureTheory.Measure.addHaar_preimage_linearMap, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, Orientation.kahler_mul, SchwartzMap.instLocallyConvexSpace, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, ProperCone.dual_dual_flip, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Algebra.trace_complex_apply, ArchimedeanClass.ofArchimedean_stdPart, Orientation.rightAngleRotation_trans_neg_orientation, Orientation.volumeForm_robust', Quaternion.inner_self, CongruenceSubgroup.strictPeriods_Gamma, Polynomial.Chebyshev.one_le_abs_eval_T_real, ModularGroup.tendsto_lcRow0, cosetToCuspOrbit_apply_mk, Quaternion.norm_exp, Quaternion.continuous_coe, ContinuousMap.comp_attachBound_mem_closure, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, AffineSubspace.isPreconnected_setOf_sOppSide, Complex.selfAdjointEquiv_symm_apply, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, Polynomial.Chebyshev.roots_T_real, SchwartzMap.fderivCLM_fourier_eq, Orientation.volumeForm_zero_neg, Polynomial.Chebyshev.complex_ofReal_eval_U, det_fderivPiPolarCoordSymm, UpperHalfPlane.det_J, AffineSubspace.isConnected_setOf_sOppSide, ModularGroup.coe_one, Polynomial.Chebyshev.one_lt_eval_T_real, realPart_imaginaryPart, Subgroup.strictPeriods_SL2Z, CongruenceSubgroup.mem_conjGL', ContDiffPointwiseHolderAt.fderiv, fourierIntegral_continuousLinearMap_apply', skewAdjointPart_eq_I_smul_imaginaryPart, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, AlternatingMap.measure_def, Polynomial.Chebyshev.one_le_eval_T_real, BumpCovering.exists_finset_toPOUFun_eventuallyEq, Polynomial.Chebyshev.eval_T_real_eq_one_iff, ModularForm.prod_fintype_slash, Polynomial.Chebyshev.U_real_cosh, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Convex.subset_interior_image_homothety_of_one_lt, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, SlashInvariantForm.vAdd_width_periodic, TestFunction.instLocallyConvexSpaceReal, Orientation.kahler_apply_apply, imaginaryPart_imaginaryPart, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_imageβ, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, ModularForm.slash_def, Affine.Simplex.sSameSide_point_excenter_singleton, hasFDerivAt_integral_of_dominated_of_fderiv_le'', Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, ModularForm.is_invariant_one', EisensteinSeries.eisensteinSeriesSIF_apply, det_rotation, instContinuousStarReal, imaginaryPart_smul, CliffordAlgebraComplex.toComplex_involute, VectorFourier.fourierIntegral_probChar, ContinuousMap.polynomial_comp_attachBound, Orientation.kahler_rotation_right, CliffordAlgebraComplex.toComplex_ofComplex, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, realPart_apply_coe, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, OrthonormalBasis.same_orientation_iff_det_eq_det, ContDiffMapSupportedIn.continuous_iff_comp, Orientation.finOrthonormalBasis_orientation, CliffordAlgebraComplex.reverse_eq_id, SchwartzMap.fourier_fderivCLM_eq, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_real, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Subgroup.IsArithmetic.finiteIndex_comap, Quaternion.coe_ofComplex, Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero, TestFunction.instContinuousSMulReal, ModularForm.SL_slash_apply, Zsqrtd.toReal_apply, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_real, ContinuousMap.polynomial_comp_attachBound_mem, Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange, Polynomial.Chebyshev.isLocalExtr_T_real, ContDiffPointwiseHolderAt.iteratedFDeriv, EisensteinSeries.eisSummand_SL2_apply, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, OrthonormalBasis.orientation_adjustToOrientation, Quaternion.hasSum_expSeries_of_imaginary, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, Polynomial.Chebyshev.isExtrOn_T_real, IsSelfAdjoint.coe_realPart, CliffordAlgebraComplex.ofComplex_comp_toComplex, realPart_smul, Quaternion.instNormOneClassReal, Convex.closure_subset_image_homothety_interior_of_one_lt, ModularGroup.det_coe, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, zero_at_infty_vector_fourierIntegral, Orientation.kahler_rightAngleRotation_right, NumberField.Units.finrank_mul_regulator_eq_det, Quaternion.linearIsometryEquivTuple_apply, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, Orientation.norm_kahler, MeasureTheory.weightedSMul_smul_measure, ProperCone.innerDual_toSubmodule, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, NumberField.Units.regulator_eq_det', ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, Polynomial.Chebyshev.abs_eval_T_real_le_one_iff, skewAdjoint.I_smul_neg_I, CongruenceSubgroup.IsCongruenceSubgroup.conjGL, Orientation.oangle_neg_orientation_eq_neg, Quaternion.coeComplex_one, Quaternion.hasSum_coe, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, OrthonormalBasis.abs_det_adjustToOrientation, ModularGroup.coeHom_apply, Subgroup.strictWidthInfty_SL2Z, IsSelfAdjoint.imaginaryPart, volume_preserving_transvectionStruct, VectorFourier.fourierIntegral_fderiv, Quaternion.coe_real_complex_mul, NumberField.Units.regOfFamily_eq_det', Polynomial.card_roots_toFinset_le_derivative, SchwartzMap.denseRange_toLpCLM, Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_one, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, fourierIntegral_continuousMultilinearMap_apply', Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, UpperHalfPlane.smulAux'_im, Orientation.rightAngleRotation_neg_orientation, MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar, Quaternion.continuous_normSq, Subgroup.IsArithmetic.conj, Complex.det_conjLIE, Polynomial.Chebyshev.C_two_mul_real_cos, Polynomial.Chebyshev.roots_U_real, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, Quaternion.exp_coe, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, AffineSubspace.isConnected_setOf_sSameSide, Quaternion.exp_eq, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, Complex.ofReal_choose, ModularGroup.smul_eq_lcRow0_add, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, ContDiffMapSupportedIn.structureMapLM_eq, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, Quaternion.nnnorm_coe, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, SlashInvariantForm.T_zpow_width_invariant, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, ZLattice.covolume_eq_det, ModularForm.slash_apply, Affine.Simplex.sSameSide_point_incenter, Polynomial.Chebyshev.C_two_mul_real_cosh, CliffordAlgebraComplex.reverse_apply, AffineSubspace.isPreconnected_setOf_sSameSide, Quaternion.norm_star, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, UpperHalfPlane.petersson_slash, MeasureTheory.Measure.addHaar_image_homothety
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decidableEq π | CompOp | 32 mathmath: Complex.log_conj_eq_ite, RCLike.sqrt_eq_ite, OnePoint.isBoundedAt_iff_exists_SL2Z, IsCusp.smul_of_mem, OnePoint.isZeroAt_iff_exists_SL2Z, Complex.log_inv_eq_ite, ENNReal.top_rpow_def, isCusp_SL2Z_iff', Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, Complex.inv_cpow_eq_ite', Complex.inv_cpow_eq_ite, OnePoint.IsZeroAt.smul_iff, Complex.arg_conj, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, Complex.conj_cpow_eq_ite, ENNReal.zero_rpow_def, WithLp.prod_dist_eq_card, OnePoint.IsBoundedAt.smul_iff, WithLp.prod_norm_eq_card, BoxIntegral.Prepartition.splitMany_insert, BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le, rpow_def_of_nonneg, Complex.arg_inv, cosetToCuspOrbit_apply_mk, Polynomial.Chebyshev.roots_T_real, sinc_apply, rpow_def_of_nonpos, Matrix.IsHermitian.rank_eq_card_non_zero_eigs, Polynomial.card_roots_toFinset_le_derivative, Polynomial.Chebyshev.roots_U_real, IsCusp.smul, HurwitzZeta.hasSum_int_evenKernelβ
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decidableLE π | CompOp | 20 mathmath: intervalIntegral.intervalIntegral_eq_integral_uIoc, ProbabilityTheory.cdf_expMeasure_eq, ContinuousMap.HomotopyRel.trans_apply, ContMDiff.piecewise_Iic, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, Path.Homotopy.hcomp_apply, ProbabilityTheory.exponentialPDF_eq, ContinuousMap.HomotopyWith.trans_apply, RCLike.sqrt_eq_real_add_ite, unitInterval.qRight_zero_right, Path.Homotopy.trans_apply, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, ContinuousMap.Homotopy.trans_apply, ProbabilityTheory.paretoPDF_eq, ProbabilityTheory.exponentialCDFReal_eq, Complex.sqrt_eq_real_add_ite, Path.trans_apply, ProbabilityTheory.gammaPDF_eq, MeasureTheory.JordanDecomposition.real_smul_def, ENNReal.log_ofReal
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decidableLT π | CompOp | 52 mathmath: HurwitzZeta.hasSum_int_hurwitzZetaOdd, hasSum_mellin_pi_mul_sq', ProbabilityTheory.betaPDF_eq, deriv_abs, Affine.Simplex.sign_excenterWeights_singleton_pos, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Affine.Simplex.sign_touchpointWeights_empty, HasStrictFDerivAt.abs, ENNReal.top_rpow_def, hasDerivWithinAt_abs, NormedSpace.normalize_smul, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, isMIntegralCurveOn_piecewise, HasFDerivAt.abs, HasFDerivWithinAt.abs, sum_div_nat_floor_pow_sq_le_div_sq, ENNReal.mul_rpow_eq_ite, Icc_chartedSpaceChartAt, EReal.sign_coe, Affine.Simplex.sign_excenterWeights_singleton_neg, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, eventually_nhdsWithin_sign_eq_of_deriv_neg, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, hasStrictDerivAt_abs, Orientation.oangle_sign_smul_left, AddCircle.coe_real_preimage_closedBall_inter_eq, Orientation.oangle_sign_smul_add_smul_smul_add_smul, eventually_nhdsWithin_sign_eq_of_deriv_pos, UpperHalfPlane.ofComplex_apply_eq_ite, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, ENNReal.zero_rpow_def, Affine.Simplex.ExcenterExists.sign_touchpointWeights, Affine.Simplex.sign_touchpointWeights_singleton_pos, Orientation.oangle_sign_smul_right, signedDist_smul, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, Affine.Simplex.sign_touchpointWeights_singleton_neg, ENNReal.coe_rpow_def, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, Affine.Simplex.sign_signedInfDist_touchpoint_empty, hasDerivAt_abs, Affine.Simplex.sign_excenterWeights_empty, Affine.Simplex.ExcenterExists.signedInfDist_excenter, eqOn_piecewise_of_isMIntegralCurveOn_Ioo, Angle.sign_toReal, sum_div_pow_sq_le_div_sq, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, Orientation.oangle_sign_smul_add_smul_right, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, Orientation.oangle_sign_smul_add_smul_left
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equivCauchy π | CompOp | β |
instAdd π | CompOp | 1272 mathmath: AddGroupNorm.add_apply, cos_add_nat_mul_pi, arctan_eq_arccos, MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnreal, HurwitzZeta.hasSum_int_hurwitzZetaOdd, norm_sub_sq_real, Circle.periodic_exp, MeasureTheory.setToFun_add_left, le_log_one_add_of_nonneg, EuclideanGeometry.dist_smul_vadd_sq, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, cos_pi_div_five, dist_triangle, rpow_add_of_nonneg, Complex.mul_im, gold_sq, norm_lt_of_mem_ball', sin_add_sin, Bundle.ContMDiffRiemannianMetric.contMDiff, expNear_succ, goldenConj_mul_fib_succ_add_fib, CircleDeg1Lift.translationNumber_mul_of_commute, QuotientAddGroup.exists_norm_mk_lt, InformationTheory.integral_llr_add_mul_log_nonneg, Angle.toReal_add_of_sign_eq_neg_sign, HolderTriple.inv_add_inv_eq_inv, sin_arctan, deriv_arctan, MeasureTheory.levyProkhorovDist_triangle, HasStrictDerivAt.rpow, CircleDeg1Lift.translate_inv_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, IsPicardLindelof.of_contDiffAt_one, AddDissociated.randomisation, ProbabilityTheory.measure_ge_le_exp_cgf, intervalIntegral.intervalIntegrable_one_div_one_add_sq, SzemerediRegularity.energy_increment, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, hasDerivAt_sqrt_mul_log, cos_add_pi, InnerProductGeometry.angle_add_angle_sub_add_angle_sub_eq_pi, arctan_eq_arcsin, HurwitzZeta.hasSum_int_hurwitzZetaEven, intervalIntegral.inv_smul_integral_comp_div_add, hasDerivAt_sigmoid, UnitAddCircle.lintegral_preimage, gold_add_goldConj, rpow_add_natCast', CircleDeg1Lift.map_add_nat, sqrt_one_add_le, sin_add_two_pi, Complex.norm_le_abs_re_add_abs_im, sinh_add, ProbabilityTheory.mgf_const_add, cos_eq_zero_iff, young_inequality, norm_add_eq_iff_real, UnitAddCircle.intervalIntegral_preimage, BoxIntegral.unitPartition.mem_box_iff', log_div_le_sum_range_add, real_sqrt_le_nat_sqrt_succ, IsLprojection.Lnorm, countingFunction_finsum_eq_finsum_add, Complex.add_im, Wbtw.dist_add_dist, ProbabilityTheory.covariance_add_left, MeasureTheory.measureReal_symmDiff_le, Complex.equivRealProdAddHom_symm_apply, sin_periodic, NumberField.mixedEmbedding.convexBodySumFun_add_le, ValueDistribution.characteristic_mul_top_le, Complex.locally_lipschitz_exp, dist_sq_lineMap_lineMap_of_inner_eq_zero, integral_const_on_unit_interval, InformationTheory.mul_log_le_klDiv, isMIntegralCurve_comp_add, CircleDeg1Lift.commute_nat_add, ENNReal.rpow_add, Gamma_nat_add_half, posLog_norm_add_le, Metric.cthickening_cthickening_subset, CircleDeg1Lift.iterate_pos_le_iff, LiouvilleWith.rat_add_iff, goldConj_sq, dist_triangle4_right, Metric.hausdorffDist_triangle, one_add_mul_le_cos, Affine.Simplex.dist_point_faceOppositeCentroid, MeasureTheory.lpNorm_add_le', Polynomial.logMahlerMeasure_C_mul, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, ValueDistribution.logCounting_zero_mul_le, AddCircle.coe_real_preimage_closedBall_eq_iUnion, CircleDeg1Lift.iterate_pos_lt_iff, EuclideanGeometry.Sphere.IsExtTangent.dist_center, Ioo_eq_ball, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ENNReal.toReal_add, MeasureTheory.Integrable.hasSum_intervalIntegral, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, summable_log_one_add_of_summable, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, tsum_eq_tsum_fourierIntegral_of_rpow_decay_of_summable, WithLp.prod_norm_eq_idemFst_of_L1, hasDerivAt_bernoulliFun, bernoulliFun_two, ValueDistribution.proximity_zero_mul_le, ProbabilityTheory.sum_prob_mem_Ioc_le, BoxIntegral.unitPartition.box_upper, add_sqrt_self_sq_sub_one_inv, derivWithin_arctan, closedBall_sub_ball, TopologicalSpace.Opens.CompleteCopy.dist_eq, HasGradientAt.hasDerivAt', SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, tendsto_one_add_pow_exp_of_tendsto, integral_pow, summable_one_div_nat_add_rpow, Height.logHeightβ_sum_le, Height.logHeightβ_add_le, add_neg_lt_sSup, hasSum_log_one_add_inv, schnirelmannDensity_le_iff_forall, HasConstantSpeedOnWith.ratio, norm_add_pow_two_real, EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi, tan_sub', ProbabilityTheory.cgf_gaussianReal, norm_sub_mul_self, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_compProd, monomial_has_deriv_aux, norm_le_norm_add_const_of_dist_le, Archimedean.embedRealFun_add, hasDerivAt_mul_log, setOf_liouvilleWith_subset_aux, Metric.dist_lt_add_of_nonempty_ball_inter_ball, dist_le_norm_add_norm, ConvexOn.univ_sSup_of_countable_affine_eq, cos_le_one_div_sqrt_sq_add_one, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, cfcβHom_nnreal_eq_restrict, Height.logHeightβ_sub_le, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, hasDerivWithinAt_abs_pos, tendsto_mul_log_one_add_of_tendsto, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, antideriv_bernoulliFun, NNReal.coe_add, OrthogonalFamily.norm_sq_diff_sum, norm_sub_mul_le', CircleDeg1Lift.translationNumber_eq_rat_iff, HolderTriple.one_div_eq, Complex.normSq_mk, integral_exp_neg_mul_rpow, RCLike.realRingEquiv_symm_apply, norm_div_le, ball_eq_Ioo, AddGroupNorm.coe_add, cos_add_int_mul_two_pi, Metric.cthickening_thickening_subset, parallelogram_law_with_norm, norm_le_norm_add_norm_sub', InformationTheory.klFun_apply, Complex.integral_rpow_mul_exp_neg_rpow, integral_Ioi_rpow_of_lt, Complex.arg_mul_eq_add_arg_iff, logb_mul, Circle.exp_eq_exp, Complex.volume_sum_rpow_le, signedDist_triangle, Irrational.natCast_add, Complex.norm_log_one_add_le, Metric.iUnion_ball_nat_succ, closedBall_add_closedBall, norm_le_add_norm_add, HasDerivAt.arctan, dist_sub_sub_le, toNNReal_add, Irrational.intCast_add, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, RCLike.norm_sq_eq_def_ax, BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSet, MeromorphicOn.extract_zeros_poles_log, ValueDistribution.logCounting_add_top_le, integral_rpow_mul_exp_neg_rpow, AddCircle.scaled_exp_map_periodic, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, norm_addβ_le, one_add_rpow_hasFPowerSeriesOnBall_zero, sin_add_int_mul_pi, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, integral_cos_pow, HasFDerivAt.arctan, NumberField.mixedEmbedding.convexBodySumFun_apply', Stirling.log_stirlingSeq_diff_hasSum, MeasureTheory.measureReal_symmDiff_eq, sin_antiperiodic, log_list_prod, Polynomial.logMahlerMeasure_of_degree_eq_one, norm_sub_pow_two_real, Asymptotics.IsEquivalent.add_add_of_nonneg, Polynomial.cyclotomic_eval_lt_add_one_pow_totient, RCLike.mul_im_ax, intervalIntegral.intervalIntegrable_inv_one_add_sq, artanh_eq_half_log, LipschitzWith.le_add_mul, cos_add_two_pi, norm_le_norm_add_norm_sub, EisensteinSeries.r1_aux_bound, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_comp, ValueDistribution.logCounting_mul_zero_eventuallyLE, norm_sub_sq, WithLp.prod_dist_eq_of_L2, WithLp.prod_norm_eq_of_nat, stereoInvFunAux_apply, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, integrable_one_add_norm, Gamma_mul_Gamma_add_half, HasStrictFDerivAt.arsinh, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, integrableOn_add_rpow_Ioi_of_lt, Polynomial.logMahlerMeasure_mul_eq_add_logMahelerMeasure, closedBall_eq_Icc, sin_add_nat_mul_pi, NNReal.rpow_add_intCast', singleton_eq_inter_Icc, MeasureTheory.Measure.haar.prehaar_sup_le, CircleDeg1Lift.map_one_add, AddCircle.intervalIntegral_preimage, Stirling.le_log_factorial_stirling, IntervalIntegrable.comp_sub_right, ValueDistribution.logCounting_mul_top_eventuallyLE, MeasureTheory.probReal_add_probReal_compl, IsMIntegralCurve.periodic_xor_injective, tsum_geometric_le_of_norm_lt_one, Complex.arg_of_re_neg_of_im_nonneg, ZLattice.tsum_norm_rpow_le, integral_sin_sq, norm_add_eq_sqrt_iff_real_inner_eq_zero, hasDerivAt_arsinh, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, Angle.cos_sq_add_sin_sq, HasStrictDerivAt.arctan, CircleDeg1Lift.map_le_of_map_zero, norm_sub_le, CircleDeg1Lift.le_map_of_map_zero, gronwallBound_of_K_ne_0, exp_list_sum, isBigO_norm_Icc_restrict_atTop, sin_sq_arctan, hasDerivAt_abs_neg, intervalIntegral.integral_comp_add_div, norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero, Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure, norm_le_of_mem_closedBall, cos_add_cos, Nat.closedBall_eq_Icc, hasDerivWithinAt_abs, ProbabilityTheory.IndepFun.variance_fun_add, AkraBazziRecurrence.sumTransform_def, dist_div_div_le, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, CircleDeg1Lift.dist_map_map_zero_lt, Tactic.ComputeAsymptotics.Majorized.mul, InformationTheory.hasDerivAt_klFun, integral_cos_pow_aux, negMulLog_mul, InformationTheory.toReal_klDiv, UpperHalfPlane.vadd_re, MeasureTheory.lpNorm_add_le, ProbabilityTheory.covariance_add_const_right, dist_triangle4, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, MeasureTheory.integral_exp_tilted, cos_pi_div_sixteen, CircleDeg1Lift.lt_map_of_nat_lt_translationNumber, MeasureTheory.llr_tilted_right, one_add_tan_sq_mul_cos_sq_eq_one, dist_le_of_approx_trajectories_ODE, holderTriple_iff, arctan_add_arctan_lt_pi_div_two, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, Angle.coe_add, Function.hasTemperateGrowth_iff_isBigO, hasSum_log_one_add, CircleDeg1Lift.map_int_of_map_zero, AkraBazziRecurrence.GrowsPolynomially.add, HasDerivWithinAt.norm_sq, Complex.norm_add_eq, HasGradientAtFilter.hasDerivAtFilter', Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, ProbabilityTheory.covariance_add_const_left, inv_one_add_tan_sq, exp_arcosh, Complex.integral_exp_neg_rpow, bernoulliFun_eval_one, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, Complex.norm_log_sub_logTaylor_le, LiouvilleWith.int_add, ball_add_ball, AddCircle.add_projection_respects_measure, InnerProductGeometry.norm_add_eq_add_norm_of_angle_eq_zero, controlled_closure_of_complete, LiouvilleWith.add_rat, tan_div_sqrt_one_add_tan_sq, MeasureTheory.Measure.haar.prehaar_sup_eq, eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo, closedBall_add_ball, ZLattice.tsumNormRPowBound_spec, WithCStarModule.prod_norm_le_norm_add, sigmoid_def, UpperHalfPlane.dist_triangle, isAddFundamentalDomain_Ioc, norm_le_add_norm_add', one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, isMIntegralCurveOn_comp_add, AkraBazziRecurrence.one_add_smoothingFn_le_two, MeasureTheory.lpNorm_le_add_lpNorm_add, TrivSqZeroExt.norm_def, HurwitzZeta.hasSum_nat_hurwitzZetaEven, fib_golden_exp', MeasureTheory.volume_sum_rpow_lt, hasDerivAt_abs_rpow, Irrational.add_natCast, ZetaAsymptotics.term_tsum_of_lt, ENNReal.ofReal_add_le, LiouvilleWith.add_rat_iff, Metric.hausdorffDist_triangle', dist_midpoint_midpoint_le, deriv_Gamma_nat, trapezoidal_integral_ext, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, MeasureTheory.integrable_add_iff_of_nonneg, EuclideanGeometry.angle_le_angle_add_angle, BoxIntegral.unitPartition.mem_box_iff, stereoInvFun_apply, CircleDeg1Lift.map_map_zero_lt, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi, Complex.normSq_add, Polynomial.Chebyshev.S_two_mul_real_cos, MeasureTheory.lintegral_mul_prod_lintegral_pow_le, integrable_rpow_neg_one_add_norm_sq, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, NNReal.rpow_add_natCast', hasDerivAt_qaryEntropy, AkraBazziRecurrence.GrowsPolynomially.add_isLittleO, UpperHalfPlane.cosh_dist, le_rpow_add, MeasureTheory.measureReal_union_le, Monotone.ae_hasDerivAt, PseudoMetricSpace.dist_triangle, Int.ball_eq_Ioo, real_sqrt_lt_nat_sqrt_succ, PiNat.dist_triangle, Complex.norm_add_eq_iff, norm_le_insert', ConvexOn.sSup_of_countable_affine_eq, MeasureTheory.measureReal_unionβ', UpperHalfPlane.dist_coe_center, norm_sub_eq_sqrt_iff_real_inner_eq_zero, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, tendsto_measure_Icc, sqrtTwoAddSeries_two, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, norm_le_norm_add_norm_div', ProbabilityTheory.gaussianReal_add_const, Complex.arg_neg_eq_arg_add_pi_iff, Chebyshev.primeCounting_eq_theta_div_log_add_integral, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, ArchimedeanClass.stdPart_add, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, Metric.uniformity_basis_dist_inv_nat_succ, ModularGroup.re_T_smul, LiouvilleWith.add_int, ProbabilityTheory.variance_add_const, Metric.dist_le_infDist_add_diam, Metric.diam_thickening_le, ValueDistribution.proximity_sum_top_le, Nat.realSqrt_mem_Ico, HurwitzKernelBounds.F_nat_one_le, ProbabilityTheory.variance_sub, CircleDeg1Lift.lt_map_of_int_lt_translationNumber, cthickening_thickening, MeasureTheory.SimpleFunc.norm_approxOn_yβ_le, CircleDeg1Lift.tendsto_translation_number', MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, ball_eq_openSegment, Complex.HadamardThreeLines.norm_invInterpStrip, dist_div_div_le_of_le, intervalIntegral.integral_comp_add_mul, Complex.ofReal_add, WithLp.prod_norm_eq_add, tsum_eq_tsum_fourier_of_rpow_decay_of_summable, MeasureTheory.Measure.haar.addCHaar_sup_le, IsContMDiffRiemannianBundle.exists_contMDiff, Complex.add_re, Seminorm.coe_add, MeasureTheory.volume_sum_rpow_le, ofDigits_eq_sum_add_ofDigits, dist_triangle_right, HasDerivWithinAt.arsinh, MeasureTheory.measureReal_add_apply, exists_natCast_add_one_lt_pow_of_one_lt, SeminormedSpace.Core.norm_triangle, ball_add_closedBall, integral_rpow_mul_exp_neg_mul_rpow, ProbabilityTheory.paretoPDF_of_le, gronwallBound_K0, CircleDeg1Lift.map_nat_add, le_rpow_one_add_norm_iff_norm_le, Complex.normSq_sub, ProbabilityTheory.covariance_const_add_left, ProbabilityTheory.mgf_add_measure, MeasureTheory.integral_llr_tilted_left, CircleDeg1Lift.commute_add_int, InformationTheory.integral_klFun_rnDeriv, MeasureTheory.Measure.haar.addPrehaar_sup_eq, LiouvilleWith.add_int_iff, norm_add_le, leftDeriv_mul_log, exists_nat_abs_mul_sub_round_le, pow_mul_norm_iteratedFDeriv_fourier_le, LiouvilleWith.int_add_iff, ConvexOn.real_univ_sSup_of_countable_affine_eq, Set.Icc.coe_convexCombo, AddGroupSeminorm.add_bddBelow_range_add, AkraBazziRecurrence.asympBound_def, ProbabilityTheory.integral_condVar_add_variance_condExp, ProbabilityTheory.Kernel.HasSubgaussianMGF.add, UniformConcaveOn.sub, Hyperreal.IsSt.add, ValueDistribution.proximity_mul_zero_le, InformationTheory.klDiv_of_ac_of_integrable, RCLike.ofReal_add, MeasureTheory.lpNorm_sub_le, tendsto_rpow_div_mul_add, exp_abs_le, abs_log_sub_add_sum_range_le, UniformSpace.ofDist_aux, InformationTheory.klDiv_def, WithLp.prod_norm_eq_add_idemFst, BoxIntegral.Box.mem_splitCenterBox, sin_add, InnerProductSpace.volume_ball, cosh_sq, MeasureTheory.measureReal_inter_add_diffβ, ProbabilityTheory.covariance_add_right, deriv_mulExpNegMulSq, cos_pi_div_eight, tan_sq_div_one_add_tan_sq, quotient_norm_add_le, ValueDistribution.proximity_add_top_le, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, NumberField.mixedEmbedding.normAtPlace_add_le, deriv_qaryEntropy, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, deriv_arctan, dist_mul_mul_le_of_le, MeasureTheory.tilted_tilted, GroupSeminorm.inf_apply, HasDerivWithinAt.rpow, CStarModule.norm_triangle, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, Submodule.norm_sq_eq_add_norm_sq_projection, goldenRatio_mul_fib_succ_add_fib, exp_arsinh, Complex.equivRealProdAddHom_symm_apply_re, integral_sin_pow_aux, dist_triangle_left, Circle.exp_add_two_pi, harmonic_le_one_add_log, RCLike.sqrt_eq_real_add_ite, integral_div_sq_add_sq, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub', ProbabilityTheory.mgf_fun_id_gaussianReal, Polynomial.Chebyshev.S_two_mul_real_cosh, MeasureTheory.measureReal_add_measureReal_complβ, IsMIntegralCurve.comp_add, ContinuousLinearMap.rayleighQuotient_add, Complex.equivRealProdAddHom_symm_apply_im, exp_mul_le_cosh_add_mul_sinh, AddGroupSeminorm.coe_add, Orientation.areaForm'_apply, HurwitzZeta.hasSum_int_evenKernel, NormedAddGroupHom.IsQuotient.norm_lift, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, EuclideanGeometry.exterior_angle_eq_angle_add_angle, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, Besicovitch.SatelliteConfig.inter', ConvexOn.sSup_of_nat_affine_eq, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', Seminorm.ball_add_ball_subset, CircleDeg1Lift.commute_add_nat, sum_range_le_log_div, cos_eq_cos_iff, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, hasDerivWithinAt_taylor_coeff_within, Complex.arg_neg_eq_arg_add_pi_of_im_neg, ProbabilityTheory.gaussianReal_conv_gaussianReal, intervalIntegral.inv_mul_integral_comp_add_div, AkraBazziRecurrence.strictAntiOn_one_add_smoothingFn, InnerProductGeometry.angle_add_angle_eq_pi_of_angle_eq_pi, tendsto_integral_mul_one_add_inv_smul_sq_pow, UniformConvexOn.add, MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_sub, integral_sin_pow_even_mul_cos_pow_even, tendsto_nat_mul_log_one_add_of_tendsto, sameRay_iff_norm_add, mk_add, NormedAddGroupHom.opNorm_add_le, Metric.dist_lt_add_of_nonempty_closedBall_inter_ball, Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots, ValueDistribution.characteristic_add_top_eventuallyLE, Lp_add_le_tsum_of_nonneg, ProbabilityTheory.gaussianPDFReal_sub, hasStrictDerivAt_abs, norm_mul_le_of_le', cos_int_mul_two_pi_add_pi, strongConcaveOn_iff_convex, ModularGroup.re_T_zpow_smul, ProbabilityTheory.Fernique.normThreshold_eq, sin_eq_sin_iff, CircleDeg1Lift.le_map_map_zero, Asymptotics.IsBigOWith.triangle, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, tendsto_measure_Icc_nhdsWithin_right, Complex.ofReal_comp_add, irrational_add_intCast_iff, Seminorm.add_apply, signedDist_vadd_right, HolderTriple.of_pos, HasStrictFDerivAt.arctan, ProbabilityTheory.gaussianReal_const_add, CFC.monotoneOn_one_sub_one_add_inv_real, Gamma_add_one, NNReal.rpow_add_natCast, Complex.log_mul_eq_add_log_iff, ContinuousLinearMap.opNorm_add_le, StieltjesFunction.add_apply, InnerProductGeometry.angle_le_angle_add_angle, Complex.integral_exp_neg_mul_rpow, ValueDistribution.logCounting_add_top_eventuallyLE, two_mul_cos_mul_cos, tendsto_mul_log_one_add_div_atTop, sqrtTwoAddSeries_succ, taylorWithinEval_succ, HasDerivAt.norm_sq, ZetaAsymptotics.term_one, rpow_one_add', ValueDistribution.logCounting_mul_top_le, norm_sup_le_add, thickening_closedBall, fderiv_arctan, dist_sub_sub_le_of_le, Circle.exp_add, IntervalIntegrable.comp_add_right, finite_integral_one_add_norm, toNNReal_add_le, cos_add, norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, ValueDistribution.proximity_mul_top_le, CircleDeg1Lift.translate_apply, ContinuousMultilinearMap.opNorm_add_le, Int.toNat_add_toNat_neg_eq_norm, InformationTheory.mul_log_le_toReal_klDiv, ValueDistribution.characteristic_mul_zero_eventuallyLE, InnerProductGeometry.norm_sub_eq_add_norm_iff_angle_eq_pi, circleAverage_eq_integral_add, ValueDistribution.characteristic_top_mul_le, summable_Lp_add_of_nonneg, Gamma_nat_add_one_add_half, harmonic_floor_le_one_add_log, Polynomial.Chebyshev.rootMultiplicity_T_real, tan_periodic, periodic_circleMap, HasDerivWithinAt.arctan, ValueDistribution.logCounting_top_mul_eventually_le, HurwitzKernelBounds.F_int_eq_of_mem_Icc, intervalIntegral.mul_integral_comp_add_mul, NNReal.rpow_add', Complex.volume_sum_rpow_lt, dist_add_add_le, ProbabilityTheory.IndepFun.cgf_add, hasStrictDerivAt_arsinh, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, LiouvilleWith.add_nat, integral_univ_inv_one_add_sq, ProbabilityTheory.add_half_inf_sub_mem_Ioo, multipliable_one_add_of_summable, HolderConjugate.mul_eq_add, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, integral_exp_neg_rpow, RCLike.realLinearIsometryEquiv_symm_apply, Polynomial.Chebyshev.U_real_cos, WithLp.prod_norm_eq_of_L1, inv_sqrt_two_sub_one, NNReal.rpow_add, norm_mulβ_le', sin_add_pi_div_two, MeasureTheory.measureReal_union_add_interβ, rpow_add_one, closedBall_eq_segment, Angle.sin_add, dist_add_add_le_of_le, unique_unit_speed, WithLp.prod_dist_eq_add, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Nat.realSqrt_lt_ratSqrt_add_inv_prec, add_rpow_le_rpow_add, Complex.HadamardThreeLines.sSupNormIm_eps_pos, ProbabilityTheory.mgf_add_const, Complex.cpow_inv_two_re, ZetaAsymptotics.zeta_limit_aux1, Tactic.ComputeAsymptotics.Majorized.add, Chebyshev.psi_eq_theta_add_sum_theta, EisensteinSeries.r1_eq, MeasureTheory.GridLines.T_empty, Complex.div_re, MeasureTheory.integrable_add_iff_of_nonpos, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, HasDerivAt.arsinh, UniformConcaveOn.add, inv_logb_mul_base, ProbabilityTheory.variance_add_prod, Metric.thickening_ball, rightDeriv_mul_log, dist_add_dist_eq_iff, AkraBazziRecurrence.asympBound_def', ValueDistribution.characteristic_sum_top_le, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, circleMap_neg_radius, Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, goldenRatio_add_goldenConj, WithLp.unitization_norm_def, hasStrictDerivAt_abs_neg, cosh_add_sinh, InnerProductGeometry.angle_eq_angle_add_angle_iff, EReal.toReal_add, HasDerivAt.rpow, arctan_inv_2_add_arctan_inv_3, cthickening_closedBall, InnerProductSpaceable.parallelogram_identity, ValueDistribution.characteristic_add_top_le, MeasureTheory.Measure.haar.chaar_sup_eq, norm_le_norm_sub_add, AddGroupSeminorm.add_le', MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, binEntropy_eq_negMulLog_add_negMulLog_one_sub', LipschitzOnWith.le_add_mul, trapezoidal_integral_one, ConvexOn.real_univ_sSup_affine_eq, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, irrational_ratCast_add_iff, circleMap_zero_mul, tan_add_int_mul_pi, Irrational.ratCast_add, ValueDistribution.characteristic_mul_zero_le, ProbabilityTheory.variance_fun_sub, WithLp.prod_dist_eq_of_L1, WithLp.prod_dist_eq_card, ZetaAsymptotics.term_sum_of_lt, disjoint_ball_closedBall_iff, mul_add_one_le_add_one_pow, deriv_mul_log, rpowIntegrandββ_eq_pow_div, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, norm_sub_sq_eq_norm_sq_add_norm_sq_real, ProbabilityTheory.gaussianReal_add_gaussianReal_of_indepFun, norm_le_mul_norm_add', integral_inv_sq_add_sq, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, ProbabilityTheory.paretoPDF_eq, norm_div_le_of_le, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub, CircleDeg1Lift.map_add_int, Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_zsmul_add_eq_zero_of_sign_eq, preCantorSet_succ, cfcHom_nnreal_eq_restrict, ContractingWith.dist_inequality, Lp_add_le, integral_rpow, Lp_add_le_of_nonneg, rpow_add', ValueDistribution.logCounting_zero_mul_eventually_le, MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt, NNReal.rpow_add_intCast, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, exists_rat_abs_sub_le_and_den_le, tendsto_log_comp_add_sub_log, InnerProductGeometry.norm_sub_eq_add_norm_of_angle_eq_pi, Asymptotics.IsBigOWith.add, norm_sub_le_of_le, cos_pi_div_thirty_two, UnitAddCircle.measurePreserving_mk, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, inv_sqrt_one_add_tan_sq, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, dist_sq_of_inner_eq_zero, CircleDeg1Lift.commute_int_add, goldenConj_sq, Liouville.exists_pos_real_of_irrational_root, Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.cgf_const', HolderConjugate.inv_add_inv_eq_one, pow_mul_le_of_le_of_pow_mul_le, AkraBazziRecurrence.growsPolynomially_one_add_smoothingFn, GroupNorm.coe_add, Seminorm.inf_apply, integral_log, CFC.rpow_add, NonarchAddGroupSeminorm.add_bddBelow_range_add, QuotientGroup.exists_norm_mk_lt, integrable_inv_one_add_sq, Complex.norm_add_mul_I, Polynomial.Chebyshev.rootMultiplicity_U_real, HasFDerivWithinAt.arsinh, MeromorphicOn.circleAverage_log_norm, variationOnFromTo.add, not_sameRay_iff_norm_add_lt, Complex.equivRealProdAddHom_apply, hasStrictDerivAt_arctan, IntervalIntegrable.comp_add_left, sub_isBigO_norm_rpow_add_one_of_fderiv, sin_pi_div_thirty_two, NNReal.rpow_add_one, LipschitzOnWith.iff_le_add_mul, GroupNorm.add_apply, MeasureTheory.norm_stoppedValue_leastGE_le, MeasureTheory.Measure.haar.chaar_sup_le, NumberField.mixedEmbedding.logMap_unit_smul, cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, intervalIntegral.smul_integral_comp_mul_add, WithLp.prod_norm_eq_card, hasDerivAt_mulExpNegMulSq, EuclideanGeometry.angle_add_of_ne_of_ne, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, NNReal.rpow_add_one', Probability.cauchyPDFReal_def', WithLp.prod_norm_sq_eq_of_L2, sin_sq_add_cos_sq, ProbabilityTheory.HasSubgaussianMGF.add, fourierCoeff_eq_intervalIntegral, Seminorm.bddBelow_range_add, irrational_add_natCast_iff, doublingGamma_add_one, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, intervalIntegral.integral_comp_add_right, tan_add', MeasureTheory.average_add_measure, GromovHausdorff.HD_below_aux2, MeasureTheory.measureReal_union_add_interβ', isBigO_norm_rpow_add_one_of_fderiv_of_apply_eq_zero, norm_div_le_norm_div_add_norm_div, rpow_add_rpow_le_add, ProbabilityTheory.variance_add, controlled_closure_range_of_complete, holderConjugate_iff, pi_lt_sqrtTwoAddSeries, MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles, Orientation.inner_sq_add_areaForm_sq, dist_triangle4_left, disjoint_closedBall_closedBall_iff, bernoulliFun_mul, norm_add_sq_real, hasFPowerSeriesOnBall_linear_zero, sin_sub_sin, hasDerivAt_Gamma_one_half, HasStrictDerivAt.arsinh, MeasureTheory.measureReal_unionβ, ProbabilityTheory.IndepFun.variance_add, HurwitzZeta.hasSum_int_oddKernel, Gamma_mul_Gamma_add_half_of_pos, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, Cardinal.cantorFunction_succ, Angle.toReal_add_of_sign_pos_sign_neg, ConvexOn.univ_sSup_affine_eq, one_add_rpow_hasFPowerSeriesAt_zero, Complex.sqrt_eq_real_add_ite, thickening_thickening, CircleDeg1Lift.lt_iterate_pos_iff, cos_sq_add_sin_sq, ConvexOn.real_univ_sSup_of_nat_affine_eq, norm_add_sq, cos_sub_cos, tendsto_sum_range_one_div_nat_succ_atTop, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, thickening_cthickening, dist_mul_mul_le, bernoulliFun_eq_integral, binEntropy_two_inv_add, AddGroupSeminorm.add_apply, norm_add_mul_self, Irrational.add_ratCast, hasDerivAt_abs, EuclideanSpace.volume_ball, dist_vsub_vsub_le, LipschitzWith.iff_le_add_mul, ConvexOn.real_sSup_of_countable_affine_eq, toNNReal_add_toNNReal, tendsto_logb_comp_add_sub_logb, ValueDistribution.characteristic_zero_mul_eventually_le, hasDerivAt_Gamma_one, Complex.HadamardThreeLines.norm_lt_sSupNormIm_eps, OpenPartialHomeomorph.univUnitBall_apply, cauchy_add, cos_half, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, ofCauchy_add, ProbabilityTheory.variance_dual_prod', HasFDerivWithinAt.arctan, UpperHalfPlane.exp_half_dist, QuotientGroup.exists_norm_mul_lt, Complex.normSq_add_mul_I, TensorProduct.dist_tmul_le, dist_le_of_approx_trajectories_ODE_of_mem, real_inner_sub_sub_self, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, cos_antiperiodic, cos_periodic, one_add_rpow_hasFPowerSeriesAt_zero, Asymptotics.IsLittleO.add_add, cosh_arsinh, Metric.infDist_le_infDist_add_dist, signedDist_vadd_left, CircleDeg1Lift.exists_eq_add_translationNumber, CircleDeg1Lift.lt_map_map_zero, strictMonoOn_one_add_div_one_sub, ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGF, tendsto_mul_add_inv_atTop_nhds_zero, rpow_add_rpow_le, Int.closedBall_eq_Icc, quadratic_le_exp_of_nonneg, ProbabilityTheory.HasSubgaussianMGF.add_of_indepFun, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, hasDerivAt_gronwallBound, uniformContinuous_add, hasDerivAt_norm_rpow, GromovHausdorff.ghDist_le_of_approx_subsets, Hyperreal.coe_add, Ideal.Quotient.norm_mk_lt, norm_le_norm_add_norm_div, sin_add_nat_mul_two_pi, BoundedContinuousFunction.integral_add_const, ENNReal.toReal_add_le, Metric.mem_closure_range_iff_nat, RCLike.norm_sq_eq_def, Complex.circleTransformDeriv_periodic, tsum_eq_tsum_fourier_of_rpow_decay, rexp_neg_quadratic_isLittleO_rpow_atTop, intervalIntegral.mul_integral_comp_mul_add, Polynomial.Chebyshev.roots_T_real, ProbabilityTheory.gaussianReal_map_add_const, two_mul_arctan_add_pi, pow_mul_norm_iteratedFDeriv_fourierIntegral_le, norm_le_mul_norm_add, abs_sin_eq_one_iff, disjoint_ball_ball_iff, MeasureTheory.measureReal_union, sInf_le_iff, hasDerivAt_arctan', Wallis.W_eq_factorial_ratio, Chebyshev.psi_le, logb_mul_base, ConvexBody.iInter_smul_eq_self, integral_zpow, CircleDeg1Lift.map_int_add, isMIntegralCurveAt_comp_sub, ValueDistribution.characteristic_zero_mul_le, isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo, sin_eq_neg_one_iff, HasFDerivAt.arsinh, cos_lt_one_div_sqrt_sq_add_one, EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi, MeasureTheory.L1.setToL1_add_left, sin_pi_div_sixteen, AddCircle.lintegral_preimage, Metric.diam_union', integral_one_div_one_add_sq, EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_mem, BoundedContinuousFunction.add_norm_nonneg, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, UpperHalfPlane.sinh_half_dist_add_dist, two_mul_arctan_inv_3_add_arctan_inv_7, cos_add_pi_div_two, isBigO_norm_Icc_restrict_atBot, tendsto_one_add_rpow_exp_of_tendsto, lt_log_one_add_of_pos, tendsto_sum_pi_div_four, rpow_neg_one_add_norm_sq_le, Complex.dist_mk, ValueDistribution.logCounting_top_mul_le, tendsto_mul_exp_add_div_pow_atTop, ContinuousAffineMap.norm_comp_le, LiouvilleNumber.partialSum_succ, ENNReal.ofReal_add, tendsto_div_pow_mul_exp_add_atTop, AddCircle.measurePreserving_mk, RCLike.realRingEquiv_apply, MeasureTheory.SimpleFunc.norm_approxOn_zero_le, MeasureTheory.llr_tilted_left, RCLike.mul_im, rpow_add, polarCoord_apply, dist_dist_dist_le, SameRay.norm_add, MeasureTheory.measureReal_union_add_inter', exp_artanh, CircleDeg1Lift.le_iterate_pos_iff, MeasureTheory.Measure.haar.addCHaar_sup_eq, tendsto_measure_Icc_nhdsWithin_right', intervalIntegral.integral_comp_div_add, cosh_sq', OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, cosh_log, rpow_add_le_add_rpow, MeasureTheory.measureReal_union', ProbabilityTheory.variance_const_add, LiouvilleNumber.partialSum_add_remainder, ExistsContDiffBumpBase.y_support, EisensteinSeries.abs_norm_eq_max_natAbs, Polynomial.Chebyshev.U_real_cosh, Complex.integral_rpow_mul_exp_neg_mul_rpow, NNReal.rpow_one_add', dist_le_norm_add_norm', InnerProductSpace.Core.cauchy_schwarz_aux', MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, integral_pow_mul_le_of_le_of_pow_mul_le, tendsto_pow_logb_div_mul_add_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_add, dist_lt_dist_add_dist_iff, hasDerivWithinAt_abs_neg, StieltjesFunction.ae_hasDerivAt, Stirling.log_stirlingSeq_diff_le_geo_sum, EReal.coe_add, Irrational.add_intCast, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ProbabilityTheory.mgf_gaussianReal, isMIntegralCurveAt_comp_add, add_one_lt_exp, HolderTriple.inv_inv_add_inv, SzemerediRegularity.coe_m_add_one_pos, HolderTriple.inv_eq, ProbabilityTheory.gaussianReal_map_const_add, cos_nat_mul_two_pi_add_pi, rpow_one_add_lt_one_add_mul_self, tanh_eq, ProbabilityTheory.mgf_id_gaussianReal, norm_sup_sub_sup_le_add_norm, exp_bound', norm_addβ_le, Polynomial.cyclotomic_eval_le_add_one_pow_totient, Metric.nhds_basis_ball_inv_nat_succ, sinh_add_cosh, BoundingSieve.siftedSum_le_mainSum_errSum_of_upperMoebius, Metric.infDist_le_infDist_add_hausdorffDist, tendsto_abs_tan_atTop, NumberField.house_add_le, UniformConvexOn.sub, SzemerediRegularity.edgeDensity_chunk_not_uniform, rpow_add_natCast, integral_inv_one_add_sq, EisensteinSeries.abs_norm_eq_max_natAbs_neg, AkraBazziRecurrence.h_rec, CircleDeg1Lift.map_lt_add_translationNumber_add_one, EuclideanGeometry.law_cos, BoundingSieve.multSum_eq_main_err, norm_le_norm_add_const_of_dist_le', intervalIntegral.integral_comp_add_left, CircleDeg1Lift.map_add_one', HolderTriple.one_div_add_one_div, ProbabilityTheory.variance_dual_prod, integral_sin_pow_odd, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, LiouvilleWith.rat_add, MeasureTheory.DominatedFinMeasAdditive.add, BohrMollerup.logGammaSeq_add_one, ZetaAsymptotics.term_welldef, Submodule.orthogonalProjectionFn_norm_sq, Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_nsmul_add_eq_zero_of_sign_eq, ZetaAsymptotics.term_sum_one, young_inequality_of_nonneg, cos_sq, ProbabilityTheory.IndepFun.integrable_exp_mul_add, InnerProductSpace.volume_closedBall, ProbabilityTheory.hasDerivAt_mgf, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, MeasureTheory.Measure.volumeIoiPow_apply_Iio, Polynomial.logMahlerMeasure_C_mul_X_add_C, norm_add_le_of_le, dist_midpoint_midpoint_le', sum_range_sub_log_div_le, CircleDeg1Lift.map_lt_of_translationNumber_lt_nat, exp_approx_end, cthickening_cthickening, ProbabilityTheory.aestronglyMeasurable_exp_mul_add, norm_add_mul_self_real, tendsto_euler_sin_prod, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq', zero_lt_one_add_norm_sq, arctan_add, FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2, Angle.toReal_add_eq_toReal_add_toReal, Complex.arg_eq_nhds_of_re_neg_of_im_pos, UniformSpace.Completion.dist_triangle, AddCircle.integral_liftIoc_eq_intervalIntegral, integral_Ioi_inv_one_add_sq, hasDerivAt_arctan, Complex.volume_sum_rpow_lt_one, BoundedContinuousFunction.coe_le_coe_add_dist, ENNReal.rpow_add_of_nonneg, cthickening_ball, ValueDistribution.proximity_top_mul_le, UpperHalfPlane.dist_coe_center_sq, Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle, Complex.normSq_apply, irrational_add_ratCast_iff, norm_add_pow_two, ProbabilityTheory.IndepFun.mgf_add, ProbabilityTheory.gaussianPDFReal_add, half_mul_log_add_log_abs, QuotientAddGroup.exists_norm_add_lt, le_sSup_iff, real_inner_add_add_self, tan_add_nat_mul_pi, LiouvilleWith.nat_add_iff, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq', BoxIntegral.unitPartition.tag_apply, intervalIntegral.integral_comp_mul_add, RCLike.normSq_add, GroupSeminorm.coe_add, RCLike.div_re, integral_sin_pow, MeasureTheory.stoppedAbove_le, arctan_add_eq_sub_pi, cosh_eq, MeasureTheory.measureReal_add_diff, Complex.norm_eq_sqrt_sq_add_sq, UpperHalfPlane.cosh_dist', hasSum_pow_div_log_of_abs_lt_one, ProbabilityTheory.covariance_const_add_right, Complex.borelCaratheodory, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, cos_add_nat_mul_two_pi, Besicovitch.SatelliteConfig.inter, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, gauge_add_le, Metric.Sigma.dist_triangle, Lp_add_le_hasSum_of_nonneg, ringEquivCauchy_apply, norm_le_insert, fderivWithin_arctan, norm_inf_le_add, integral_mul_rpow_one_add_sq, irrational_intCast_add_iff, ModularGroup.lcRow0_apply, tendsto_log_nat_add_one_sub_log, norm_inf_sub_inf_le_add_norm, thickening_ball, NNReal.coe_list_sum, norm_sub_pow_two, Angle.toReal_coe_eq_self_add_two_pi_iff, rpow_add_intCast, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, SchwartzMap.tsum_eq_tsum_fourierIntegral, NNReal.rpow_add_of_nonneg, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, integral_Iic_inv_one_add_sq, tendsto_pow_log_div_mul_add_atTop, one_add_mul_self_lt_rpow_one_add, cantorSet_eq_union_halves, unitInterval.add_pos, Asymptotics.IsBigOWith.sub, cos_eq_neg_one_iff, ValueDistribution.characteristic_top_mul_eventually_le, add_one_le_exp, cos_sub, Wallis.W_succ, integral_cos_sq, ENNReal.toReal_le_add', closedBall_sub_closedBall, RCLike.normSq_apply, tanh_arsinh, sinh_three_mul, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, zero_lt_one_add_norm_sq', Icc_eq_closedBall, ball_sub_ball, norm_sub_mul_le, GroupSeminorm.add_apply, ConvexOn.exists_affine_le_of_lt, Submodule.Quotient.norm_mk_lt, Gamma_nat_eq_factorial, hasDerivAt_Gamma_nat, ENNReal.toReal_le_add, ConvexOn.real_sSup_of_nat_affine_eq, posLog_sum, sin_add_pi, cos_add_int_mul_pi, ValueDistribution.characteristic_sum_top_eventuallyLE, ZLattice.sum_piFinset_Icc_rpow_le, norm_le_norm_div_add, cosh_add, MeasureTheory.exists_upperSemicontinuous_lt_integral_gt, MeasureTheory.integral_llr_tilted_right, irrational_natCast_add_iff, CircleDeg1Lift.map_map_zero_le, dist_add_dist_of_mem_segment, norm_sub_mul_self_real, sqrt_one_add_norm_sq_le, MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int, Metric.thickening_cthickening_subset, MeasureTheory.measure_unitBall_eq_integral_div_gamma, Subadditive.apply_mul_add_le, ProbabilityTheory.HasSubgaussianMGF_add_of_HasCondSubgaussianMGF, ZetaAsymptotics.term_of_lt, MeasureTheory.average_union, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, MeasureTheory.Measure.haar.addPrehaar_sup_le, Function.hasTemperateGrowth_one_add_norm_sq_rpow, IsMIntegralCurveAt.comp_add, sin_eq_one_iff, ProbabilityTheory.measure_le_le_exp_cgf, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, HurwitzZeta.hasSum_nat_cosKernelβ, rpow_add_intCast', intervalIntegral.inv_mul_integral_comp_div_add, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, ProbabilityTheory.Fernique.normThreshold_add_one, rpow_one_add_le_one_add_mul_self, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, CircleDeg1Lift.iterate_pos_eq_iff, norm_le_of_mem_closedBall', tsum_eq_tsum_fourierIntegral_of_rpow_decay, Metric.dist_lt_add_of_nonempty_ball_inter_closedBall, InnerProductGeometry.angle_eq_angle_add_add_angle_add_of_mem_span, CircleDeg1Lift.translationNumber_eq_int_iff, ProbabilityTheory.variance_fun_add, WithLp.prod_norm_eq_of_L2, cos_sq_arctan, dist_sq_lineMap_of_inner_eq_zero, Rat.AbsoluteValue.apply_le_sum_digits, Metric.diam_union, log_mul, sin_add_int_mul_two_pi, tendsto_prod_pi_div_two, SchwartzMap.one_add_le_sup_seminorm_apply, UnitAddCircle.integral_preimage, Polynomial.Chebyshev.roots_U_real_nodup, GroupSeminorm.mul_bddBelow_range_add, MeasureTheory.measureReal_diff_le_iff_le_add, cosh_two_mul, Chebyshev.eventually_primeCounting_le, exp_add, IsMIntegralCurve.periodic_of_eq, Affine.Simplex.ninePointCircle_center, ConvexOn.sSup_affine_eq, deriv_sqrt_mul_log', isAddFundamentalDomain_Ioc', MeasureTheory.measureReal_add_measureReal_compl, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Chebyshev.psi_le_const_mul_self, norm_add_sq_eq_norm_sq_add_norm_sq_real, tendsto_one_add_div_rpow_exp, rpow_add_one', Polynomial.Chebyshev.roots_T_real_nodup, Behrend.exists_large_sphere_aux, MeasureTheory.measureReal_union_add_inter, CircleDeg1Lift.map_add_one, smoothTransition.pos_denom, ringEquivCauchy_symm_apply_cauchy, Function.HasTemperateGrowth.isBigO_uniform, dist_vadd_vadd_le, integral_pow_abs_sub_uIoc, EuclideanSpace.volume_closedBall, MeasureTheory.measureReal_diff_add_inter, AddGroupSeminorm.inf_apply, AddCircle.integral_preimage, two_mul_sin_mul_sin, one_add_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.measureReal_inter_add_diff, isBigO_norm_restrict_cocompact, tendsto_harmonic_sub_log_add_one, norm_add_lt_of_not_sameRay, Metric.diam_cthickening_le, posLog_nat_mul, one_add_mul_self_le_rpow_one_add, ConvexOn.real_sSup_affine_eq, posLog_mul, dist_triangle8, one_div_sub_sq_hasFPowerSeriesOnBall_zero, norm_mul_le', disjoint_closedBall_ball_iff, LiouvilleWith.add_nat_iff, RCLike.normSq_sub, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, exists_int_int_abs_mul_sub_le, LiouvilleWith.nat_add, sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, norm_sub_le_norm_sub_add_norm_sub, MeasureTheory.llr_smul_left, Hyperreal.st_add, MeasureTheory.volume_sum_rpow_lt_one, ball_sub_closedBall, CircleDeg1Lift.tendsto_translation_numberβ', RCLike.realLinearIsometryEquiv_apply, Metric.thickening_thickening_subset, EuclideanGeometry.angle_add_angle_add_angle_eq_pi, Polynomial.Chebyshev.roots_U_real, norm_lt_of_mem_ball, Seminorm.closedBall_add_closedBall_subset, hasSum_log_sub_log_of_abs_lt_one, posLog_norm_sum_le, norm_mulβ_le', NumberField.mixedEmbedding.logMap_mul, ConvexOn.univ_sSup_of_nat_affine_eq, integral_sin_pow_even, summable_one_div_int_add_rpow, lt_sInf_add_pos, Function.HasTemperateGrowth.isBigO, ValueDistribution.characteristic_mul_top_eventuallyLE, hasDerivAt_abs_pos, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', Archimedean.ratLt'_add, log_doublingGamma_eq, two_mul_sin_mul_cos, tendsto_one_add_div_pow_exp, binEntropy_eq_negMulLog_add_negMulLog_one_sub, rpowIntegrandββ_eqOn_pow_div, ValueDistribution.logCounting_mul_zero_le, sum_trapezoidal_integral_adjacent_intervals, AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T, InnerProductGeometry.angle_eq_angle_add_add_angle_add, Stirling.tendsto_self_div_two_mul_self_add_one, intervalIntegral.inv_smul_integral_comp_add_div, Wallis.le_W, SchwartzMap.tsum_eq_tsum_fourier, ZLattice.exists_finsetSum_norm_rpow_le_tsum, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, MeasureTheory.Measure.integrable_pow_neg_integrablePower, CircleDeg1Lift.map_lt_of_translationNumber_lt_int, GromovHausdorff.HD_below_aux1, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero, ProbabilityTheory.IndepFun.mgf_add', posLog_add, IsMIntegralCurveOn.comp_add, MeasureTheory.SignedMeasure.rnDeriv_add, HurwitzZeta.hasSum_int_evenKernelβ, tan_add_pi, Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall, Complex.dist_eq_re_im, cos_arctan, Metric.Sigma.dist_ne, goldenRatio_sq, intervalIntegral.smul_integral_comp_add_mul, GromovHausdorff.HD_candidatesBDist_le, Probability.cauchyPDFReal_def, GroupSeminorm.mul_le', Lp_add_le_tsum_of_nonneg', arctan_add_eq_add_pi, PiTensorProduct.projectiveSeminormAux_add_le, one_add_norm_le_sqrt_two_mul_sqrt, tendsto_logb_nat_add_one_sub_logb
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instAddCommGroup π | CompOp | 790 mathmath: IsLocalMaxOn.fderivWithin_nonpos, AddCircle.measure_univ, HurwitzZeta.hasSum_int_hurwitzZetaOdd, differentiableOn_arcosh, hasDerivAt_arccos, HurwitzZeta.isBigO_atTop_evenKernel_sub, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, HurwitzZeta.expZeta_zero, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, uniqueDiffOn_Icc, Bundle.ContMDiffRiemannianMetric.contMDiff, MonotoneOn.intervalIntegral_slope_le, differentiable_arctan, differentiableAt_mulExpNegMulSq, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, differentiableAt_arcsin, fourierCoeff_tsum_comp_add, tendsto_tsum_div_pow_atTop_integral, ConvexOn.rightDeriv_le_slope_of_mem_interior, hasDerivAt_sqrt_mul_log, NumberField.Units.logEmbedding_fundSystem, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, HurwitzZeta.hasSum_int_cosKernelβ, HurwitzZeta.hasSum_int_hurwitzZetaEven, RightDerivMeasurableAux.D_subset_differentiable_set, CliffordAlgebraComplex.ofComplex_conj, tsum_eq_tsum_fourier, deriv_negMulLog, hasDerivAt_sigmoid, HurwitzZeta.LSeriesHasSum_cos, UnitAddCircle.lintegral_preimage, deriv_abs, EuclideanSpace.closedBall_zero_eq, ZMod.LFunction_stdAddChar_eq_expZeta, ProbabilityTheory.covarianceBilinDual_apply', nnnorm_deriv_mulExpNegMulSq_le_one, deriv_binEntropy, uniqueDiffWithinAt_Iic, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, HurwitzZeta.cosZeta_two_mul_nat', UnitAddCircle.intervalIntegral_preimage, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, AddCircle.homeomorphCircle'_apply_mk, hasStrictDerivAt_rpow_const_of_ne, MeasureTheory.Measure.toJordanDecomposition_toSignedMeasure_sub, span_fourier_closure_eq_top, AddCircle.volume_eq_smul_haarAddCircle, ZLattice.covolume_eq_det_inv, ProbabilityTheory.covarianceBilinDual_apply, intervalIntegral.fderiv_integral_of_tendsto_ae, Orientation.volumeForm_robust_neg, differentiableWithinAt_abs_pos, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, AddCircle.coe_real_preimage_closedBall_eq_iUnion, differentiable_sinh, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, tsum_eq_tsum_fourierIntegral_of_rpow_decay_of_summable, Complex.angle_exp_one, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, hasSum_one_div_nat_pow_mul_fourier, AddCircle.toCircle_add, ProbabilityTheory.uncenteredCovarianceBilin_apply, deriv_log, not_differentiableAt_norm_zero, uniqueDiffOn_Iic, HurwitzZeta.cosZeta_two_mul_nat, NumberField.mixedEmbedding.mem_idealLattice, Complex.re_balance, BoxIntegral.unitPartition.mem_smul_span_iff, HasGradientAt.hasDerivAt', one_mem_posTangentConeAt_iff_frequently, hasDerivAt_sin, MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_toSignedMeasure, differentiableOn_log, Differentiable.fderiv_norm_rpow, Behrend.sphere_subset_preimage_metric_sphere, lintegral_fderiv_lineMap_eq_edist, UnitAddTorus.mFourierSubalgebra_coe, OrthonormalBasis.det_eq_neg_det_of_opposite_orientation, signedDist_right_congr, differentiableOn_arcsin, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, uniqueDiffOn_Ioc, monomial_has_deriv_aux, HurwitzZeta.evenKernel_def, UnitAddTorus.mFourierSubalgebra_closure_eq_top, hasDerivAt_mul_log, differentiableWithinAt_abs, deriv_arccos, hasStrictDerivAt_sinh, AddCircle.homeomorphCircle'_symm_apply, LocallyBoundedVariationOn.ae_differentiableWithinAt, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, hasDerivWithinAt_abs_pos, IsLocalMax.fderiv_eq_zero, MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_sub, HasFDerivAt.norm_sq, antideriv_bernoulliFun, AddCircle.integral_haarAddCircle, hasStrictFDerivAt_rpow_of_pos, differentiableAt_sigmoid, RCLike.ofReal_balance, CliffordAlgebraComplex.ofComplex_toComplex, deriv_abs_neg, differentiableWithinAt_arccos_Ici, CliffordAlgebraComplex.toComplex_comp_ofComplex, HurwitzZeta.hurwitzZetaEven_zero, HarmonicAt.analyticAt_complex_partial, signedDist_left_congr, exists_deriv_eq_zero, InformationTheory.leftDeriv_klFun_one, RCLike.ofReal_comp_balance, ZMod.completedLFunction_def_even, MeasureTheory.withDensityα΅₯_eq_withDensity_pos_part_sub_withDensity_neg_part, signedDist_triangle, hasDerivAt_arcosh, ConvexOn.monotoneOn_rightDeriv, enorm_fderiv_norm_rpow_le, LocallyBoundedVariationOn.ae_differentiableAt, Polynomial.toAddCircle_X_pow_eq_fourier, MonotoneOn.intervalIntegrable_deriv, Angle.toReal_coe, signedDist_linear_apply_apply, HurwitzZeta.oddKernel_def', fourier_norm, hasStrictDerivAt_arccos, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, HurwitzZeta.hasSum_nat_sinZeta, BoxIntegral.unitPartition.integralSum_eq_tsum_div, norm_deriv_mulExpNegMulSq_le_one, Complex.log_exp_eq_re_add_toIocMod, signedDist_le_dist, not_continuousAt_deriv_mul_log_zero, ZMod.LFunction_def_odd, Orientation.areaForm_neg_orientation, tendsto_card_div_pow_atTop_volume, Monotone.ae_differentiableAt, AddCircle.intervalIntegral_preimage, AddCircle.norm_div_natCast, signedDist_apply_apply, differentiableAt_rpow_const_of_ne, UnitAddTorus.mFourierCoeff_toLp, hasDerivAt_arsinh, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, HurwitzZeta.completedSinZeta_neg, hasDerivAt_abs_neg, deriv_sqrt_aux, HasStrictDerivAt.real_of_complex, AddCircle.instIsAddHaarMeasureRealVolume, deriv_rpow_const, DifferentiableWithinAt.dist, hasDerivWithinAt_abs, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, HurwitzZeta.evenKernel_eq_cosKernel_of_zero, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, HurwitzZeta.hurwitzZetaEven_apply_zero, deriv_sinh, orthonormal_fourier, ZLattice.covolume.tendsto_card_div_pow, InformationTheory.hasDerivAt_klFun, HurwitzZeta.expZeta_one_sub, ae_differentiableAt_norm, MeasureTheory.memLp_haarAddCircle_iff, AddCircle.ergodic_nsmul_add, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, AddCircle.dense_addSubgroup_iff_ne_zmultiples, Bundle.ContinuousRiemannianMetric.continuous, NumberField.Units.span_basisOfIsMaxRank, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, HasDerivWithinAt.norm_sq, HasGradientAtFilter.hasDerivAtFilter', IsLocalExtr.fderiv_eq_zero, fourier_one, differentiableOn_rpow_const, AddCircle.denseRange_zsmul_iff, hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, InformationTheory.leftDeriv_klFun, tendsto_integral_exp_smul_cocompact, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, AddCircle.exists_norm_nsmul_le, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MeasureTheory.MemLp.memLp_liftIoc, ProbabilityTheory.differentiableAt_mgf, HurwitzZeta.hasSum_nat_completedCosZeta, Polynomial.toAddCircle.integrable, fourier_zero, fourier_neg', differentiable_cos, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, Complex.re_comp_balance, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, AddCircle.norm_coe_mul, ZMod.toAddCircle_inj, HurwitzZeta.hasSum_nat_hurwitzZetaEven, HurwitzZeta.hasSum_int_cosKernel, ZMod.completedLFunction_def_odd, hasDerivAt_abs_rpow, signedDist_eq_zero_of_orthogonal, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, AddCircle.ergodic_add_left, AddCircle.norm_half_period_eq, HurwitzZeta.hurwitzZeta_neg_nat, deriv_Gamma_nat, HurwitzZeta.sinKernel_neg, Complex.ofReal_balance, hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, UnitAddTorus.mFourier_add, hasDerivAt_qaryEntropy, Monotone.ae_hasDerivAt, HurwitzZeta.oddKernel_def, AffineSubspace.signedInfDist_eq_signedDist_of_mem, one_mem_posTangentConeAt_iff_mem_closure, Affine.Simplex.signedInfDist_apply_self, MeasureTheory.SignedMeasure.toMeasureOfLEZero_toSignedMeasure, differentiableAt_rpow_of_ne, AddCircle.ergodic_add_right, differentiableAt_log, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, HarmonicAt.differentiableAt_complex_partial, UnitAddTorus.mFourier_zero, deriv_inv_log, ProbabilityTheory.covarianceBilinDual_eq_covariance, signedDist_zero, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, NumberField.mixedEmbedding.span_idealLatticeBasis, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, AddCircle.instIsUnifLocDoublingMeasureRealVolume, ProbabilityTheory.covarianceBilinDual_zero, differentiable_exp, ProbabilityTheory.differentiableOn_mgf, HurwitzZeta.hurwitzEvenFEPair_zero_symm, CliffordAlgebraComplex.ofComplex_I, hasStrictDerivAt_arcosh, Complex.log_exp_eq_sub_toIocDiv, UnitAddTorus.coeFn_mFourierLp, differentiableAt_cos, deriv_log', signedDist_triangle_left, tsum_eq_tsum_fourier_of_rpow_decay_of_summable, IsContMDiffRiemannianBundle.exists_contMDiff, deriv2_binEntropy, UnitAddTorus.mFourier_neg, hasDerivAt_arcsin, HurwitzZeta.cosZeta_eq, hasDerivAt_tan, HurwitzZeta.hasSum_int_cosZeta, Complex.arg_exp_mul_I, deriv_tan_sub_id, AddCircle.volume_closedBall, leftDeriv_mul_log, differentiableAt_Gamma, hasStrictDerivAt_cosh, NumberField.mixedEmbedding.mem_span_latticeBasis, gradient_eq_deriv', Orientation.kahler_neg_orientation, hasStrictDerivAt_log, MonotoneOn.intervalIntegrable_slope, differentiableOn_Gamma_Ioi, differentiableOn_mul_log, fderiv_norm_smul_neg, HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat, deriv_mulExpNegMulSq, fourier_coe_apply, periodizedBernoulli.continuous, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, fourierSubalgebra_separatesPoints, dense_differentiableAt_norm, HurwitzZeta.hasSum_nat_cosZeta, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, fourierCoeff.const_smul, MonotoneOn.intervalIntegral_deriv_mem_uIcc, EuclideanSpace.sphere_zero_eq, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, deriv_qaryEntropy, deriv_arctan, HurwitzZeta.completedHurwitzZetaEven_eq, monotoneOn_deriv_descPochhammer_eval, AddCircle.instIsProbabilityMeasureRealHaarAddCircle, has_antideriv_at_fourier_neg, differentiableAt_log_iff, UnitAddTorus.mFourier_norm, Orientation.rotation_neg_orientation_eq_neg, DifferentiableAt.norm_sq, HurwitzZeta.hasSum_expZeta_of_one_lt_re, HurwitzZeta.hasSum_int_evenKernel, signedDist_smul_of_pos, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, hasStrictDerivAt_const_rpow_of_neg, IsContinuousRiemannianBundle.exists_continuous, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, intervalIntegral.integral_hasStrictFDerivAt, signedDist_lineMap_lineMap, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, HurwitzZeta.completedCosZetaβ_neg, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, signedDist_vadd_left_swap, HasFDerivWithinAt.norm_sq, differentiableAt_abs_neg, hasDerivAt_fourier_neg, norm_fderiv_norm_rpow_le, deriv_abs_zero, hasStrictDerivAt_abs, fourier_eval_zero, hasDerivAt_cos, AffineSubspace.signedInfDist_eq_const_of_mem, ZMod.toAddCircle_natCast, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, fourierCoeff_toLp, Differentiable.norm_rpow, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, coe_fourierBasis, differentiableWithinAt_arcsin_Ici, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, AddCircle.ergodic_nsmul, AddCircle.injective_toCircle, HurwitzZeta.sinKernel_zero, deriv_abs_pos, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, HurwitzZeta.completedCosZetaβ_zero, HurwitzZeta.oddKernel_zero, differentiableAt_cosh, HasDerivAt.norm_sq, MeasureTheory.SignedMeasure.toJordanDecomposition_neg, AddCircle.coe_real_preimage_closedBall_inter_eq, Polynomial.hermite_eq_deriv_gaussian', AddCircle.toCircle_zero, AddCircle.continuous_toCircle, uniqueDiffWithinAt_Ioo, ProbabilityTheory.covarianceBilinDual_self_eq_variance, HurwitzZeta.hasSum_int_sinKernel, hasStrictFDerivAt_norm_sq, deriv_exp, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, tendsto_integral_exp_smul_cocompact_of_inner_product, HurwitzZeta.LSeriesHasSum_exp, hasDerivAt_rpow_const, Complex.ofReal_comp_balance, differentiableAt_norm_smul, MeasureTheory.SignedMeasure.singularPart_neg, iter_deriv_exp, differentiable_iteratedDeriv_cos, Differentiable.norm_sq, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, HurwitzKernelBounds.F_int_eq_of_mem_Icc, AddCircle.toCircle_zsmul, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, uniqueDiffWithinAt_Ioi, signedDist_lineMap_left, HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat, tendsto_rightDeriv_mul_log_atTop, hasStrictDerivAt_arsinh, NumberField.mixedEmbedding.span_latticeBasis, OrthonormalBasis.det_adjustToOrientation, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, HurwitzZeta.sinZeta_two_mul_nat_add_one', signedDist_anticomm, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, uniqueDiffOn_Icc_zero_one, modelWithCornersEuclideanHalfSpace_zero, UnitAddCircle.mem_approxAddOrderOf_iff, differentiableAt_arctan, uniqueDiffWithinAt_Iio, Complex.im_balance, differentiableWithinAt_abs_neg, differentiableOn_negMulLog, hasDerivAt_fourier, HurwitzZeta.completedHurwitzZetaOdd_neg, rightDeriv_mul_log, ZMod.LFunction_def_even, fourier_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, hasStrictDerivAt_abs_neg, CliffordAlgebraComplex.equiv_symm_apply, HurwitzZeta.hasSum_nat_completedSinZeta, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, AddCircle.norm_coe_eq_abs_iff, HurwitzZeta.oddKernel_neg, HurwitzZeta.evenKernel_neg, ProbabilityTheory.deriv_mgf, AddCircle.measurePreserving_equivIoc, AddCircle.toCircle_apply_mk, HurwitzZeta.cosZeta_zero, differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, hasFDerivAt_polarCoord_symm, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, deriv_arcsin, abs_signedDist_eq_dist_iff_vsub_mem_span, AddCircle.closedBall_eq_univ_of_half_period_le, ConvexOn.monotoneOn_leftDeriv, NumberField.Units.instDiscrete_unitLattice, differentiable_sin, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, CliffordAlgebraComplex.toComplex_ΞΉ, eulerMascheroniConstant_eq_neg_deriv, MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply, not_differentiableAt_inv_log_zero, deriv_mul_log, AddCircle.denseRange_zsmul_coe_iff, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, signedDist_neg, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, differentiableAt_tan, differentiable_cosh, fourierSubalgebra_coe, Polynomial.toAddCircle_monomial_eq_smul_fourier, signedDist_vsub_self_rev, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, signedDist_linear_apply, UnitAddCircle.measurePreserving_mk, hasDerivAt_log, Complex.im_comp_balance, signedDist_self, signedDist_vsub_self, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, signedDist_smul, hasStrictDerivAt_arctan, ZLattice.volume_image_eq_volume_div_covolume, map_linearMap_volume_pi_eq_smul_volume_pi, uniqueDiffOn_Iio, intervalIntegral.differentiable_integral_of_continuous, AddCircle.norm_neg_period, AddCircle.compactSpace, MeasureTheory.SignedMeasure.totalVariation_neg, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, AddCircle.ergodic_zsmul, hasDerivAt_mulExpNegMulSq, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, UnitAddTorus.mFourierSubalgebra_separatesPoints, differentiableOn_arccos, IsLocalMin.deriv_eq_zero, hasDerivAt_cosh, tendsto_deriv_mul_log_atTop, LipschitzOnWith.ae_differentiableWithinAt_real, UnitAddCircle.norm_eq, fourierCoeff_eq_intervalIntegral, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, span_fourierLp_closure_eq_top, differentiableWithinAt_arccos_Iic, ZLattice.covolume.tendsto_card_le_div, signedDist_smul_of_neg, Complex.toIocMod_arg, MeasureTheory.SignedMeasure.singularPart_sub, nnnorm_fderiv_norm_rpow_le, differentiableAt_abs_pos, HurwitzZeta.completedHurwitzZetaEven_zero, Angle.coe_toIocMod, HurwitzZeta.cosKernel_def, hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, fderiv_norm_smul, EuclideanSpace.ball_zero_eq, HurwitzZeta.hasSum_int_oddKernel, ZMod.toAddCircle_intCast, HurwitzZeta.sinZeta_two_mul_nat_add_one, Affine.Simplex.sign_signedInfDist_touchpoint_empty, signedDist_vadd_right_swap, differentiable_mulExpNegMulSq, AddCircle.coe_real_preimage_closedBall_period_zero, Polynomial.fourierCoeff_toAddCircle_natCast, differentiableAt_arccos, not_DifferentiableAt_log_mul_zero, fourierCoeffOn_of_hasDerivAt_Ioo, ZMod.toAddCircle_apply, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, HurwitzZeta.hurwitzZetaOdd_eq, Angle.toIocMod_toReal, CliffordAlgebraComplex.equiv_apply, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, InformationTheory.rightDeriv_klFun, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, AddCircle.addWellApproximable_ae_empty_or_univ, HurwitzZeta.hurwitzZeta_zero, hasDerivAt_Gamma_one, hasStrictDerivAt_cos, IntervalIntegrable.intervalIntegrable_slope, AddCircle.isFiniteMeasure, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, not_differentiableAt_rpow_const_zero, Differentiable.dist, RightDerivMeasurableAux.differentiable_set_eq_D, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, ProbabilityTheory.iteratedDeriv_two_cgf, measurableSet_of_differentiableWithinAt_Ioi, differentiable_iteratedDeriv_sin, ProbabilityTheory.deriv_mgf_zero, fourier_neg, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, deriv_sigmoid, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, Orientation.rightAngleRotation_trans_neg_orientation, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume, signedDist_vadd_left, HurwitzZeta.hurwitzZeta_one_sub, ProbabilityTheory.deriv_cgf, intervalIntegral.integral_hasFDerivWithinAt, hasDerivAt_gronwallBound, MeasureTheory.JordanDecomposition.toSignedMeasure_neg, hasDerivAt_norm_rpow, differentiableAt_tan_of_mem_Ioo, not_continuousAt_deriv_qaryEntropy_zero, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, AffineSubspace.signedInfDist_singleton, tsum_eq_tsum_fourier_of_rpow_decay, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, AkraBazziRecurrence.differentiableAt_smoothingFn, HurwitzZeta.completedHurwitzZetaEvenβ_neg, HurwitzZeta.completedHurwitzZetaEvenβ_zero, deriv_cos, Orientation.volumeForm_zero_neg, differentiableAt_binEntropy, hasDerivAt_arctan', deriv_bernoulliFun, det_fderivPiPolarCoordSymm, deriv2_qaryEntropy, differentiableAt_exp, hasStrictDerivAt_arcsin, LipschitzWith.ae_differentiableAt_of_real, Angle.coe_toIcoMod, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, AddCircle.lintegral_preimage, differentiable_iteratedDeriv_cosh, hasStrictDerivAt_sin, ZMod.toAddCircle_injective, uniqueDiffOn_Ioi, HurwitzZeta.sinZeta_neg, hasFDerivAt_pi_polarCoord_symm, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, DifferentiableWithinAt.norm_sq, HurwitzZeta.completedCosZeta_eq, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_neg, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, AddCircle.measurePreserving_mk, differentiable_fourierChar, uniqueDiffOn_Ico, HurwitzZeta.hurwitzEvenFEPair_neg, deriv_cos', isBigO_deriv_rpow_const_atTop, AddCircle.measurable_mk', DifferentiableOn.dist, deriv_rpow_const', differentiableAt_arcosh, IsLocalMaxOn.fderivWithin_eq_zero, AddCircle.norm_le_half_period, hasStrictDerivAt_sqrt, HurwitzZeta.completedHurwitzZetaEven_neg, hasDerivAt_tan_of_mem_Ioo, iter_deriv_rpow_const, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, hasDerivAt_exp, fourierSubalgebra_closure_eq_top, volume_euclideanSpace_eq_dirac, HurwitzZeta.cosKernel_neg, Affine.Simplex.ExcenterExists.signedInfDist_excenter, fourier_zero', HurwitzZeta.hasSum_int_sinZeta, UnitAddCircle.mem_addWellApproximable_iff, hasDerivWithinAt_abs_neg, StieltjesFunction.ae_hasDerivAt, hasSum_sq_fourierCoeff, differentiableAt_negMulLog, MeasureTheory.SignedMeasure.rnDeriv_neg, HurwitzZeta.completedCosZeta_zero, fourierBasis_repr, AffineSubspace.signedInfDist_def, NumberField.Units.unitLattice_rank, HurwitzZeta.completedCosZeta_neg, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, MeasureTheory.Measure.toSignedMeasure_sub_apply, CliffordAlgebraComplex.toComplex_involute, differentiable_norm_rpow, HurwitzZeta.cosZeta_neg, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, CliffordAlgebraComplex.toComplex_ofComplex, uniqueDiffWithinAt_Ici, HurwitzZeta.sinKernel_def, ZSpan.discreteTopology_pi_basisFun, Affine.Simplex.signedInfDist_affineCombination, signedDist_apply, AddCircle.norm_eq, fourier_coe_apply', NumberField.Units.logEmbeddingEquiv_apply, fourierCoeffOn_eq_integral, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, differentiableAt_sinh, signedDist_eq_dist_iff_vsub_mem_span, uniqueDiffOn_Ioo, differentiable_iteratedDeriv_sinh, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, UnitAddTorus.mFourier_single, differentiableOn_abs, ProbabilityTheory.hasDerivAt_mgf, tendsto_card_div_pow_atTop_volume', CliffordAlgebraComplex.reverse_eq_id, HurwitzZeta.hurwitzZetaOdd_neg, hasStrictDerivAt_tan, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ProbabilityTheory.deriv_cgf_zero, NumberField.mixedEmbedding.euclidean.finrank, DifferentiableAt.norm, fderiv_norm_smul_pos, AddCircle.integral_liftIoc_eq_intervalIntegral, hasDerivAt_arctan, fourierCoeff_liftIoc_eq, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, ZMod.toAddCircle_eq_zero, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, ContinuousMapZero.toNNReal_neg_smul, Complex.arg_exp, deriv_arcsin_aux, fourier_add', IsLocalMin.fderiv_eq_zero, differentiableAt_qaryEntropy, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, tsum_sq_fourierCoeff, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, differentiable_arsinh, CliffordAlgebraComplex.ofComplex_comp_toComplex, fderiv_norm_rpow, Polynomial.toAddCircle_X_eq_fourier_one, hasStrictDerivAt_const_rpow, AddCircle.closedBall_ae_eq_ball, fourier_add_half_inv_index, fourierCoeffOn_of_hasDerivAt, AffineSubspace.signedInfDist_apply_self, ProbabilityTheory.covarianceBilinDual_of_not_memLp, HurwitzZeta.completedHurwitzZetaEven_residue_zero, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, AddCircle.pathConnectedSpace, differentiable_rpow_const, tsum_eq_tsum_fourierIntegral, zero_at_infty_vector_fourierIntegral, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, AddCircle.norm_eq', fourier_add, instNonemptySeedRatReal, HurwitzZeta.hasSum_int_completedCosZeta, abs_signedDist_le_dist, HurwitzZeta.LSeriesHasSum_sin, hasStrictFDerivAt_rpow_of_neg, hasStrictDerivAt_rpow_const, intervalIntegral.integral_hasFDerivAt, HurwitzZeta.sinZeta_eq, intervalIntegral.fderiv_integral, ProbabilityTheory.IsGaussian.charFunDual_eq', AffineSubspace.signedInfDist_apply_of_mem, hasDerivAt_Gamma_nat, differentiableAt_abs, not_continuousAt_deriv_qaryEntropy_one, DifferentiableOn.norm, Orientation.oangle_neg_orientation_eq_neg, AddCircle.toCircle_nsmul, HurwitzZeta.hasSum_int_completedSinZeta, signedDist_apply_linear, differentiableAt_sin, parallelepiped_orthonormalBasis_one_dim, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, hasDerivAt_sinh, Polynomial.toAddCircle_C_eq_smul_fourier_zero, InformationTheory.not_differentiableAt_klFun_zero, deriv_cosh, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, deriv_sin, AddCircle.homeomorphCircle'_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp', instIsAddHaarMeasureUnitAddCircleVolume, ZMod.LFunction_dft, HurwitzZeta.hasSum_nat_cosKernelβ, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, AddCircle.homeomorphCircle_apply, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, expNegInvGlue.differentiable_polynomial_eval_inv_mul, tsum_eq_tsum_fourierIntegral_of_rpow_decay, norm_fderiv_norm_id_rpow, NumberField.Units.basisOfIsMaxRank_fundSystem, Affine.Simplex.signedInfDist_apply_of_ne, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, deriv_mul_log_zero, hasDerivAt_sqrt, IccRightChart_extend_top, UnitAddCircle.integral_preimage, hasDerivWithinAt_arccos_Iic, measurableSet_of_differentiableWithinAt_Ici, deriv_sqrt_mul_log', differentiableAt_binEntropy_iff_ne_zero_one, deriv_tan, AddCircle.toCircle_neg, AddCircle.norm_eq_of_zero, Orientation.rightAngleRotation_neg_orientation, hasStrictDerivAt_exp, fourierCoeffOn_of_hasDeriv_right, AddCircle.integral_preimage, InformationTheory.deriv_klFun, differentiable_sigmoid, MeasureTheory.Measure.toSignedMeasure_restrict_sub, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, ProbabilityTheory.integral_tilted_mul_self, integrableOn_Ioi_deriv_norm_ofReal_cpow, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, HurwitzZeta.hurwitzZetaEven_neg, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, coeFn_fourierLp, Differentiable.norm, fourierCoeff_liftIco_eq, DifferentiableAt.dist, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, ConvexOn.slope_le_leftDeriv_of_mem_interior, uniqueDiffOn_Ici, fderiv_norm_sq, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, hasDerivWithinAt_arcsin_Iic, hasDerivAt_abs_pos, HurwitzZeta.hurwitzZetaEven_eq, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, AddCircle.ergodic_zsmul_add, deriv2_sqrt_mul_log, hasStrictDerivAt_log_of_pos, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, parallelepiped_single, deriv2_negMulLog, SchwartzMap.tsum_eq_tsum_fourier, Urysohns.CU.lim_eq_midpoint, ZLattice.covolume_eq_det, HurwitzZeta.hasSum_int_evenKernelβ, intervalIntegral.differentiableOn_integral_of_continuous, differentiable_circleMap, Complex.angle_exp_exp, CliffordAlgebraComplex.reverse_apply, differentiableAt_negMulLog_iff, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, IsLocalMinOn.fderivWithin_eq_zero, deriv2_mul_log, MeasureTheory.SignedMeasure.rnDeriv_sub, hasDerivAt_negMulLog, fourierCoeff_fourier, Affine.Simplex.signedInfDist_incenter
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instAddCommMonoid π | CompOp | 1009 mathmath: ZLattice.summable_norm_zpow, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, aux_hasSum_of_le_geometric, Seminorm.isBounded_const, norm_prod_le_of_le, Bundle.ContMDiffRiemannianMetric.isVonNBounded, dist_le_range_sum_dist, NNReal.summable_coe, exists_continuous_sum_one_of_isOpen_isCompact, Bundle.ContMDiffRiemannianMetric.contMDiff, summable_sigma_of_nonneg, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ProbabilityTheory.gaussianReal_map_const_mul, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, IsSelfAdjoint.quasispectrumRestricts, sSup_smul_of_nonpos, BoxIntegral.Prepartition.measure_iUnion_toReal, RCLike.ofRealCLM_apply, hasFDerivAt_fourierChar_neg_bilinear_left, NumberField.Units.finrank_eq_rank, AddDissociated.randomisation, ZLattice.summable_norm_sub_inv_pow, tendsto_tsum_div_pow_atTop_integral, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, NumberField.Units.logEmbedding_fundSystem, ZSpan.volume_real_fundamentalDomain, Complex.ofRealCLM_coe, Complex.areaForm, summable_riemannZetaSummand, ProbabilityTheory.gaussianReal_const_mul, EuclideanSpace.closedBall_zero_eq, MeasureTheory.sum_measureReal_singleton, MeasureTheory.Submartingale.sum_mul_sub', AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, ProbabilityTheory.covarianceBilinDual_apply', ProbabilityTheory.variance_fun_sum', summable_ofDigitsTerm, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, log_div_le_sum_range_add, norm_iteratedFDerivWithin_smul_le, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, countingFunction_finsum_eq_finsum_add, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, Seminorm.finset_sup_apply, ProbabilityTheory.covarianceBilinDual_apply, strictConcaveOn_rpow, fderiv_fourierChar_neg_bilinear_right_apply, norm_iteratedFDeriv_mul_le, intervalIntegral.fderiv_integral_of_tendsto_ae, LipschitzWith.ae_lineDeriv_sum_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, det_fderivPolarCoordSymm, RCLike.norm_expect_le, norm_iteratedFDerivWithin_clm_apply, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, EuclideanSpace.norm_sq_eq, AkraBazziRecurrence.tendsto_atTop_sumCoeffsExp, Orientation.volumeForm_neg_orientation, ProbabilityTheory.iIndepFun.mgf_sumβ, log_prod, Metric.exists_forall_closedEBall_subset_auxβ, instArchimedean, ProbabilityTheory.uncenteredCovarianceBilin_apply, Complex.ofRealCLM_norm, Complex.reLm_coe, Antitone.tendsto_alternating_series_of_tendsto_zero, NumberField.mixedEmbedding.mem_idealLattice, ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFun, BoxIntegral.unitPartition.mem_smul_span_iff, Set.Countable.exists_pos_hasSum_le, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, Bundle.RiemannianMetric.isVonNBounded, Complex.convexHull_reProdIm, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, summable_one_div_nat_add_rpow, Matrix.linfty_opNorm_replicateRow, Height.logHeightβ_sum_le, hasSum_log_one_add_inv, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, sum_geometric_two_le, MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iff, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, Complex.im_expect, summable_one_div_int_pow, MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul, MeasureTheory.SignedMeasure.exists_compl_positive_negative, summable_norm_mul_geometric_of_norm_lt_one, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, vector_fourierIntegral_eq_integral_exp_smul, lp.sum_rpow_le_norm_rpow, lp.norm_sum_single, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, RCLike.hasSum_ofReal, cfcβHom_nnreal_eq_restrict, norm_iteratedFDeriv_clm_apply, summable_norm_mul_geometric_of_norm_lt_one', MeasureTheory.Submartingale.sum_upcrossingStrat_mul, NumberField.mixedEmbedding.commMap_apply_of_isComplex, hasStrictFDerivAt_rpow_of_pos, exists_dist_slope_lt_pairwiseDisjoint_hasSum, rpow_sum_le_const_mul_sum_rpow_of_nonneg, OrthogonalFamily.norm_sq_diff_sum, Orientation.volumeForm_map, dist_birkhoffSum_birkhoffSum_le, OrthonormalBasis.sum_sq_inner_right, MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, summable_condensed_iff_of_eventually_nonneg, summable_nat_rpow_inv, exp_bound, ENNReal.ofReal_sum_of_nonneg, Affine.Simplex.sum_mongePointWeightsWithCircumcenter, ProbabilityTheory.HasSubgaussianMGF.const_mul, QuadraticForm.equivalent_signType_weighted_sum_squared, strictConvexOn_pow, Complex.volume_sum_rpow_le, MeasureTheory.SignedMeasure.toComplexMeasure_apply, sum_ofDigitsTerm_digits_le, convexOn_univ_dist, lp.sum_rpow_le_of_tendsto, Orientation.abs_volumeForm_apply_of_orthonormal, MeromorphicOn.extract_zeros_poles_log, NumberField.mixedEmbedding.negAt_apply_snd, hasSum_sinh, VectorFourier.fourierPowSMulRight_eq_comp, norm_multiset_sum_le, UniformConvexOn.strictConvexOn, NumberField.mixedEmbedding.convexBodySumFun_apply', Chebyshev.psi_eq_sum_theta, Stirling.log_stirlingSeq_diff_hasSum, Complex.reCLM_nnnorm, MeasureTheory.SignedMeasure.toJordanDecomposition_zero, ENNReal.hasSum_toReal, NumberField.mixedEmbedding.negAt_preimage, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, Chebyshev.psi_sub_theta_eq_sum_not_prime, Pi.sum_norm_apply_le_norm', NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MeasureTheory.SignedMeasure.singularPart_smul, ProbabilityTheory.covarianceBilin_apply_basisFun_self, Orientation.areaForm_to_volumeForm, lp.norm_rpow_eq_tsum, strictConvexOn_exp, Finsupp.logb_prod, Affine.Simplex.inv_height_lt_sum_inv_height, Orientation.areaForm_neg_orientation, tendsto_card_div_pow_atTop_volume, hasSum_cosh, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, PartitionOfUnity.sum_eq_one', SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, SmoothPartitionOfUnity.sum_finsupport', not_summable_indicator_one_div_natCast, ZLattice.tsum_norm_rpow_le, strictConcaveOn_log_Iio, ProbabilityTheory.gaussianReal_map_continuousLinearMap, logb_prod, exp_sub_sum_range_succ_isLittleO_pow, strictConcaveOn_univ_of_deriv2_neg, MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iff, Orientation.areaForm_swap, hasSum_zeta_four, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, Bundle.ContinuousRiemannianMetric.symm, summable_abs_int_rpow, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, strongConcaveOn_zero, Metric.PiNatEmbed.dist_def, ContinuousMap.HomotopyRel.trans_apply, MeasureTheory.SignedMeasure.mutuallySingular_singularPart, convexOn_rpow_left, PartitionOfUnity.exists_finset_nhds, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, AkraBazziRecurrence.sumTransform_def, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, toNNReal_sum_of_nonneg, not_summable_of_antitone_of_neg, MultilinearMap.norm_image_sub_le_of_bound', VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, ZLattice.covolume.tendsto_card_div_pow, MonotoneOn.sum_le_integral, tsum_exp_neg_mul_int_sq, Seminorm.ball_smul, Even.strictConvexOn_pow, LiouvilleNumber.summable, hasSum_cos, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, lp.summable_mul, Orientation.volumeForm_zero_pos, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, NormedSpace.norm_expSeries_summable, LSeries.summable_real_of_abscissaOfAbsConv_lt, NumberField.Units.span_basisOfIsMaxRank, convexOn_dist, MeasureTheory.Submartingale.sum_mul_sub, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, Complex.equivRealProdCLM_symm_apply, hasSum_log_one_add, ProbabilityTheory.covariance_sum_right', Seminorm.convexOn, strictConcaveOn_sqrt_mul_log_Ioi, MonotoneOn.integral_le_sum_Ico, CompactlySupportedContinuousMap.coe_toRealLinearMap, memβp_gen_iff, NumberField.Units.basisOfIsMaxRank_apply, exists_extension_of_le_sublinear, le_ofDigits_cantorToTernary_sum, MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityα΅₯_rnDeriv_eq, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, integral_le_sum_mul_Ico_of_antitone_monotone, ProbabilityTheory.covariance_sum_right, MeasureTheory.SignedMeasure.totalVariation_zero, summable_schlomilch_iff_of_nonneg, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, convexOn_univ_norm, ZLattice.tsumNormRPowBound_spec, RCLike.summable_ofReal, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, EisensteinSeries.summable_norm_eisSummand, RCLike.imLm_coe, log_nat_eq_sum_factorization, Path.Homotopy.hcomp_apply, Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter, concaveOn_rpow, MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real, MeasureTheory.volume_sum_rpow_lt, hasSum_ofDigitsTerm_digits, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, ZSpan.volume_fundamentalDomain, ProbabilityTheory.covarianceBilin_zero, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, NumberField.mixedEmbedding.convexBodySumFun_apply, VectorFourier.differentiable_fourierIntegral, ZetaAsymptotics.term_tsum_of_lt, fourierIntegral_convergent_iff', MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff, PartitionOfUnity.sum_le_one', Bundle.ContMDiffRiemannianMetric.symm, Filter.Tendsto.cesaro, RealRMK.rieszMeasure_le_of_eq_one, NormedSpace.norm_expSeries_summable_of_mem_ball', VectorFourier.iteratedFDeriv_fourierIntegral, differentiableAt_rpow_of_ne, ProbabilityTheory.gaussianReal_map_linearMap, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, PiLp.dist_eq_of_L1, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Seminorm.comp_smul, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, OrthonormalBasis.sum_sq_norm_inner_right, EMetric.exists_forall_closedBall_subset_auxβ, CompactlySupportedContinuousMap.toRealLinearMap_apply, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, PartitionOfUnity.sum_eq_one, HurwitzZeta.hasSum_nat_sinKernel, ProbabilityTheory.covarianceBilinDual_zero, RealRMK.integral_rieszMeasure, bernstein.variance, tsum_geometric_of_lt_one, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, logb_nat_eq_sum_factorization, LiouvilleNumber.remainder_summable, sum_div_nat_floor_pow_sq_le_div_sq, Orthonormal.inner_products_summable, ValueDistribution.proximity_sum_top_le, LinearMap.extendToπ_apply, norm_sum_neg_one_pow_le, innerβ_apply, MeasureTheory.measureReal_biUnion_finset, ModularGroup.lcRow0Extend_apply, ball_eq_openSegment, Seminorm.bound_of_continuous, Bundle.ContMDiffRiemannianMetric.pos, sum_le_exp_of_nonneg, IsContMDiffRiemannianBundle.exists_contMDiff, sum_Ico_le_integral_of_le, MeasureTheory.volume_sum_rpow_le, ProbabilityTheory.covariance_sum_left, ProbabilityTheory.covariance_fun_sum_right', MeasureTheory.SignedMeasure.singularPart_add, Complex.hasSum_ofReal, ofDigits_eq_sum_add_ofDigits, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, ProbabilityTheory.mgf_sum_of_identDistribβ, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, Matrix.frobenius_norm_def, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, ProperCone.innerDual_singleton, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, PiLp.norm_eq_sum, inner_le_weight_mul_Lp_of_nonneg, Finset.norm_prod_one_add_sub_one_le, circleIntegrable_log_norm_factorizedRational, Complex.isCauSeq_norm_exp, rpow_sum_le_const_mul_sum_rpow, pow_mul_norm_iteratedFDeriv_fourier_le, NumberField.mixedEmbedding.mem_span_latticeBasis, norm_multiset_prod_le, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm, strictConvexOn_mul_log, ProbabilityTheory.covarianceBilin_comm, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, sin_eq_tsum, rpow_sum_of_pos, NonarchAddGroupSeminormClass.toAddGroupSeminormClass, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, abs_log_sub_add_sum_range_le, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.norm_expSeries_summable_of_mem_ball, StrictMono.strictConvexOn_univ_of_deriv, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos, NumberField.house_sum_le_sum_house, ProbabilityTheory.iIndepFun.integrable_exp_mul_sum, Nat.Primes.not_summable_one_div, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, MeasureTheory.SignedMeasure.re_toComplexMeasure, AntitoneOn.sum_le_integral_Ico, IsPreconnected.convex, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, MeasureTheory.SignedMeasure.mutuallySingular_iff, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, EuclideanSpace.sphere_zero_eq, SmoothPartitionOfUnity.sum_eq_one', OrthonormalBasis.sum_sq_inner_left, Circle.exp_inj, sinh_eq_tsum, MeasureTheory.uniformIntegrable_average_real, cos_eq_tsum, NumberField.mixedEmbedding.negAt_apply_isComplex, AkraBazziRecurrence.p_def, MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE, MeasureTheory.Measure.toSignedMeasure_smul, dist_le_range_sum_of_dist_le, summable_nat_pow_inv, norm_sum_le_of_le, ContinuousMap.HomotopyWith.trans_apply, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, ZLattice.summable_norm_rpow, norm_iteratedFDerivWithin_prod_le, convexOn_log_Gamma, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, Complex.selfAdjointEquiv_apply, tsum_geometric_two, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, ProbabilityTheory.sum_variance_truncation_le, Orientation.areaForm'_apply, PiCountable.dist_summable, HurwitzZeta.hasSum_int_evenKernel, summable_exp_neg_nat, RCLike.ofReal_finsupp_sum, hasSum_one_div_nat_pow_mul_cos, ProbabilityTheory.iIndepFun.cgf_sum, ProbabilityTheory.covariance_fun_sum_left, MeasureTheory.SignedMeasure.singularPart_zero, IsContinuousRiemannianBundle.exists_continuous, ProbabilityTheory.covariance_sum_sum, sum_range_le_log_div, MonotoneOn.sum_le_integral_Ico, Complex.equivRealProdLm_apply, intervalIntegral.integral_hasStrictFDerivAt, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, Complex.ofRealCLM_apply, sum_trapezoidal_error_adjacent_intervals, cfcHom_real_eq_restrict, UniformConvexOn.convexOn, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, ArithmeticFunction.vonMangoldt_sum, AkraBazziRecurrence.strictAnti_sumCoeffsExp, IsSelfAdjoint.spectrumRestricts, Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots, Seminorm.const_isBounded, sum_mul_Ico_le_integral_of_monotone_antitone, Complex.summable_ofReal, ProbabilityTheory.isGaussian_gaussianReal, ProbabilityTheory.variance_fun_sum, VectorFourier.fderiv_fourierIntegral, doublingGamma_log_convex_Ioi, BoundingSieve.siftedSum_eq_sum_support_mul_ite, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Bundle.RiemannianMetric.symm, strongConcaveOn_iff_convex, smul_iInf_of_nonpos, le_sum_ofDigitsTerm_digits, summable_pow_div_add, MeasureTheory.measureReal_iUnion_fintype, ProbabilityTheory.gaussianReal_mul_const, MeasureTheory.Submartingale.sum_mul_upcrossingStrat_le, concaveOn_univ_of_deriv2_nonpos, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, tsum_geometric_of_abs_lt_one, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, SzemerediRegularity.edgeDensity_chunk_uniform, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, hasSum_sq_fourierCoeffOn, ProbabilityTheory.strong_law_aux6, convexOn_descPochhammer_eval, IsMIntegralCurveAt.hasMFDerivAt, MeasureTheory.tendsto_sum_indicator_atTop_iff', SpectrumRestricts.real_iff, hasSum_geometric_two, Pi.sum_norm_apply_le_norm, concaveOn_negMulLog, NNReal.coe_tsum_of_nonneg, PiLp.norm_sq_eq_of_L2, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, Complex.ofReal_sum, MeasureTheory.Measure.toSignedMeasure_apply, ProbabilityTheory.covarianceBilin_self_nonneg, PiLp.norm_eq_of_L1, NNReal.coe_sum, ProbabilityTheory.integral_linearMap_gaussianReal, ZSpan.norm_fract_le, ProbabilityTheory.covarianceBilinDual_self_eq_variance, Path.Homotopy.trans_apply, Orientation.areaForm_comp_linearIsometryEquiv, EisensteinSeries.norm_le_tsum_norm, QuasispectrumRestricts.real_iff, EisensteinSeries.summable_one_div_norm_rpow, Affine.Simplex.inradius_eq_abs_inv_sum, AntitoneOn.integral_le_sum_Ico, convexOn_Gamma, summable_dirichletSummand, ContinuousMap.Homotopy.trans_apply, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, ZetaAsymptotics.term_tsum_one, ProbabilityTheory.covarianceBilinDual_self_nonneg, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, Complex.equivRealProdLm_symm_apply, Complex.equivRealProdLm_symm_apply_im, Complex.volume_sum_rpow_lt, ProbabilityTheory.aestronglyMeasurable_exp_mul_sum, lp.norm_compl_sum_single, MeasureTheory.Measure.toSignedMeasure_add, ProbabilityTheory.covarianceBilin_real_self, BoundingSieve.siftedSum_le_sum_of_upperMoebius, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, SmoothPartitionOfUnity.sum_le_one', NumberField.mixedEmbedding.span_latticeBasis, tsum_geometric_two', ProbabilityTheory.covariance_fun_sum_fun_sum', AlternatingMap.norm_image_sub_le_of_bound', HurwitzKernelBounds.summable_f_nat, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, OrthonormalBasis.sum_sq_norm_inner_left, VectorFourier.fourierSMulRight_apply, StrongConcaveOn.strictConcaveOn, closedBall_eq_segment, Seminorm.closedBall_smul, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, SmoothPartitionOfUnity.sum_nonneg, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Orientation.areaForm_comp_rightAngleRotation, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, not_summable_indicator_mod_of_antitone_of_neg, ZetaAsymptotics.zeta_limit_aux1, Complex.ofReal_expect, Affine.Simplex.sum_circumcenterWeightsWithCircumcenter, Chebyshev.psi_eq_theta_add_sum_theta, GroupNorm.groupNormClass, convex_iff_isPreconnected, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, InformationTheory.convexOn_klFun, summable_one_div_nat_rpow, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, ProbabilityTheory.gaussianReal_map_mul_const, ZLattice.summable_norm_pow_inv, AkraBazziRecurrence.asympBound_def', ValueDistribution.characteristic_sum_top_le, BoxIntegral.BoxAdditiveMap.toSMul_apply, Nat.roughNumbersUpTo_card_le', ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, EuclideanSpace.norm_eq, Orientation.inner_rightAngleRotation_left, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, ProbabilityTheory.covarianceBilin_apply_pi, Affine.Simplex.sum_excenterWeights_eq_one_iff, ProbabilityTheory.covariance_fun_sum_right, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', UniformConcaveOn.concaveOn, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, NormedSpace.norm_expSeries_summable', NormedSpace.norm_expSeries_div_summable_of_mem_ball, Complex.hasSum_re, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, summable_exp_nat_mul_of_ge, NumberField.Units.instDiscrete_unitLattice, summable_one_div_pow_of_le, RCLike.hasSum_re, ZetaAsymptotics.term_sum_of_lt, uniformConcaveOn_zero, Orientation.abs_areaForm_le, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, Quaternion.summable_coe, summable_iff_not_tendsto_nat_atTop_of_nonneg, ProbabilityTheory.covarianceBilin_apply_basisFun, hasSum_geometric_two', ContinuousAlternatingMap.norm_image_sub_le', NumberField.mixedEmbedding.negAt_symm, VectorFourier.contDiff_fourierIntegral, cfcHom_nnreal_eq_restrict, Polynomial.sum_sq_norm_coeff_eq_circleAverage, Lp_add_le, Lp_add_le_of_nonneg, tsum_geometric_inv_two_ge, strictConvexOn_rpow, UniformConcaveOn.strictConcaveOn, ofDigits_cantorToTernary_sum_le, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, QuadraticForm.posDef_of_toMatrix', NumberField.mixedEmbedding.volume_negAt_plusPart, SmoothPartitionOfUnity.sum_eq_one, exp_multiset_sum, PiLp.dist_sq_eq_of_L2, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, rank_rat_real, ENNReal.tsum_coe_ne_top_iff_summable_coe, MeasureTheory.SignedMeasure.rnDeriv_smul, MeasureTheory.sum_measureReal_preimage_singleton, RCLike.im_tsum, MeromorphicOn.circleAverage_log_norm, ProbabilityTheory.gaussianPDFReal_inv_mul, NNReal.coe_expect, Quaternion.tsum_coe, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, map_linearMap_volume_pi_eq_smul_volume_pi, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Chebyshev.theta_eq_sum_Icc, rpow_sum_of_nonneg, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, cfcβHom_real_eq_restrict, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, Complex.equivRealProdLm_symm_apply_re, MeasureTheory.ComplexMeasure.im_apply, Monotone.convexOn_univ_of_deriv, RCLike.ofReal_expect, Orientation.abs_areaForm_of_orthogonal, lp.hasSum_norm, innerβ_apply_apply, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, Polynomial.sum_derivRootWeight_pos, CompactlySupportedContinuousMap.toNNRealLinear_apply, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, PiLp.norm_eq_of_nat, ValueDistribution.logCounting_sum_top_eventuallyLE, MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles, ZLattice.covolume.tendsto_card_le_div, Complex.re_tsum, Orientation.inner_sq_add_areaForm_sq, bernoulliFun_mul, dist_prod_prod_le_of_le, lp.tsum_mul_le_mul_norm', RCLike.reLm_coe, eigenvalue_mem_ball, ODE.FunSpace.dist_iterate_next_le, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, EuclideanSpace.ball_zero_eq, HurwitzZeta.hasSum_int_oddKernel, ProbabilityTheory.strong_law_aux7, WithCStarModule.pi_norm_le_sum_norm, sum_mul_le_sqrt_mul_sqrt, ZLattice.summable_norm_sub_rpow, hahnEmbedding_isOrderedModule_rat, summable_geometric_of_abs_lt_one, posLog_prod, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, Complex.im_sum, Complex.coe_selfAdjointEquiv, summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, Affine.Simplex.sum_reflectionCircumcenterWeightsWithCircumcenter, summable_condensed_iff_of_nonneg, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, tendsto_sum_range_one_div_nat_succ_atTop, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, tsum_geometric_inv_two, not_summable_one_div_natCast, norm_iteratedFDeriv_prod_le, Affine.Simplex.exradius_eq_abs_inv_sum, NumberField.mixedEmbedding.stdBasis_apply_isReal, BumpCovering.sum_toPartitionOfUnity_eq, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, Affine.Simplex.ExcenterExists.sum_excenterWeights_eq_one, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, PartitionOfUnity.sum_le_one, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_symm_apply, RCLike.hasSum_iff, MeasureTheory.measureReal_iUnion_fintype_le, Path.trans_apply, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, NumberField.mixedEmbedding.convexBodyLT_convex, tsum_sq_fourierCoeffOn, ProbabilityTheory.covarianceBilinDual_comm, ArithmeticFunction.sum_moebius_mul_log_eq, ProperCone.dual_dual_flip, flip_innerβ, intervalIntegral.fderivWithin_integral_of_tendsto_ae, Orientation.volumeForm_robust', lp.norm_sub_norm_compl_sub_single, strictConcaveOn_sqrt, MeasureTheory.ae_mem_limsup_atTop_iff, ModularGroup.tendsto_lcRow0, Complex.imCLM_coe, intervalIntegral.integral_hasFDerivWithinAt, circleAverage_log_norm_factorizedRational, InformationTheory.strictConvexOn_klFun, summable_pow_mul_exp_neg_nat_mul, ProbabilityTheory.covarianceBilin_apply, Monotone.tendsto_alternating_series_of_tendsto_zero, norm_prod_le, GroupSeminorm.groupSeminormClass, FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1, NumberField.mixedEmbedding.latticeBasis_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, Complex.selfAdjointEquiv_symm_apply, ProbabilityTheory.covariance_sum_left', ProbabilityTheory.covarianceBilin_map, dist_sum_sum_le_of_le, gauge_sum_le, hasSum_one_div_nat_pow_mul_sin, Asymptotics.IsBigOWith.sum, Bundle.ContinuousRiemannianMetric.pos, ProbabilityTheory.strong_law_aux4, MeasureTheory.Measure.toBoxAdditive_apply, StrictAnti.strictConcaveOn_univ_of_deriv, pow_mul_norm_iteratedFDeriv_fourierIntegral_le, IsCoercive.continuousLinearEquivOfBilin_apply, Orientation.volumeForm_zero_neg, ProbabilityTheory.mgf_sum_of_identDistrib, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, SmoothPartitionOfUnity.sum_finsupport, Orientation.areaForm_map, det_fderivPiPolarCoordSymm, ENNReal.tsum_coe_eq_top_iff_not_summable_coe, ENNReal.summable_toReal, NumberField.mixedEmbedding.commMap_apply_of_isReal, AddGroupSeminorm.addGroupSeminormClass, Seminorm.finset_sup_smul, Bundle.RiemannianMetric.pos, tendsto_sub_mul_tsum_nat_rpow, MeasureTheory.lpNorm_sum_le, hasSum_zeta_two, convexOn_exp, Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, log_multiset_prod, strictConvexOn_univ_of_deriv2_pos, Complex.equivRealProdCLM_symm_apply_re, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, Chebyshev.psi_eq_sum_Icc, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, tendsto_sum_pi_div_four, NumberField.mixedEmbedding.latticeBasis_repr_apply, sInf_smul_of_nonpos, fourierIntegral_continuousLinearMap_apply', LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, ProbabilityTheory.uncenteredCovarianceBilin_zero, Affine.Simplex.sum_touchpointWeights, InformationTheory.convexOn_Ioi_klFun, Affine.Simplex.sum_pointWeightsWithCircumcenter, VectorFourier.fourierPowSMulRight_apply, Nat.Primes.summable_rpow, RCLike.ofReal_tsum, not_summable_natCast_inv, SeminormClass.toAddGroupSeminormClass, EuclideanSpace.dist_eq, NumberField.mixedEmbedding.normAtPlace_negAt, AlternatingMap.measure_def, strictConcaveOn_sin_Icc, convexOn_univ_of_deriv2_nonneg, integral_le_sum_Ico_of_le, Finsupp.log_prod, Orientation.areaForm_map_complex, NNReal.coe_multiset_sum, NumberField.mixedEmbedding.finrank, inner_le_Lp_mul_Lq, ZLattice.summable_norm_sub_zpow, Complex.imCLM_nnnorm, ValueDistribution.logCounting_sum_top_le, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, Orientation.inner_rightAngleRotation_right, NNReal.summable_mk, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Summable.norm, summable_norm_iff, Affine.Simplex.ExcenterExists.signedInfDist_excenter, hasSum_sin, Orientation.volumeForm_apply_le, absolutelyContinuousOnInterval_iff, BoxIntegral.Box.volume_apply, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, NumberField.mixedEmbedding.negAt_apply_norm_isReal, hasSum_geometric_of_abs_lt_one, Complex.hasSum_im, MonotoneOn.integral_le_sum, Metric.exists_subseq_summable_dist_of_cauchySeq, AntitoneOn.sum_le_integral, BohrMollerup.f_add_nat_eq, AddGroupNorm.addGroupNormClass, OrthogonalFamily.norm_sum, MeasureTheory.Measure.toSignedMeasure_apply_measurable, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, not_summable_iff_tendsto_nat_atTop_of_nonneg, hasSum_sq_fourierCoeff, ProbabilityTheory.strong_law_aux1, PartitionOfUnity.sum_nonneg, dist_prod_prod_le, StrongConvexOn.strictConvexOn, Orientation.kahler_apply_apply, PiLp.dist_eq_of_L2, Orientation.inner_rightAngleRotationAuxβ_left, strictConvexOn_zpow, riesz_extension, Orientation.areaForm_apply_self, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, differentiable_fourierChar_neg_bilinear_right, ProbabilityTheory.variance_linearMap_gaussianReal, ENNReal.toReal_sum, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, NumberField.Units.unitLattice_rank, exp_bound', sum_div_pow_sq_le_div_sq, smul_iSup_of_nonpos, Complex.imCLM_enorm, MeasureTheory.Measure.toSignedMeasure_sub_apply, hasSum_arctan, strictConcave_binEntropy, SzemerediRegularity.edgeDensity_chunk_not_uniform, VectorFourier.fourierIntegral_probChar, VectorFourier.norm_fourierSMulRight_le, AlternatingMap.measure_parallelepiped, summable_norm_geometric_of_norm_lt_one, EuclideanSpace.dist_sq_eq, AkraBazziRecurrence.h_rec, summable_geometric_two', Memβp.summable, Complex.ofRealCLM_enorm, ZSpan.discreteTopology_pi_basisFun, Antitone.cauchySeq_alternating_series_of_tendsto_zero, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, ProbabilityTheory.strong_law_aux2, NumberField.Units.logEmbeddingEquiv_apply, UnitAddTorus.hasSum_sq_mFourierCoeff, Complex.re_expect, strictConcaveOn_log_Ioi, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm_of_integrable, CliffordAlgebraComplex.Q_apply, ProbabilityTheory.IndepFun.variance_sum, MeasureTheory.measureReal_biUnion_finset_le, VectorFourier.norm_fourierPowSMulRight_le, NormedSpace.norm_expSeries_div_summable, dist_birkhoffAverage_birkhoffAverage_le, Complex.equivRealProdCLM_symm_apply_im, summable_pow_mul_jacobiThetaβ_term_bound, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, hasFDerivAt_fourierChar_neg_bilinear_right, Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos, lp.norm_eq_tsum_rpow, not_summable_one_div_on_primes, ProbabilityTheory.strong_law_aux3, norm_iteratedFDerivWithin_mul_le, VectorFourier.norm_fourierSMulRight, cantorSequence_eq_self_sub_sum_cantorToTernary, LinearMap.mem_span_iff_bound, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, summable_geometric_two, strongConvexOn_iff_convex, tendsto_card_div_pow_atTop_volume', strongConvexOn_zero, sum_range_sub_log_div_le, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, ProbabilityTheory.strong_law_ae_real, summable_one_div_nat_pow, ProbabilityTheory.covariance_sum_sum', ProbabilityTheory.strong_law_aux5, ProbabilityTheory.variance_sum', MeasureTheory.measureReal_biUnion_finsetβ, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, MeasureTheory.JordanDecomposition.toSignedMeasure_zero, FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2, differentiable_fourierChar_neg_bilinear_left, MeasureTheory.lpNorm_expect_le, Antitone.concaveOn_univ_of_deriv, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, fourierCoeff_liftIoc_eq, Complex.volume_sum_rpow_lt_one, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, ProbabilityTheory.geometricPMFRealSum, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, bernstein.probability, AkraBazziRecurrence.one_mem_range_sumCoeffsExp, Complex.reCLM_norm, ContinuousMapZero.toNNReal_neg_smul, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, FormalMultilinearSeries.summable_norm_mul_pow, instIsOrderedAddMonoid, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NumberField.mixedEmbedding.convexBodySum_convex, Affine.Simplex.sum_excenterWeights, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, Orientation.areaForm_rightAngleRotation_right, NNReal.hasSum_coe, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, tsum_sq_fourierCoeff, Set.Countable.exists_pos_forall_sum_le, AntitoneOn.integral_le_sum, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, norm_iteratedFDeriv_smul_le, Complex.ofReal_tsum, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_apply, PiCountable.dist_eq_tsum, hasSum_pow_div_log_of_abs_lt_one, summable_norm_pow_mul_geometric_of_norm_lt_one, dist_le_Ico_sum_of_dist_le, MeasureTheory.SignedMeasure.null_of_totalVariation_zero, AkraBazziRecurrence.continuous_sumCoeffsExp, ContinuousMapZero.toNNReal_smul, MeasureTheory.Measure.toSignedMeasure_restrict_eq_restrict_toSignedMeasure, ProbabilityTheory.covarianceBilinDual_of_not_memLp, MeasureTheory.measureReal_biUnion_eq_sum_powerset, ModularGroup.lcRow0_apply, Complex.imCLM_apply, ProbabilityTheory.gaussianPDFReal_mul, summable_geometric_of_lt_one, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NNReal.coe_tsum, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, NumberField.mixedEmbedding.fundamentalCone.expMap_sum, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Monotone.cauchySeq_alternating_series_of_tendsto_zero, compact_inner_le_weight_mul_Lp_of_nonneg, ProbabilityTheory.HasSubgaussianMGF.sum_of_hasCondSubgaussianMGF, NumberField.mixedEmbedding.disjoint_span_commMap_ker, NumberField.Units.sum_mult_mul_log, hasStrictFDerivAt_rpow_of_neg, MeasureTheory.integrable_count_iff, intervalIntegral.integral_hasFDerivAt, PartitionOfUnity.exists_finset_nhds', cosh_eq_tsum, PiLp.norm_eq_of_L2, RCLike.ofRealCLM_coe, intervalIntegral.fderiv_integral, ProbabilityTheory.IsGaussian.charFunDual_eq', sum_sqrt_mul_sqrt_le, RealRMK.le_rieszMeasure_tsupport_subset, posLog_sum, hasSum_zeta_nat, MeasureTheory.sum_measureReal_le_measureReal_univ, ValueDistribution.characteristic_sum_top_eventuallyLE, ZLattice.sum_piFinset_Icc_rpow_le, FormalMultilinearSeries.summable_norm_apply, MeasureTheory.mul_upcrossingsBefore_le, Quaternion.hasSum_coe, signedDist_apply_linear, MeasureTheory.Measure.toSignedMeasure_zero, Bundle.RiemannianMetric.continuousAt, AkraBazziRecurrence.injective_sumCoeffsExp, hasSum_iff_tendsto_nat_of_nonneg, Complex.reCLM_enorm, VectorFourier.hasFDerivAt_fourierChar_smul, strictConcaveOn_cos_Icc, norm_sum_le, ProbabilityTheory.iIndepFun.cgf_sumβ, dist_sum_sum_le, ProbabilityTheory.covarianceBilinDual_of_not_memLp', Complex.re_sum, RCLike.hasSum_im, HurwitzZeta.hasSum_nat_cosKernelβ, ProbabilityTheory.poissonPMFRealSum, AkraBazziRecurrence.sumCoeffsExp_p_eq_one, Orientation.volumeForm_comp_linearIsometryEquiv, exp_sum, log_of_ne_zero, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, ModularForm.summable_eta_q, Complex.hasSum_iff, NumberField.mixedEmbedding.norm_negAt, SmoothPartitionOfUnity.sum_le_one, VectorFourier.fourierIntegral_fderiv, one_half_le_sum_primes_ge_one_div, exp_sub_sum_range_isBigO_pow, dist_le_Ico_sum_dist, convexOn_mul_log, Orthonormal.sum_inner_products_le, PartitionOfUnity.sum_finsupport', strictConcaveOn_negMulLog, ProbabilityTheory.mgf_sum_measure, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, fderiv_fourierChar_neg_bilinear_left_apply, OrthogonalFamily.summable_iff_norm_sq_summable, summable_partition, fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.norm_image_sub_le', Polynomial.mahlerMeasure_le_sum_norm_coeff, BumpCovering.sum_toPOUFun_eq, RCLike.ofReal_sum, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, Complex.imLm_coe, MeasureTheory.summable_measure_toReal, summable_nat_rpow, MeasureTheory.Measure.toSignedMeasure_restrict_sub, summable_exp_nat_mul_iff, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, inner_le_Lp_mul_Lq_of_nonneg, RCLike.re_tsum, summable_prod_of_nonneg, ProbabilityTheory.HasSubgaussianMGF_sum_of_HasCondSubgaussianMGF, MeasureTheory.volume_sum_rpow_lt_one, ProbabilityTheory.convex_integrableExpSet, NonarchAddGroupNormClass.toAddGroupNormClass, strictConcaveOn_qaryEntropy, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Complex.im_tsum, Orientation.areaForm_rightAngleRotation_left, ProbabilityTheory.iIndepFun.mgf_sum, ENNReal.tsum_toReal_eq, fourierCoeff_liftIco_eq, NumberField.mixedEmbedding.disjoint_negAt_plusPart, hasSum_log_sub_log_of_abs_lt_one, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, posLog_norm_sum_le, convexOn_rpow, arcsin_projIcc, summable_one_div_int_add_rpow, Seminorm.smul_le_smul, Complex.nonempty_linearEquiv_real, Complex.equivRealProdCLM_apply, PiLp.dist_eq_sum, NumberField.mixedEmbedding.convexBodySum_mem, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', hasSum_L_function_mod_four_eval_three, ModularGroup.smul_eq_lcRow0_add, ProbabilityTheory.variance_sum, hasSum_geometric_of_lt_one, summable_geometric_two_encode, NumberField.mixedEmbedding.convexBodyLT'_convex, Bundle.ContinuousRiemannianMetric.isVonNBounded, PartitionOfUnity.sum_finsupport, MeasureTheory.hasFiniteIntegral_count_iff, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, HurwitzKernelBounds.summable_f_int, Orientation.inner_mul_areaForm_sub, ofDigits_digits_sum_eq, uniformConvexOn_zero, SmoothPartitionOfUnity.contMDiff_sum, MeasureTheory.Measure.zero_le_toSignedMeasure, sum_trapezoidal_integral_adjacent_intervals, MeasureTheory.SignedMeasure.im_toComplexMeasure, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ProbabilityTheory.covariance_fun_sum_left', BoxIntegral.unitPartition.tag_mem_smul_span, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Cardinal.summable_cantor_function, ZLattice.covolume_eq_det, lp.tsum_mul_le_mul_norm, convexOn_norm, MeasureTheory.SignedMeasure.rnDeriv_add, HurwitzZeta.hasSum_int_evenKernelβ, Affine.Simplex.sum_centroidWeightsWithCircumcenter, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, Orthonormal.tsum_inner_products_le, summable_indicator_mod_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, Complex.reCLM_apply, Orientation.abs_volumeForm_apply_le, instIsOrderedCancelAddMonoid, ProbabilityTheory.covariance_fun_sum_fun_sum
|
instAddCommSemigroup π | CompOp | β |
instAddGroup π | CompOp | 595 mathmath: EuclideanGeometry.Sphere.mul_dist_eq_abs_power, MeasureTheory.Measure.integral_comp_inv_smul, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Angle.abs_toReal_neg_coe_eq_self_iff, HurwitzZeta.isBigO_atTop_evenKernel_sub, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, Angle.sign_two_zsmul_eq_sign_iff, Angle.neg_coe_abs_toReal_of_sign_nonpos, ProbabilityTheory.gaussianReal_map_const_mul, norm_torusIntegral_le_of_norm_le_const, HasStrictFDerivAt.abs_of_pos, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, MeasureTheory.Measure.addHaar_image_continuousLinearMap, abs_sinc_le_one, smul_map_volume_mul_right, ContinuousMap.abs_mem_subalgebra_closure, 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, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, Asymptotics.IsBigOWith.abs_right, Asymptotics.isBigO_abs_abs, ModularForm.mul_slash, ProbabilityTheory.gaussianReal_const_mul, deriv_abs, Complex.norm_le_abs_re_add_abs_im, abs_cos_le_one, HasDerivWithinAt.liminf_right_slope_le, isLittleO_exp_neg_mul_sq_cocompact, young_inequality, range_circleMap, Asymptotics.IsBigO.abs_left, Polynomial.exists_partition_polynomial, ZLattice.covolume_eq_det_inv, Angle.eq_iff_sign_eq_and_abs_toReal_eq, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, differentiableWithinAt_abs_pos, NumberField.dedekindZeta_residue_def, AddCircle.coe_real_preimage_closedBall_eq_iUnion, Asymptotics.isLittleO_abs_abs, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Complex.angle_exp_one, log_abs, cosh_abs, UpperHalfPlane.im_smul_eq_div_normSq, BoxIntegral.unitPartition.mem_smul_span_iff, TopologicalSpace.Opens.CompleteCopy.dist_eq, NumberField.Units.regOfFamily_eq_det, summable_one_div_nat_add_rpow, abs_tanh_lt_one, PNat.dist_eq, RCLike.abs_im_div_norm_le_one, ModularForm.prod_slash, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, CompactlySupportedContinuousMap.nnrealPart_smul_neg, setOf_liouvilleWith_subset_aux, differentiableWithinAt_abs, Polynomial.exists_partition_polynomial_aux, ProbabilityTheory.integrable_pow_abs_of_integrable_exp_mul, CFC.negPart_algebraMap, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, Rat.dist_eq, Circle.isAddQuotientCoveringMap_exp, Asymptotics.IsLittleO.abs_left, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, smul_map_diagonal_volume_pi, deriv_abs_neg, 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, Angle.abs_toReal_le_pi, ProbabilityTheory.HasSubgaussianMGF.const_mul, MeasureTheory.Measure.addHaar_preimage_smul, abs_sinh, RCLike.abs_re_le_norm, Asymptotics.isBigO_abs_left, 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, Orientation.abs_volumeForm_apply_of_orthonormal, RCLike.norm_ofReal, abs_lt_norm_sub_of_not_sameRay, image_circleMap_Ioc, cauSeq_converges, 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, Angle.sign_two_nsmul_eq_neg_sign_iff, RCLike.abs_re_div_norm_le_one, BoxIntegral.unitPartition.integralSum_eq_tsum_div, NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, log_two_near_10, coe_toNNReal_le, Differentiable.abs, abs_real_inner_le_norm, MeasureTheory.Measure.integral_comp_inv_mul_left, ModularGroup.tendsto_abs_re_smul, BoundedContinuousFunction.integral_const_sub, UnitAddTorus.mFourierCoeff_toLp, isTheta_exp_comp_one, SameRay.norm_sub, volume_preimage_mul_left, summable_abs_int_rpow, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, hasDerivAt_abs_neg, ProbabilityTheory.integrable_exp_mul_abs, norm_circleMap_zero, sqrt_sq_eq_abs, map_matrix_volume_pi_eq_smul_volume_pi, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', hasDerivWithinAt_abs, Asymptotics.IsLittleO.abs_abs, HurwitzZeta.hurwitzZetaEven_apply_zero, intervalIntegral.abs_intervalIntegral_eq, AddSubgroup.tendsto_zmultiples_subtype_cofinite, smul_map_volume_mul_left, NumberField.Units.span_basisOfIsMaxRank, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, Complex.abs_re_eq_norm, Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, Angle.abs_toReal_neg, ZSpan.measureReal_fundamentalDomain, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, ProbabilityTheory.abs_truncation_le_bound, NumberField.Units.regulator_eq_det, ConvexOn.isBoundedUnder_abs, 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, eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, exists_rat_abs_sub_lt_and_lt_of_irrational, AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, abs_le_sqrt, isAddFundamentalDomain_Ioc, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, norm_cauchyPowerSeries_le, abs_dist_sub_le, Angle.coe_abs_toReal_of_sign_nonneg, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, Complex.abs_arg_le_pi, AddCircle.norm_coe_mul, HurwitzZeta.hasSum_nat_hurwitzZetaEven, NumberField.Units.finrank_mul_regOfFamily_eq_det, instIsCompleteAbs, MeasureTheory.volume_sum_rpow_lt, Asymptotics.isBigOWith_abs_left, hasDerivAt_abs_rpow, Angle.coe_eq_zero_iff, ZSpan.volume_fundamentalDomain, abs_dist_sub_le_dist_mul_mul, AddCircle.norm_half_period_eq, ZSpan.measure_fundamentalDomain, logb_abs_base, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, MeasureTheory.crossing_pos_eq, Complex.abs_im_le_norm, MeasureTheory.Measure.integral_comp_smul, HasFDerivAt.abs_of_pos, abs_cos_int_mul_pi, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, HasFDerivAt.abs, abs_iteratedDeriv_cos_le_one, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, HasStrictFDerivAt.abs_of_neg, HasFDerivWithinAt.abs, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_integrable_exp_mul, MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin, Complex.abs_im_eq_norm, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, DifferentiableWithinAt.abs, NumberField.mixedEmbedding.convexBodySumFun_smul, abs_mulExpNegMulSq_comp_le_norm, contDiffOn_abs, coe_nnabs, EReal.coe_zsmul, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, dist_integral_mulExpNegMulSq_comp_le, ProbabilityTheory.integrable_exp_abs_mul_abs_add, exp_one_near_20, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, MeasureTheory.volume_sum_rpow_le, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul', MeasureTheory.integral_image_eq_integral_abs_deriv_smul, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, intervalIntegral.abs_integral_mono_interval, Complex.isCauSeq_norm_exp, ContDiffOn.abs, rpow_sum_le_const_mul_sum_rpow, exists_nat_abs_mul_sub_round_le, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, exp_abs_le, Nat.dist_eq, RCLike.abs_wInner_le, exists_polynomial_near_of_continuousOn, NumberField.mixedEmbedding.covolume_idealLattice, HurwitzZeta.completedHurwitzZetaEven_eq, Complex.angle_eq_abs_arg, Function.locallyFinsuppWithin.toClosedBall_divisor, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, 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, ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, integral_comp_abs, MeasureTheory.Measure.addHaar_parallelepiped, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, posLog_eq_zero_iff, UpperHalfPlane.im_smul, abs_sin_sub_sin_le, rpow_logb_eq_abs, Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_pi, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, abs_rpow_of_nonneg, ModularGroup.exists_row_one_eq_and_min_re, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, ValueDistribution.characteristic_sub_characteristic_inv_le, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, 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, deriv_abs_zero, hasStrictDerivAt_abs, RCLike.abs_im_le_norm, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', ProbabilityTheory.gaussianReal_mul_const, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, HasFDerivAt.abs_of_neg, ContinuousLinearMap.rayleighQuotient_le_norm, abs_norm_sub_norm_le, NumberField.Ideal.tendsto_norm_le_div_atTopβ, MeasureTheory.lpNorm_abs, deriv_abs_pos, exists_polynomial_near_continuousMap, abs_sin_half, DifferentiableOn.abs, abs_sin_eq_sqrt_one_sub_cos_sq, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, AkraBazziRecurrence.GrowsPolynomially.abs, abs_rpow_le_abs_rpow, MeasureTheory.Measure.integral_comp_mul_left, Asymptotics.isBigOWith_abs_abs, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, Liouville.frequently_exists_num, Complex.norm_ratCast, Complex.abs_im_lt_norm, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul, Affine.Simplex.inradius_eq_abs_inv_sum, MeasureTheory.setIntegral_abs_condExp_le, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, MeasurableEmbedding.gaussianReal_comap_apply, Angle.sign_two_nsmul_eq_sign_iff, enorm_eq_ofReal_abs, NumberField.mixedEmbedding.norm_smul, circleMap_preimage_codiscrete, Complex.abs_arg_inv, MeasureTheory.integral_comp_rpow_Ioi, posLog_abs, Int.tendsto_zmultiplesHom_cofinite, InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm, abs_real_inner_div_norm_mul_norm_le_one, MeasureTheory.Measure.addHaar_image_linearMap, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, intervalIntegral.abs_integral_le_integral_abs, differentiableWithinAt_abs_neg, Complex.abs_arg_le_pi_div_two_iff, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, ProbabilityTheory.gaussianReal_map_mul_const, LiouvilleWith.frequently_lt_rpow_neg, Asymptotics.IsBigOWith.abs_abs, Polynomial.exists_approx_polynomial, hasStrictDerivAt_abs_neg, RCLike.isCauSeq_norm, DifferentiableWithinAt.abs_of_neg, abs_cos_sub_cos_le, AddCircle.norm_coe_eq_abs_iff, AbsoluteValue.IsAdmissible.exists_approx, ZLattice.covolume_eq_det_mul_measureReal, RCLike.isCauSeq_im, NumberField.mixedEmbedding.covolume_integerLattice, nnnorm_abs, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul, abs_signedDist_eq_dist_iff_vsub_mem_span, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, ProbabilityTheory.integrable_exp_mul_abs_add, Angle.sign_two_zsmul_eq_neg_sign_iff, not_sameRay_iff_abs_lt_norm_sub, Orientation.abs_areaForm_le, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, tendsto_abs_tan_of_cos_eq_zero, Angle.abs_cos_eq_of_two_zsmul_eq, sin_div_le_inv_abs, MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part, ProbabilityTheory.integrable_exp_abs_mul_abs, Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_zsmul_add_eq_zero_of_sign_eq, Lp_add_le, exists_rat_abs_sub_le_and_den_le, abs_sin_lt_abs, MeasureTheory.measureReal_abs_gt_le_integral_charFun, EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, AbsoluteValue.IsAdmissible.exists_partition, MeasureTheory.addHaarMeasure_eq_volume_pi, cosh_lt_cosh, NumberField.Units.abs_det_eq_abs_det, abs_circleAverage_le_circleAverage_abs, HasFDerivWithinAt.abs_of_pos, Liouville.exists_pos_real_of_irrational_root, volume_real_interval, Complex.abs_im_div_norm_le_one, ProbabilityTheory.integrable_rpow_abs_of_integrable_exp_mul, instIsUniformAddGroupReal, ConcaveOn.isBoundedUnder_abs, ProbabilityTheory.gaussianPDFReal_inv_mul, abs_log_mul_self_rpow_lt, Complex.abs_re_le_norm, map_linearMap_volume_pi_eq_smul_volume_pi, Int.dist_eq, mellin_comp_rpow, abs_mulExpNegMulSq_one_le_one, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, AbsoluteValue.IsAdmissible.exists_partition', MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, ContDiffWithinAt.abs, dist_eq, Orientation.abs_areaForm_of_orthogonal, UnitAddCircle.norm_eq, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, sqrt_mul_self_eq_abs, MeasureTheory.Measure.map_addHaar_smul, LiouvilleWith.exists_pos, HasDerivWithinAt.limsup_slope_le', intervalIntegral.norm_integral_le_of_norm_le_const_ae, differentiableAt_abs_pos, NNReal.abs_eq, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, isTheta_exp_comp_exp_comp, Complex.abs_arg_lt_pi_div_two_iff, Angle.abs_toReal_coe_eq_self_iff, NumberField.exists_ideal_in_class_of_norm_le, circleIntegrable_sub_zpow_iff, dist_0_eq_abs, cosh_le_cosh, abs_dist, Affine.Simplex.exradius_eq_abs_inv_sum, NumberField.Ideal.tendsto_norm_le_div_atTop, hasDerivAt_abs, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', dense_addSubgroupClosure_pair_iff, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, abs_cos_eq_sqrt_one_sub_sin_sq, Asymptotics.isLittleO_abs_right, MeasureTheory.Measure.addHaar_preimage_linearMap, sameRay_iff_norm_sub, uniformContinuous_abs, volume_uIoo, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Orientation.volumeForm_robust', InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, EuclideanGeometry.angle_eq_abs_oangle_toReal, Complex.lim_im, ExistsContDiffBumpBase.w_def, MeasureTheory.Measure.setIntegral_comp_smul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, circleAverage_log_norm_factorizedRational, toNNReal_abs, Complex.ofReal_zsmul, EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, ProbabilityTheory.rpow_abs_le_mul_max_exp, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Complex.norm_sub_eq_iff, abs_sin_eq_one_iff, Orientation.angle_eq_abs_oangle_toReal, Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, circleIntegral.norm_integral_le_of_norm_le_const', abs_dist_sub_le_dist_add_add, instIsAddHaarMeasureProdRealVolume, abs_iteratedDeriv_sin_le_one, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, MeasureTheory.abs_integral_le_integral_abs, isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo, DifferentiableAt.abs, IntervalIntegrable.abs, Complex.ofReal_comp_zsmul, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, ProbabilityTheory.rpow_abs_le_mul_exp_abs, Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples, BoundedContinuousFunction.norm_sub_nonneg, EReal.abs_def, HurwitzZeta.completedCosZeta_eq, Complex.isCauSeq_im, ProbabilityTheory.integrable_pow_abs_mul_exp_of_integrable_exp_mul, logb_abs, MeasureTheory.lintegral_image_eq_lintegral_abs_deriv_mul, ContDiff.abs, intervalIntegral.norm_integral_le_of_norm_le_const, ProbabilityTheory.abs_truncation_le_abs_self, MeasureTheory.isAddHaarMeasure_volume_pi, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, AddCircle.norm_le_half_period, NumberField.mixedEmbedding.normAtPlace_smul, BumpCovering.exists_finset_toPOUFun_eventuallyEq, Complex.abs_re_lt_norm, intervalIntegral.abs_integral_eq_abs_integral_uIoc, inner_le_Lp_mul_Lq, ProbabilityTheory.meas_ge_le_evariance_div_sq, map_volume_mul_right, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul', Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, ModularForm.prod_fintype_slash, circleIntegrable_sub_inv_iff, AbsoluteValue.IsAdmissible.exists_approx_aux, BoxIntegral.Box.volume_apply, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, tendsto_abs_logb_atTop, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Complex.angle_one_left, InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero, CFC.posPart_algebraMap, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, abs_norm_sub_norm_le', hasDerivWithinAt_abs_neg, contDiffWithinAt_abs, abs_sin_le_abs, ProbabilityTheory.strong_law_aux1, Hyperreal.coe_abs, ContinuousLinearMap.bddAbove_rayleighQuotient, Asymptotics.IsBigO.abs_abs, Complex.angle_one_right, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_imageβ, ModularForm.slash_def, Complex.lim_norm, abs_sin_le_one, Complex.re_zsmul, CFC.negPart_def, instIsTopologicalAddGroupReal, Angle.coe_zsmul, tendsto_abs_tan_atTop, enorm_abs, SchwartzMap.le_seminorm', NumberField.mixedEmbedding.norm_real, AlternatingMap.measure_parallelepiped, abs_mulExpNegMulSq_le, intervalIntegral.norm_integral_le_abs_integral_norm, AddCircle.norm_eq, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, MeasureTheory.addHaarMeasure_eq_volume, exp_one_near_10, AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, Angle.abs_cos_eq_of_two_nsmul_eq, Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_nsmul_add_eq_zero_of_sign_eq, Complex.isCauSeq_norm, ENNReal.abs_toReal, Complex.IsExpCmpFilter.tendsto_abs_re, Asymptotics.IsBigO.abs_right, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, differentiableOn_abs, abs_ofDigits_sub_ofDigits_le, circleAverage_abs_radius, CFC.posPart_def, ContDiffAt.abs, EReal.coe_abs, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, NNReal.dist_eq, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Angle.abs_sin_eq_of_two_zsmul_eq, NumberField.mixedEmbedding.instIsAddHaarMeasureRealMixedSpaceVolume, abs_norm, 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, abs_rpow_le_exp_log_mul, UpperHalfPlane.mem_verticalStrip_iff, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, half_mul_log_add_log_abs, MeasurableEquiv.gaussianReal_map_symm_apply, Circle.exp_zsmul, abs_real_inner_div_norm_mul_norm_eq_one_iff, Angle.abs_sin_eq_of_two_nsmul_eq, GaussianFourier.verticalIntegral_norm_le, volume_uIoc, HurwitzZeta.completedHurwitzZetaEven_residue_zero, CircleIntegrable.abs, TFAE_exists_lt_isLittleO_pow, ProbabilityTheory.gaussianPDFReal_mul, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, AddCircle.norm_eq', NumberField.Units.finrank_mul_regulator_eq_det, abs_cos_eq_one_iff, abs_signedDist_le_dist, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Complex.im_zsmul, 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, MeasureTheory.integral_abs_condExp_le, Complex.norm_intCast, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, mem_closure_iff, Asymptotics.IsLittleO.abs_right, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, OrthonormalBasis.abs_det_adjustToOrientation, RCLike.isCauSeq_re, Subgroup.strictPeriods_eq_zmultiples_strictWidthInfty, log_of_ne_zero, MeasureTheory.upcrossingsBefore_pos_eq, Function.Periodic.intervalIntegral_add_zsmul_eq, exp_log_eq_abs, NumberField.Units.regOfFamily_eq_det', CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_neg, isAddFundamentalDomain_Ioc', Asymptotics.IsBigOWith.abs_left, sinc_le_inv_abs, AddCircle.norm_eq_of_zero, abs_log_mul_self_lt, volume_preimage_mul_right, UpperHalfPlane.smulAux'_im, integral_pow_abs_sub_uIoc, MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar, Complex.isCauSeq_re, Subgroup.periods_eq_zmultiples_widthInfty, isCauSeq_iff_lift, ODE.FunSpace.dist_iterate_next_apply_le, DifferentiableAt.abs_of_pos, circleMap_mem_sphere', CompactlySupportedContinuousMap.nnrealPart_neg_eq_zero_of_nonneg, norm_eq_abs, DifferentiableAt.abs_of_neg, exists_int_int_abs_mul_sub_le, not_differentiableAt_abs_zero, MeasureTheory.volume_sum_rpow_lt_one, Complex.dist_conj_self, arcsin_projIcc, summable_one_div_int_add_rpow, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, cos_abs, MeasureTheory.Measure.integral_comp_div, 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, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, Complex.abs_re_div_norm_le_one, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, contDiffAt_abs, volume_interval, Angle.eq_iff_abs_toReal_eq_of_sign_eq, Complex.lim_re, BoxIntegral.unitPartition.tag_mem_smul_span, HasDerivWithinAt.limsup_slope_le, Asymptotics.isBigO_abs_right, Asymptotics.isLittleO_abs_left, ZLattice.covolume_eq_det, NumberField.mixedEmbedding.normAtPlace_real, HurwitzZeta.hasSum_int_evenKernelβ, PowerSeries.IsRestricted.isRestricted_iff_abs, ModularForm.slash_apply, Complex.angle_exp_exp, abs_exp, Complex.lim_eq_lim_im_add_lim_re, MeasureTheory.Measure.integral_comp_inv_mul_right, MeasureTheory.BorelCantelli.process_difference_le, MeasureTheory.Measure.addHaar_smul, Orientation.abs_volumeForm_apply_le, UpperHalfPlane.petersson_slash, map_volume_mul_left, MeasureTheory.Measure.addHaar_image_homothety, ModularGroup.coe_truncatedFundamentalDomain
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instAddLeftCancelSemigroup π | CompOp | 2 mathmath: fourierCoeff_liftIoc_eq, fourierCoeff_liftIco_eq
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instAddMonoid π | CompOp | 384 mathmath: ValueDistribution.logCounting_zero, RCLike.conj_re, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, RCLike.sqrt_eq_ite, Complex.im_qsmul, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, RCLike.one_re, RCLike.map_apply, RCLike.geometric_hahn_banach_point_open, sSup_smul_of_nonpos, hasFDerivAt_fourierChar_neg_bilinear_left, RCLike.reCLM_apply, CircleDeg1Lift.translate_inv_apply, RCLike.div_re_ofReal, RCLike.separate_convex_open_set, NumberField.Units.logEmbedding_fundSystem, RCLike.re_add_im, InnerProductSpace.Core.inner_mul_inner_self_le, Complex.real_smul, fourierIntegral_eq, Submodule.re_inner_starProjection_eq_normSq, fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.IsPositive.re_inner_nonneg_right, LinearMap.IsSymmetric.im_inner_self_apply, RCLike.sub_conj, RCLike.re_sqrt_ofReal, RCLike.pos_iff, BoxIntegral.unitPartition.mem_smul_span_iff, Circle.starRingEnd_addChar, RCLike.ofReal_re, RCLike.re_add_im_ax, exp_nsmul, RCLike.is_real_TFAE, RCLike.abs_im_div_norm_le_one, norm_sub_mul_self, CompactlySupportedContinuousMap.nnrealPart_smul_neg, Matrix.IsHermitian.eigenvalues_eq, ValueDistribution.logCounting_pow_top, UpperHalfPlane.isometry_real_vadd, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, ConvexOn.univ_sSup_of_countable_affine_eq, RCLike.ofNat_re, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, RCLike.nonpos_iff, RCLike.smul_re, ValueDistribution.proximity_pow_zero, Function.locallyFinsuppWithin.logCounting_nonneg, RCLike.abs_re_le_norm, RCLike.geometric_hahn_banach_closed_point, AEMeasurable.im, Archimedean.embedReal_apply, RCLike.norm_sq_eq_def_ax, Complex.im_nnqsmul, RCLike.intCast_re, RCLike.im_eq_zero_iff_isSelfAdjoint, inner_mul_inner_self_le, RCLike.mul_im_ax, Function.locallyFinsuppWithin.logCounting_eval_zero, InnerProductSpace.Core.norm_eq_sqrt_re_inner, Pi.sum_norm_apply_le_norm', RCLike.abs_re_div_norm_le_one, norm_sub_sq, ValueDistribution.logCounting_top, RCLike.I_re_ax, RCLike.re_nonneg_of_nonneg, LinearMap.IsSymmetric.coe_re_inner_self_apply, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, pow_mem_closedBall, Function.locallyFinsuppWithin.logCounting_eventually_le, inner_re_zero_right, UpperHalfPlane.vadd_re, RCLike.re_monotone, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, CircleDeg1Lift.translate_iterate, RCLike.im_ofReal_pow, NumberField.Units.logEmbeddingQuot_apply, LowerSemicontinuousOn.isClosed_re_epigraph, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, NumberField.Units.basisOfIsMaxRank_apply, inner_self_im, tendsto_integral_exp_smul_cocompact, inner_re_zero_left, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, inner_self_ofReal_re, RCLike.imLm_coe, RCLike.div_im, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, RCLike.im_to_real, fourier_real_eq, RCLike.ext_iff, Angle.coe_coeHom, fourierIntegral_convergent_iff', RCLike.re_eq_norm_of_mul_conj, RCLike.conj_eq_iff_re, Function.locallyFinsuppWithin.logCounting_eventuallyLE, ConvexOn.sSup_of_countable_affine_eq, RCLike.ofNat_mul_re, InnerProductSpace.Core.inner_im_symm, continuous_probChar, RCLike.I_eq_zero_or_im_I_eq_one, RCLike.le_iff_re_im, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, RCLike.measurable_re, real_inner_eq_re_inner, RCLike.add_conj, RCLike.ofReal_re_ax, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, RCLike.im_eq_conj_sub, RCLike.conj_im_ax, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, Angle.sin_two_nsmul, RCLike.im_mul_ofReal, RCLike.geometric_hahn_banach_point_point, LinearMap.extendToπ'_apply_re, fourierIntegral_eq_half_sub_half_period_translate, RCLike.re_to_real, RCLike.neg_iff, RCLike.sqrt_eq_real_add_ite, RCLike.inv_im, InnerProductSpaceable.inner_.norm_sq, ConvexOn.sSup_of_nat_affine_eq, RCLike.one_im, RCLike.natCast_re, InnerProductSpace.Core.inner_self_nonneg, inner_re_symm, ProbabilityTheory.gaussianReal_conv_gaussianReal, tendsto_integral_mul_one_add_inv_smul_sq_pow, RCLike.norm_le_re_iff_eq_norm, RCLike.ofReal_im, RCLike.abs_im_le_norm, smul_iInf_of_nonpos, RCLike.nonneg_iff, Circle.star_addChar, RCLike.continuous_re, NumberField.mixedEmbedding.logMap_eq_logEmbedding, nsmul_mem_closedBall, RCLike.zero_re, Archimedean.embedReal_injective, InnerProductSpace.Core.inner_re_symm, RCLike.smul_im, Pi.sum_norm_apply_le_norm, RCLike.re_eq_add_conj, fourier_eq, ContinuousLinearMap.reApplyInnerSelf_apply, inner_self_eq_norm_mul_norm, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, RCLike.norm_nsmul, CircleDeg1Lift.translate_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, LinearMap.re_inner_adjoint_mul_self_nonneg, MeasureTheory.Integrable.re_im_iff, ValueDistribution.characteristic_pow_zero, Complex.ofReal_nsmul, Measurable.im, RCLike.norm_im_le_norm, NNReal.coe_nnqsmul, ConvexOn.convex_re_epigraph, ValueDistribution.characteristic_sub_characteristic_inv, RCLike.sqrt_of_nonneg, LinearMap.isPositive_iff_complex, inner_self_eq_norm_sq, RCLike.lipschitzWith_re, Measurable.re, NNReal.coe_nsmul, MeasureTheory.lpNorm_nsmul, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, MeasureTheory.AEStronglyMeasurable.re, RCLike.I_im, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, RCLike.ofNat_mul_im, RCLike.isCauSeq_im, InnerProductSpace.norm_sq_eq_re_inner, CircleDeg1Lift.translate_zpow, RCLike.hasSum_re, locallyFinsuppWithin.logCounting_divisor, Complex.coe_imAddGroupHom, RCLike.mul_im_I_ax, probChar_apply', PreInnerProductSpace.Core.re_inner_nonneg, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, CompactlySupportedContinuousMap.toReal_add, RCLike.re_mul_ofReal, RCLike.im_tsum, RCLike.norm_re_le_norm, re_inner_self_pos, NumberField.mixedEmbedding.logMap_unit_smul, ValueDistribution.characteristic_pow_top, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, Complex.im_nsmul, ENNReal.toReal_nsmul, RCLike.geometric_hahn_banach_open, fourierIntegral_convergent_iff, ENNReal.ofReal_nsmul, hasDerivAt_fourierChar, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, Complex.re_qsmul, RCLike.re_le_re, RCLike.reLm_coe, Angle.coe_nsmul, RCLike.natCast_im, MeasureTheory.MemLp.re, RCLike.ratCast_re, MeasureTheory.AEStronglyMeasurable.im, RCLike.ofReal_eq_re_of_isSelfAdjoint, Matrix.IsHermitian.coe_re_apply_self, MeasureTheory.Integrable.re, integral_coe_re_add_coe_im, RCLike.lt_iff_re_im, ConvexOn.univ_sSup_affine_eq, norm_add_sq, RCLike.norm_sq_re_conj_add, norm_add_mul_self, RCLike.conj_im, fourierChar_apply, fourier_bilin_convolution_eq_integral, InnerProductSpace.Core.inner_self_ofReal_re, RCLike.hasSum_iff, RCLike.measurable_im, tendsto_integral_exp_smul_cocompact, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, UpperHalfPlane.vadd_right_cancel_iff, RCLike.re_eq_ofReal_of_isSelfAdjoint, Archimedean.exists_orderAddMonoidHom_real_injective, Matrix.PosSemidef.re_dotProduct_nonneg, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, RCLike.re_le_norm, Complex.ofReal_qsmul, ContinuousLinearMap.isPositive_iff_complex, fourierIntegral_half_period_translate, RCLike.ofNat_im, NumberField.Units.logEmbeddingQuot_injective, BoundedContinuousFunction.integral_add_const, RCLike.norm_sq_eq_def, Matrix.IsHermitian.coe_re_diag, RCLike.ratCast_im, RCLike.I_mul_re, RCLike.conj_eq_iff_im, Function.locallyFinsuppWithin.logCounting_mono, EReal.coe_nsmul, RCLike.conj_re_ax, Complex.ofReal_comp_nsmul, BoundedContinuousFunction.add_norm_nonneg, inner_mul_symm_re_eq_norm, CompactlySupportedContinuousMap.toReal_smul, Submodule.re_inner_starProjection_nonneg, sInf_smul_of_nonpos, MeasureTheory.MemLp.im, fourierChar_apply', RCLike.realRingEquiv_apply, differentiable_fourierChar, ValueDistribution.proximity_pow_top, RCLike.mul_im, ValueDistribution.logCounting_pow_zero, RCLike.im_sq_le_normSq, continuous_fourierChar, RCLike.re_ofReal_pow, re_inner_self_nonpos, RCLike.norm_sq_re_add_conj, LinearMap.IsSymmetric.im_inner_apply_self, RCLike.im_to_complex, expMonoidHom_apply, InnerProductSpace.Core.cauchy_schwarz_aux', SlashInvariantForm.vAdd_width_periodic, UpperHalfPlane.coe_vadd, Function.locallyFinsuppWithin.logCounting_le, deriv_fourierChar, RCLike.re_eq_complex_re, RCLike.norm_to_complex, RCLike.re_sq_le_normSq, differentiable_fourierChar_neg_bilinear_right, RCLike.mul_re, smul_iSup_of_nonpos, tendsto_integral_exp_inner_smul_cocompact, Seminorm.coeFnAddMonoidHom_apply, RCLike.re_le_neg_norm_iff_eq_neg_norm, CompactlySupportedContinuousMap.nnrealPart_smul_pos, RCLike.to_complex_nonneg_iff, UpperHalfPlane.modular_T_zpow_smul, NumberField.Units.logEmbeddingEquiv_apply, RCLike.im_ofReal_mul, inner_self_re_eq_norm, Circle.expHom_apply, RCLike.I_re, hasFDerivAt_fourierChar_neg_bilinear_right, Complex.re_nnqsmul, RCLike.im_eq_complex_im, RCLike.ofReal_im_ax, InnerProductSpace.Core.inner_self_im, CircleDeg1Lift.translationNumber_translate, differentiable_fourierChar_neg_bilinear_left, pow_mem_ball, AEMeasurable.re, fourierCoeff_liftIoc_eq, ContinuousMapZero.toNNReal_neg_smul, RCLike.re_ofReal_mul, norm_add_pow_two, norm_eq_sqrt_re_inner, RCLike.iInter_halfSpaces_eq, inner_self_nonneg, RCLike.continuous_im, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, RCLike.normSq_add, RCLike.div_re, setIntegral_re_add_im, RCLike.geometric_hahn_banach_compact_closed, RCLike.geometric_hahn_banach_point_closed, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, ContinuousMapZero.toNNReal_smul, norm_sub_pow_two, fourierInv_eq, Module.Basis.opNorm_le, Archimedean.embedReal_one, RCLike.conj_eq_re_sub_im, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, Complex.re_nsmul, integral_re, RCLike.normSq_apply, Complex.ofReal_nnqsmul, ConvexOn.exists_affine_le_of_lt, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, probChar_apply, NumberField.Units.regulator_eq_det', re_inner_le_norm, ValueDistribution.logCounting_coe, RCLike.mul_re_ax, LinearMap.im_inner_adjoint_mul_self_eq_zero, ValueDistribution.log_counting_zero_sub_logCounting_top, integral_re_add_im, NumberField.Units.dirichletUnitTheorem.logEmbedding_ker, VectorFourier.hasFDerivAt_fourierChar_smul, fourierIntegral_real_eq, RCLike.norm_le_im_iff_eq_I_mul_norm, RCLike.re_to_complex, nsmul_mem_ball, RCLike.hasSum_im, RCLike.isCauSeq_re, RCLike.I_im', CircleDeg1Lift.translate_pow, Seminorm.coeFnAddMonoidHom_injective, hasLipschitzAdd, fourierIntegralInv_eq, NumberField.Units.regOfFamily_eq_det', ConvexOn.sSup_affine_eq, LinearMap.IsSymmetric.coe_re_inner_apply_self, fderiv_fourierChar_neg_bilinear_left_apply, Function.locallyFinsuppWithin.logCounting_even, RCLike.geometric_hahn_banach_closed_compact, RCLike.intCast_im, SlashInvariantForm.vAdd_apply_of_mem_strictPeriods, inner_im_symm, RCLike.re_extendToπ'β, MeasureTheory.memLp_re_im_iff, RCLike.normSq_sub, RCLike.re_tsum, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, UpperHalfPlane.vadd_im, Circle.exp_nsmul, fourierCoeff_liftIco_eq, RCLike.imCLM_apply, ConvexOn.univ_sSup_of_nat_affine_eq, UpperHalfPlane.modular_T_smul, RCLike.geometric_hahn_banach_open_open, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, RCLike.lipschitzWith_im, Complex.coe_reAddGroupHom, MeasureTheory.charFun_eq_integral_probChar, UpperHalfPlane.vadd_left_injective, integral_im, hahnEmbedding_isOrderedAddMonoid, RCLike.im_le_norm, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, BoxIntegral.unitPartition.tag_mem_smul_span, RCLike.inv_re, Matrix.PosDef.re_dotProduct_pos, MeasureTheory.Integrable.im, LinearMap.IsPositive.re_inner_nonneg_left, RCLike.zero_im, RCLike.im_eq_zero, RCLike.geometric_hahn_banach_open_point
|
instAddRightCancelSemigroup π | CompOp | β |
instAddSemigroup π | CompOp | β |
instCommMonoid π | CompOp | 220 mathmath: NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Orientation.kahler_map_complex, SchwartzMap.lineDerivOpCLM_eq, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, norm_torusIntegral_le_of_norm_le_const, SchwartzMap.instLineDerivLeftSMulReal, AddDissociated.randomisation, Complex.kahler, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_le, Height.mulHeightβ_eq, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, Complex.integral_comp_pi_polarCoord_symm, BumpCovering.toPartitionOfUnity_apply, ContDiffMapSupportedIn.iteratedFDerivLM_apply, ContinuousMultilinearMap.norm_map_snoc_le, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, Orientation.kahler_comp_rightAngleRotation', Polynomial.Chebyshev.zero_lt_prod_node_sub_node, ProbabilityTheory.iIndepFun.mgf_sumβ, log_prod, ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, Polynomial.one_le_prod_max_one_norm_roots, OrderedFinpartition.norm_applyOrderedFinpartition_le, NumberField.FinitePlace.prod_eq_inv_abs_norm, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, SchwartzMap.fderivCLM_apply, NumberField.prod_abs_eq_one, Multipliable.norm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, toNNReal_prod_of_nonneg, NumberField.FinitePlace.prod_eq_inv_abs_norm_int, MeasureTheory.L1.setToL1_smul_left, Finsupp.logb_prod, harm_mean_le_geom_mean_weighted, ProbabilityTheory.iCondIndep_iff, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, SchwartzMap.smulLeftCLM_real_smul, Orientation.kahler_eq_zero_iff, logb_prod, multiset_prod_map_rpow, Orientation.kahler_swap, multipliable_norm_one_add_of_summable_norm, Orientation.kahler_comp_rightAngleRotation, NumberField.mulHeight_eq, NNReal.coe_prod, SchwartzMap.laplacianCLM_eq', SmoothBumpCovering.toSmoothPartitionOfUnity_apply, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, harm_mean_le_geom_mean, PiTensorProduct.projectiveSeminorm_tprod_le, NNReal.coe_multiset_prod, ContinuousMultilinearMap.le_opNorm, volume_Icc_pi_toReal, ContinuousAlternatingMap.le_opNorm, MultilinearMap.exists_bound_of_continuous, ContDiffMapSupportedIn.uniformSpace_eq_iInf, volume_pi_Ioc_toReal, BoxIntegral.BoxAdditiveMap.volume_apply, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, BumpCovering.toPartitionOfUnity_eq_mul_prod, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, FormalMultilinearSeries.compAlongComposition_bound, AlternatingMap.exists_bound_of_continuous, geom_mean_eq_arith_mean_weighted_iff', SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff, Complex.ofReal_prod, Orientation.kahler_neg_orientation, rpow_sum_of_pos, ContinuousMultilinearMap.norm_map_init_le, SchwartzMap.smulRightCLM_apply_apply, MeasureTheory.setToFun_smul_left, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, ProbabilityTheory.iCondIndepSets_singleton_iff, norm_iteratedFDerivWithin_prod_le, RCLike.ofReal_prod, BoxIntegral.Box.volume_face_mul, Distribution.mapCLM_apply, RCLike.ofReal_finsuppProd, MeasureTheory.integral_posConvolution, Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line, BoxIntegral.Box.volume_apply', ContDiffMapSupportedIn.locallyConvexSpace, Height.mulHeightβ_sum_le, Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod, ProbabilityTheory.iCondIndepSet_iff, SchwartzMap.fourier_evalCLM_eq, SchwartzMap.evalCLM_apply_apply, Multipliable.norm_tprod, Height.mulHeight_eq, ContinuousLinearMap.norm_map_tail_le, multipliable_one_add_of_summable, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, ContinuousMultilinearMap.ratio_le_opNorm, volume_pi_Ioo_toReal, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, SchwartzMap.integral_bilinear_laplacian_right_eq_left, FormalMultilinearSeries.compAlongComposition_norm, Orientation.kahler_apply_self, Finset.norm_prod_le', Orientation.kahler_rotation_left', norm_prod, ContDiff.fourierPowSMulRight, Orientation.normSq_kahler, ContinuousAlternatingMap.norm_image_sub_le', ProbabilityTheory.iCondIndepSets_iff, geom_mean_lt_arith_mean_weighted_iff_of_pos, ENNReal.toReal_prod, exp_multiset_sum, ContinuousAlternatingMap.le_of_opNorm_le, Orientation.kahler_rightAngleRotation_left, rpow_sum_of_nonneg, Orientation.kahler_comp_linearIsometryEquiv, ENNReal.ofReal_prod_of_nonneg, SchwartzMap.tsupport_fderivCLM_subset, Orientation.kahler_rotation_left, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, posLog_prod, norm_iteratedFDeriv_prod_le, BumpCovering.sum_toPartitionOfUnity_eq, Orientation.kahler_mul, SchwartzMap.instLocallyConvexSpace, PiTensorProduct.mapL_opNorm, geom_mean_eq_arith_mean_weighted_iff, geom_mean_le_arith_mean, ProbabilityTheory.iCondIndepFun_iff, volume_pi_Ico_toReal, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1, SchwartzMap.fderivCLM_fourier_eq, det_fderivPiPolarCoordSymm, log_multiset_prod, ContinuousMultilinearMap.bound, ContDiffPointwiseHolderAt.fderiv, ContinuousAlternatingMap.opNorm_le_iff, VectorFourier.fourierPowSMulRight_apply, Finsupp.log_prod, BumpCovering.exists_finset_toPOUFun_eventuallyEq, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, ContinuousMultilinearMap.le_of_opNorm_le, Orientation.volumeForm_apply_le, BoxIntegral.Box.volume_apply, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, TestFunction.instLocallyConvexSpaceReal, Orientation.kahler_apply_apply, hasFDerivAt_integral_of_dominated_of_fderiv_le'', Orientation.kahler_rotation_right, integral_sin_pow_odd, geom_mean_eq_arith_mean_weighted_of_constant, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, geom_mean_weighted_of_constant, SchwartzMap.fourier_fderivCLM_eq, tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Complex.norm_prod, TestFunction.instContinuousSMulReal, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, ContDiffPointwiseHolderAt.iteratedFDeriv, NumberField.house_prod_le, ContinuousMultilinearMap.opNorm_le_iff, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, ContinuousMultilinearMap.norm_map_cons_le, BumpCovering.toPOUFun_eq_mul_prod, ContinuousAlternatingMap.bound, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, HasSum.rexp, NumberField.mixedEmbedding.fundamentalCone.expMap_sum, Orientation.kahler_rightAngleRotation_right, NumberField.InfinitePlace.prod_eq_abs_norm, PiTensorProduct.injectiveSeminorm_tprod_le, NumberField.mulHeightβ_eq, Orientation.norm_kahler, MeasureTheory.weightedSMul_smul_measure, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, rexp_tsum_eq_tprod, multipliable_of_summable_log', Height.AdmissibleAbsValues.product_formula, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, finset_prod_rpow, Finset.norm_prod_le, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, hasProd_of_hasSum_log, exp_sum, tendsto_prod_pi_div_two, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, HasProd.norm, SchwartzMap.denseRange_toLpCLM, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.norm_image_sub_le', NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, BumpCovering.sum_toPOUFun_eq, integral_comp_pi_polarCoord_symm, ProbabilityTheory.iIndepFun.mgf_sum, integral_sin_pow_even, ContinuousAlternatingMap.ratio_le_opNorm, sqrt_prod, ContDiffMapSupportedIn.structureMapLM_eq, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, NumberField.mixedEmbedding.norm_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, unitInterval.prod_mem, BoundingSieve.prod_primeFactors_nu, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, multipliable_of_summable_log, geom_mean_le_arith_mean_weighted, Orientation.abs_volumeForm_apply_le
|
instCommMonoidWithZero π | CompOp | β |
instCommSemigroup π | CompOp | β |
instCommSemiring π | CompOp | 736 mathmath: range_cfcβ_nnreal, HasStrictFDerivAt.log, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Seminorm.isBounded_const, MeasureTheory.mulEquivHaarChar_smul_integral_map, Bundle.ContMDiffRiemannianMetric.isVonNBounded, SpectrumRestricts.nnreal_of_nonneg, Bundle.ContMDiffRiemannianMetric.contMDiff, ProbabilityTheory.isGaussian_iff_gaussian_charFun, IsSelfAdjoint.quasispectrumRestricts, Matrix.IsHermitian.isClosedEmbedding_cfcAux, hasFDerivAt_fourierChar_neg_bilinear_left, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, CFC.abs_eq_cfc_norm, tendsto_tsum_div_pow_atTop_integral, CFC.sqrt_eq_one_iff', CFC.posPart_one, ContinuousMap.abs_mem_subalgebra_closure, nnnorm_cfcβ_nnreal_le_iff, Complex.ofRealCLM_coe, Complex.areaForm, CliffordAlgebraComplex.ofComplex_conj, PositiveLinearMap.apply_le_of_isSelfAdjoint, Matrix.IsHermitian.det_abs, ProbabilityTheory.covarianceBilinDual_apply', CFC.posPart_natCast, CFC.tendsto_cfc_rpow_sub_one_log, SchwartzMap.pairing_apply_apply, Complex.real_algHom_eq_id_or_conj, Matrix.IsHermitian.cfc_eq, CFC.sq_sqrt, ContinuousLinearMap.integral_apply, RCLike.algebraMap_eq_ofReal, ProbabilityTheory.covarianceBilinDual_apply, CFC.exists_pos_algebraMap_le_iff, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, strictConcaveOn_rpow, fderiv_fourierChar_neg_bilinear_right_apply, Unitization.real_cfcβ_eq_cfc_inr, geom_goldenRatio_isSol_fibRec, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Orientation.volumeForm_neg_orientation, QuasispectrumRestricts.nnreal_iff, CFC.nnnorm_sqrt, Metric.exists_forall_closedEBall_subset_auxβ, ProbabilityTheory.uncenteredCovarianceBilin_apply, CStarAlgebra.norm_or_neg_norm_mem_spectrum, SchwartzMap.bilinLeftCLM_apply, Bundle.RiemannianMetric.isVonNBounded, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, CFC.sqrt_rpow, InnerProductSpace.canonicalCovariantTensor_eq_sum, RCLike.re_add_im_ax, Matrix.PosSemidef.sqrt_eq_zero_iff, Differentiable.fderiv_norm_rpow, signedDist_right_congr, ContinuousMap.toNNReal_neg_algebraMap, SchwartzMap.laplacianCLM_eq, vector_fourierIntegral_eq_integral_exp_smul, cfc_complex_eq_real, fderivWithin_sinh, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, TestFunction.continuous_iff_continuous_comp, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, CFC.negPart_algebraMap, cfcβHom_nnreal_eq_restrict, TestFunction.toBoundedContinuousFunctionCLM_apply, ContinuousLinearMap.norm_extendToπ, hasStrictFDerivAt_rpow_of_pos, SpectrumRestricts.nnreal_iff, smul_map_diagonal_volume_pi, CliffordAlgebraComplex.ofComplex_toComplex, Orientation.volumeForm_map, toMatrix_rotation, CliffordAlgebraComplex.toComplex_comp_ofComplex, signedDist_left_congr, instStarModuleNNRealReal, QuadraticForm.equivalent_signType_weighted_sum_squared, strictConvexOn_pow, signedDist_triangle, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, convexOn_univ_dist, Continuous.cfc_nnreal', signedDist_linear_apply_apply, VectorFourier.fourierPowSMulRight_eq_comp, sameRay_iff_inv_norm_smul_eq_of_ne, UniformConvexOn.strictConvexOn, HasFDerivAt.arctan, HasStrictFDerivAt.abs, IsUnit.cfcSqrt, CFC.continuousOn_log, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, BoxIntegral.unitPartition.integralSum_eq_tsum_div, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, ProbabilityTheory.covarianceBilin_apply_basisFun_self, Orientation.areaForm_to_volumeForm, signedDist_le_dist, NNReal.algebraMap_eq_coe, HasStrictFDerivAt.arsinh, strictConvexOn_exp, HasFDerivWithinAt.exp, SchwartzMap.fourier_lineDerivOp_eq, TemperedDistribution.instLineDerivLeftSMulReal, Orientation.areaForm_neg_orientation, tendsto_card_div_pow_atTop_volume, fderivWithin_sin, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, CFC.continuousOn_sqrt, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, SchwartzMap.smulLeftCLM_real_smul, BoundedContinuousFunction.integral_const_sub, signedDist_apply_apply, Complex.liftAux_apply, strictConcaveOn_log_Iio, strictConcaveOn_univ_of_deriv2_neg, Orientation.areaForm_swap, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, Bundle.ContinuousRiemannianMetric.symm, fderiv.log, Complex.sameRay_of_arg_eq, strongConcaveOn_zero, Matrix.PosSemidef.det_sqrt, IsSelfAdjoint.coe_mem_spectrum_complex, map_matrix_volume_pi_eq_smul_volume_pi, convexOn_rpow_left, MeasureTheory.convolution_precompR_apply, ZLattice.covolume.tendsto_card_div_pow, norm_injOn_ray_right, ContinuousMap.toNNReal_algebraMap, StarAlgHom.continuous_realContinuousMapOfNNReal, Seminorm.ball_smul, Even.strictConvexOn_pow, Complex.lift_apply, Commute.cfc_real, Orientation.volumeForm_zero_pos, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, Matrix.IsHermitian.charpoly_cfc_eq, convexOn_dist, nnnorm_cfcβ_nnreal_lt, CFC.sqrt_eq_rpow, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ProbabilityTheory.covariance_smul_left, Seminorm.convexOn, strictConcaveOn_sqrt_mul_log_Ioi, Polynomial.ofReal_eval, continuousMap_mem_polynomialFunctions_closure, MeasureTheory.lpNorm_smul_measure_of_ne_zero, SchwartzMap.smulLeftCLM_sum, cfc_real_eq_nnreal, Matrix.PosSemidef.posSemidef_sqrt, StarAlgHom.realContinuousMapOfNNReal_apply, TestFunction.postcompCLM_apply, IsSelfAdjoint.neg_algebraMap_norm_le_self, Orientation.oangle_eq_zero_iff_sameRay, convexOn_univ_norm, ProbabilityTheory.condVar_smul, Orientation.angle_eq_iff_oangle_eq_or_sameRay, Orientation.rotation_map, hasFDerivAt_norm_rpow, sameRay_iff_of_norm_eq, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, concaveOn_rpow, geom_gold_isSol_fibRec, signedDist_eq_zero_of_orthogonal, ProbabilityTheory.covarianceBilin_zero, CFC.posPart_algebraMap_nnreal, RCLike.conjCLE_coe, contDiffOn_stereoToFun, SchwartzMap.smulLeftCLM_fun_neg, Matrix.PosSemidef.sqrt_eq_one_iff, coe_mem_spectrum_real_of_nonneg, fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, Bundle.ContMDiffRiemannianMetric.symm, SchwartzMap.pairing_apply, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, Quaternion.expSeries_odd_of_imaginary, AffineSubspace.signedInfDist_eq_signedDist_of_mem, HasFDerivAt.abs, CFC.sqrt_eq_one_iff, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, HasFDerivWithinAt.abs, CStarAlgebra.norm_posPart_le, Seminorm.comp_smul, IsGreatest.nnnorm_cfcβ_nnreal, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, EMetric.exists_forall_closedBall_subset_auxβ, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, HasCompactSupport.hasFDerivAt_convolution_right, ProbabilityTheory.covarianceBilinDual_zero, CFC.continuous_abs, NumberField.mixedEmbedding.convexBodySumFun_smul, continuousOn_cfc_nnreal, NumberField.mixedEmbedding.logMap_real_smul, fderivWithin_cos, CliffordAlgebraComplex.ofComplex_I, LinearMap.extendToπ_apply, innerβ_apply, ball_eq_openSegment, cfc_nnreal_eq_real, Complex.liftAux_neg_I, Seminorm.bound_of_continuous, cfcβ_real_eq_complex, Bundle.ContMDiffRiemannianMetric.pos, HasStrictFDerivAt.sqrt, signedDist_triangle_left, IsContMDiffRiemannianBundle.exists_contMDiff, HasDerivWithinAt.arsinh, HasStrictFDerivAt.rpow, ContinuousMap.sup_mem_closed_subalgebra, RCLike.ofReal_re_ax, CFC.abs_natCast, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, hasFDerivAt_integral_of_dominated_loc_of_lip', stereoToFun_apply, strictConvexOn_mul_log, ProbabilityTheory.covarianceBilin_comm, Complex.det_conjAe, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, Orientation.kahler_neg_orientation, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, SchwartzMap.smulRightCLM_apply_apply, taylor_mean_remainder, StrictMono.strictConvexOn_univ_of_deriv, EuclideanHalfSpace.convex, Complex.liftAux_I, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, Quaternion.exp_of_re_eq_zero, CStarAlgebra.instNonnegSpectrumClass, IsPreconnected.convex, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, IsSelfAdjoint.spectrum_nonempty, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, SchwartzMap.smulLeftCLM_const, Orientation.rightAngleRotation_map', MeasureTheory.Measure.toSignedMeasure_smul, Complex.algHom_ext_iff, Continuous.cfc_nnreal_of_mem_nhdsSet, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, convexOn_log_Gamma, Orientation.rotation_neg_orientation_eq_neg, Matrix.instNonnegSpectrumClass, HasFDerivWithinAt.log, Complex.range_liftAux, Orientation.areaForm'_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, Continuous.cfcβ_nnreal, Complex.liftAux_apply_I, signedDist_smul_of_pos, CFC.rpow_map_prod, IsContinuousRiemannianBundle.exists_continuous, signedDist_lineMap_lineMap, UniformConvexOn.convexOn, ContinuousAt.cfcβ_nnreal, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, tendsto_integral_mul_one_add_inv_smul_sq_pow, sameRay_iff_norm_add, signedDist_vadd_left_swap, Seminorm.const_isBounded, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, CFC.abs_algebraMap, doublingGamma_log_convex_Ioi, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, Bundle.RiemannianMetric.symm, strongConcaveOn_iff_convex, IsStrictlyPositive.nnrpow, fderiv_cos, concaveOn_univ_of_deriv2_nonpos, ContinuousMap.sup_mem_subalgebra_closure, Complex.conjAe_coe, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, signedDist_vadd_right, HasStrictFDerivAt.arctan, hasSum_sq_fourierCoeffOn, Matrix.instFiniteElemRealSpectrum, not_sameRay_iff_of_norm_eq, CFC.monotoneOn_one_sub_one_add_inv_real, convexOn_descPochhammer_eval, concaveOn_negMulLog, ContinuousWithinAt.cfcβ_nnreal, Polynomial.aeval_conj, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, ContinuousMap.inf_mem_subalgebra_closure, ProbabilityTheory.covarianceBilin_self_nonneg, WeakBilin.locallyConvexSpace, EuclideanQuadrant.convex, ContinuousMap.inf_mem_closed_subalgebra, CFC.continuousOn_nnrpow, fderiv_exp, fderiv_arctan, ProbabilityTheory.covarianceBilinDual_self_eq_variance, Orientation.areaForm_comp_linearIsometryEquiv, QuasispectrumRestricts.real_iff, TemperedDistribution.instLineDerivSMulReal, range_cfcβ_nnreal_eq_image_cfcβ_real, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, IsSelfAdjoint.sq_spectrumRestricts, Filter.Tendsto.cfcβ_nnreal, fderivWithin.log, HasFDerivWithinAt.sinh, convexOn_Gamma, IsUnit.cfcNNRpow, isConnected_setOf_sameRay_and_ne_zero, ProbabilityTheory.covarianceBilinDual_self_nonneg, HasFDerivAt.log, Complex.coe_basisOneI_repr, signedDist_lineMap_left, ProbabilityTheory.covarianceBilin_real_self, ContinuousOn.cfc_nnreal, nnnorm_cfcβ_nnreal_lt_iff, NumberField.mixedEmbedding.norm_smul, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, VectorFourier.fourierSMulRight_apply, geom_goldConj_isSol_fibRec, StrongConcaveOn.strictConcaveOn, closedBall_eq_segment, Seminorm.closedBall_smul, nnnorm_cfc_nnreal_lt, isScalarTower, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, HasFDerivAt.exp, signedDist_anticomm, SchwartzMap.smulLeftCLM_add, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Orientation.areaForm_comp_rightAngleRotation, IsStrictlyPositive.sqrt, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, tsirelson_inequality, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, convex_iff_isPreconnected, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, InformationTheory.convexOn_klFun, cfcβ_real_eq_nnreal, HasDerivAt.arsinh, nnnorm_cfc_nnreal_le, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, Continuous.cfc_nnreal, Orientation.inner_rightAngleRotation_left, CliffordAlgebraComplex.equiv_symm_apply, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, nnnorm_cfc_nnreal_le_iff, Quaternion.im_exp, fderivWithin_exp, CFC.sqrt_sq, Algebra.leftMulMatrix_complex, ProbabilityTheory.covarianceBilin_apply_pi, CFC.rpow_sqrt_nnreal, signedDist_triangle_right, UniformConcaveOn.concaveOn, Orientation.inner_mul_areaForm_sub', HasFDerivWithinAt.rpow_const, abs_signedDist_eq_dist_iff_vsub_mem_span, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, CliffordAlgebraComplex.toComplex_ΞΉ, ContinuousLinearMap.extendToπ_apply, HasFDerivAt.sinh, not_sameRay_iff_abs_lt_norm_sub, uniformConcaveOn_zero, Complex.linearEquiv_det_conjAe, Orientation.abs_areaForm_le, ContinuousMapZero.toContinuousMapHom_toNNReal, Complex.instStarModuleReal, signedDist_neg, CStarAlgebra.mul_star_le_algebraMap_norm_sq, ProbabilityTheory.covarianceBilin_apply_basisFun, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, sameRay_iff_inv_norm_smul_eq, cfcHom_nnreal_eq_restrict, Tactic.ComputeAsymptotics.Majorized.smul, strictConvexOn_rpow, Matrix.PosSemidef.sq_sqrt, signedDist_vsub_self_rev, HasFDerivAt.rpow_const, UniformConcaveOn.strictConcaveOn, ContinuousOn.cfcβ_nnreal', signedDist_linear_apply, isBoundedSMul, Orientation.rotation_eq_matrix_toLin, QuadraticForm.posDef_of_toMatrix', HasStrictFDerivAt.const_rpow, range_cfc_nnreal, ContinuousLinearMap.instNonnegSpectrumClassRealId, HasStrictFDerivAt.cos, signedDist_self, Unitization.nnreal_cfcβ_eq_cfc_inr, ProperCone.dual_flip_dual, signedDist_vsub_self, MeasureTheory.SignedMeasure.rnDeriv_smul, signedDist_smul, CStarAlgebra.norm_le_iff_le_algebraMap, HasFDerivWithinAt.arsinh, not_sameRay_iff_norm_add_lt, CFC.abs_ofNat, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, CFC.negPart_one, CFC.log_smul', isConformalMap_complex_linear_conj, Matrix.PosSemidef.inv_sqrt, Matrix.finite_real_spectrum, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, SchwartzMap.tsupport_smulLeftCLM_subset, CFC.abs_algebraMap_nnreal, Monotone.convexOn_univ_of_deriv, Complex.coe_algebraMap, HasFDerivAt.sin, Orientation.abs_areaForm_of_orthogonal, innerβ_apply_apply, ProbabilityTheory.mgf_smul_left, ContinuousLinearMap.intervalIntegral_apply, SchwartzMap.smulLeftCLM_neg, CFC.nnnorm_rpow, Continuous.cfcβ_nnreal_of_mem_nhdsSet, Orientation.inner_sq_add_areaForm_sq, signedDist_smul_of_neg, CStarAlgebra.star_mul_le_algebraMap_norm_sq, ProbabilityTheory.isPosSemidef_covarianceBilinDual, HasStrictDerivAt.arsinh, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, cfc_comp_norm, CFC.abs_intCast, apply_le_nnnorm_cfc_nnreal, HasFDerivWithinAt.sqrt, SchwartzMap.pairing_continuous_left, range_cfc_nnreal_eq_image_cfc_real, signedDist_vadd_right_swap, SchwartzMap.integralCLM_apply, fderivWithin_sqrt, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, fderiv_sinh, SchwartzMap.lineDerivOp_fourierInv_eq, CliffordAlgebraComplex.equiv_apply, ProbabilityTheory.covarianceBilin_of_not_memLp, Complex.lift_symm_apply_coe, Orientation.oangle_map, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, StarAlgHom.realContinuousMapOfNNReal_injective, HasFDerivWithinAt.arctan, NumberField.mixedEmbedding.convexBodyLT_convex, tsum_sq_fourierCoeffOn, sameRay_iff_norm_sub, ProbabilityTheory.covarianceBilinDual_comm, HasFDerivWithinAt.rpow, ProbabilityTheory.covariance_smul_right, NormedAlgebra.Real.nonempty_algEquiv_or, ProperCone.dual_dual_flip, flip_innerβ, Orientation.rightAngleRotation_trans_neg_orientation, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, CFC.spectrum_abs, strictConcaveOn_sqrt, signedDist_vadd_left, ExistsContDiffBumpBase.w_def, Polynomial.aeval_ofReal, instContinuousMapUniqueHom, InformationTheory.strictConvexOn_klFun, ProbabilityTheory.covarianceBilin_apply, HasFDerivAt.cos, ContinuousMap.comp_attachBound_mem_closure, Orientation.kahler_map, IsSelfAdjoint.map_spectrum_real, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, Matrix.IsHermitian.cfcAux_id, ProbabilityTheory.covarianceBilin_map, BoundedContinuousFunction.integral_add_const, AffineSubspace.signedInfDist_singleton, HasFDerivAt.const_rpow, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, SchwartzMap.derivCLM_apply, StrictAnti.strictConcaveOn_univ_of_deriv, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', IsCoercive.continuousLinearEquivOfBilin_apply, Orientation.volumeForm_zero_neg, Orientation.areaForm_map, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.logMap_real, AlgHom.map_coe_real_complex, Seminorm.finset_sup_smul, Bundle.RiemannianMetric.pos, CStarAlgebra.instNonnegSpectrumClass', convexOn_exp, Seminorm.isBounded_sup, CFC.sqrt_eq_cfc, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, HasFDerivAt.arsinh, strictConvexOn_univ_of_deriv2_pos, QuasispectrumRestricts.nnreal_of_nonneg, Filter.Tendsto.cfc_nnreal, IsSelfAdjoint.instContinuousFunctionalCalculus, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, CFC.abs_eq_cfcβ_norm, continuousOn_cfcβ_nnreal, CFC.abs_sq, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, InformationTheory.convexOn_Ioi_klFun, hasFDerivAt_integral_of_dominated_of_fderiv_le, VectorFourier.fourierPowSMulRight_apply, strictConcaveOn_sin_Icc, convexOn_univ_of_deriv2_nonneg, Complex.sameRay_iff, RCLike.conj_to_real, NumberField.mixedEmbedding.normAtPlace_smul, Orientation.inner_rightAngleRotation_right, CStarAlgebra.isStrictlyPositive_TFAE, fderiv_sqrt, Complex.sameRay_iff_arg_div_eq_zero, nonempty_algEquiv_or, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, CStarAlgebra.norm_negPart_le, cfcβ_nnreal_eq_real, CFC.sqrt_algebraMap, CFC.posPart_algebraMap, CFC.sqrt_one, stereographic_apply, Complex.toMatrix_conjAe, ContinuousLinearMap.IsPositive.spectrumRestricts, CFC.nnrpow_eq_cfcβ_real, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, polynomialFunctions.topologicalClosure, StrongConvexOn.strictConvexOn, Orientation.kahler_apply_apply, Orientation.inner_rightAngleRotationAuxβ_left, strictConvexOn_zpow, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, Orientation.areaForm_apply_self, differentiable_fourierChar_neg_bilinear_right, AffineSubspace.signedInfDist_def, CFC.negPart_def, signedDist_lineMap_right, SchwartzMap.tsupport_derivCLM_subset, CFC.sqrt_rpow_nnreal, strictConcave_binEntropy, nnnorm_cfc_nnreal_lt_iff, CliffordAlgebraComplex.toComplex_involute, VectorFourier.fourierIntegral_probChar, RCLike.conjAe_coe, ContinuousMap.polynomial_comp_attachBound, Orientation.rightAngleRotation_map, VectorFourier.norm_fourierSMulRight_le, CliffordAlgebraComplex.toComplex_ofComplex, signedDist_apply, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, cfc_real_eq_complex, CFC.norm_rpow, strictConcaveOn_log_Ioi, HasStrictFDerivAt.sin, signedDist_eq_dist_iff_vsub_mem_span, HasFDerivWithinAt.const_rpow, CliffordAlgebraComplex.Q_apply, fderivWithin_cosh, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, VectorFourier.norm_fourierPowSMulRight_le, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, hasFDerivAt_fourierChar_neg_bilinear_right, MonotoneOn.nnnorm_cfc, VectorFourier.norm_fourierSMulRight, RCLike.ofReal_im_ax, LinearMap.mem_span_iff_bound, ContinuousOn.cfcβ_nnreal, SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, Orientation.oangle_eq_pi_iff_sameRay_neg, CFC.posPart_def, strongConvexOn_zero, CliffordAlgebraComplex.reverse_eq_id, CFC.nnrpow_eq_rpow, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, Complex.adjoin_I, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, differentiable_fourierChar_neg_bilinear_left, Antitone.concaveOn_univ_of_deriv, Quaternion.coe_ofComplex, polynomialFunctions_closure_eq_top', ContinuousMapZero.toNNReal_neg_smul, continuousOn_cfc_nnreal_setProd, NumberField.mixedEmbedding.convexBodySum_convex, ContinuousMap.polynomial_comp_attachBound_mem, HasFDerivAt.sqrt, CFC.abs_one, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, CStarAlgebra.nonneg_TFAE, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, Quaternion.hasSum_expSeries_of_imaginary, CliffordAlgebraComplex.ofComplex_comp_toComplex, SchwartzMap.smulLeftCLM_ofReal, MeasureTheory.lpNorm_smul_measure_of_ne_top, fderiv_norm_rpow, HasStrictFDerivAt.cosh, CStarAlgebra.norm_mem_spectrum_of_nonneg, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, ContinuousMapZero.toNNReal_smul, CFC.log_algebraMap, ProbabilityTheory.covarianceBilinDual_of_not_memLp, fderivWithin_arctan, Complex.ofRealAm_coe, MeasureTheory.charFun_map_eq_charFunDual_smul, CFC.isUnit_nnrpow_iff, isConformalMap_complex_linear, zero_at_infty_vector_fourierIntegral, SchwartzMap.smulLeftCLM_apply, norm_injOn_ray_left, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, CFC.monotoneOn_cfcβ_rpowIntegrandββ, fderiv_cosh, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, TemperedDistribution.derivCLM_apply_apply, HasStrictFDerivAt.sinh, abs_signedDist_le_dist, hasStrictFDerivAt_rpow_of_neg, RCLike.ofRealCLM_coe, ProbabilityTheory.IsGaussian.charFunDual_eq', isConnected_setOf_sameRay, ContinuousAt.cfc_nnreal, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', Complex.coe_basisOneI, HasFDerivAt.cosh, Orientation.oangle_neg_orientation_eq_neg, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, signedDist_apply_linear, Bundle.RiemannianMetric.continuousAt, Subalgebra.SeparatesPoints.rclike_to_real, polynomialFunctions_closure_eq_top, VectorFourier.hasFDerivAt_fourierChar_smul, strictConcaveOn_cos_Icc, HasFDerivWithinAt.cos, ContinuousWithinAt.cfc_nnreal, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, exists_extension_norm_eq, nnnorm_cfcβ_nnreal_le, RCLike.ofRealAm_coe, CFC.sqrt_eq_real_sqrt, IsSelfAdjoint.le_algebraMap_norm_self, apply_le_nnnorm_cfcβ_nnreal, ProbabilityTheory.covarianceBilinDual_of_not_memLp', SchwartzMap.fourier_convolution, continuousOn_cfcβ_nnreal_setProd, ENNReal.toReal_smul, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, CFC.continuousOn_rpow, signedDist_left_lineMap, MonotoneOn.nnnorm_cfcβ, volume_preserving_transvectionStruct, Quaternion.coe_real_complex_mul, convexOn_mul_log, ProbabilityTheory.variance_smul, TestFunction.injective_toBoundedContinuousFunctionCLM, strictConcaveOn_negMulLog, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, CFC.nnnorm_nnrpow, fderiv_fourierChar_neg_bilinear_left_apply, CFC.rpow_eq_rpow_prod, Matrix.PosDef.posDef_sqrt, Orientation.rightAngleRotation_neg_orientation, CFC.norm_nnrpow, RCLike.re_extendToπ'β, CFC.log_smul, Commute.cfcβ_real, rpowIntegrandββ_eqOn_mul_rpowIntegrandββ_one, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, HasFDerivAt.rpow, sameRay_iff_norm_smul_eq, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, SpectrumRestricts.nnreal_iff_nnnorm, ProbabilityTheory.convex_integrableExpSet, strictConcaveOn_qaryEntropy, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, Orientation.areaForm_rightAngleRotation_left, HasFDerivWithinAt.sin, cfcβ_complex_eq_real, SchwartzMap.smulLeftCLM_smul, geom_goldenConj_isSol_fibRec, HasStrictFDerivAt.exp, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, Matrix.IsHermitian.instContinuousFunctionalCalculus, fderiv_sin, convexOn_rpow, Quaternion.exp_eq, Seminorm.smul_le_smul, MeasureTheory.addEquivAddHaarChar_smul_integral_map, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', HasCompactSupport.hasFDerivAt_convolution_left, NumberField.mixedEmbedding.convexBodyLT'_convex, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, CFC.rpow_eq_cfc_real, Complex.conjCLE_coe, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Orientation.inner_mul_areaForm_sub, uniformConvexOn_zero, signedDist_vadd_vadd, Continuous.cfcβ_nnreal', hasFDerivAt_integral_of_dominated_loc_of_lip, HasFDerivWithinAt.cosh, CFC.isUnit_sqrt_iff, convexOn_norm, HasStrictFDerivAt.rpow_const, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, CliffordAlgebraComplex.reverse_apply, CFC.rpow_sqrt, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm
|
instDistribLattice π | CompOp | β |
instDivInvMonoid π | CompOp | 1457 mathmath: CuspFormClass.qExpansion_isBigO, InnerProductGeometry.cos_angle_add_of_inner_eq_zero, pi_div_four_le_arcsin, ZLattice.summable_norm_zpow, Polynomial.Chebyshev.isExtrOn_T_real_iff, hasDerivAt_arccos, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, BoundedContinuousFunction.tietze_extension_step, aux_hasSum_of_le_geometric, MeasureTheory.setIntegral_tilted, le_log_one_add_of_nonneg, tan_pi_div_four, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, cos_pi_div_five, real_inner_div_norm_mul_norm_eq_neg_one_iff, EulerSine.integral_cos_mul_cos_pow, PiLp.nndist_eq_sum, sin_add_sin, Complex.div_ofReal_re, expNear_succ, Angle.sign_two_zsmul_eq_sign_iff, EuclideanGeometry.Sphere.thales_theorem, sinh_eq, sinh_log, mellin_eq_fourier, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, sin_arctan, MeasureTheory.norm_indicatorConstLp_le, ProbabilityTheory.gammaPDF_of_nonneg, deriv_arctan, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, arcsin_eq_pi_div_two_sub_arccos, InnerProductSpace.volume_closedBall_of_dim_even, RCLike.div_re_ofReal, Orientation.inner_rotation_pi_div_two_right_smul, intervalIntegral.intervalIntegrable_one_div_one_add_sq, tendsto_tsum_div_pow_atTop_integral, Orientation.oangle_add_left_smul_rotation_pi_div_two, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, SzemerediRegularity.energy_increment, hasDerivAt_sqrt_mul_log, arctan_eq_arcsin, ContinuousLinearMap.opNorm_bound_of_ball_bound, ContractingWith.dist_fixedPoint_le, sin_pi_div_two, intervalIntegral.inv_smul_integral_comp_div_add, ProbabilityTheory.betaPDF_eq, MeasureTheory.eLpNorm'_const', Angle.two_zsmul_eq_pi_iff, sqrt_one_add_le, integral_sin_mul_cosβ, EuclideanGeometry.dist_inversion_inversion, Angle.sin_add_pi_div_two, Stirling.factorial_isEquivalent_stirling, Complex.norm_sub_mem_Icc_angle, cos_eq_zero_iff, young_inequality, MeasureTheory.lpNorm_fun_div_natCast, log_div_le_sum_range_add, neg_pi_div_two_eq_arcsin, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, log_sqrt, UpperHalfPlane.im_div_exp_dist_le, InformationTheory.mul_log_le_klDiv, integral_exp_mul_Iic, Complex.arg_neg_I, Gamma_nat_add_half, InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero, eulerMascheroniConstant_lt_two_thirds, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, ProbabilityTheory.Fernique.lt_normThreshold_zero, NumberField.dedekindZeta_residue_def, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, Ioo_eq_ball, InnerProductGeometry.sin_angle, MeasureTheory.norm_indicatorConstLp, circleMap_neg_pi_div_two, Complex.div_ofNat_im, sqrt_div_self, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, Complex.arg_of_re_nonneg, BoxIntegral.unitPartition.box_upper, derivWithin_arctan, intervalIntegral.integral_comp_sub_div, UpperHalfPlane.im_smul_eq_div_normSq, TopologicalSpace.Opens.CompleteCopy.dist_eq, HolderTriple.holderConjugate_div_div, tendsto_cos_pi_div_two, rpow_zpow_comm, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, interval_average_eq_div, MeasureTheory.toReal_rnDeriv_tilted_left, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, MeasureTheory.le_eLpNorm_of_bddBelow, InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero, CFC.sqrt_rpow, integral_pow, summable_one_div_nat_add_rpow, PadicInt.norm_p_pow, hasSum_log_one_add_inv, integral_log_sin_zero_pi_div_two, lt_zpow_of_log_lt, LiouvilleNumber.partialSum_eq_rat, MeasureTheory.Measure.addHaarScalarFactor_eq_integral_div, schnirelmannDensity_le_iff_forall, HasConstantSpeedOnWith.ratio, ProbabilityTheory.sub_half_inf_sub_mem_Ioo, sum_geometric_two_le, EuclideanGeometry.pi_div_three_le_angle_of_le_of_le, NNReal.rpow_add_rpow_le_add, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, tan_sub', summable_one_div_int_pow, ProbabilityTheory.cgf_gaussianReal, le_schnirelmannDensity_iff, integral_inv_of_pos, UpperHalfPlane.moebius_im, RCLike.abs_im_div_norm_le_one, ModularForm.prod_slash, ProbabilityTheory.HasSubgaussianMGF.mgf_le, NumberField.abs_discr_ge', MeasureTheory.lintegral_prod_lintegral_pow_le, range_arctan, IsLowerSet.exists_subset_ball, NumberField.abs_discr_ge, WithLp.prod_nnnorm_eq_add, setOf_liouvilleWith_subset_aux, MeasureTheory.integral_tilted, deriv_arccos, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, integral_sin_pow_three, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, ENNReal.orderIsoRpow_symm_apply, deriv_sqrt_mul_log, Function.Periodic.norm_qParam_lt_iff, Wallis.W_le, one_sub_sq_div_two_le_cos, antideriv_bernoulliFun, Irrational.ratCast_div, CircleDeg1Lift.translationNumber_eq_rat_iff, HolderTriple.one_div_eq, SimpleGraph.antitoneOn_extremalNumber_div_choose_two, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, integral_exp_neg_mul_rpow, Mathlib.Meta.NormNum.rpow_isRat_eq_inv_rpow, Angle.abs_toReal_eq_pi_div_two_iff, ModularForm.prod_slash_sum_weights, Stirling.log_stirlingSeq_formula, Complex.neg_pi_div_two_lt_arg_iff, deriv.log, exp_bound, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, tendsto_exp_div_pow_atTop, log_div_log, Behrend.bound_aux', BoxIntegral.Box.upper_sub_lower_splitCenterBox, WeakFEPair.h_feq, NNReal.coe_div, ENNReal.lintegral_mul_rpow_le_lintegral_rpow_mul_lintegral_rpow, Complex.integral_rpow_mul_exp_neg_rpow, NNReal.sqrt_eq_rpow, sin_pi_div_three, integral_Ioi_rpow_of_lt, Complex.volume_sum_rpow_le, inv_logb_div_base, zpow_le_iff_le_log, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, Complex.norm_log_one_add_le, dist_inv_invβ, Complex.mul_angle_le_norm_sub, Polynomial.Chebyshev.isLocalMin_T_real, HasDerivAt.arctan, Complex.arg_le_pi_div_two_iff, HasDerivAt.sqrt, InnerProductGeometry.sin_angle_div_norm_eq_sin_angle_div_norm, rpow_mul_intCast, ContDiffBump.normed_def, intervalIntegral.intervalIntegrable_zpow, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, arctan_mem_Ioo, Angle.two_zsmul_coe_div_two, integral_rpow_mul_exp_neg_rpow, AddCircle.scaled_exp_map_periodic, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, MeasureTheory.measure_lt_one_eq_integral_div_gamma, tan_arccos, Orientation.neg_rotation_neg_pi_div_two, hasSum_sinh, LiouvilleNumber.aux_calc, sin_add_int_mul_pi, exists_of_schnirelmannDensity_eq_zero, Polynomial.isRoot_cos_pi_div_five, integral_cos_pow, neg_pi_div_two_lt_arctan, HasFDerivAt.arctan, hasStrictDerivAt_arccos, Chebyshev.psi_eq_sum_theta, Stirling.log_stirlingSeq_diff_hasSum, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, zpow_lt_iff_lt_log, artanh_eq_half_log, Complex.sin_bound, sin_sub_pi_div_two, tan_int_mul_pi_div_two, Wallis.tendsto_W_nhds_pi_div_two, zpow_lt_of_lt_log, Angle.sign_two_nsmul_eq_neg_sign_iff, NNReal.eventually_pow_one_div_le, RCLike.abs_re_div_norm_le_one, BoxIntegral.unitPartition.integralSum_eq_tsum_div, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, EuclideanGeometry.angle_orthogonalProjection_self, WithLp.prod_norm_eq_of_nat, Complex.norm_dslope_le_div_of_mapsTo_ball, Gamma_mul_Gamma_add_half, ContDiffBump.one_lt_rOut_div_rIn, sin_gt_sub_cube, two_mul_arctan_inv_2_sub_arctan_inv_7, EulerSine.integral_cos_mul_cos_pow_aux, Affine.Simplex.ninePointCircle_radius, Angle.toReal_neg_pi_div_two, LindemannWeierstrass.exp_polynomial_approx, tendsto_card_div_pow_atTop_volume, Complex.tan_arg, hasSum_cosh, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, EuclideanGeometry.inversion_vsub_center, harm_mean_le_geom_mean_weighted, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, log_two_near_10, InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, pi_div_two_le_two, NNReal.dist_agmSequences_fst_snd, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, AddCircle.norm_div_natCast, Stirling.le_log_factorial_stirling, ContDiffBump.measure_closedBall_div_le_integral, tanh_eq_sinh_div_cosh, curveIntegralFun_trans_aeeq_right, not_summable_indicator_one_div_natCast, EuclideanGeometry.Sphere.IsTangentAt.angle_eq_pi_div_two, UpperHalfPlane.dist_eq_iff_eq_sinh, Complex.arg_of_re_neg_of_im_nonneg, integral_sin_sq, arcsin_eq_pi_div_two, exp_sub_sum_range_succ_isLittleO_pow, EuclideanSpace.volume_closedBall_fin_three, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, hasSum_zeta_four, rescale_to_shell_semi_normed_zpow, cos_pi_div_four, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, descPochhammer_eval_div_factorial_le_sum_choose, HasStrictDerivAt.arctan, ENNReal.ofReal_div_of_pos, gronwallBound_of_K_ne_0, Complex.ofReal_zpow, sin_sq_arctan, intervalIntegral.integral_comp_add_div, deriv_sqrt_aux, ContinuousMap.HomotopyRel.trans_apply, Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, arccos_eq_pi_div_two_sub_arcsin, cos_add_cos, tendsto_smoothingFun_comp, ModularGroup.exists_bound_of_subgroup_invariant_of_isBigO, AkraBazziRecurrence.sumTransform_def, Complex.arg_of_im_pos, Gamma_mul_Gamma_one_sub, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Padic.norm_eq_zpow_log_mulValuation, arcsin_le_pi_div_two, NNReal.arith_mean_le_rpow_mean, SimpleGraph.triangleRemovalBound_mul_cube_lt, ZLattice.covolume.tendsto_card_div_pow, MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, niven_sin, tsum_exp_neg_mul_int_sq, tan_two_mul, Seminorm.ball_smul, LiouvilleNumber.summable, NNReal.isGreatest_Lp, hasSum_cos, ContDiffBump.normed_le_div_measure_closedBall_rOut, InnerProductGeometry.angle_zero_right, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, MeasureTheory.integral_exp_tilted, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', cos_pi_div_sixteen, zpow_le_of_le_log, rpow_sub', LSeries.summable_real_of_abscissaOfAbsConv_lt, Complex.norm_exp_I_mul_ofReal_sub_one, Angle.cos_add_pi_div_two, arctan_add_arctan_lt_pi_div_two, CFC.sqrt_eq_rpow, InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two, Complex.arg_cos_add_sin_mul_I_sub, Asymptotics.IsBigOWith.right_le_sub_of_lt_one, hasSum_log_one_add, Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, tanh_arcosh, Gamma_one_half_eq, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, pi_div_two_eq_arcsin, Complex.norm_cpow_of_ne_zero, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, Chebyshev.integral_one_div_log_sq_isBigO, ENNReal.lintegral_rpow_add_le_add_eLpNorm_mul_lintegral_rpow_add, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, toNNReal_div, Complex.integral_exp_neg_rpow, harm_mean_le_geom_mean, Complex.norm_log_sub_logTaylor_le, taylor_mean_remainder_lagrange_iteratedDeriv, le_zpow_iff_log_le, two_mul_arctan, hasDerivWithinAt_arccos_Ici, pi_div_two_pos, tan_div_sqrt_one_add_tan_sq, AddCircle.exists_norm_nsmul_le, arctan_eq_neg_pi_div_four, isEquivalent_choose, Complex.div_ofNat, InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, circleMap_pi_div_two, exists_rat_abs_sub_lt_and_lt_of_irrational, ZLattice.covolume_div_covolume_eq_relIndex, Complex.norm_cderiv_le, PiLp.edist_eq_sum, ContinuousLinearMap.exists_approx_preimage_norm_le, sqrt_two_lt_three_halves, cos_le_one_sub_mul_cos_sq, Complex.norm_cpow_of_imp, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, RCLike.div_im, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, trapezoidal_error_le_of_c2, dist_birkhoffAverage_apply_birkhoffAverage, ENNReal.eventually_pow_one_div_le, Path.Homotopy.hcomp_half, Stirling.stirlingSeq_one, logb_div, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Path.Homotopy.hcomp_apply, InnerProductGeometry.cos_angle, expNear_sub, PadicInt.norm_eq_zpow_neg_valuation, norm_sub_le_of_geometric_bound_of_hasSum, Seminorm.rescale_to_shell_zpow, cot_eq_cos_div_sin, quarters_mem_preCantorSet, MeasureTheory.volume_sum_rpow_lt, cos_one_le, EuclideanGeometry.preimage_inversion_perpBisector, MeasureTheory.integrable_comp_div_iff, Complex.div_ratCast_re, InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero, StrictMonoOn.exists_slope_lt_deriv_aux, EuclideanGeometry.angle_le_pi_div_three_of_le_of_le, ZetaAsymptotics.term_tsum_of_lt, HasDerivAt.log, AddCircle.norm_half_period_eq, Polynomial.Chebyshev.isLocalMax_T_real, Complex.norm_log_one_add_sub_self_le, tendsto_cos_neg_pi_div_two, dist_midpoint_midpoint_le, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, inner_le_Lp_mul_Lq_tsum_of_nonneg', BoxIntegral.unitPartition.mem_box_iff, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, tan_pi_div_two, dist_le_of_le_geometric_of_tendstoβ, ContractingWith.apriori_dist_iterate_fixedPoint_le, integrable_rpow_neg_one_add_norm_sq, arccos_le_pi_div_two, HasDerivWithinAt.sqrt, WithLp.prod_edist_eq_of_L2, UpperHalfPlane.cosh_dist, Padic.norm_p_pow, real_inner_div_norm_mul_norm_eq_one_iff, Chebyshev.sum_PrimePow_eq_sum_sum, Quaternion.expSeries_odd_of_imaginary, Complex.div_im, sq_cos_pi_div_six, spectrum.gelfand_formula, MeasureTheory.enorm_indicatorConstLp_le, sqrt_div', Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, one_div_one_sub_hasFPowerSeriesOnBall_zero, Irrational.intCast_div, InnerProductGeometry.sin_angle_sub_of_inner_eq_zero, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, tendsto_sin_neg_pi_div_two, Stirling.le_factorial_stirling, EuclideanGeometry.angle_self_right, ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mul, coe_fib_eq, deriv_inv_log, log_le_rpow_div, EulerSine.sin_pi_mul_eq, ContinuousLinearMap.ratio_le_opNorm, CircleDeg1Lift.transnumAuxSeq_dist_lt, Chebyshev.primeCounting_eq_theta_div_log_add_integral, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, Metric.uniformity_basis_dist_inv_nat_succ, bernstein.variance, NormedSpace.polar_ball_subset_closedBall_div, arcsin_neg_one, LiouvilleNumber.remainder_summable, sum_div_nat_floor_pow_sq_le_div_sq, Nat.realSqrt_mem_Ico, HurwitzKernelBounds.F_nat_one_le, EuclideanGeometry.image_inversion_perpBisector, CircleDeg1Lift.tendsto_translation_number', Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO, Affine.Triangle.acuteAngled_iff_angle_lt, ProbabilityTheory.betaPDF_of_pos_lt_one, sin_pi_div_two_sub, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, one_div_sub_hasFPowerSeriesOnBall_zero, log_zpow, WithLp.prod_norm_eq_add, exp_one_near_20, StrictMonoOn.exists_deriv_lt_slope_aux, irrational_div_natCast_iff, arccos_eq_pi_div_two, HasStrictFDerivAt.sqrt, sum_le_exp_of_nonneg, arcsin_mem_Icc, MeasureTheory.Lp.norm_const_le, MeasureTheory.volume_sum_rpow_le, deriv2_binEntropy, cos_pi_div_two, integral_rpow_mul_exp_neg_mul_rpow, Convex.taylor_approx_two_segment, Matrix.frobenius_norm_def, hasDerivAt_arcsin, Orientation.inner_rotation_pi_div_two_right, RingSeminorm.exists_index_pow_le, Complex.arg_one_add_mem_Ioo, exp_bound_div_one_sub_of_interval, gauge_ball, Function.Periodic.im_invQParam, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, MeasureTheory.eLpNorm'_smul_measure, MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ, hasDerivAt_tan, CircleDeg1Lift.translationNumber_of_map_pow_eq_add_int, Complex.inv_re, integral_id, Behrend.bound, Complex.arg_of_re_neg_of_im_neg, PiLp.norm_eq_sum, deriv_tan_sub_id, WeakFEPair.h_feq', stereoToFun_apply, exists_nat_abs_mul_sub_round_le, Angle.toReal_pi_div_two, dist_birkhoffAverage_birkhoffAverage, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', arctan_inv_of_neg, Orientation.inner_rotation_pi_div_two_left, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, Chebyshev.integrableOn_theta_div_id_mul_log_sq, FormalMultilinearSeries.radius_inv_eq_limsup, sin_eq_tsum, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, tendsto_rpow_div_mul_add, arccos_le_pi_div_four, cos_int_mul_pi_sub, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, Padic.norm_eq_zpow_neg_valuation, NumberField.house.exists_ne_zero_int_vec_house_le, abs_log_sub_add_sum_range_le, SlashInvariantForm.exists_one_half_le_im_and_norm_le, Complex.arg_lt_pi_div_two_iff, taylor_mean_remainder, WithLp.prod_norm_eq_add_idemFst, BoxIntegral.Box.mem_splitCenterBox, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', sin_sq_eq_half_sub, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, InnerProductSpace.volume_ball, RCLike.ofReal_zpow, cos_pi_div_eight, InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero, norm_jacobiTheta_sub_one_le, tan_sq_div_one_add_tan_sq, Nat.Primes.not_summable_one_div, PiNat.mem_cylinder_iff_dist_le, Quaternion.exp_of_re_eq_zero, injOn_tan, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, deriv_arctan, sinh_eq_tsum, Irrational.div_intCast, MeasureTheory.uniformIntegrable_average_real, integral_sin_mul_cosβ, cos_eq_tsum, MeasureTheory.Lp.norm_const', Angle.two_zsmul_neg_pi_div_two, Orientation.inner_rotation_pi_div_two_left_smul, EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two, irrational_div_intCast_iff, InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, ProbabilityTheory.tilted_mul_apply_mgf', InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero, RingSeminorm.isBoundedUnder, ContinuousMap.HomotopyWith.trans_apply, RCLike.sqrt_eq_real_add_ite, PadicInt.norm_int_le_pow_iff_dvd, integral_div_sq_add_sq, ProbabilityTheory.mgf_fun_id_gaussianReal, RCLike.inv_im, Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, Set.Icc.eq_convexCombo, rescale_to_shell, tsum_geometric_two, arith_mean_le_rpow_mean, Angle.two_zsmul_toReal_eq_two_mul, hasSum_one_div_nat_pow_mul_cos, AkraBazziRecurrence.GrowsPolynomially.div, EuclideanGeometry.oangle_orthogonalProjection_self, ModularFormClass.exp_decay_sub_atImInfty, Finset.doubling_lt_two, MeasureTheory.tilted_apply_eq_ofReal_integral, sum_range_le_log_div, ModularFormClass.exists_petersson_le, Chebyshev.primeCounting_sub_theta_div_log_isBigO, ProbabilityTheory.gaussianPDFReal_def, Complex.div_intCast, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty, intervalIntegral.inv_smul_integral_comp_sub_div, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, Behrend.exp_neg_two_mul_le, InnerProductGeometry.angle_zero_left, intervalIntegral.inv_mul_integral_comp_add_div, Complex.arg_eq_nhds_of_im_neg, NumberField.Units.regOfFamily_div_regulator, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, div_rpow, rescale_to_shell_semi_normed, EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two, integral_sin_pow_even_mul_cos_pow_even, EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist, qaryEntropy_strictAntiOn, sinOrderIso_apply, ProbabilityTheory.meas_ge_le_variance_div_sq, Angle.cos_eq_zero_iff, Lp_add_le_tsum_of_nonneg, LinearMap.bound_of_ball_bound', InnerProductSpace.volume_ball_of_dim_odd, Irrational.natCast_div, Complex.arg_of_im_nonneg_of_ne_zero, smoothingFun_le, Finset.doubling_lt_golden_ratio, strongConcaveOn_iff_convex, Complex.dist_le_div_mul_dist_of_mapsTo_ball, lt_zpow_iff_log_lt, Quaternion.expSeries_even_of_imaginary, toNNReal_div', Complex.arg_eq_pi_div_two_iff, MeasureTheory.mul_le_integral_rnDeriv_of_ac, intervalIntegral.inv_mul_integral_comp_sub_div, ZMod.toAddCircle_natCast, UpperHalfPlane.dist_eq, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, sqrt_div_self', AddCircle.exists_norm_eq_of_isOfFinAddOrder, log_div_self, NormedAddGroupHom.ratio_le_opNorm, AkraBazziRecurrence.bi_min_div_two_pos, SzemerediRegularity.edgeDensity_chunk_uniform, CircleDeg1Lift.transnumAuxSeq_def, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero, hasDerivWithinAt_arcsin_Ici, InnerProductGeometry.cos_angle_sub_of_inner_eq_zero, HasStrictFDerivAt.arctan, NumberField.Ideal.tendsto_norm_le_div_atTopβ, unitInterval.qRight_zero_right, ProbabilityTheory.strong_law_aux6, unitary.norm_argSelfAdjoint, hasSum_geometric_two, LSeries.norm_term_eq, ModularFormClass.exists_bound, ProbabilityTheory.variance_le_sq_of_bounded, intervalIntegral.integral_comp_div, InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero, MeasureTheory.tilted_apply, ProbabilityTheory.hasFPowerSeriesAt_mgf, Complex.integral_exp_neg_mul_rpow, abs_sin_half, InnerProductGeometry.tan_angle_sub_of_inner_eq_zero, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, tendsto_mul_log_one_add_div_atTop, WithLp.prod_nndist_eq_add, ZLattice.covolume.tendsto_card_le_div', EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, ContinuousOn.isBigOWith_rev_principal, ZetaAsymptotics.term_one, log_div, Polynomial.hermite_eq_deriv_gaussian', integral_inv_of_neg, BoxIntegral.unitPartition.box_lower, fderiv_arctan, ENNReal.lintegral_Lp_add_le, Path.Homotopy.trans_apply, MeasureTheory.eLpNorm_indicator_const_le, HurwitzZeta.oddKernel_functional_equation, tan_pi_div_two_sub, arcsin_of_le_neg_one, Liouville.frequently_exists_num, tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, HasStrictDerivAt.log, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, AbsoluteValue.IsEquiv.log_div_log_pos, cos_pi_div_six, InformationTheory.mul_log_le_toReal_klDiv, sin_half_eq_neg_sqrt, range_arcsin, InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero, coe_intFib_eq, intervalIntegral.inv_smul_integral_comp_div_sub, Gamma_nat_add_one_add_half, ContinuousMap.Homotopy.trans_apply, ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_eq_top, unitInterval.div_mem, InnerProductGeometry.tan_angle_add_of_inner_eq_zero, MeasureTheory.Lp.norm_constL_le, Polynomial.Chebyshev.rootMultiplicity_T_real, HasDerivWithinAt.arctan, Complex.norm_zpow, log_div_self_antitoneOn, Angle.sign_two_nsmul_eq_sign_iff, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, sin_int_mul_pi_sub, ProbabilityTheory.add_half_inf_sub_mem_Ioo, MeasureTheory.Lp.eLpNorm'_lim_eq_lintegral_liminf, tsum_geometric_two', arcsin_le_neg_pi_div_two, integral_exp_neg_rpow, Orientation.oangle_sub_right_smul_rotation_pi_div_two, abs_real_inner_div_norm_mul_norm_le_one, Angle.sin_pi_div_two_sub, sin_add_pi_div_two, tendsto_fib_div_fib_succ_atTop, ContinuousOn.isBigOWith_principal, HolderConjugate.conjugate_eq, Seminorm.closedBall_smul, MeasureTheory.eLpNorm_const', integral_inv, WithLp.prod_dist_eq_add, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le, Nat.realSqrt_lt_ratSqrt_add_inv_prec, Complex.cos_bound, taylor_tendsto, MeasureTheory.Lp.norm_const, Complex.cpow_inv_two_im_eq_sqrt, Complex.cpow_inv_two_re, one_le_pi_div_two, UnitAddCircle.mem_approxAddOrderOf_iff, tendsto_log_div_rpow_nhdsGT_zero, ContinuousMultilinearMap.ratio_le_opNorm, ZetaAsymptotics.zeta_limit_aux1, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, NNReal.rpow_inv_rpow_self, rpow_intCast_mul, cosh_le_exp_half_sq, Chebyshev.psi_eq_theta_add_sum_theta, EisensteinSeries.r1_eq, Complex.div_re, NNReal.rpow_add_rpow_le, Complex.abs_arg_le_pi_div_two_iff, NumberField.Units.regOfFamily_div_regOfFamily, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, summable_one_div_nat_rpow, rpow_sub_one, LiouvilleWith.frequently_lt_rpow_neg, AkraBazziRecurrence.asympBound_def', MeasureTheory.Measure.haarScalarFactor_eq_integral_div, Nat.roughNumbersUpTo_card_le', Polynomial.Chebyshev.isMinOn_T_real, irrational_ratCast_div_iff, schnirelmannDensity_le_div, Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, log_div_sqrt_antitoneOn, mellin_eq_fourierIntegral, unitInterval.mul_pos_mem_iff, integral_cos_pow_three, AddCircle.norm_coe_eq_abs_iff, ModularGroup.exists_one_half_le_im_smul, ENNReal.rpow_add_rpow_le, Polynomial.Chebyshev.isLocalExtr_T_real_iff, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Quaternion.im_exp, arctan_inv_2_add_arctan_inv_3, arctan_one, integral_one_div_of_pos, EuclideanGeometry.inversion_def, arccos_eq_arctan, Complex.norm_div, AddCircle.toCircle_apply_mk, CFC.rpow_sqrt_nnreal, Angle.two_nsmul_eq_pi_iff, Polynomial.hermite_eq_deriv_gaussian, one_half_lt_eulerMascheroniSeq_six, exp_half, Orientation.inner_smul_rotation_pi_div_two_right, isLittleO_zpow_exp_pos_mul_atTop, sin_pi_over_two_pow_succ, trapezoidal_integral_one, MeasureTheory.eLpNorm_nnreal_eq_lintegral, bijOn_sin, deriv_arcsin, div_sqrt, qaryEntropy_strictMonoOn, tan_pi_div_six, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, summable_one_div_pow_of_le, HasFPowerSeriesOnBall.uniform_geometric_approx', InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero, Complex.angle_le_mul_norm_sub, Angle.sign_two_zsmul_eq_neg_sign_iff, ZetaAsymptotics.term_sum_of_lt, EuclideanSpace.volume_ball_fin_three, arctan_inv_sqrt_three, rpowIntegrandββ_eq_pow_div, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, PadicInt.norm_le_pow_iff_norm_lt_pow_add_one, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, AddCircle.denseRange_zsmul_coe_iff, cos_sub_int_mul_pi, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero, Complex.div_ofReal, hasSum_geometric_two', arcsin_of_one_le, Complex.norm_prime_cpow_le_one_half, rpow_sub_one', integral_inv_sq_add_sq, MeasureTheory.nnnorm_indicatorConstLp_le, Complex.norm_cderiv_sub_lt, sin_div_le_inv_abs, ENNReal.Lp_add_le, PiNat.dist_eq_of_ne, MeasureTheory.setLIntegral_tilted, PadicInt.norm_le_pow_iff_le_valuation, irrational_div_ratCast_iff, preCantorSet_succ, ContractingWith.dist_inequality, sin_sub_int_mul_pi, Lp_add_le, ProbabilityTheory.integral_tilted_mul_eq_mgf, integral_rpow, Lp_add_le_of_nonneg, ContDiffBump.apply, EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle, tendsto_tan_pi_div_two, Orientation.neg_rotation_pi_div_two, exists_rat_abs_sub_le_and_den_le, PadicInt.norm_le_pow_iff_mem_span_pow, Complex.normSq_div, pow_div_factorial_le_exp, cos_pi_div_thirty_two, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, bernoulliFun_one, niven_angle_eq, Orientation.oangle_sub_left_smul_rotation_pi_div_two, Liouville.exists_pos_real_of_irrational_root, Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.HasSubgaussianMGF.cgf_le, ZLattice.covolume.tendsto_card_div_pow', UpperHalfPlane.dist_le_dist_coe_div_sqrt, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, Polynomial.Chebyshev.isMaxOn_T_real, Complex.abs_im_div_norm_le_one, circleMap_zero_div, CuspFormClass.exists_bound, ofCauchy_div, integral_sqrt_one_sub_sq, Polynomial.Chebyshev.rootMultiplicity_U_real, MeasureTheory.rnDeriv_tilted_left, Orientation.oangle_add_right_smul_rotation_pi_div_two, abs_log_mul_self_rpow_lt, hasStrictDerivAt_arctan, sin_bound, ENNReal.lintegral_mul_le_Lp_mul_Lq, Orientation.inner_smul_rotation_pi_div_two_left, surjOn_sin, sin_pi_div_thirty_two, intervalIntegral.inv_mul_integral_comp_div_sub, neg_pi_div_two_lt_arcsin, trapezoidal_error_le, rpow_sub_intCast', Complex.div_ofNat_re, cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, sin_pi_div_six, EulerSine.integral_cos_pow_eq, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, image_tan_Ioo, Probability.cauchyPDFReal_def', fourierCoeff_eq_intervalIntegral, tendsto_mod_div_atTop_nhds_zero_nat, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, inner_sum_smul_sum_smul_of_sum_eq_zero, norm_div, one_half_lt_eulerMascheroniConstant, numDerangements_tendsto_inv_e, tan_add', le_integral_rpowIntegrandββ_one, MeasureTheory.average_add_measure, EuclideanGeometry.inner_weightedVSub, intervalIntegral.inv_smul_integral_comp_div, LiouvilleWith.exists_pos, MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ, rpow_add_rpow_le_add, PiLp.norm_eq_of_nat, pi_lt_sqrtTwoAddSeries, ZLattice.covolume.tendsto_card_le_div, SzemerediRegularity.hundred_div_Ξ΅_pow_five_le_m, coe_fib_eq', injOn_sin, bernoulliFun_mul, Complex.div_intCast_re, ContractingWith.dist_le_of_fixedPoint, hasFPowerSeriesOnBall_linear_zero, sin_sub_sin, EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero, ODE.FunSpace.dist_iterate_next_le, hasDerivAt_Gamma_one_half, quarter_mem_preCantorSet, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, isMIntegralCurveAt_comp_mul_ne_zero, Gamma_mul_Gamma_add_half_of_pos, Complex.arg_of_im_neg, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, ProbabilityTheory.strong_law_aux7, RCLike.ofReal_div, MeasureTheory.eLpNorm'_add_le_of_le_one, ZMod.toAddCircle_intCast, Complex.abs_arg_lt_pi_div_two_iff, HasFDerivWithinAt.sqrt, lt_sin_mul, NumberField.exists_ideal_in_class_of_norm_le, Complex.sqrt_eq_real_add_ite, inner_le_Lp_mul_Lq_tsum_of_nonneg, summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, SimpleGraph.tendsto_turanDensity, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, fderivWithin_sqrt, eulerMascheroniSeq'_six_lt_two_thirds, cos_sub_cos, tendsto_sum_range_one_div_nat_succ_atTop, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, CircleDeg1Lift.tendsto_translation_numberβ, ZMod.toAddCircle_apply, tendsto_tan_neg_pi_div_two, Angle.tan_eq_sin_div_cos, ModularGroup.exists_bound_of_subgroup_invariant_of_isArithmetic_of_isBigO, MeasureTheory.SimpleFunc.eLpNorm'_eq, ModularGroup.exists_bound_of_invariant_of_isBigO, ModularGroup.im_smul_eq_div_normSq, cos_pi_over_two_pow, not_summable_one_div_natCast, one_sub_div_pow_le_exp_neg, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, UpperHalfPlane.cosh_half_dist, ProbabilityTheory.tilted_mul_apply_mgf, EuclideanSpace.volume_ball, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, dense_addSubgroupClosure_pair_iff, toNNReal_zpow, Angle.sign_coe_pi_div_two, Seminorm.rescale_to_shell, gaugeRescale_def, Angle.zsmul_eq_iff, Complex.div_ratCast_im, AkraBazziRecurrence.deriv_smoothingFn, cos_half, Path.trans_apply, HasFDerivWithinAt.arctan, MeasureTheory.setIntegral_tilted', UpperHalfPlane.exp_half_dist, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, ProbabilityTheory.iteratedDeriv_two_cgf, tendsto_arctan_atTop, integral_exp_mul_Ioi, tendsto_rpow_div, integral_sin_mul_cos_sq, HurwitzKernelBounds.F_nat_zero_zero_sub_le, quadratic_root_cos_pi_div_five, NNReal.orderIsoRpow_symm_eq, rpow_sub_natCast', geom_mean_le_arith_mean, rescale_to_shell_zpow, MeasureTheory.lpNorm_div_natCast, AkraBazziRecurrence.dist_r_b, ArchimedeanClass.stdPart_div, Complex.div_natCast_im, strictMonoOn_one_add_div_one_sub, ProbabilityTheory.deriv_cgf, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, WeakFEPair.hf_modif_FE, NNReal.Lp_add_le_tsum', rpow_add_rpow_le, Asymptotics.isBigO_iff_isBoundedUnder_le_div, quadratic_le_exp_of_nonneg, one_sub_sq_div_two_lt_cos, ProbabilityTheory.gammaPDF_eq, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, PadicInt.exists_pow_neg_lt, EuclideanGeometry.hasFDerivAt_inversion, dist_div_norm_sq_smul, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, two_mul_arctan_sub_pi, GromovHausdorff.ghDist_le_of_approx_subsets, tan_pi_div_three, ProbabilityTheory.rpow_abs_le_mul_max_exp, pi_div_two_le_arcsin, arccos_lt_pi_div_two, tendsto_rpow_neg_div, Seminorm.smul_closedBall_preimage, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, tan_eq_zero_iff, Metric.mem_closure_range_iff_nat, zero_mem_lowerBounds_smoothingSeminormSeq_range, hasSum_one_div_nat_pow_mul_sin, Polynomial.Chebyshev.roots_T_real, tendsto_arctan_atBot, two_mul_arctan_add_pi, Complex.norm_deriv_le_div_of_mapsTo_ball, Angle.two_nsmul_coe_div_two, SchwartzMap.isBigO_cocompact_zpow_neg_nat, abs_sin_eq_one_iff, Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, mapsTo_sin_Ioo, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter, Complex.GammaSeq_eq_approx_Gamma_integral, SimpleGraph.triangleRemovalBound_le, Wallis.W_eq_factorial_ratio, deriv2_qaryEntropy, hasStrictDerivAt_arcsin, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, smoothingSeminormSeq_bddBelow, integral_zpow, tendsto_sub_mul_tsum_nat_rpow, exists_hasDerivAt_eq_slope, hasSum_zeta_two, norm_midpoint_lt_iff, sin_eq_neg_one_iff, sin_pi_div_sixteen, integral_one_div_one_add_sq, AkraBazziRecurrence.GrowsPolynomially.zpow, UpperHalfPlane.sinh_half_dist_add_dist, ProbabilityTheory.lintegral_betaPDF, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one, Complex.ofReal_div, two_mul_arctan_inv_3_add_arctan_inv_7, NumberField.abs_discr_ge_of_isTotallyComplex, Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, cos_add_pi_div_two, ProbabilityTheory.rpow_abs_le_mul_exp_abs, arctan_inv_of_pos, lt_log_one_add_of_pos, MeasureTheory.lintegral_tilted, tendsto_sum_pi_div_four, rpow_neg_one_add_norm_sq_le, derivWithin_sqrt, ModularFormClass.qExpansion_isBigO, Angle.cos_pi_div_two_sub, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm_toReal, ProbabilityTheory.iteratedDeriv_two_cgf_eq_integral, Finset.card_mul_finset_lt_two, EuclideanGeometry.oangle_self_orthogonalProjection, tendsto_mul_exp_add_div_pow_atTop, LiouvilleNumber.partialSum_succ, MeasureTheory.eLpNorm_indicator_const', tendsto_div_pow_mul_exp_add_atTop, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, le_zpow_of_log_le, Seminorm.smul_ball_preimage, Complex.inv_im, RCLike.normSq_div, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg, Chebyshev.integral_theta_div_log_sq_isBigO, InnerProductGeometry.sin_angle_add_of_inner_eq_zero, exp_artanh, Hyperreal.coe_div, IsUpperSet.exists_subset_ball, AddCircle.norm_le_half_period, LinearMap.bound_of_sphere_bound, intervalIntegral.integral_comp_div_add, hasStrictDerivAt_sqrt, InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero, integral_gaussian, arcsin_lt_pi_div_two, integral_one_div, Function.Periodic.norm_qParam, inner_le_Lp_mul_Lq, ZLattice.summable_norm_sub_zpow, HurwitzZeta.hurwitzOddFEPair_k, cosh_log, arctan_lt_pi_div_two, norm_zpow, fderiv_sqrt, Polynomial.Chebyshev.eval_T_real_eq_one_iff, logb_div_base, MeasureTheory.pow_mul_meas_ge_le_eLpNorm, NNReal.inner_le_Lp_mul_Lq_tsum', integral_sin_sq_mul_cos, arctan_sqrt_three, hasSum_sin, Complex.arg_eq_nhds_of_im_pos, MeasureTheory.eLpNorm_const, EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_ne, rpow_one_sub', NNReal.Lp_add_le, curveIntegralFun_trans_aeeq_left, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, Complex.integral_rpow_mul_exp_neg_mul_rpow, rpow_sub_natCast, Chebyshev.integral_theta_div_log_sq_isLittleO, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, EulerSine.integral_cos_pow_pos, Asymptotics.isBigOWith_const_const, IsMIntegralCurveAt.comp_mul_ne_zero, schnirelmannDensity_lt_iff, sin_sq_pi_over_two_pow, sq_sin_pi_div_three, UnitAddCircle.mem_addWellApproximable_iff, stereographic_apply, tendsto_pow_logb_div_mul_add_atTop, homeomorphSphereProd_apply_snd_coe, Stirling.log_stirlingSeq_diff_le_geo_sum, Complex.neg_pi_div_two_le_arg_iff, Behrend.le_sqrt_log, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, Behrend.two_div_one_sub_two_div_e_le_eight, MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ, ProbabilityTheory.mgf_gaussianReal, monotoneOn_sin, Complex.div_ofReal_im, strictConvexOn_zpow, Irrational.div_natCast, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, Complex.norm_log_one_sub_inv_sub_self_le, tanh_eq, ProbabilityTheory.mgf_id_gaussianReal, Complex.norm_deriv_le_of_forall_mem_sphere_norm_le, exp_bound', sum_div_pow_sq_le_div_sq, tendsto_fib_succ_div_fib_atTop, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm, Behrend.bound_aux, arcsin_image_Icc, MeasureTheory.eLpNorm_indicator_constβ, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, Metric.nhds_basis_ball_inv_nat_succ, integral_rpow_mul_exp_neg_mul_Ioi, CFC.sqrt_rpow_nnreal, setOf_liouville_eq_iInter_iUnion, hasSum_arctan, Complex.cpow_inv_two_im_eq_neg_sqrt, tendsto_abs_tan_atTop, ENNReal.lintegral_Lp_add_le_of_le_one, ContDiffBump.normed_le_div_measure_closedBall_rIn, Complex.arg_eq_nhds_of_re_pos, Irrational.div_ratCast, SzemerediRegularity.edgeDensity_chunk_not_uniform, sinc_of_ne_zero, log_natCast_le_rpow_div, EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_ne, summable_geometric_two', tendsto_exp_div_rpow_atTop, HolderTriple.one_div_pos, Gamma_integrand_isLittleO, one_div_sub_pow_hasFPowerSeriesOnBall_zero, neg_pi_div_two_le_arcsin, EuclideanGeometry.angle_self_orthogonalProjection, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, ZLattice.covolume.tendsto_card_le_div'', Unitary.norm_argSelfAdjoint, fourierCoeffOn_eq_integral, HurwitzKernelBounds.F_nat_zero_le, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, HolderTriple.one_div_add_one_div, sinc_apply, tendsto_pow_const_div_const_pow_of_one_lt, integral_sin_pow_odd, EuclideanGeometry.dist_affineCombination, ContractingWith.fixedPoint_lipschitz_in_map, Angle.nsmul_toReal_eq_mul, HolderTriple.one_div_nonneg', ZetaAsymptotics.term_welldef, PiLp.nnnorm_eq_sum, exp_one_near_10, rpow_div_two_eq_sqrt, EuclideanGeometry.dist_smul_vadd_eq_dist, dist_birkhoffAverage_birkhoffAverage_le, intervalIntegral.integral_comp_div_sub, young_inequality_of_nonneg, InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero, cos_sq, intervalIntegral.inv_mul_integral_comp_div, lp.norm_eq_tsum_rpow, AffineSubspace.mem_perpBisector_iff_inner_eq, not_summable_one_div_on_primes, Orientation.rotation_pi_div_two, MeasureTheory.setLIntegral_tilted', InnerProductSpace.volume_closedBall, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, Matrix.frobenius_nnnorm_def, Padic.norm_le_pow_iff_norm_lt_pow_add_one, MeasureTheory.Measure.volumeIoiPow_apply_Iio, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, taylor_mean_remainder_cauchy, summable_geometric_two, HurwitzZeta.evenKernel_functional_equation, strongConvexOn_iff_convex, Complex.norm_log_natCast_le_rpow_div, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip', EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, tendsto_card_div_pow_atTop_volume', dist_midpoint_midpoint_le', EReal.coe_div, sum_range_sub_log_div_le, exists_deriv_eq_slope, exp_approx_end, CircleDeg1Lift.tendsto_translationNumber, HolderTriple.one_div_pos', UpperHalfPlane.sinh_half_dist, ProbabilityTheory.strong_law_ae_real, summable_one_div_nat_pow, hasStrictDerivAt_tan, MeasureTheory.eLpNorm'_eq_lintegral_enorm, InnerProductSpace.volume_closedBall_of_dim_odd, UpperHalfPlane.dist_le_iff_le_sinh, tendsto_euler_sin_prod, ProbabilityTheory.deriv_cgf_zero, sin_pi_div_eight, arctan_add, Complex.arg_eq_nhds_of_re_neg_of_im_pos, Bertrand.real_main_inequality, arctan_eq_pi_div_four, integral_Ioi_inv_one_add_sq, hasDerivAt_arctan, Complex.volume_sum_rpow_lt_one, taylor_mean_remainder_bound, Complex.betaIntegral_convergent_left, Nat.ratSqrt_mem_Ioc, MeasureTheory.norm_indicatorConstLp', exp_sub, rpow_sub_intCast, sqrt_div, DiffContOnCl.ball_subset_image_closedBall, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, Polynomial.Chebyshev.isLocalExtr_T_real, setOf_liouville_eq_irrational_inter_iInter_iUnion, HasFDerivAt.sqrt, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, ruzsaSzemerediNumberNat_lower_bound, rpow_sub, deriv_arcsin_aux, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter, MeasureTheory.tilted_eq_withDensity_nnreal, Complex.div_intCast_im, BoxIntegral.unitPartition.tag_apply, IsPrimitiveRoot.arg, tendsto_sin_pi_div_two, Angle.cos_sub_pi_div_two, arccos_zero, Polynomial.Chebyshev.isExtrOn_T_real, RCLike.div_re, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, MeasureTheory.eLpNorm_sub_le_of_dist_bdd, integral_gaussian_Ioi, arctan_add_eq_sub_pi, cosh_eq, abs_real_inner_div_norm_mul_norm_eq_one_iff, strictMonoOn_sin, unitInterval.half_le_symm_iff, UpperHalfPlane.cosh_dist', NNReal.inner_le_Lp_mul_Lq_tsum, EuclideanGeometry.dist_center_inversion, hasSum_pow_div_log_of_abs_lt_one, Orientation.inner_smul_rotation_pi_div_two_smul_right, Complex.borelCaratheodory, Complex.div_natCast, zpow_arith_mean_le_arith_mean_zpow, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, fourier_add_half_inv_index, Affine.Simplex.Equilateral.angle_eq_pi_div_three, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, StrictMonoOn.exists_slope_lt_deriv, Angle.two_nsmul_neg_pi_div_two, CuspFormClass.exp_decay_atImInfty, integral_sin_sq_mul_cos_sq, fderivWithin_arctan, integral_mul_rpow_one_add_sq, StrictMonoOn.exists_deriv_lt_slope, SchwartzMap.isBigO_cocompact_zpow, exp_bound_div_one_sub_of_interval', UpperHalfPlane.tanh_half_dist, rpow_add_intCast, ENNReal.fun_eq_funMulInvSnorm_mul_eLpNorm, dist_le_of_le_geometric_of_tendsto, NNReal.rpow_self_rpow_inv, Chebyshev.intervalIntegrable_one_div_log_sq, Complex.norm_cpow_le, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, strictMonoOn_tan, Polynomial.tendsto_div_exp_atTop, integral_Iic_inv_one_add_sq, Complex.arg_eq_nhds_of_re_neg_of_im_neg, div_logb, tendsto_pow_log_div_mul_add_atTop, rothNumberNat_le_ruzsaSzemerediNumberNat', Asymptotics.IsBigOWith.right_le_add_of_lt_one, cantorSet_eq_union_halves, ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le', BoxIntegral.unitPartition.box.upper_sub_lower, Wallis.W_succ, integral_cos_sq, ENNReal.toReal_div, arcsin_eq_arctan, Complex.arg_mul_cos_add_sin_mul_I_sub, NNReal.coe_zpow, irrational_intCast_div_iff, tanh_arsinh, rpow_neg_natCast, cosh_eq_tsum, cos_pi_div_three, Icc_eq_closedBall, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, seminormFromBounded_bddAbove_range, le_sin_mul, holderConjugate_one_div, EuclideanGeometry.dist_inversion_center, spectralValueTerms_of_lt_natDegree, Angle.toReal_eq_pi_div_two_iff, ordinaryHypergeometricSeries_norm_div_succ_norm, Complex.abs_cpow_inv_two_im, le_gauge_of_subset_closedBall, tendsto_const_div_pow, unitInterval.two_mul_sub_one_mem_iff, hasSum_zeta_nat, cos_add_int_mul_pi, MeasureTheory.tilted_apply_eq_ofReal_integral', tan_arcsin, AddChar.zmod_intCast, BoxIntegral.unitPartition.diam_boxIcc, surjOn_tan, arcsin_eq_neg_pi_div_two, ENNReal.inner_le_Lp_mul_Lq, Metric.nhds_basis_ball_inv_nat_pos, EuclideanGeometry.Sphere.secondInter_eq_lineMap, Padic.norm_lt_pow_iff_norm_le_pow_sub_one, ZLattice.covolume.tendsto_card_div_pow'', LiouvilleNumber.remainder_lt, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter, Complex.norm_fderiv_le_div_of_mapsTo_ball, InnerProductGeometry.sin_angle_add, InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero, MeasureTheory.rnDeriv_tilted_left_self, cos_sub_pi_div_two, strictConcaveOn_cos_Icc, MeasureTheory.measure_unitBall_eq_integral_div_gamma, CStarAlgebra.exists_sum_four_unitary, exp_neg_one_lt_half, ZetaAsymptotics.term_of_lt, MeasureTheory.average_union, gauge_closedBall, log_div_self_rpow_antitoneOn, EuclideanGeometry.angle_self_left, MeasureTheory.eLpNorm'_const, taylor_mean_remainder_lagrange, Complex.borelCaratheodory_zero, sin_eq_one_iff, rpow_add_intCast', InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, intervalIntegral.inv_mul_integral_comp_div_add, rpow_intCast, tendsto_factorial_div_pow_self_atTop, Angle.sin_sub_pi_div_two, holderConjugate_iff_eq_conjExponent, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, EuclideanSpace.edist_eq, EuclideanGeometry.inversion_eq_lineMap, intervalIntegral.intervalIntegrable_one_div, MeasureTheory.Lp.pow_mul_meas_ge_le_enorm, HasDerivWithinAt.log, cos_sq_arctan, NNReal.Lp_add_le_tsum, rpowIntegrandββ_one_ge_rpow_sub_two, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, seminormFromConst_seq_def, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, tendsto_prod_pi_div_two, one_half_le_sum_primes_ge_one_div, exp_sub_sum_range_isBigO_pow, hasDerivAt_sqrt, integral_one_div_of_neg, Polynomial.Chebyshev.roots_U_real_nodup, hasDerivWithinAt_arccos_Iic, Complex.approx_Gamma_integral_tendsto_Gamma_integral, Chebyshev.eventually_primeCounting_le, Padic.norm_int_le_pow_iff_dvd, Affine.Simplex.ninePointCircle_center, Gamma_three_div_two_lt_one, deriv_sqrt_mul_log', Padic.norm_p_zpow, sinh_artanh, FormalMultilinearSeries.radius_eq_liminf, deriv_tan, tendsto_one_add_div_rpow_exp, cos_int_mul_pi, Polynomial.Chebyshev.roots_T_real_nodup, Behrend.exists_large_sphere_aux, cos_pi_div_two_sub, NNReal.dist_gm_am_le, Stirling.second_wallis_limit, UpperHalfPlane.smulAux'_im, InnerProductSpace.volume_ball_of_dim_even, integral_pow_abs_sub_uIoc, EuclideanSpace.volume_closedBall, tendsto_exp_mul_div_rpow_atTop, sqrt_eq_rpow, Angle.toReal_eq_neg_pi_div_two_iff, sin_half_eq_sqrt, AkraBazziRecurrence.bi_min_div_two_lt_one, CFC.conjugate_rpow_neg_one_half, WithLp.prod_edist_eq_add, Complex.arg_I, Orientation.cos_oangle_eq_inner_div_norm_mul_norm, ODE.FunSpace.dist_iterate_next_apply_le, one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.div_natCast_re, irrational_natCast_div_iff, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, inner_le_Lp_mul_Lq_of_nonneg, exists_int_int_abs_mul_sub_le, four_mul_arctan_inv_5_sub_arctan_inv_239, sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, le_iff_norm_sqrt_mul_rpow, Mathlib.Meta.NormNum.nnreal_rpow_isRat_eq_inv_nnreal_rpow, Complex.sin_arg, MeasureTheory.volume_sum_rpow_lt_one, HolderTriple.one_div_nonneg, CircleDeg1Lift.tendsto_translation_numberβ', derivWithin.log, ZMod.toCircle_eq_circleExp, Polynomial.Chebyshev.roots_U_real, Complex.div_ratCast, cosh_artanh, AbsoluteValue.IsEquiv.log_div_log_eq_log_div_log, ZLattice.covolume_div_covolume_eq_relIndex', CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux, Metric.uniformity_basis_dist_inv_nat_pos, hasSum_log_sub_log_of_abs_lt_one, NNReal.inner_le_Lp_mul_Lq, Complex.cos_arg, Complex.arg_eq_neg_pi_div_two_iff, AkraBazziRecurrence.growsPolynomially_zpow, EulerSine.integral_cos_mul_cos_pow_even, ENNReal.rpow_add_rpow_le_add, integral_sin_pow_even, InformationTheory.mul_klFun_le_toReal_klDiv, ContinuousAlternatingMap.ratio_le_opNorm, Affine.Simplex.points_vsub_eulerPoint, bernoulliFun_eval_half, summable_one_div_int_add_rpow, Quaternion.exp_eq, Angle.two_nsmul_toReal_eq_two_mul, cos_bound, Angle.sign_coe_neg_pi_div_two, MeasureTheory.Measure.integral_comp_div, Int.Matrix.exists_ne_zero_int_vec_norm_le, HasStrictDerivAt.sqrt, LiouvilleNumber.remainder_lt', PiLp.dist_eq_sum, niven, hasSum_L_function_mod_four_eval_three, Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, NNReal.lintegral_mul_le_Lp_mul_Lq, MeasureTheory.tilted_apply', hasDerivWithinAt_arcsin_Iic, Function.Periodic.exp_decay_sub_of_bounded_at_inf, PiLp.edist_eq_of_L2, quarter_mem_cantorSet, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, MeasureTheory.eLpNorm_indicator_const, Complex.norm_cderiv_lt, summable_geometric_two_encode, log_doublingGamma_eq, tan_eq_sin_div_cos, Complex.abs_re_div_norm_le_one, deriv_sqrt, tendsto_one_add_div_pow_exp, arcsin_one, HolderConjugate.div_conj_eq_sub_one, Function.Periodic.exp_decay_of_zero_at_inf, deriv2_sqrt_mul_log, ConvexOn.lipschitzOnWith_of_abs_le, rpowIntegrandββ_eqOn_pow_div, rpow_neg_ofNat, EisensteinSeries.div_max_sq_ge_one, coe_sinOrderIso_apply, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, Stirling.tendsto_self_div_two_mul_self_add_one, intervalIntegral.inv_smul_integral_comp_add_div, Wallis.le_W, Angle.nsmul_eq_iff, sin_pi_div_four, RCLike.inv_re, GaussianFourier.integral_rexp_neg_mul_sq_norm, Behrend.exists_large_sphere, sin_sq_pi_over_two_pow_succ, Int.Matrix.exists_ne_zero_int_vec_norm_le', cos_arctan, AkraBazziRecurrence.isLittleO_self_div_log_id, continuousOn_tan_Ioo, circleMap_zero_zpow, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', CFC.rpow_sqrt, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, Lp_add_le_tsum_of_nonneg', InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero, ConcaveOn.lipschitzOnWith_of_abs_le, arctan_add_eq_add_pi, ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_ne_top, ModularGroup.coe_truncatedFundamentalDomain, MeasureTheory.Integrable.comp_div
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instDivisionRing π | CompOp | 91 mathmath: Complex.im_qsmul, Affine.Simplex.finiteDimensional_direction_altitude, Affine.Simplex.dist_point_faceOppositeCentroid, CongruenceSubgroup.exists_Gamma_le_conj', GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Affine.Triangle.dist_point_faceOppositeCentroid, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, EuclideanGeometry.oangle_sign_eq_zero_iff_collinear, Complex.instFiniteDimensionalReal, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, OrthonormalBasis.measurePreserving_repr, EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq, EuclideanGeometry.Sphere.secondInter_collinear, Affine.Simplex.ninePointCircle_eq_circumsphere_medial, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, EuclideanSpace.volume_closedBall_fin_three, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, FiniteDimensional.complexToReal, FiniteDimensional.rclike_to_real, PiLp.volume_preserving_toLp, LinearIsometryEquiv.reflections_generate_dim_aux, Affine.Triangle.dist_circumcenter_reflection_orthocenter, EuclideanGeometry.collinear_of_angle_eq_zero, instIsTopologicalDivisionRingReal, EuclideanSpace.volume_closedBall_fin_two, LinearIsometryEquiv.reflections_generate, CongruenceSubgroup.IsArithmetic.conj, Affine.Simplex.mongePlane_def, stereoToFun_apply, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, CongruenceSubgroup.isArithmetic_conj_SL2Z, Orientation.areaForm'_apply, Affine.Triangle.dist_orthocenter_reflection_circumcenter, hasSum_one_div_nat_pow_mul_cos, PiLp.volume_preserving_ofLp, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, Affine.Simplex.dist_point_centroid, Submodule.reflection_sub, EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero, CongruenceSubgroup.finiteIndex_conjGL, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, EuclideanGeometry.Concyclic.Coplanar, EuclideanSpace.volume_ball_fin_three, EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, exists_convs_eq_rat, OrthonormalBasis.measurePreserving_repr_symm, rank_rat_real, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, EuclideanGeometry.collinear_of_sin_eq_zero, Complex.re_qsmul, convs_eq_convergent, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, EuclideanSpace.volume_ball_fin_two, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, EuclideanSpace.volume_ball, Complex.ofReal_qsmul, EuclideanGeometry.hasFDerivAt_inversion, EuclideanGeometry.collinear_of_angle_eq_pi, AffineSubspace.signedInfDist_singleton, hasSum_one_div_nat_pow_mul_sin, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear, Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle, EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, Module.Basis.parallelepiped_map, LinearIsometryEquiv.reflections_generate_dim, volume_euclideanSpace_eq_dirac, stereographic_apply, Complex.subfield_eq_of_closed, Affine.Simplex.isDiameter_ninePointCircle, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, AffineBasis.centroid_mem_interior_convexHull, EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, CongruenceSubgroup.IsCongruenceSubgroup.conjGL, subfield_eq_of_closed, OrthonormalBasis.measurePreserving_measurableEquiv, exists_extension_norm_eq, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, Affine.Simplex.circumcenter_eq_centroid, Affine.Simplex.ninePointCircle_center, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, EuclideanSpace.volume_closedBall, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, Subgroup.IsArithmetic.conj, NNRat.instContinuousSMulRatReal, Complex.nonempty_linearEquiv_real, Affine.Triangle.dist_point_centroid
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instField π | CompOp | 282 mathmath: ProbabilityTheory.cdf_measure_stieltjesFunction, SpectrumRestricts.nnreal_of_nonneg, MonotoneOn.intervalIntegral_slope_le, ConvexOn.le_slope_of_hasDerivAt, StrictConvexOn.slope_lt_leftDeriv, AddDissociated.randomisation, CFC.abs_eq_cfc_norm, Complex.lim_conj, CFC.sqrt_eq_one_iff', CFC.posPart_one, ConvexOn.rightDeriv_le_slope_of_mem_interior, rank_le_card_isVisible, Complex.instIsComplete, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, Matrix.IsHermitian.det_abs, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', HasDerivWithinAt.liminf_right_slope_le, CFC.posPart_natCast, CFC.sq_sqrt, StrictConvexOn.deriv_lt_slope, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, OnePoint.isBoundedAt_iff_exists_SL2Z, QuadraticForm.posDef_toMatrix', not_bounded_iff_exists_ne_zero_mem_asymptoticCone, StrictConcaveOn.lt_slope_of_hasDerivAt, IsCusp.smul_of_mem, RCLike.norm_expect_le, StrictConcaveOn.slope_lt_rightDeriv, StrictConvexOn.rightDeriv_lt_slope, Complex.re_balance, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, CFC.sqrt_rpow, Matrix.PosSemidef.sqrt_eq_zero_iff, Complex.im_expect, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, CFC.negPart_algebraMap, cfcβHom_nnreal_eq_restrict, ENNReal.orderIsoRpow_symm_apply, StrictConcaveOn.slope_lt_derivWithin, centerMass_mem_ball_of_strictConvexSpace, exists_dist_slope_lt_pairwiseDisjoint_hasSum, RCLike.ofReal_balance, SpectrumRestricts.nnreal_iff, IsometryEquiv.midpoint_fixed, toMatrix_rotation, volume_val, Complex.isCauSeq_conj, AffineIsometryEquiv.pointReflection_midpoint_left, ConcaveOn.slope_le_of_hasDerivAt, Complex.exp_def, RCLike.ofReal_comp_balance, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, EuclideanGeometry.oangle_midpoint_right, OnePoint.isZeroAt_iff_exists_SL2Z, StrictConvexOn.lt_slope_of_hasDerivAt, Complex.im_nnqsmul, one_add_rpow_hasFPowerSeriesOnBall_zero, cauSeq_converges, IsUnit.cfcSqrt, StrictConcaveOn.deriv_lt_slope, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, StrictConcaveOn.slope_lt_deriv, ConvexOn.slope_le_deriv, Matrix.PosSemidef.det_sqrt, StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iio, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, isCusp_SL2Z_iff', ModularGroup.lcRow0Extend_symm_apply, StrictConvexOn.slope_lt_deriv, volume_eq_stieltjes_id, CFC.sqrt_eq_rpow, Matrix.PosSemidef.posSemidef_sqrt, EuclideanGeometry.oangle_midpoint_rev_left, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, Complex.re_comp_balance, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, instIsCompleteAbs, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, CFC.posPart_algebraMap_nnreal, dist_midpoint_midpoint_le, Matrix.PosSemidef.sqrt_eq_one_iff, Matrix.PosSemidef.sqrt_sq, Complex.ofReal_balance, Monotone.ae_hasDerivAt, Quaternion.expSeries_odd_of_imaginary, ConcaveOn.slope_le_of_hasDerivWithinAt_Ioi, CFC.sqrt_eq_one_iff, one_div_one_sub_hasFPowerSeriesOnBall_zero, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, StieltjesFunction.measurable_measure, ModularGroup.lcRow0Extend_apply, one_div_sub_hasFPowerSeriesOnBall_zero, IsClosed.exists_wbtw_isVisible, isBounded_iff_asymptoticCone_subset_singleton, CFC.abs_natCast, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, Complex.isCauSeq_norm_exp, IsometryEquiv.map_midpoint, MonotoneOn.intervalIntegrable_slope, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, ConvexOn.slope_le_leftDeriv, Quaternion.exp_of_re_eq_zero, ConvexOn.le_slope_of_hasDerivWithinAt_Ioi, EuclideanGeometry.oangle_midpoint_left, Quaternion.re_exp, SzemerediRegularity.biUnion_star_subset_nonuniformWitness, StrictConcaveOn.slope_lt_of_hasDerivAt, OnePoint.IsZeroAt.smul_iff, cfcHom_real_eq_restrict, IsSelfAdjoint.spectrumRestricts, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, CFC.abs_algebraMap, Quaternion.expSeries_even_of_imaginary, IsStrictlyPositive.nnrpow, SpectrumRestricts.real_iff, ProbabilityTheory.hasFPowerSeriesAt_mgf, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, imaginaryPart_eq_neg_I_smul_skewAdjointPart, StrictConcaveOn.derivWithin_lt_slope, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, IsSelfAdjoint.sq_spectrumRestricts, StrictConvexOn.slope_lt_derivWithin, Complex.ofReal_comp_balance, ConvexOn.slope_le_of_hasDerivWithinAt, szemeredi_regularity, IsUnit.cfcNNRpow, StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iio, NNReal.coe_nnqsmul, ConcaveOn.le_slope_of_hasDerivWithinAt, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, IsStrictlyPositive.sqrt, Quaternion.normSq_exp, Matrix.PosSemidef.isUnit_sqrt_iff, Complex.im_balance, Complex.ofReal_expect, ProbabilityTheory.instIsProbabilityMeasureCondCDF, Quaternion.im_exp, CFC.sqrt_sq, CauSeq.tendsto_limit, CFC.rpow_sqrt_nnreal, RCLike.isCauSeq_im, ConcaveOn.slope_le_derivWithin, CauSeq.cauchySeq, ProbabilityTheory.measure_cdf, ConcaveOn.leftDeriv_le_slope, cfcHom_nnreal_eq_restrict, ConcaveOn.derivWithin_le_slope, Matrix.PosSemidef.sq_sqrt, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, Complex.im_comp_balance, ConcaveOn.deriv_le_slope, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, isCauSeq_iff_cauchySeq, OnePoint.IsBoundedAt.smul_iff, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, NNReal.coe_expect, CFC.abs_ofNat, CFC.negPart_one, Matrix.PosSemidef.inv_sqrt, ConcaveOn.slope_le_of_hasDerivWithinAt, cfcβHom_real_eq_restrict, CFC.abs_algebraMap_nnreal, RCLike.ofReal_expect, ConcaveOn.le_slope_of_hasDerivWithinAt_Iio, StrictConvexOn.lt_slope_of_hasDerivWithinAt, AffineSubspace.midpoint_mem_perpBisector, nndist_midpoint_midpoint_le, HasDerivWithinAt.limsup_slope_le', hasFPowerSeriesOnBall_linear_zero, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, cfc_comp_norm, CFC.abs_intCast, Affine.Triangle.eulerPoint_eq_midpoint, StrictConcaveOn.slope_lt_of_hasDerivWithinAt, ConvexOn.derivWithin_le_slope, one_add_rpow_hasFPowerSeriesAt_zero, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, ceil_logb_natCast, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, StrictConcaveOn.slope_lt_of_hasDerivWithinAt_Ioi, IntervalIntegrable.intervalIntegrable_slope, EuclideanGeometry.oangle_midpoint_rev_right, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, NNReal.orderIsoRpow_symm_eq, one_add_rpow_hasFPowerSeriesAt_zero, CFC.spectrum_abs, Complex.lim_im, AffineSpace.asymptoticNhds_le_cobounded, cosetToCuspOrbit_apply_mk, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, Quaternion.norm_exp, exists_deriv_eq_slope', EuclideanGeometry.angle_midpoint_eq_pi, StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioi, floor_logb_natCast, ConvexOn.slope_le_of_hasDerivAt, CFC.sqrt_eq_cfc, IsClosed.convexHull_subset_affineSpan_isVisible, Complex.isCauSeq_im, ConvexOn.deriv_le_slope, CFC.abs_sq, ConvexOn.rightDeriv_le_slope, skewAdjointPart_eq_I_smul_imaginaryPart, StrictConcaveOn.lt_slope_of_hasDerivWithinAt, StrictConvexOn.derivWithin_lt_slope, CStarAlgebra.isStrictlyPositive_TFAE, asymptoticCone_subset_singleton_of_bounded, CFC.sqrt_algebraMap, CFC.posPart_algebraMap, CFC.sqrt_one, ContinuousLinearMap.IsPositive.spectrumRestricts, StieltjesFunction.ae_hasDerivAt, ProbabilityTheory.measure_condCDF_Iic, ProbabilityTheory.measurable_measure_condCDF, Complex.lim_norm, StrictConvexOn.slope_lt_of_hasDerivWithinAt, ConcaveOn.slope_le_rightDeriv, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, CFC.sqrt_rpow_nnreal, ConvexOn.le_slope_of_hasDerivWithinAt, ConvexOn.slope_le_derivWithin, one_div_sub_pow_hasFPowerSeriesOnBall_zero, Complex.re_expect, Complex.re_nnqsmul, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, ProbabilityTheory.measure_condCDF_univ, Complex.equiv_limAux, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, CFC.nnrpow_eq_rpow, SpectrumRestricts.nnreal_iff_spectralRadius_le, MeasureTheory.lpNorm_expect_le, Quaternion.coe_ofComplex, CFC.abs_one, Matrix.PosSemidef.sqrt_mul_self, Quaternion.hasSum_expSeries_of_imaginary, PadicInt.complete, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, ProbabilityTheory.gaussianPDFReal_mul, CFC.isUnit_nnrpow_iff, compact_inner_le_weight_mul_Lp_of_nonneg, Complex.ofReal_nnqsmul, Padic.complete, OpenPartialHomeomorph.unitBallBall_symm_apply, StrictConcaveOn.leftDeriv_lt_slope, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, CauchySeq.isCauSeq, Complex.isCauSeq_exp, RCLike.isCauSeq_re, OpenPartialHomeomorph.unitBallBall_apply, ConcaveOn.slope_le_deriv, ConvexOn.slope_le_of_hasDerivWithinAt_Iio, eq_midpoint_of_dist_eq_half, ArchimedeanClass.stdPart_real, Matrix.PosDef.posDef_sqrt, ConcaveOn.le_slope_of_hasDerivAt, Complex.isCauSeq_re, one_add_rpow_hasFPowerSeriesOnBall_zero, isCauSeq_iff_lift, one_div_sub_sq_hasFPowerSeriesOnBall_zero, SpectrumRestricts.nnreal_iff_nnnorm, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, Quaternion.exp_coe, ConvexOn.slope_le_leftDeriv_of_mem_interior, Quaternion.exp_eq, Complex.ofReal_choose, IsCusp.smul, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, AffineIsometryEquiv.pointReflection_midpoint_right, Complex.lim_re, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, HasDerivWithinAt.limsup_slope_le, ProbabilityTheory.instIsProbabilityMeasurecdf, Urysohns.CU.lim_eq_midpoint, CFC.isUnit_sqrt_iff, RCLike.norm_nnqsmul, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Complex.lim_eq_lim_im_add_lim_re, CFC.rpow_sqrt, StrictConvexOn.slope_lt_of_hasDerivAt
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instInhabited π | CompOp | 2 mathmath: AkraBazziRecurrence.p_def, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real
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instIntCast π | CompOp | 287 mathmath: CuspFormClass.qExpansion_isBigO, HurwitzZeta.hasSum_int_hurwitzZetaOdd, exists_floor, EisensteinSeries.linear_inv_isBigO_left, CircleDeg1Lift.map_sub_int, HurwitzZeta.hasSum_int_cosKernelβ, Int.cast_complex_isTheta_cast_real, HurwitzZeta.hasSum_int_hurwitzZetaEven, GaussianInt.intCast_im, norm_jacobiThetaβ_term_le, cos_eq_zero_iff, norm_jacobiThetaβ_term_fderiv_ge, le_log_of_zpow_le, BoxIntegral.unitPartition.mem_box_iff', tan_int_mul_pi, countingFunction_finsum_eq_finsum_add, ENNReal.rpow_intCast_mul, Polynomial.exists_partition_polynomial, LiouvilleWith.int_sub, CircleDeg1Lift.iterate_pos_le_iff, cos_int_mul_two_pi, NumberField.dedekindZeta_residue_def, CircleDeg1Lift.iterate_pos_lt_iff, MeasureTheory.Integrable.hasSum_intervalIntegral, BoxIntegral.unitPartition.box_upper, LiouvilleWith.mul_int_iff, EisensteinSeries.abs_le_right_of_norm, NNReal.rpow_intCast_mul, summable_one_div_int_pow, NumberField.abs_discr_ge', LiouvilleWith.sub_int, NumberField.abs_discr_ge, setOf_liouvilleWith_subset_aux, Polynomial.exists_partition_polynomial_aux, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, CircleDeg1Lift.translationNumber_eq_rat_iff, GaussianInt.toComplex_defβ, cos_add_int_mul_two_pi, Circle.exp_eq_exp, zpow_le_iff_le_log, irrational_sqrt_intCast_iff, Irrational.intCast_add, NNReal.rpow_mul_intCast, rpow_mul_intCast, MeromorphicOn.extract_zeros_poles_log, Circle.exp_two_pi_mul_int, GaussianInt.toComplex_div_re, RCLike.intCast_re, LiouvilleWith.int_sub_iff, sin_add_int_mul_pi, zpow_lt_iff_lt_log, NumberField.FinitePlace.prod_eq_inv_abs_norm_int, AbsoluteValue.exists_partition_int, tan_int_mul_pi_div_two, NumberField.house_intCast, CircleDeg1Lift.floor_sub_le_translationNumber, NNReal.rpow_add_intCast', Irrational.mul_intCast, Irrational.intCast_mul, Polynomial.Chebyshev.T_real_cos, summable_abs_int_rpow, CircleDeg1Lift.map_le_of_map_zero, CircleDeg1Lift.le_map_of_map_zero, irrational_intCast_sub_iff, ModularGroup.lcRow0Extend_symm_apply, tsum_exp_neg_mul_int_sq, Complex.arg_cos_add_sin_mul_I_sub, CircleDeg1Lift.map_int_of_map_zero, LiouvilleWith.int_add, le_zpow_iff_log_le, HurwitzZeta.hasSum_int_cosKernel, norm_jacobiThetaβ_term, BoxIntegral.unitPartition.mem_box_iff, Polynomial.Chebyshev.S_two_mul_real_cos, LinearGrowth.Real.eventually_atTop_exists_int_between, Int.ball_eq_Ioo, abs_cos_int_mul_pi, Irrational.intCast_div, Int.dist_eq', LiouvilleWith.add_int, irrational_mul_intCast_iff, Int.isClosedEmbedding_coe_real, ModularGroup.lcRow0Extend_apply, log_zpow, Complex.ofReal_intCast, GaussianInt.toComplex_im_div, LiouvilleWith.mul_int, CircleDeg1Lift.commute_add_int, LiouvilleWith.add_int_iff, circleIntegrable_log_norm_factorizedRational, exists_nat_abs_mul_sub_round_le, LiouvilleWith.int_add_iff, irrational_sqrt_intCast_iff_of_nonneg, cos_int_mul_pi_sub, LiouvilleWith.sub_int_iff, Complex.intCast_re, NumberField.mixedEmbedding.covolume_idealLattice, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, CircleDeg1Lift.commute_sub_int, Irrational.div_intCast, Int.norm_eq_abs, irrational_div_intCast_iff, Polynomial.Chebyshev.S_two_mul_real_cosh, HurwitzZeta.hasSum_int_evenKernel, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, Complex.div_intCast, cos_eq_cos_iff, ArchimedeanClass.stdPart_intCast, Angle.angle_eq_iff_two_pi_dvd_sub, cos_int_mul_two_pi_add_pi, lt_zpow_iff_log_lt, ModularGroup.re_T_zpow_smul, sin_eq_sin_iff, CircleDeg1Lift.le_map_map_zero, irrational_add_intCast_iff, NumberField.Ideal.tendsto_norm_le_div_atTopβ, lt_log_of_zpow_lt, GaussianInt.to_real_re, Angle.intCast_mul_eq_zsmul, BoxIntegral.unitPartition.box_lower, HurwitzZeta.hasSum_int_sinKernel, Liouville.frequently_exists_num, sin_int_mul_two_pi_sub, CircleDeg1Lift.translationNumber_le_ceil_sub, coe_intFib_eq, ENNReal.rpow_intCast, Irrational.sub_intCast, Complex.normSq_intCast, sin_int_mul_pi_sub, GaussianInt.to_real_im, Polynomial.Chebyshev.U_real_cos, EisensteinSeries.linear_inv_isBigO_right_add, GaussianInt.toComplex_re_div, irrational_sqrt_of_multiplicity_odd, GaussianInt.toComplex_re, rpow_intCast_mul, LiouvilleWith.frequently_lt_rpow_neg, Polynomial.exists_approx_polynomial, LiouvilleWith.int_mul, AbsoluteValue.IsAdmissible.exists_approx, NumberField.mixedEmbedding.covolume_integerLattice, CircleDeg1Lift.translate_zpow, NNReal.rpow_intCast, tan_add_int_mul_pi, irrational_sub_intCast_iff, ZLattice.exists_forall_abs_repr_le_norm, cos_sub_int_mul_pi, Int.dist_cast_real, CircleDeg1Lift.map_add_int, sin_sub_int_mul_pi, ofCauchy_intCast, NNReal.rpow_add_intCast, AbsoluteValue.IsAdmissible.exists_partition, RCLike.ofReal_intCast, CircleDeg1Lift.commute_int_add, Liouville.exists_pos_real_of_irrational_root, Complex.norm_int_of_nonneg, CuspFormClass.exists_bound, MeromorphicOn.circleAverage_log_norm, Int.dist_eq, rpow_sub_intCast', AbsoluteValue.IsAdmissible.exists_partition', Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, LiouvilleWith.int_mul_iff, EisensteinSeries.linear_isTheta_left, UnitAddCircle.norm_eq, LiouvilleWith.exists_pos, GaussianInt.intCast_real_norm, Int.not_irrational, MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles, Complex.div_intCast_re, HurwitzZeta.hasSum_int_oddKernel, ZMod.toAddCircle_intCast, GaussianInt.toComplex_im, GaussianInt.im_toComplex, NumberField.exists_ideal_in_class_of_norm_le, CircleDeg1Lift.lt_iterate_pos_iff, norm_jacobiThetaβ'_term_le, NumberField.Ideal.tendsto_norm_le_div_atTop, cauchy_intCast, tan_int_mul_pi_sub, Angle.zsmul_eq_iff, Polynomial.Chebyshev.T_real_cosh, Circle.exp_int_mul_two_pi, CFC.rpow_intCast, convergent_of_int, ArithmeticFunction.sum_moebius_mul_log_eq, EisensteinSeries.linear_isTheta_right_add, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, circleAverage_log_norm_factorizedRational, Int.closedBall_eq_Icc, Irrational.intCast_sub, GaussianInt.re_toComplex, log_intCast_nonneg, tan_eq_zero_iff, tsum_eq_tsum_fourier_of_rpow_decay, Circle.exp_intCast_mul, abs_sin_eq_one_iff, integral_zpow, CircleDeg1Lift.map_int_add, sin_eq_neg_one_iff, NumberField.abs_discr_ge_of_isTotallyComplex, cos_int_mul_two_pi_sub_pi, EisensteinSeries.abs_le_left_of_norm, CircleDeg1Lift.le_iterate_pos_iff, norm_intCast_eq_abs_mul_norm_one, AbsoluteValue.IsAdmissible.exists_approx_aux, cos_eq_one_iff, Polynomial.Chebyshev.U_real_cosh, SlashInvariantForm.vAdd_width_periodic, Irrational.add_intCast, ENNReal.rpow_mul_intCast, setOf_liouville_eq_iInter_iUnion, sin_eq_zero_iff, ZLattice.normBound_spec, tendsto_abs_tan_atTop, cos_sub_int_mul_two_pi, Int.preimage_ball, UpperHalfPlane.modular_T_zpow_smul, AddCircle.norm_eq, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, summable_pow_mul_jacobiThetaβ_term_bound, cos_int_mul_two_pi_sub, EisensteinSeries.linear_isTheta_right, Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_real, Int.isUniformEmbedding_coe_real, Zsqrtd.toReal_apply, rpow_sub_intCast, Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_real, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, setOf_liouville_eq_irrational_inter_iInter_iUnion, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, Complex.div_intCast_im, BoxIntegral.unitPartition.tag_apply, IsPrimitiveRoot.arg, Circle.exp_eq_one, fourier_add_half_inv_index, irrational_intCast_add_iff, ModularGroup.lcRow0_apply, Int.tendsto_coe_cofinite, rpow_add_intCast, SchwartzMap.tsum_eq_tsum_fourierIntegral, AddCircle.norm_eq', cos_eq_neg_one_iff, abs_cos_eq_one_iff, Complex.arg_mul_cos_add_sin_mul_I_sub, irrational_intCast_div_iff, cos_add_int_mul_pi, AddChar.zmod_intCast, sin_sub_int_mul_two_pi, CircleDeg1Lift.map_map_zero_le, MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int, Complex.norm_intCast, sin_eq_one_iff, rpow_add_intCast', HurwitzZeta.hasSum_int_completedHurwitzZetaEven, rpow_intCast, CircleDeg1Lift.iterate_pos_eq_iff, tsum_eq_tsum_fourierIntegral_of_rpow_decay, CircleDeg1Lift.translationNumber_eq_int_iff, qaryEntropy_one, sin_add_int_mul_two_pi, tan_sub_int_mul_pi, cos_int_mul_pi, sign_intCast, exists_int_int_abs_mul_sub_le, Polynomial.Chebyshev.C_two_mul_real_cos, Int.preimage_closedBall, tan_eq_zero_iff', CircleDeg1Lift.translationNumber_zpow, summable_one_div_int_add_rpow, GaussianInt.intCast_re, NNReal.rpow_sub_intCast', cast_natAbs_eq_nnabs_cast, sin_int_mul_pi, GaussianInt.toComplex_div_im, EisensteinSeries.div_max_sq_ge_one, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, SchwartzMap.tsum_eq_tsum_fourier, ZLattice.abs_repr_le, norm_jacobiThetaβ_term_fderiv_le, Int.norm_cast_real, irrational_intCast_mul_iff, EisensteinSeries.linear_inv_isBigO_right, HurwitzZeta.hasSum_int_evenKernelβ, Polynomial.Chebyshev.C_two_mul_real_cosh, circleMap_zero_zpow
|
instInv π | CompOp | 513 mathmath: CFC.rpow_inv_rpow, arctan_eq_arccos, MeasureTheory.Measure.integral_comp_inv_smul, HasStrictFDerivAt.log, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, Polynomial.mahlerMeasure_def_of_ne_zero, not_continuousAt_inv_log_neg_one, sinh_log, EisensteinSeries.linear_inv_isBigO_left, HolderTriple.inv_add_inv_eq_inv, HasDerivWithinAt.liminf_right_slope_norm_le, MeasureTheory.charFun_eq_fourierIntegral', gauge_def', ValueDistribution.proximity_zero, dist_midpoint_right, TsirelsonInequality.sqrt_two_inv_mul_self, ZLattice.summable_norm_sub_inv_pow, tendsto_tsum_div_pow_atTop_integral, Orientation.oangle_add_left_smul_rotation_pi_div_two, NNReal.rpow_rpow_inv, MeasureTheory.Measure.integral_comp_mul_right, intervalIntegral.inv_smul_integral_comp_div_add, taylorWithinEval_hasDerivAt_Ioo, tan_inv_eq_cot, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, CFC.tendsto_cfc_rpow_sub_one_log, dist_mulExpNegMulSq_le_two_mul_sqrt, countingFunction_finsum_eq_finsum_add, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, hasDerivWithinAt_taylorWithinEval, ZLattice.covolume_eq_det_inv, inv_rpow, bernoulliFun_eval_half_eq_zero, lt_rpow_inv_iff_of_pos, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, dist_left_midpoint, sqrt_div_self, bernoulliFun_two, add_sqrt_self_sq_sub_one_inv, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, intervalIntegral.intervalIntegrable_inv, deriv_log, rpow_neg_one, PiCountable.min_dist_le_dist_pi, intervalIntegral.integral_comp_mul_left, BoxIntegral.unitPartition.mem_smul_span_iff, intervalIntegral.integral_comp_mul_sub, rpow_eq_const_mul_integral, MeasureTheory.Lp.nnnorm_le_of_ae_bound, HasDerivWithinAt.liminf_right_norm_slope_le, ENNReal.rpow_inv_rpow, not_IntegrableOn_Ioi_inv, Complex.sqrt_I, hasSum_log_one_add_inv, HolderConjugate.inv_inv, integral_inv_of_pos, NNReal.pow_rpow_inv_natCast, HolderTriple.inv_nonneg', MeasureTheory.eLpNorm_smul_measure_of_ne_top', Complex.norm_one_add_mul_inv_le, AddCircle.integral_haarAddCircle, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, circleMap_zero_inv, logb_inv, Mathlib.Meta.NormNum.rpow_isRat_eq_inv_rpow, summable_nat_rpow_inv, Polynomial.Chebyshev.integral_measureT, ContinuousMap.toLp_norm_le, MeasureTheory.Measure.addHaar_preimage_smul, sign_inv, hasDerivAt_arcosh, inv_logb_div_base, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, inv_goldenConj, Complex.norm_log_one_add_le, rpow_inv_log, NNReal.rpow_inv_lt_iff_of_pos, Metric.continuousAt_inv_infDist_pt, LiouvilleNumber.aux_calc, sameRay_iff_inv_norm_smul_eq_of_ne, inv_goldenRatio, intervalIntegral.intervalIntegrable_inv_one_add_sq, MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo, NumberField.FinitePlace.prod_eq_inv_abs_norm_int, ENNReal.pow_rpow_inv_natCast, BoxIntegral.unitPartition.integralSum_eq_tsum_div, stereoInvFunAux_apply, sqrt_inv, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, HasStrictFDerivAt.arsinh, two_mul_arctan_inv_2_sub_arctan_inv_7, Affine.Simplex.inv_height_lt_sum_inv_height, tendsto_card_div_pow_atTop_volume, harm_mean_le_geom_mean_weighted, MeasureTheory.Measure.integral_comp_inv_mul_left, tsum_geometric_le_of_norm_lt_one, hasDerivAt_arsinh, taylor_tendsto, rescale_to_shell_semi_normed_zpow, volume_preimage_mul_left, fderiv.log, Metric.PiNatEmbed.dist_def, map_matrix_volume_pi_eq_smul_volume_pi, SameRay.inv_norm_smul_eq, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, MeasureTheory.Measure.integral_comp_smul_of_nonneg, ZLattice.covolume.tendsto_card_div_pow, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, NNReal.rpow_inv_rpow, HolderConjugate.one_sub_inv, finite_integral_rpow_sub_one_pow_aux, holderTriple_iff, ProbabilityTheory.strong_law_ae, HolderTriple.inv_nonneg, inv_one_add_tan_sq, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, MeasureTheory.lpNorm_smul_measure_of_ne_zero, harm_mean_le_geom_mean, Complex.norm_log_sub_logTaylor_le, Metric.Snowflaking.image_ofSnowflaking_eball, le_ofDigits_cantorToTernary_sum, has_fderiv_at_filter_real_equiv, Metric.Snowflaking.preimage_toSnowflaking_emetricClosedBall, sigmoid_def, norm_cauchyPowerSeries_le, ofDigitsTerm_le, ENNReal.rpow_inv_le_iff, CFC.rpow_rpow_inv, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, Metric.Snowflaking.ediam_image_ofSnowflaking, Seminorm.rescale_to_shell_zpow, BoundedContinuousFunction.Lp_nnnorm_le, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, norm_commutator_sub_one_le, NNReal.eq_rpow_inv_iff, Complex.norm_log_one_add_sub_self_le, RCLike.normSq_inv, stereoInvFun_apply, Irrational.inv, MeasureTheory.Measure.integral_comp_smul, Filter.Tendsto.cesaro, not_IntegrableOn_Ici_inv, Metric.Snowflaking.image_ofSnowflaking_ball, dist_right_midpoint, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, uniformContinuous_inv, deriv_inv_log, le_rpow_inv_iff_of_neg, posLog_sub_posLog_inv, tsum_geometric_of_lt_one, sum_div_nat_floor_pow_sq_le_div_sq, ENNReal.toReal_inv, ENNReal.lt_rpow_inv_iff, hasStrictDerivAt_arcosh, inv_norm_smul_mem_unitClosedBall, deriv_log', intervalIntegrable_sub_inv_iff, one_div_sub_hasFPowerSeriesOnBall_zero, intervalIntegral.integral_comp_add_mul, ofDigits_eq_sum_add_ofDigits, HasDerivWithinAt.arsinh, convergent_succ, le_rpow_one_add_norm_iff_norm_le, Behrend.bound, inner_le_weight_mul_Lp_of_nonneg, arctan_inv_of_neg, Affine.Simplex.excenterWeights_empty_lt_inv_two, hasStrictDerivAt_log, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Metric.Snowflaking.image_ofSnowflaking_closedEBall, norm_inv_mul_rpow_sub_one_sub_log_le, Metric.Snowflaking.preimage_toSnowflaking_closedBall, NumberField.mixedEmbedding.covolume_idealLattice, toNNReal_inv, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_self, summable_nat_pow_inv, hasDerivWithinAt_taylorWithinEval_at_Icc, tendsto_rpow_sub_one_log, Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, rescale_to_shell, hasFDerivAt_iff_tendsto, ProbabilityTheory.sum_variance_truncation_le, HasFDerivWithinAt.log, ENNReal.rpow_rpow_inv, cauchy_inv, PiCountable.dist_summable, ENNReal.le_rpow_inv_iff, neg_inv_le_log, HasDerivWithinAt.limsup_norm_slope_le, ProbabilityTheory.gaussianPDFReal_def, Complex.inv_def, Asymptotics.isBigOWith_self_const_mul, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, intervalIntegral.inv_smul_integral_comp_sub_div, hasDerivWithinAt_taylor_coeff_within, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, intervalIntegral.inv_mul_integral_comp_add_div, tendsto_integral_mul_one_add_inv_smul_sq_pow, expNegInvGlue.tendsto_polynomial_inv_mul_zero, NNReal.lt_rpow_inv_iff, rescale_to_shell_semi_normed, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, irrational_inv_iff, le_sum_ofDigitsTerm_digits, Angle.tan_eq_inv_of_two_nsmul_add_two_nsmul_eq_pi, intervalIntegral.inv_mul_integral_comp_sub_div, ProbabilityTheory.Fernique.lintegral_closedBall_diff_exp_logRatio_mul_sq_le, tsum_geometric_of_abs_lt_one, HasDerivWithinAt.limsup_slope_norm_le, NNReal.rpow_inv_eq_iff, circleAverage_def, HolderTriple.of_pos, hasSum_sq_fourierCoeffOn, CFC.monotoneOn_one_sub_one_add_inv_real, MeasureTheory.lpNorm_nnreal_eq_integral_norm_rpow, MeasureTheory.setAverage_eq, le_rpow_inv_iff_of_pos, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, NNReal.rpow_inv_le_iff_of_pos, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, taylorWithinEval_succ, pow_rpow_inv_natCast, MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm, integral_inv_of_neg, MeasureTheory.Measure.integral_comp_mul_left, MeasureTheory.eLpNormLESNormFDerivOneConst_def, tan_pi_div_two_sub, Hyperreal.IsSt.inv, Affine.Simplex.excenterWeightsUnnorm_empty_apply, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, NNReal.rpow_inv_le_iff, Affine.Simplex.inradius_eq_abs_inv_sum, fderivWithin.log, circleAverage_eq_integral_add, intervalIntegral.inv_smul_integral_comp_div_sub, Hyperreal.coe_inv, BoundedContinuousFunction.Lp_norm_le, HasFDerivAt.log, hasStrictDerivAt_arsinh, integral_univ_inv_one_add_sq, norm_inv, inv_sqrt_two_sub_one, MeasureTheory.eLpNorm_le_of_ae_enorm_bound, Orientation.oangle_sub_right_smul_rotation_pi_div_two, EisensteinSeries.linear_inv_isBigO_right_add, rpow_neg_eq_inv_rpow, Metric.Snowflaking.preimage_toSnowflaking_eball, lt_rpow_inv_iff_of_neg, integral_inv, imaginaryPart_apply_coe, NNReal.le_rpow_inv_iff, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, rpow_inv_le_iff_of_neg, hasGradientAt_iff_tendsto, HasDerivAt.arsinh, logb_inv_base, inv_logb_mul_base, ZLattice.summable_norm_pow_inv, HolderTriple.inv_pos, EisensteinSeries.isBigO_linear_add_const_vec, arctan_inv_2_add_arctan_inv_3, intervalIntegral.integral_comp_sub_mul, homeomorphUnitSphereProd_apply_fst_coe, NumberField.mixedEmbedding.covolume_integerLattice, NNReal.rpow_inv_le_iff_of_neg, MeasureTheory.uniformIntegrable_average, not_differentiableAt_inv_log_zero, arctan_inv_sqrt_three, Metric.Snowflaking.preimage_toSnowflaking_closedEBall, MeasureTheory.Lp.norm_le_of_ae_bound, NNReal.coe_inv, integral_inv_sq_add_sq, Complex.normSq_inv, sin_div_le_inv_abs, sameRay_iff_inv_norm_smul_eq, mellin_comp_inv, ContDiffBump.apply, Mathlib.Meta.NormNum.IsInt.rpow_eq_inv_pow, HasFDerivAt.lim_real, tsum_geometric_inv_two_ge, rpow_inv_log_le_exp_one, NNReal.le_rpow_inv_iff_of_neg, MeasureTheory.measureReal_abs_gt_le_integral_charFun, hasDerivAt_log, inv_sqrt_one_add_tan_sq, continuous_inv, ZLattice.covolume.tendsto_card_div_pow', binEntropy_eq_log_two, HolderConjugate.inv_add_inv_eq_one, ENNReal.ofReal_inv_of_pos, hasDerivAtFilter_iff_tendsto, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, integrable_inv_one_add_sq, NNReal.lt_rpow_inv_iff_of_neg, HasFDerivWithinAt.arsinh, MeromorphicOn.circleAverage_log_norm, ProbabilityTheory.gaussianPDFReal_inv_mul, map_linearMap_volume_pi_eq_smul_volume_pi, intervalIntegral.inv_mul_integral_comp_div_sub, mellin_comp_rpow, mulExpNegMulSq_eq_sqrt_mul_mulExpNegMulSq_one, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, tendstoLocallyUniformlyOn_rpow_sub_one_log, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, ENNReal.inner_le_weight_mul_Lp_of_nonneg, NNReal.inner_le_weight_mul_Lp, Probability.cauchyPDFReal_def', NNReal.lt_rpow_inv_iff_of_pos, Complex.exp_bound, MeasureTheory.Measure.map_addHaar_smul, intervalIntegral.inv_smul_integral_comp_div, holderConjugate_iff, tendsto_integral_cexp_sq_smul, Metric.Snowflaking.preimage_toSnowflaking_ball, HasStrictDerivAt.arsinh, expNegInvGlue.continuous_polynomial_eval_inv_mul, rpow_inv_natCast_pow, sigmoid_zero, Complex.sqrt_neg_I, MeasureTheory.lpNorm_one, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, NormedSpace.polar_ball, RCLike.sqrt_neg_I, ProbabilityTheory.strong_law_Lp, tsum_geometric_inv_two, binEntropy_two_inv_add, Affine.Simplex.exradius_eq_abs_inv_sum, NumberField.mixedEmbedding.fundamentalCone.expMap_apply, Seminorm.rescale_to_shell, AkraBazziRecurrence.deriv_smoothingFn, OpenPartialHomeomorph.univUnitBall_apply, MeasureTheory.Measure.addHaar_preimage_linearMap, RCLike.inv_def, RCLike.sqrt_I, tsum_sq_fourierCoeffOn, geom_mean_le_arith_mean, rescale_to_shell_zpow, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, ofCauchy_inv, NormedSpace.sInter_polar_eq_closedBall, ExistsContDiffBumpBase.w_def, MeasureTheory.Measure.setIntegral_comp_smul, inv_sign, tendsto_mul_add_inv_atTop_nhds_zero, expNegInvGlue.contDiff_polynomial_eval_inv_mul, HolderConjugate.one_sub_inv_inv, NumberField.mixedEmbedding.logMap_apply, PadicInt.norm_p, inv_gold, HolderConjugate.inv_one_sub_inv, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, rpow_inv_lt_iff_of_neg, exists_nat_pos_inv_lt, hasDerivAt_arctan', logb_mul_base, NNReal.rpow_inv_lt_iff, MeasureTheory.integral_comp_mul_right_Ioi, HasFDerivAt.arsinh, two_mul_arctan_inv_3_add_arctan_inv_7, BoundedContinuousFunction.toLp_norm_le, arctan_inv_of_pos, Metric.Snowflaking.image_ofSnowflaking_emetricClosedBall, Metric.Snowflaking.edist_ofSnowflaking_ofSnowflaking, ContinuousLinearEquiv.homothety_inverse, not_summable_natCast_inv, map_volume_mul_right, cosh_log, logb_div_base, Complex.norm_cpow_inv_nat, hasSum_geometric_of_abs_lt_one, hasFDerivAtFilter_iff_tendsto, rpow_inv_eq, HolderTriple.inv_inv_add_inv, HolderTriple.inv_eq, HolderTriple.inv_lt_inv, ProbabilityTheory.strong_law_ae_simpleFunc_comp, closedBall_rpow_sub_one_eq_empty_aux, schnirelmannDensity_setOf_modeq_one, Complex.norm_log_one_sub_inv_sub_self_le, sum_div_pow_sq_le_div_sq, NormedSpace.closedBall_inv_subset_polar_closedBall, schnirelmannDensity_le_of_notMem, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, Filter.Tendsto.cesaro_smul, Hyperreal.st_inv, ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul, EReal.coe_inv, integral_inv_one_add_sq, abs_mulExpNegMulSq_le, one_div_sub_pow_hasFPowerSeriesOnBall_zero, AddCircle.norm_eq, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, not_integrableOn_Ici_inv, realPart_apply_coe, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, intervalIntegral.integral_comp_mul_right, not_integrableOn_Ioi_inv, intervalIntegral.inv_mul_integral_comp_div, Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, homeomorphSphereProd_apply_fst_coe, ENNReal.rpow_inv_lt_iff, abs_ofDigits_sub_ofDigits_le, MeasureTheory.Egorov.exists_notConvergentSeq_lt, Metric.Snowflaking.image_ofSnowflaking_closedBall, not_continuousAt_inv_log_one, tendsto_card_div_pow_atTop_volume', CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, binEntropy_strictAntiOn, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, MeasureTheory.lpNorm_eq_integral_norm_rpow_toReal, integral_Ioi_inv_one_add_sq, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, MeasureTheory.Measure.integral_isAddLeftInvariant_isAddRightInvariant_combo, MeasureTheory.integral_comp_mul_left_Ioi, schnirelmannDensity_setOf_Odd, Metric.Snowflaking.ediam_preimage_toSnowflaking, Padic.norm_p, binEntropy_two_inv, half_mul_log_add_log_abs, hasGradientWithinAt_iff_tendsto, log_inv, unitInterval.eq_closedBall, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, intervalIntegral.integral_comp_mul_add, rpow_inv_lt_iff_of_pos, hasDerivAt_iff_tendsto, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, MeasureTheory.condExp_bot', MeasureTheory.lpNorm_smul_measure_of_ne_top, PiCountable.dist_eq_tsum, ContinuousLinearEquiv.coord_norm, MeasureTheory.lpNorm_one', NNReal.rpow_inv_natCast_pow, le_inv_mul_exp, NormedSpace.polar_closedBall, ProbabilityTheory.strong_law_ae_of_measurable, ProbabilityTheory.gaussianPDFReal_mul, AddCircle.norm_eq', ENNReal.rpow_inv_natCast_pow, MeasureTheory.lpNorm_const, integral_Iic_inv_one_add_sq, rpow_rpow_inv, compact_inner_le_weight_mul_Lp_of_nonneg, interval_average_eq, HolderConjugate.inv_sub_one, dist_midpoint_left, Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi, ValueDistribution.proximity_coe, HolderTriple.inv_pos', ordinaryHypergeometricSeries_norm_div_succ_norm, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', MeasureTheory.eLpNorm_smul_measure_of_ne_zero', hasFDerivWithinAt_iff_tendsto, Asymptotics.isBigOWith_inv, rpow_inv_le_iff_of_pos, exp_neg, ZLattice.covolume.tendsto_card_div_pow'', RCLike.ofReal_inv, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, OpenPartialHomeomorph.univUnitBall_symm_apply, Metric.Snowflaking.image_ofSnowflaking_emetricBall, schnirelmannDensity_setOf_mod_eq_one, rpow_inv_rpow, rpow_neg, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, intervalIntegral.inv_mul_integral_comp_div_add, expNegInvGlue.differentiable_polynomial_eval_inv_mul, Complex.ofReal_inv, AkraBazziRecurrence.GrowsPolynomially.inv, NNReal.le_rpow_inv_iff_of_pos, cot_inv_eq_tan, taylor_within_apply, EisensteinSeries.vec_add_const_isTheta, MeasureTheory.lpNorm_const', sinc_le_inv_abs, volume_preimage_mul_right, HolderTriple.inv_sub_inv_eq_inv, ArchimedeanClass.stdPart_inv, Metric.Snowflaking.preimage_toSnowflaking_emetricBall, intervalIntegrable_inv_iff, inv_logb, one_div_sub_sq_hasFPowerSeriesOnBall_zero, rpowIntegrandββ_eqOn_mul_rpowIntegrandββ_one, four_mul_arctan_inv_5_sub_arctan_inv_239, one_sub_inv_le_log_of_pos, hasDerivWithinAt_iff_tendsto, MeasureTheory.eLpNorm_le_of_ae_bound, mul_pow_le_nat_floor_pow, NNReal.rpow_inv_lt_iff_of_neg, bernoulliFun_eval_half, MeasureTheory.condExp_bot_ae_eq, LiouvilleNumber.remainder_lt', hasSum_geometric_of_lt_one, hasStrictDerivAt_log_of_pos, BoxIntegral.unitPartition.tag_mem_smul_span, deriv2_negMulLog, intervalIntegral.inv_smul_integral_comp_add_div, ZLattice.abs_repr_le, EisensteinSeries.linear_inv_isBigO_right, eq_rpow_inv, binEntropy_strictMonoOn, MeasureTheory.average_eq, MeasureTheory.Measure.integral_comp_inv_mul_right, Probability.cauchyPDFReal_def, deriv2_mul_log, inv_goldConj, Asymptotics.IsBigOWith.const_mul_right, map_volume_mul_left
|
instLE π | CompOp | 2088 mathmath: List.norm_prod_le, SchwartzMap.norm_toLp_le_seminorm, IsLocalMaxOn.fderivWithin_nonpos, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, Behrend.roth_lower_bound, SpectrumRestricts.le_nnreal_iff, geometric_hahn_banach_open, Angle.abs_toReal_neg_coe_eq_self_iff, pi_div_four_le_arcsin, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, CircleDeg1Lift.instOrderHomClassReal, BoundedContinuousFunction.tietze_extension_step, EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two, norm_smul_le, smoothTransition.eq_one_iff_one_le, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, NNReal.orderIsoIccZeroCoe_apply_coe_coe, lp.norm_apply_le_norm, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, SemiNormedGrp.explicitCokernelDesc_norm_le, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, dist_le_range_sum_dist, dist_triangle, AddGroupNorm.coe_le_coe, MeasureTheory.SignedMeasure.toMeasureOfZeroLE_apply, one_le_sqrt, WithLp.norm_fst_le, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, PadicInt.coe_sub, HasDerivAt.le_of_lipschitz, exists_floor, Finset.Nonempty.norm_sum_le_sup'_norm, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ProbabilityTheory.gaussianReal_map_const_mul, EReal.coe_le_coe_iff, InformationTheory.integral_llr_add_mul_log_nonneg, CStarMatrix.norm_entry_le_norm, BoundedContinuousMapClass.map_bounded, MeasureTheory.setIntegral_nonpos_ae, one_le_cosh, HasCompactSupport.convolution_integrand_bound_left, ContDiffBump.nonneg_normed, lp.isLUB_norm, LipschitzOnWith.norm_sub_le, unitInterval.sigmoid_le_iff, ContinuousLinearMap.norm_inr_le_one, Stirling.log_stirlingSeq_bounded_aux, MeasureTheory.norm_indicatorConstLp_le, pi_le_four, ModularGroup.exists_bound_of_invariant, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, MeasureTheory.levyProkhorovDist_triangle, ConvexOn.le_slope_of_hasDerivAt, logb_le_iff_le_rpow, ProbabilityTheory.condCDF_nonneg, abs_sinc_le_one, sqrt_eq_cases, ConvexOn.continuousOn_tfae, ContinuousLinearMap.exists_preimage_norm_le, ConvexOn.rightDeriv_le_slope_of_mem_interior, gauge_le_one_of_mem, Seminorm.le_finset_sup_apply, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, norm_eq_iInf_iff_real_inner_le_zero, Seminorm.norm_sub_map_le_sub, MeasureTheory.MeasuredSets.real_sub_real_le_dist, Filter.hasBasis_cobounded_norm', ProbabilityTheory.Kernel.densityProcess_antitone_kernel_right, SchwartzMap.norm_le_seminorm, ContractingWith.dist_fixedPoint_le, spectrum.norm_le_norm_of_mem, PadicInt.mem_subring_iff, ProbabilityTheory.IsCondKernelCDF.le_one, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, GroupNorm.le_def, Metric.uniformContinuous_iff_le, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Mathlib.Tactic.Rify.ratCast_le, MeasureTheory.exists_notMem_null_le_integral, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Metric.diam_mono, PadicInt.coe_zero, ProbabilityTheory.gaussianReal_const_mul, Complex.norm_le_abs_re_add_abs_im, abs_cos_le_one, MeasureTheory.upcrossingStrat_nonneg, RightDerivMeasurableAux.norm_sub_le_of_mem_A, InnerProductSpace.Core.inner_mul_inner_self_le, BoundedContinuousFunction.norm_compContinuous_le, BoxIntegral.Box.splitUpper_eq_bot, ProbabilityTheory.Kernel.densityProcess_mono_set, young_inequality, norm_jacobiThetaβ_term_fderiv_ge, NormedAddGroupHom.norm_comp_le, ContinuousLinearMap.norm_inl_le_one, MeasureTheory.norm_condExpL2_le, IsLocalMaxOn.hasFDerivWithinAt_nonpos, dist_mulExpNegMulSq_le_two_mul_sqrt, BoxIntegral.unitPartition.mem_box_iff', PadicInt.val_mkUnits, norm_iteratedFDerivWithin_smul_le, real_sqrt_le_nat_sqrt_succ, ContinuousMultilinearMap.norm_map_snoc_le, NumberField.InfinitePlace.le_iff_le, Padic.withValUniformEquiv_norm_le_one_iff, NumberField.norm_norm_le_norm_mul_house_pow, Valued.toNormedField.norm_le_one_iff, neg_pi_div_two_eq_arcsin, log2_le_logb, dist_smul_le, MeasureTheory.measureReal_symmDiff_le, sinh_nonneg_iff, SeminormedGroup.disjoint_nhds, Matrix.l2_opNorm_mulVec, frontier_halfSpace, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, NumberField.mixedEmbedding.convexBodySumFun_add_le, Metric.infDist_le_dist_of_mem, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, UpperHalfPlane.im_div_exp_dist_le, Seminorm.finset_sup_apply, AddSubgroup.norm_normedMk_le, isBounded_iff_forall_norm_le', EuclideanGeometry.angle_le_pi, CStarAlgebra.inr_mem_Icc_iff_norm_le, MeasureTheory.submartingale_iff_expected_stoppedValue_mono, arctan_nonneg, intervalIntegral.intervalIntegral_eq_integral_uIoc, ProbabilityTheory.mgf_nonneg, ProbabilityTheory.gammaPDFReal_nonneg, LinearMap.polar_eq_iInter, posLog_norm_add_le, ProbabilityTheory.Kernel.densityProcess_mono_kernel_left, CircleDeg1Lift.iterate_pos_le_iff, LipschitzWith.dist_le_mul, LinearMap.IsPositive.re_inner_nonneg_right, eventually_cobounded_le_norm, ConvexOn.map_set_average_le, norm_iteratedFDeriv_mul_le, toNNReal_le_toNNReal_iff', dist_triangle4_right, Metric.hausdorffDist_triangle, ContinuousLinearMap.norm_compLp_le, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, logb_le_logb_of_base_lt_one, MeasureTheory.lpNorm_add_le', SeparationQuotient.norm_liftNormedAddGroupHom_apply_le, Orientation.areaForm_le, log_neg_natCast_nonneg, ENNReal.toReal_mono', schnirelmannDensity_le_one, RCLike.norm_expect_le, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, MeasureTheory.norm_setToFun_le_mul_norm', MeasureTheory.lpNorm_nonneg, le_pow_iff_log_le, ProbabilityTheory.Kernel.densityProcess_le_one, isBoundedUnder_le_exp_comp, norm_iteratedFDerivWithin_clm_apply, MeasureTheory.Integrable.measure_norm_ge_lt_top, isBoundedUnder_ge_exp_comp, Seminorm.bddAbove_range_iff, NormedSpace.image_isVonNBounded_iff, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, UpperHalfPlane.dist_le_iff_dist_coe_center_le, SmoothPartitionOfUnity.nonneg, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, ValueDistribution.proximity_zero_mul_le, QuasispectrumRestricts.nnreal_iff, sin_arctan_nonneg, IsUltrametricDist.norm_intCast_le_one, norm_abs_sub_abs, ContinuousMap.dist_le_two_norm, MeasureTheory.measureReal_le_measureReal_union_left, NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_one, NormedAddGroupHom.norm_id_le, NNReal.canLift, NumberField.mixedEmbedding.norm_le_convexBodySumFun, Complex.frontier_setOf_re_le, SchwartzMap.decay', PiCountable.min_dist_le_dist_pi, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, ContinuousLinearMap.opNorm_lsmul_apply_le, IsUltrametricDist.norm_add_one_le_max_norm_one, ContinuousMap.norm_coe_le_norm, Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, Polynomial.one_le_prod_max_one_norm_roots, NormedAddGroupHom.opNorm_le_of_lipschitz, LinearMap.IsPositive.nonneg_eigenvalues, Set.Countable.exists_pos_hasSum_le, Affine.Simplex.circumradius_nonneg, IsOpen.exists_msmooth_support_eq, OrderedFinpartition.norm_applyOrderedFinpartition_le, IsCompact.exists_bound_of_continuousOn', BoxIntegral.Box.le_TFAE, EuclideanHalfSpace.ext_iff, HasSolidNorm.solid, isUltrametricDist_iff_forall_norm_natCast_le_one, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, PadicInt.nonarchimedean, Polynomial.sub_one_pow_totient_le_cyclotomic_eval, QuotientAddGroup.le_norm_iff, EisensteinSeries.abs_le_right_of_norm, Module.Basis.exists_opNorm_le, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, Height.logHeightβ_sum_le, Height.logHeightβ_add_le, EisensteinSeries.r_lower_bound_on_verticalStrip, logb_le_iff_le_rpow_of_base_lt_one, Urysohns.CU.approx_le_succ, FDerivMeasurableAux.le_of_mem_A, toNNReal_le_ofNat, mulRight_bound, CStarAlgebra.mem_Icc_iff_norm_le_one, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, ConvexOn.set_average_mem_epigraph, schnirelmannDensity_le_iff_forall, Besicovitch.SatelliteConfig.hlast, PadicInt.coe_eq_zero, sum_geometric_two_le, PadicInt.padic_norm_e_of_padicInt, NNReal.coe_le_one, norm_nonneg', ENNReal.ofReal_eq_zero, le_schnirelmannDensity_iff, RCLike.abs_im_div_norm_le_one, one_le_exp_iff, ProbabilityTheory.HasSubgaussianMGF.mgf_le, Seminorm.coe_le_coe, NumberField.abs_discr_ge', log_add_one_le_harmonic, MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM, norm_exp_I_mul_ofReal_sub_one_le, Cardinal.Real.Ioc_countable_iff, HolderTriple.inv_nonneg', HasFDerivAt.le_of_lipschitzOn, lp.sum_rpow_le_norm_rpow, pi_nonneg, NumberField.abs_discr_ge, PadicInt.coe_sum, Complex.arg_le_pi, entry_norm_bound_of_unitary, Complex.norm_one_add_mul_inv_le, dist_le_norm_add_norm, log_mul_self_monotoneOn, CStarAlgebra.norm_le_natCast_iff_of_nonneg, NonUnitalIsometricContinuousFunctionalCalculus.norm_quasispectrum_le, Height.logHeightβ_sub_le, CircleDeg1Lift.dist_map_zero_translationNumber_le, norm_iteratedFDeriv_clm_apply, sin_le_one, ProbabilityTheory.IsCondKernelCDF.nonneg, ContinuousAlternatingMap.norm_def, AntilipschitzWith.mul_le_dist, SmoothBumpFunction.le_one, ProbabilityTheory.cdf_expMeasure_eq, Wallis.W_le, Submodule.norm_starProjection_apply_le, one_sub_sq_div_two_le_cos, IsUltrametricDist.exists_norm_multiset_prod_le, arcsin_nonpos, mem_closedBall_iff_norm'', SpectrumRestricts.nnreal_iff, Asymptotics.IsBigOWith_def, ProbabilityTheory.Kernel.density_le_one, Seminorm.mem_closedBall_zero, DirichletCharacter.norm_LSeries_product_ge_one, abs_setIntegral_mulExpNegMulSq_comp_sub_le_mul_measure, RCLike.nonpos_iff, RCLike.nonpos_iff_exists_ofReal, one_sub_le_exp_neg, dist_birkhoffSum_birkhoffSum_le, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, LinearMap.polar_singleton, norm_div_le, Asymptotics.isBigO_iff_div_isBoundedUnder, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, Complex.neg_pi_div_two_lt_arg_iff, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, Behrend.bound_aux', unitInterval.symm_le_symm, Besicovitch.BallPackage.r_le, Angle.abs_toReal_le_pi, ProbabilityTheory.HasSubgaussianMGF.const_mul, ConcaveOn.slope_le_of_hasDerivAt, MeasureTheory.measure_integral_le_pos, ContinuousMap.toLp_norm_le, ContinuousMultilinearMap.norm_smulRightL_le, norm_le_norm_add_norm_sub', List.norm_prod_le', MeasureTheory.Measure.haar.prehaar_le_index, RCLike.abs_re_le_norm, Behrend.log_two_mul_two_le_sqrt_log_eight, ContinuousMultilinearMap.norm_mkPiAlgebra_le, ProbabilityTheory.stieltjesOfMeasurableRat_nonneg, Seminorm.bound_of_continuous_normedSpace, Besicovitch.SatelliteConfig.h, zpow_le_iff_le_log, Complex.norm_log_one_add_le, Complex.mul_angle_le_norm_sub, sigmoid_nonneg, sum_ofDigitsTerm_digits_le, formalMultilinearSeries_geometric_apply_norm_le, norm_le_add_norm_add, Padic.norm_int_le_one, norm_pow_le_mul_norm, le_logb_iff_rpow_le, dist_sub_sub_le, Complex.arg_le_pi_div_two_iff, instZeroLEOneClass, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSet, MeasureTheory.exists_average_le, IsApproximateAddSubgroup.one_le, SemilinearMapClass.bound_of_continuous, MeasureTheory.SignedMeasure.bddBelow_measureOfNegatives, Matrix.norm_entry_le_entrywise_sup_norm, EReal.coe_nonpos, PiNat.dist_triangle_nonarch, norm_addβ_le, CStarRing.norm_mul_self_le, MeasureTheory.measureReal_mono, Height.one_le_mulHeight, norm_multiset_sum_le, le_gauge_of_notMem, antilipschitzWith_iff_le_mul_dist, inner_mul_inner_self_le, ContinuousLinearMap.norm_fst_le, CStarModule.norm_nonneg, AntilipschitzWith.le_mul_norm, IsUltrametricDist.norm_tsum_le, MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le, CovBySMul.nonneg, ContinuousLinearMap.le_opNorm, LipschitzWith.le_add_mul, norm_le_norm_add_norm_sub, Pi.sum_norm_apply_le_norm', MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae', RCLike.abs_re_div_norm_le_one, norm_sub_le_mul_volume_of_norm_lineDeriv_le, ValueDistribution.logCounting_mul_zero_eventuallyLE, norm_deriv_mulExpNegMulSq_le_one, EuclideanGeometry.angle_le_iff_dist_le, ContinuousMap.norm_le_of_nonempty, Complex.norm_dslope_le_div_of_mapsTo_ball, PadicInt.algebraMap_apply, signedDist_le_dist, ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, RCLike.re_nonneg_of_nonneg, NormedAddGroupHom.IsQuotient.norm_le, spectrum.norm_le_norm_mul_of_mem, AddGroupNorm.le_def, Complex.norm_le_norm_of_mapsTo_ball, IsPowMul.map_one_le_one, AntilipschitzWith.le_mul_dist, entrywise_sup_norm_bound_of_unitary, LindemannWeierstrass.exp_polynomial_approx, DirichletCharacter.norm_le_one, norm_iteratedFDerivWithin_clm_apply_const, CircleDeg1Lift.floor_sub_le_translationNumber, RCLike.ofReal_nonneg, harm_mean_le_geom_mean_weighted, Complex.interior_setOf_le_re, MeasureTheory.Measure.haar.prehaar_sup_le, InnerProductGeometry.angle_le_pi, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, ValueDistribution.proximity_nonneg, IsUltrametricDist.norm_tprod_le, ConvexOn.slope_le_deriv, log_two_near_10, coe_toNNReal_le, Polynomial.mahlerMeasure_nonneg, LipschitzWith.norm_div_le, Metric.Sum.one_le_dist_inr_inl, pi_div_two_le_two, Asymptotics.isLittleO_iff_nat_mul_le, NNReal.dist_agmSequences_fst_snd, EuclideanGeometry.Sphere.nonempty_iff, EReal.toReal_nonpos, Stirling.le_log_factorial_stirling, ProbabilityTheory.variance_le_sub_mul_sub, abs_real_inner_le_norm, ValueDistribution.logCounting_mul_top_eventuallyLE, tsum_geometric_le_of_norm_lt_one, Module.Basis.norm_mul_le_const_mul_norm, spectralValueTerms_bddAbove, ZLattice.tsum_norm_rpow_le, mem_closedBall_iff_norm', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, arcsin_eq_pi_div_two, NumberField.exists_conjugate_one_le_norm, isTheta_exp_comp_one, norm_lineDeriv_le_of_lipschitz, le_sqrt', ProperCone.hyperplane_separation', real_inner_mul_inner_self_le, rescale_to_shell_semi_normed_zpow, norm_indicator_le_of_subset, Function.locallyFinsuppWithin.logCounting_eventually_le, CircleDeg1Lift.map_le_of_map_zero, dist_pair_smul, FDerivMeasurableAux.norm_sub_le_of_mem_A, norm_sub_le, Metric.le_glueDist_inr_inl, arccos_eq_zero, Asymptotics.isBigO_iff, CircleDeg1Lift.le_map_of_map_zero, NonUnitalSeminormedRing.norm_mul_le, ProbabilityTheory.stieltjesOfMeasurableRat_le_one, BoxIntegral.Prepartition.mem_split_iff', UpperHalfPlane.dist_log_im_le, ContinuousMap.HomotopyRel.trans_apply, ModularGroup.exists_max_im, norm_le_of_mem_closedBall, NumberField.house_mul_le, SeparationQuotient.norm_normedMk_le, ContinuousMap.dist_apply_le_dist, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', ContDiffBump.nonneg, IsUltrametricDist.dist_triangle_max, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, Angle.toReal_coe_eq_self_iff, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, norm_pow_le, UpperHalfPlane.im_le_im_mul_exp_dist, dist_div_div_le, MeasureTheory.tendstoInMeasure_iff_norm, convex_halfSpace_re_le, AntilipschitzWith.le_mul_norm', arcsin_le_pi_div_two, UpperHalfPlane.isBoundedAtImInfty_iff, ContinuousMultilinearMap.opNorm_smul_le, Asymptotics.div_isBoundedUnder_of_isBigO, MeasureTheory.upcrossingStrat_le_one, MonotoneOn.sum_le_integral, ContinuousMultilinearMap.norm_restr, antilipschitzWith_iff_exists_mul_le_norm', ContinuousMultilinearMap.norm_image_sub_le, ProbabilityTheory.isPosSemidef_covarianceBilin, InnerProductGeometry.sin_angle_nonneg, ENNReal.le_toReal_sub, MeasureTheory.lpNorm_add_le, dist_triangle4, Urysohns.CU.approx_nonneg, NNReal.isCoboundedUnder_le_toReal, exists_norm_le_le_norm_sub_of_finset, PhragmenLindelof.eqOn_quadrant_II, UniformConvexSpace.uniform_convex, IsGreatest.norm_cfcβ, ModularGroup.exists_bound_of_subgroup_invariant, CircleDeg1Lift.coe_toOrderIso_symm, PseudoMetricSpace.le_two_mul_dist_ofPreNNDist, BoxIntegral.Box.le_iff_bounds, Multipliable.eventually_bounded_finset_prod, CuspFormClass.petersson_bounded_left, arsinh_nonpos_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, BohrMollerup.f_add_nat_ge, Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, HolderTriple.inv_nonneg, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, MonotoneOn.integral_le_sum_Ico, pi_div_two_eq_arcsin, LowerSemicontinuousOn.isClosed_re_epigraph, dist_nonneg, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, NNReal.bddBelow_coe, PhragmenLindelof.eq_zero_on_quadrant_IV, two_le_pi, ContinuousLinearMap.bounds_nonempty, MeasureTheory.measureReal_nonneg, Complex.im_le_norm, Asymptotics.bound_of_isBigO_cofinite, ProbabilityTheory.abs_truncation_le_bound, BoundingSieve.one_le_y, harm_mean_le_geom_mean, spectrum_star_mul_self_nonneg, Complex.norm_log_sub_logTaylor_le, MeasureTheory.SimpleFunc.exists_forall_norm_le, arsinh_nonneg_iff, PiTensorProduct.projectiveSeminorm_tprod_le, le_ofDigits_cantorToTernary_sum, mem_closedBall_iff_norm, le_zpow_iff_log_le, ConvexOn.isBoundedUnder_abs, Complex.closure_setOf_lt_im, ContinuousLinearMap.isPositive_def, indicator_norm_le_norm_self, MeasureTheory.Measure.haar.addCHaar_nonneg, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, toNNReal_le_one, ENNReal.ofNat_le_ofReal, le_exp_log, AddCircle.exists_norm_nsmul_le, sqrt_le_iff, PadicInt.mk_coe, ExistsContDiffBumpBase.u_le_one, CircleDeg1Lift.coe_toOrderIso_inv, IsGreatest.norm_cfc, ENNReal.ofReal_le_iff_le_toReal, InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, Asymptotics.IsLittleO.bound, ZLattice.tsumNormRPowBound_spec, RCLike.ofReal_le_ofReal, MeasureTheory.norm_condExpL2_coe_le, WithCStarModule.prod_norm_le_norm_add, ContinuousLinearMap.exists_approx_preimage_norm_le, BoundedContinuousFunction.bddAbove_range_norm_comp, coe_expOrderIso_apply, ContinuousMultilinearMap.le_opNorm, BoxIntegral.Box.splitUpper_eq_self, UpperHalfPlane.dist_triangle, norm_cauchyPowerSeries_le, norm_le_add_norm_add', abs_dist_sub_le, ofDigitsTerm_le, ProbabilityTheory.cdf_nonneg, ProbabilityTheory.exponentialPDFReal_nonneg, HasFPowerSeriesOnBall.uniform_geometric_approx, BoundedContinuousFunction.dist_eq, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, MeasureTheory.lpNorm_le_add_lpNorm_add, Complex.abs_arg_le_pi, isBigO_one_exp_comp, dist_right_le_of_mem_uIcc, arccos_le_pi, Path.Homotopy.hcomp_apply, dist_le_zero, Filter.IsIncreasingApproximateUnit.eventually_norm, Complex.re_le_re, ContinuousAlternatingMap.le_opNorm, Asymptotics.isBigO_top, Seminorm.rescale_to_shell_zpow, ProbabilityTheory.defaultRatCDF_le_one, cos_one_le, norm_commutator_sub_one_le, realPart.norm_le, isBigO_exp_comp_one, dist_le_coe, ContinuousAlternatingMap.bounds_bddBelow, MeasureTheory.Measure.haar.add_prehaar_le_addIndex, exists_seq_norm_le_one_le_norm_sub, abs_dist_sub_le_dist_mul_mul, Complex.norm_log_one_add_sub_self_le, map_pow_le_pow, Metric.hausdorffDist_triangle', dist_midpoint_midpoint_le, EuclideanGeometry.angle_le_angle_add_angle, BoxIntegral.unitPartition.mem_box_iff, PhragmenLindelof.eqOn_quadrant_I, BoxIntegral.Integrable.dist_integralSum_integral_le_of_memBaseSet, cos_nonneg_of_mem_Icc, IsUltrametricDist.exists_norm_finset_prod_le, MeasureTheory.tendstoInMeasure_iff_dist, ContractingWith.apriori_dist_iterate_fixedPoint_le, SeminormedAddGroup.disjoint_nhds_zero, PartitionOfUnity.sum_le_one', MeasureTheory.norm_integral_le_integral_norm, arccos_le_pi_div_two, Complex.abs_im_le_norm, exp_one_mul_le_exp, ContinuousMultilinearMap.isLeast_opNorm, AkraBazziRecurrence.T_nonneg, IsUltrametricDist.exists_norm_finset_prod_le_of_nonempty, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, NNReal.one_le_coe, WithCStarModule.norm_apply_le_norm, MultilinearMap.exists_bound_of_continuous, Wbtw.dist_le_max_dist, Asymptotics.isBigO_nat_atTop_iff, SmoothPartitionOfUnity.le_one, LinearGrowth.Real.eventually_atTop_exists_int_between, PadicInt.norm_ascPochhammer_le, Behrend.lower_bound_le_one, MeasureTheory.measureReal_union_le, Complex.re_sq_le_normSq, norm_mulβ_le, Asymptotics.isBigO_one_iff, BumpCovering.le_one, MeasureTheory.Measure.haar.chaar_mono, PhragmenLindelof.eqOn_quadrant_III, Function.locallyFinsuppWithin.logCounting_eventuallyLE, PseudoMetricSpace.dist_triangle, MeasureTheory.stoppedValue_lowerCrossingTime, NormedSpace.inclusionInDoubleDual_norm_le, le_log_iff_exp_le, PiNat.dist_triangle, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, ConcaveOn.slope_le_of_hasDerivWithinAt_Ioi, abs_iteratedDeriv_cos_le_one, norm_le_insert', HolderTriple.nonneg', ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, BoundedVariationOn.sub_le, convexHull_exists_dist_ge, PiTensorProduct.bddBelow_projectiveSemiNormAux, projIcc_eq_one, CStarAlgebra.norm_posPart_le, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, Polynomial.gaussNorm_intAdicAbv_le_one, Stirling.le_factorial_stirling, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, le_arcsin_iff_sin_le', Complex.equivRealProd_apply_le', memβp_infty_iff, norm_le_norm_add_norm_div', Subgroup.widthInfty_nonneg, Urysohns.CU.lim_le_one, le_rpow_inv_iff_of_neg, MeasureTheory.exists_notMem_null_le_average, LSeriesSummable.le_const_mul_rpow, ContinuousLinearMap.ratio_le_opNorm, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, norm_sub_norm_le', BoundedContinuousFunction.norm_eq, ProbabilityTheory.exponentialPDF_eq, SchwartzMap.norm_iteratedFDeriv_le_seminorm, AlgHom.norm_apply_le_self, Submodule.norm_orthogonalProjection_apply_le, ContinuousLinearMap.bounds_bddBelow, Hyperreal.coe_nonneg, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet, lp.norm_nonneg', norm_fderiv_le_of_lipschitz, Metric.dist_le_infDist_add_diam, sum_div_nat_floor_pow_sq_le_div_sq, enorm'_le_iff_norm_le, RCLike.normSq_nonneg, contraction_of_isPowMul, MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq, NNReal.isBoundedUnder_ge_toReal, Height.mulHeightβ_add_le, Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gamma, norm_exp_mul_sq_le, ValueDistribution.proximity_sum_top_le, Metric.boundedSpace_iff, ContinuousMultilinearMap.opNorm_nonneg, RCLike.le_iff_re_im, norm_sum_neg_one_pow_le, Complex.norm_exp_sub_sum_le_norm_mul_exp, CircleDeg1Lift.iterate_mono, MeasureTheory.SimpleFunc.norm_approxOn_yβ_le, Polynomial.le_supNorm, dist_integral_mulExpNegMulSq_comp_le, norm_snd_le, lipschitz_with_lipschitz_const_mul, Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO, lipschitzOnWith_iff_norm_div_le, FormalMultilinearSeries.compAlongComposition_bound, AlternatingMap.exists_bound_of_continuous, HasCompactSupport.exists_bound_of_continuous, WithLp.dist_snd_le, two_mul_le_exp, exp_one_near_20, MeasureTheory.norm_setToFun_le', PseudoMetricSpace.dist_ofPreNNDist_le, norm_le_pi_norm, log_of_pos, Height.zero_le_logHeightβ, MeasureTheory.Measure.haar.addCHaar_sup_le, IsUltrametricDist.exists_norm_multiset_sum_le, MeasureTheory.Lp.norm_const_le, toNNReal_le_natCast, dist_triangle_right, Affine.Simplex.exradius_nonneg, MeasureTheory.tendsto_indicator_ge, artanh_le_artanh_iff, SeminormedSpace.Core.norm_triangle, Complex.dist_le_dist_of_mapsTo_ball, MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zero, interior_halfSpace, MeasureTheory.measure_le_setAverage_pos, Height.one_le_mulHeightβ, Matrix.PosSemidef.eigenvalues_nonneg, exists_continuous_nonneg_pos, le_rpow_one_add_norm_iff_norm_le, RingSeminorm.exists_index_pow_le, ContinuousAffineMap.norm_contLinear_le, ENNReal.ofReal_le_ofNat, MeasureTheory.Measure.haar.prehaar_nonneg, Urysohns.CU.bddAbove_range_approx, spectralNorm_mul, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, IsLocalMinOn.hasFDerivWithinAt_nonneg, mul_gauge_le_norm, norm_add_le, Finset.norm_prod_one_add_sub_one_le, Angle.toReal_nonneg_iff_sign_nonneg, PiTensorProduct.norm_eval_le_injectiveSeminorm, unitInterval.one_minus_le_one, exists_nat_abs_mul_sub_round_le, pow_mul_norm_iteratedFDeriv_fourier_le, Metric.thickening_eq_empty_iff, norm_deriv_le_of_lipschitzOn, PadicInt.coe_one, AddGroupSeminorm.add_bddBelow_range_add, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', norm_multiset_prod_le, QuasispectrumRestricts.le_nnreal_iff, ProbabilityTheory.cdf_le_one, BoundedContinuousFunction.neg_norm_le_apply, ValueDistribution.proximity_mul_zero_le, Metric.nonneg_of_mem_sphere, MeasureTheory.lpNorm_sub_le, real_inner_self_nonneg, exp_abs_le, arccos_le_pi_div_four, Seminorm.bddAbove_iff, BoxIntegral.Box.dist_le_distortion_mul, ContinuousMultilinearMap.norm_map_init_le, IsApproximateSubgroup.card_mul_self_le, abs_log_sub_add_sum_range_le, SlashInvariantForm.exists_one_half_le_im_and_norm_le, Filter.hasBasis_cobounded_norm, ConvexOn.slope_le_leftDeriv, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem, NumberField.house_sum_le_sum_house, PositiveLinearMap.exists_norm_apply_le, EuclideanHalfSpace.convex, norm_le_norm_of_abs_le_abs, NormedStarGroup.norm_star_le, Complex.interior_setOf_le_im, Polynomial.supNorm_nonneg, MeasureTheory.Integrable.exists_boundedContinuous_integral_sub_le, norm_jacobiTheta_sub_one_le, GromovHausdorff.ghDist_le_hausdorffDist, unitInterval.mul_le_left, PiNat.mem_cylinder_iff_dist_le, quotient_norm_add_le, enorm_le_iff_norm_le, MeasureTheory.Measure.haar.addPrehaar_mono, AntitoneOn.sum_le_integral_Ico, NNReal.val_eq_coe, FormalMultilinearSeries.ofScalars_norm_le, IsCoercive.bounded_below, ValueDistribution.proximity_add_top_le, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, ContractingWith.dist_le_mul, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, NumberField.mixedEmbedding.normAtPlace_add_le, closure_of_rat_image_lt, IsUltrametricDist.norm_fwdDiff_iter_apply_le, SpectrumRestricts.nnreal_le_iff, NumberField.house_pow_le, one_le_gauge_of_notMem, CStarModule.norm_triangle, MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le, Matrix.permMatrix_l2_opNorm_le, MeasureTheory.norm_condExpIndL1_le, ConvexOn.le_slope_of_hasDerivWithinAt_Ioi, ProperCone.hyperplane_separation_point, MeasureTheory.Measure.haar.prehaar_mono, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, ENNReal.toReal_nonneg, sqrtTwoAddSeries_zero_nonneg, MeasureTheory.norm_integral_le_lintegral_norm, arcsin_le_iff_le_sin', AbsolutelyContinuousOnInterval.exists_bound, artanh_eq_zero_iff, InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero, ContinuousLinearMap.norm_precompR_le, PadicInt.coe_natCast, MeasureTheory.Measure.haar.chaar_nonneg, RingSeminorm.mul_le', dist_triangle_left, ContinuousMap.HomotopyWith.trans_apply, harmonic_le_one_add_log, AkraBazziRecurrence.min_bi_le, RCLike.sqrt_eq_real_add_ite, PadicInt.norm_int_le_pow_iff_dvd, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub', NormedSpace.isVonNBounded_iff', LipschitzWith.dist_iterate_succ_le_geometric, PadicInt.valuation_coe_nonneg, Metric.isBounded_iff, NormedAddGroupHom.bound', MeasureTheory.norm_condExpInd_apply_le, norm_iteratedFDerivWithin_prod_le, IsOpen.exists_contMDiff_support_eq, CStarModule.norm_inner_le, rescale_to_shell, posLog_eq_zero_iff, MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_le_of_meas, norm_sub_le_norm_mul, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, Asymptotics.isBigO_const_iff, IsApproximateAddSubgroup.card_nsmul_le, UniformContinuousOn.cexp, ENNReal.ofReal_le_ofReal_iff', Polynomial.one_le_mahlerMeasure_of_ne_zero, abs_sin_sub_sin_le, Asymptotics.IsTheta.isBoundedUnder_le_iff, FormalMultilinearSeries.norm_compContinuousLinearMap_le, spectralValueTerms_nonneg, Metric.diam_nonneg, norm_zsmul_le, logb_nonpos_iff_of_base_lt_one, Besicovitch.SatelliteConfig.inter', ENNReal.lt_iff_exists_real_btwn, ModularFormClass.exists_petersson_le, MonotoneOn.sum_le_integral_Ico, ContinuousLinearMap.opNorm_comp_le, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, MeasureTheory.Lp.norm_smul_le, Valued.integer.norm_le_one, Bornology.IsBounded.exists_norm_le', ModularGroup.exists_row_one_eq_and_min_re, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, InnerProductSpace.Core.inner_self_nonneg, lipschitzWith_iff_norm_div_le, dist_triangle_max, dist_le_of_mem_Icc, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, ValueDistribution.characteristic_sub_characteristic_inv_le, BoundedContinuousFunction.norm_le_of_nonempty, Submodule.starProjection_norm_le, RCLike.norm_le_re_iff_eq_norm, le_rpow_iff_log_le, BoundedContinuousFunction.norm_integral_le_norm, MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_sub, rescale_to_shell_semi_normed, Complex.dist_le_dist_of_mapsTo_ball_self, NormedAddGroupHom.opNorm_add_le, diam_stdSimplex_le, imaginaryPart.norm_le, Seminorm.preimage_metric_closedBall, sinOrderIso_apply, ProbabilityTheory.IsMeasurableRatCDF.le_one, ValueDistribution.characteristic_eventually_nonneg, MeasureTheory.norm_weightedSMul_le, PartitionOfUnity.nonneg, ProbabilityTheory.meas_ge_le_variance_div_sq, BoundedContinuousFunction.apply_le_norm, ValueDistribution.characteristic_add_top_eventuallyLE, NNReal.mk_one, Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, norm_fderiv_norm_rpow_le, NumberField.FinitePlace.add_le, Complex.nonpos_iff, leTotal_R, NumberField.FinitePlace.instNonnegHomClassReal, expNegInvGlue.nonneg, Asymptotics.isBigOWith_iff, ContinuousAlternatingMap.isLeast_opNorm, Complex.arg_lt_pi_iff, RCLike.abs_im_le_norm, MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le, smoothingFun_le, BoundedContinuousFunction.dist_coe_le_dist, MeasureTheory.stoppedValue_upperCrossingTime, OneHomClass.bound_of_antilipschitz, Complex.dist_le_div_mul_dist_of_mapsTo_ball, closure_open_halfSpace, eventually_norm_pow_le, RCLike.nonneg_iff, le_sum_ofDigitsTerm_digits, ENNReal.truncateToReal_le, ProbabilityTheory.IsMeasurableRatCDF.nonneg, log_le_iff_le_exp, MeasureTheory.mul_le_integral_rnDeriv_of_ac, ProbabilityTheory.gaussianReal_mul_const, PadicInt.coe_adicCompletionIntegersEquiv_apply, CircleDeg1Lift.le_map_map_zero, Asymptotics.IsBigO.exists_mem_basis, NormedAddGroupHom.ratio_le_opNorm, norm_nsmul_le, sign_mul_nonneg, ContinuousMultilinearMap.bounds_bddBelow, ContinuousLinearMap.rayleighQuotient_le_norm, mem_balancedHull_iff, ContinuousLinearMap.norm_def, lipschitzWith_iff_norm_sub_le, mem_closedBall_iff_norm''', Height.mulHeightβ_sum_le, abs_norm_sub_norm_le, BoxIntegral.Prepartition.upper_le_upper, Set.infsep_nonneg, CuspFormClass.petersson_bounded_right, Polynomial.exists_forall_norm_le, Stirling.sqrt_pi_le_stirlingSeq, NumberField.Ideal.tendsto_norm_le_div_atTopβ, GroupNorm.coe_le_coe, smoothTransition.le_one, ProbabilityTheory.IsRatCondKernelCDFAux.mono', unitInterval.qRight_zero_right, NormedSpace.equicontinuous_TFAE, ProbabilityTheory.Kernel.rnDerivAux_le_one, dist_le_of_mem_uIcc, ProbabilityTheory.norm_complexMGF_le_mgf, Pi.sum_norm_apply_le_norm, ModularFormClass.exists_bound, ProbabilityTheory.variance_le_sq_of_bounded, Metric.le_infDist, norm_div_sub_norm_div_le_norm_div, ContinuousLinearMap.opNorm_add_le, Valued.toNormedField.norm_le_iff, sin_nonneg_of_mem_Icc, unitInterval.mul_le_right, padic_polynomial_dist, Height.mulHeightβ_sub_le, InnerProductGeometry.angle_le_angle_add_angle, ContinuousLinearMap.NonlinearRightInverse.bound, iInter_halfSpaces_eq, ValueDistribution.logCounting_add_top_eventuallyLE, ProbabilityTheory.covarianceBilin_self_nonneg, add_mem_closedBall_iff_norm, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, InnerProductSpace.Core.norm_inner_le_norm, unitInterval.nonneg', MeasureTheory.integral_le_liminf_integral_of_forall_isOpen_measure_le_liminf_measure, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, norm_sup_le_add, AntilipschitzWith.le_mul_norm_div, abs_rpow_le_abs_rpow, unitInterval.le_one', ENNReal.natCast_le_ofReal, NormedAddGroupHom.bounds_nonempty, CompactlySupportedContinuousMap.integralLinearMap_apply, Path.Homotopy.trans_apply, MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le, NumberField.one_le_house_of_isIntegral, unitInterval.symm_le_comm, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, ENNReal.ofReal_le_one, ConcaveOn.le_map_integral, Complex.interior_setOf_im_le, cos_arcsin_nonneg, EisensteinSeries.norm_le_tsum_norm, NumberField.mixedEmbedding.convexBodySumFun_nonneg, ValueDistribution.proximity_mul_top_le, ContinuousMultilinearMap.opNorm_add_le, eventually_cobounded_le_norm', PadicInt.one_le_norm_iff, unitary.two_mul_one_sub_le_norm_sub_one_sq, rpow_le_rpow_left_iff, ProbabilityTheory.condVar_ae_le_condExp_sq, InformationTheory.mul_log_le_toReal_klDiv, ENNReal.one_le_ofReal, Nat.pairwise_one_le_dist, sqrt_le_one, CircleDeg1Lift.translationNumber_le_ceil_sub, LinearMap.re_inner_adjoint_mul_self_nonneg, range_euclideanHalfSpace, NNReal.isBoundedUnder_le_toReal, ValueDistribution.characteristic_mul_zero_eventuallyLE, real_inner_le_norm, arccos_eq_pi, ConvexOn.slope_le_of_hasDerivWithinAt, ContinuousLinearMap.norm_map_tail_le, AntitoneOn.integral_le_sum_Ico, NonarchAddGroupNorm.le_def, MeasureTheory.setIntegral_abs_condExp_le, NumberField.mixedEmbedding.norm_nonneg, ContinuousMap.Homotopy.trans_apply, exists_dual_vector'', ConcaveOn.set_average_mem_hypograph, Metric.infDist_le_infDist_of_subset, BoundedContinuousFunction.Lp_norm_le, MeasureTheory.exists_integral_le, Complex.norm_sub_le_angle, MeasureTheory.Lp.norm_constL_le, ProbabilityTheory.covarianceBilinDual_self_nonneg, Metric.mem_closedBall', ContDiffBump.measure_closedBall_le_integral, Metric.Sum.one_le_dist_inl_inr, ValueDistribution.logCounting_top_mul_eventually_le, log_div_self_antitoneOn, PiCountable.dist_le_dist_pi_of_dist_lt, norm_prod_le_iff, Cardinal.Real.Icc_countable_iff, Hyperreal.IsSt.le, ProbabilityTheory.IsRatCondKernelCDFAux.le_one', NNReal.isCoboundedUnder_ge_toReal, RCLike.norm_im_le_norm, ProbabilityTheory.Kernel.densityProcess_nonneg, Metric.hausdorffDist_le_diam, MeasureTheory.ae_le_lpNorm_exponent_top, dist_add_add_le, contraction_of_isPowMul_of_boundedWrt, BoundingSieve.siftedSum_le_sum_of_upperMoebius, ConvexOn.convex_re_epigraph, SmoothPartitionOfUnity.sum_le_one', real_inner_le_one_of_norm_eq_one, arcsin_le_neg_pi_div_two, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, ProbabilityTheory.Kernel.rnDerivAux_nonneg, Asymptotics.isBigOWith_top, norm_sub_le_of_mem_segment, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, toNNReal_eq_zero, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, norm_mulβ_le', ConcaveOn.le_slope_of_hasDerivWithinAt, Urysohns.CU.approx_le_one, abs_real_inner_div_norm_mul_norm_le_one, LinearMap.isPositive_iff_complex, bernstein_nonneg, PiLp.dist_apply_le, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', NormedAddGroupHom.bound, SmoothPartitionOfUnity.sum_nonneg, MeasureTheory.norm_charFun_le_one, unitInterval.le_one, IsOpen.measure_eq_biSup_integral_continuous, EuclideanGeometry.dist_le_of_wbtw_of_mem_perpBisector, norm_deriv_le_of_lipschitz, sinhOrderIso_apply, MeasureTheory.SimpleFunc.norm_integral_le_integral_norm, one_le_pi_div_two, ofDigits_nonneg, IsUltrametricDist.norm_zsmul_le, ContinuousMultilinearMap.ratio_le_opNorm, ContinuousLinearMap.norm_extendToπ'_bound, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, isBounded_iff_forall_norm_le, pi_norm_const_le', cosh_le_exp_half_sq, rpow_inv_le_iff_of_neg, Complex.abs_arg_le_pi_div_two_iff, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, AddGroupSeminorm.coe_le_coe, SeparationQuotient.norm_liftNormedAddGroupHom_le, ProbabilityTheory.gaussianReal_map_mul_const, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, ofDigitsTerm_nonneg, Metric.uniformity_basis_dist_le, UpperHalfPlane.le_dist_coe, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, ContinuousLinearMap.le_opNormβ, Nat.roughNumbersUpTo_card_le', ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, schnirelmannDensity_le_div, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, real_inner_self_nonpos, ContinuousLinearMap.opNorm_mul_le, HasCompactMulSupport.exists_bound_of_continuous, log_div_sqrt_antitoneOn, Asymptotics.IsBigO.exists_nonneg, Height.mulHeightβ_nonneg, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, abs_cos_sub_cos_le, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, AddCircle.norm_coe_eq_abs_iff, Complex.frontier_setOf_le_re, ModularGroup.exists_one_half_le_im_smul, Seminorm.le_def, self_le_sinh_iff, InnerProductGeometry.angle_nonneg, convex_halfSpace_re_ge, dist_le_tsum_dist_of_tendstoβ, NormedAddCommGroup.exists_norm_nsmul_le, norm_le_norm_sub_add, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, self_subset_gauge_le_one, AddGroupSeminorm.add_le', MeasureTheory.Martingale.bddAbove_range_iff_bddBelow_range, FormalMultilinearSeries.compAlongComposition_norm, ExistsContDiffBumpBase.y_nonneg, dist_pi_eq_iff, BoundingSieve.weights_nonneg, spectralNorm_nonneg, BoxIntegral.Box.splitLower_eq_bot, Metric.nonempty_closedBall, ModularGroup.exists_bound_fundamental_domain_of_isBigO, neg_one_le_sinc, LipschitzOnWith.le_add_mul, Metric.isBounded_image_iff, ConcaveOn.slope_le_derivWithin, IsBoundedSMul.dist_pair_smul', ProbabilityTheory.variance_nonneg, CircleDeg1Lift.coe_toOrderIso, BoxIntegral.Box.mk'_eq_bot, EReal.coe_nonneg, ConvexOn.real_univ_sSup_affine_eq, BoxIntegral.Box.coe_splitLower, SchwartzMap.le_seminorm, LipschitzWith.norm_sub_le, Finset.norm_prod_le', ENNReal.toReal_le_coe_of_le_coe, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, LipschitzOnWith.norm_div_le, Stirling.stirlingSeq'_bounded_by_pos_constant, convex_halfSpace_im_ge, NormedAddGroupHom.le_opNorm, HasFPowerSeriesOnBall.uniform_geometric_approx', IsBoundedLinearMap.bound, natLog_le_logb, Complex.angle_le_mul_norm_sub, MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply, Convex.gauge_le, LipschitzWith.norm_le_mul, Orientation.abs_areaForm_le, ZLattice.exists_forall_abs_repr_le_norm, Metric.le_glueDist_inl_inr, PadicInt.norm_le_pow_iff_norm_lt_pow_add_one, Set.Nontrivial.infsep_anti, EisensteinSeries.r_mul_max_le, Valued.norm_add_le, Asymptotics.bound_of_isBigO_nat_atTop, cauchySeq_iff_le_tendsto_0, IsUltrametricDist.norm_pow_le, Asymptotics.IsBigO.bound, Complex.norm_le_norm_of_mapsTo_ball_self, IsUltrametricDist.exists_norm_finset_sum_le, norm_lineDeriv_le_of_lipschitzOn, Complex.norm_prime_cpow_le_one_half, norm_le_mul_norm_add', log_natCast_nonneg, AkraBazziRecurrence.eventually_one_sub_smoothingFn_nonneg, Complex.closure_setOf_re_lt, sigmoid_le_one, QuotientAddGroup.norm_lift_apply_le, ENNReal.orderIsoUnitIntervalBirational_apply_coe, sigmoid_le_iff, Height.logHeight_nonneg, ProbabilityTheory.paretoPDF_eq, norm_root_le_spectralValue, sin_div_le_inv_abs, ContinuousAlternatingMap.norm_image_sub_le', norm_le_pi_norm', GromovHausdorff.hausdorffDist_optimal_le_HD, neg_one_le_real_inner_of_norm_eq_one, Stirling.log_stirlingSeq_bounded_by_constant, PadicInt.norm_le_pow_iff_le_valuation, ConcaveOn.le_map_average, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub, ConcaveOn.leftDeriv_le_slope, dist_le_tsum_dist_of_tendsto, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, Metric.dist_le_diam_of_mem, ContractingWith.dist_inequality, norm_sub_sub_norm_sub_le_norm_sub, Module.Basis.norm_nonneg, MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_le, ConcaveOn.derivWithin_le_slope, ValueDistribution.logCounting_zero_mul_eventually_le, NormedAddGroupHom.bounds_bddBelow, one_le_toNNReal, rpow_le_rpow_left_iff_of_base_lt_one, rpow_inv_log_le_exp_one, exists_rat_abs_sub_le_and_den_le, BoundedContinuousFunction.dist_le_iff_of_nonempty, ProperCone.relative_hyperplane_separation, PadicInt.norm_le_pow_iff_mem_span_pow, Int.Matrix.one_le_norm_A_of_ne_zero, BoxIntegral.IntegrationParams.RCond.min, MeasureTheory.measureReal_abs_gt_le_integral_charFun, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, PreInnerProductSpace.Core.re_inner_nonneg, UpperHalfPlane.isZeroAtImInfty_iff, ofDigits_cantorToTernary_sum_le, Padic.norm_le_one_iff_val_nonneg, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, IsPicardLindelof.norm_le, abs_circleAverage_le_circleAverage_abs, ConcaveOn.deriv_le_slope, neg_one_le_cos, sin_sq_le_sq, StrongDual.norm_toLpβ_le, sin_sq_le_one, Liouville.exists_pos_real_of_irrational_root, ContDiffMapSupportedIn.norm_apply_le_seminorm, Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.HasSubgaussianMGF.cgf_le, UpperHalfPlane.dist_le_dist_coe_div_sqrt, Asymptotics.isBigO_one_nat_atTop_iff, Complex.abs_im_div_norm_le_one, NNReal.mk_zero, LinearMap.mem_polar_singleton, exp_le_exp, CuspFormClass.exists_bound, MeasureTheory.L1.norm_integral_le, NonarchAddGroupSeminorm.add_bddBelow_range_add, spectrum.coe_le_norm_of_mem, ProbabilityTheory.exponentialCDFReal_eq, isBoundedLinearMap_iff, Complex.re_le_norm, Subgroup.strictWidthInfty_nonneg, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, ENNReal.ofReal_le_coe, ConcaveOn.isBoundedUnder_abs, ProbabilityTheory.gaussianPDFReal_inv_mul, one_le_norm_one, ContinuousMultilinearMap.norm_iteratedFDeriv_le, MeasureTheory.le_sub_of_le_upcrossingsBefore, Complex.interior_setOf_re_le, Complex.abs_re_le_norm, rpow_left_injOn, LipschitzOnWith.iff_le_add_mul, CStarModule.norm_eq_csSup, RCLike.norm_re_le_norm, BoxIntegral.Box.diam_Icc_le_of_distortion_le, arctan_le_arctan_iff, lipschitzWith_iff_dist_le_mul, MeasureTheory.MemLp.integral_indicator_norm_ge_le, ArithmeticFunction.vonMangoldt.residueClass_nonneg, ContinuousMultilinearMap.norm_iteratedFDeriv_le', MeasureTheory.Measure.haar.chaar_sup_le, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, le_toNNReal_iff_coe_le', Set.infsep_pair_le_toReal_inf, Asymptotics.isBigO_cofinite_iff, Matrix.linfty_opNorm_mulVec, MeasureTheory.setIntegral_nonpos_le, DirichletCharacter.norm_LFunction_product_ge_one, ContinuousAffineMap.norm_image_zero_le, abs_mulExpNegMulSq_one_le_one, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, IsCompact.exists_bound_of_continuousOn, ConcaveOn.slope_le_of_hasDerivWithinAt, ConvexOn.average_mem_epigraph, NormedAddGroupHom.ofLipschitz_norm_le, PowerSeries.IsRestricted.convergenceSet_BddAbove, mem_closedBall_one_iff, Complex.closure_setOf_lt_re, log_le_log_iff, RCLike.nonneg_iff_exists_ofReal, RCLike.geometric_hahn_banach_open, smoothingFun_le_self, ZeroHomClass.bound_of_antilipschitz, ConcaveOn.le_slope_of_hasDerivWithinAt_Iio, logb_nonneg_iff_of_base_lt_one, IsUltrametricDist.norm_add_le_max, gauge_nonneg, Continuous.bounded_above_of_compact_support, ProbabilityTheory.Fernique.measure_le_mul_measure_gt_normThreshold_le_of_map_rotation_eq_self, Seminorm.bddBelow_range_add, RCLike.ofReal_nonpos, EuclideanGeometry.Sphere.radius_nonneg_of_mem, NumberField.house_nonneg, le_integral_rpowIntegrandββ_one, MeasureTheory.norm_one_sub_charFun_le_two, Mathlib.Meta.Positivity.log_nonneg_of_isNegNat, GromovHausdorff.HD_below_aux2, ProbabilityTheory.variance_le_expectation_sq, WithCStarModule.norm_equiv_le_norm_prod, Rat.AbsoluteValue.padic_le_one, ArithmeticFunction.vonMangoldt.residueClass_le, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, norm_div_le_norm_div_add_norm_div, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, ValueDistribution.logCounting_sum_top_eventuallyLE, ContDiffBump.integral_le_measure_closedBall, CStarAlgebra.norm_le_norm_of_nonneg_of_le, dist_triangle4_left, ContractingWith.dist_le_of_fixedPoint, lp.tsum_mul_le_mul_norm', RCLike.re_le_re, intervalIntegral.norm_integral_le_of_norm_le_const_ae, NNReal.orderIsoIccZeroCoe_symm_apply_coe, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, coe_comp_expOrderIso, norm_le_spectralNorm, isTheta_exp_comp_exp_comp, Set.infsep_le_dist_of_mem, ODE.FunSpace.dist_iterate_next_le, ProbabilityTheory.isPosSemidef_covarianceBilinDual, dist_le_of_mem_Icc_01, ContinuousAlternatingMap.bounds_nonempty, norm_tsum_le_tsum_norm, Complex.normSq_nonneg, variationOnFromTo.nonneg_of_le, BoxIntegral.integrable_iff_cauchy_basis, Complex.arg_eq_zero_iff, WithCStarModule.pi_norm_le_sum_norm, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, PiLp.norm_apply_le, sum_mul_le_sqrt_mul_sqrt, IsometricContinuousFunctionalCalculus.norm_spectrum_le, ConvexOn.derivWithin_le_slope, MeasureTheory.setIntegral_nonneg_ae, gauge_mono, ContinuousLinearMap.norm_id_le, HasFDerivAt.le_of_lipschitz, Asymptotics.isBigO_principal, posLog_prod, cos_sq_le_one, ConvexOn.univ_sSup_affine_eq, Angle.abs_toReal_coe_eq_self_iff, NumberField.exists_ideal_in_class_of_norm_le, Complex.sqrt_eq_real_add_ite, ContinuousMap.neg_norm_le_apply, ProbabilityTheory.condCDF_le_one, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, SeminormedRing.norm_mul_le, BoundedVariationOn.dist_le, dist_mul_mul_le, cosh_le_cosh, Asymptotics.isBigO_const_left_iff_pos_le_norm, norm_iteratedFDeriv_prod_le, MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, Asymptotics.IsBigO.exists_eq_mul, toNNReal_le_toNNReal_iff_of_pos, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, ContinuousLinearMap.opNorm_lsmul_le, dist_vsub_vsub_le, AntilipschitzWith.le_mul_norm_sub, NumberField.canonicalEmbedding.norm_le_iff, MeasureTheory.Measure.haar.addPrehaar_nonneg, Unitary.two_mul_one_sub_le_norm_sub_one_sq, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, LipschitzWith.iff_le_add_mul, WeakDual.CharacterSpace.norm_le_norm_one, sinc_le_one, Padic.nonarchimedean, ValueDistribution.characteristic_zero_mul_eventually_le, MeasureTheory.L1.norm_setToL1_le_mul_norm', LipschitzOnWith.dist_le_mul, Seminorm.rescale_to_shell, PartitionOfUnity.sum_le_one, dist_le_of_mem_pi_Icc, IsUltrametricDist.exists_norm_finset_sum_le_of_nonempty, BoxIntegral.Box.lower_le_upper, ContinuousLinearMap.isPositive_def', Valued.norm_nonneg, Matrix.frobenius_norm_mul, ProbabilityTheory.Fernique.logRatio_nonneg, ConvexOn.map_integral_le, variationOnFromTo.nonpos_of_ge, ContinuousLinearMap.norm_compL_le, NonarchAddGroupNorm.coe_le_coe, NonUnitalNormedRing.norm_mul_le, rpow_le_iff_le_log, MeasureTheory.measureReal_iUnion_fintype_le, Path.trans_apply, norm_sub_le_norm_add, NormedAddGroupHom.opNorm_nonneg, natCastle_toNNReal', norm_le_zero_iff, ArithmeticFunction.vonMangoldt_nonneg, TensorProduct.dist_tmul_le, IsPicardLindelof.mul_max_le, PhragmenLindelof.eq_zero_on_quadrant_II, NumberField.InfinitePlace.one_le_mult, NNReal.forall, norm_inf_sub_inf_le_norm, HurwitzKernelBounds.F_nat_zero_zero_sub_le, PiTensorProduct.mapL_opNorm, IsBoundedSMul.dist_smul_pair', Asymptotics.IsBigOWith.exists_nonneg, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Matrix.PosSemidef.re_dotProduct_nonneg, rescale_to_shell_zpow, norm_sub_norm_le, Matrix.linfty_opNorm_mul, EuclideanGeometry.dist_le_of_wbtw_of_inner_eq_zero, Complex.norm_deriv_le_one_of_mapsTo_ball, Metric.infDist_le_infDist_add_dist, arcsin_nonneg, Complex.zero_le_real, le_norm_self, NormedAlgebra.norm_smul_le, HasLineDerivAt.le_of_lipschitzOn, ZetaAsymptotics.term_nonneg, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, ContinuousMap.norm_restrict_mono_set, ContinuousLinearMap.opNorm_mul_apply_le, RCLike.re_le_norm, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, Asymptotics.isBigO_iff_isBoundedUnder_le_div, Hyperreal.ofSeq_le_ofSeq, Chebyshev.theta_nonneg, PadicInt.valuation_coe, ContinuousLinearMap.isPositive_iff_complex, BoundedContinuousFunction.norm_coe_le_norm, smoothTransition.nonneg, NormedSpace.norm_smul_le, EReal.toReal_le_toReal, NNReal.coe_nonneg, ProbabilityTheory.gammaPDF_eq, ContinuousLinearMap.opNorm_smul_le, MeasureTheory.L1.norm_setToL1_le', isBigO_exp_comp_exp_comp, norm_prod_le, MeasureTheory.exists_le_setAverage, pi_norm_le_iff_of_nonempty, Mathlib.Meta.Positivity.log_nonneg_of_isNat, lipschitzOnWith_iff_dist_le_mul, Polynomial.leading_coeff_le_mahlerMeasure, not_bddBelow_coe, pi_div_two_le_arcsin, le_arcsin_iff_sin_le, riesz_lemma_of_norm_lt, norm_le_norm_add_norm_div, log_intCast_nonneg, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, ENNReal.toReal_add_le, zero_mem_lowerBounds_smoothingSeminormSeq_range, gauge_sum_le, SeminormedGroup.disjoint_nhds_one, ContinuousMap.apply_le_norm, Asymptotics.isBigO_iff_exists_eq_mul, ArchimedeanClass.stdPart_nonneg, Complex.norm_deriv_le_div_of_mapsTo_ball, Finset.Nonempty.norm_prod_le_sup'_norm, logb_le_logb, nat_sqrt_le_real_sqrt, NumberField.norm_embedding_le_house, neg_one_le_sin, intervalIntegral.integral_indicator, SelbergSieve.one_le_level, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, pow_mul_norm_iteratedFDeriv_fourierIntegral_le, norm_le_mul_norm_add, NumberField.mixedEmbedding.normAtPlace_nonneg, ArchimedeanClass.stdPart_le_of_le, disjoint_ball_ball_iff, abs_dist_sub_le_dist_add_add, BoundedContinuousFunction.dist_set_exists, PiTensorProduct.norm_eval_le_projectiveSeminorm, PhragmenLindelof.eqOn_quadrant_IV, ConvexOn.slope_le_of_hasDerivAt, IsUltrametricDist.norm_mul_le_max, Fourier.norm_fourierIntegral_le_integral_norm, ProperCone.mem_innerDual, WithCStarModule.norm_equiv_le_norm_pi, abs_iteratedDeriv_sin_le_one, smoothingSeminormSeq_bddBelow, MeasureTheory.measureReal_le_one, not_bddAbove_coe, MeasureTheory.lpNorm_sum_le, MeasureTheory.abs_integral_le_integral_abs, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, ConvexOn.map_average_le, IsApproximateSubgroup.card_pow_le, Metric.diam_union', MeasureTheory.measureReal_le_measureReal_union_right, PiNat.dist_nonneg, gauge_le_one_iff_mem_closure, PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one, Padic.norm_rat_le_one, IsUltrametricDist.norm_natCast_le_one, BoundedContinuousFunction.toLp_norm_le, ContDiffMapSupportedIn.seminorm_postcompLM_le, ContinuousMultilinearMap.bound, GroupSeminorm.coe_le_coe, NumberField.abs_discr_ge_of_isTotallyComplex, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, MeasureTheory.exists_setAverage_le, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, Submodule.re_inner_starProjection_nonneg, Nat.norm_cast_le, rpow_neg_one_add_norm_sq_le, Metric.Sigma.one_le_dist_of_ne, NormedAddGroupHom.norm_lift_le, ConvexOn.deriv_le_slope, integral_sin_pow_succ_le, ZLattice.le_norm_of_le_abs_repr, arcosh_le_arcosh, ContinuousAffineMap.norm_comp_le, smoothTransition.zero_iff_nonpos, PartitionOfUnity.le_one, ConvexOn.rightDeriv_le_slope, Valued.integer.mem_iff, MeasureTheory.SimpleFunc.norm_approxOn_zero_le, PiTensorProduct.projectiveSeminormAux_nonneg, Asymptotics.isBigOWith_principal, BoundedContinuousFunction.bounded, AddGroupSeminorm.le_def, BumpCovering.nonneg, MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_pos_le, dist_norm_norm_le', NormedAddGroupHom.lipschitz, MeasureTheory.L1.SimpleFunc.norm_integral_le_norm, MeasureTheory.measure_le_integral_pos, SchwartzMap.decay, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, norm_fderiv_le_of_lipschitzOn, RCLike.im_sq_le_normSq, SzemerediRegularity.pow_mul_m_le_card_part, exp_nonneg, dist_dist_dist_le, ContinuousLinearMap.opNorm_le_iff_lipschitz, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, ProbabilityTheory.abs_truncation_le_abs_self, norm_pow_le', exists_forall_sphere_dist_add_le_two_sub, Matrix.l2_opNorm_le_one_of_mem_doublyStochastic, EisensteinSeries.abs_le_left_of_norm, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg', LipschitzWith.norm_le_mul', Urysohns.CU.approx_le_approx_of_U_sub_C, MeasureTheory.lintegral_coe_le_coe_iff_integral_le, GroupSeminorm.le_def, CircleDeg1Lift.le_iterate_pos_iff, Complex.frontier_setOf_le_re_and_le_im, AddCircle.norm_le_half_period, NumberField.mixedEmbedding.normAtAllPlaces_nonneg, sSup_def, BoundedContinuousFunction.abs_diff_coe_le_dist, Hyperreal.st_le_of_le, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, inner_le_Lp_mul_Lq, ProbabilityTheory.meas_ge_le_evariance_div_sq, NormedSpace.sphere_nonempty, Complex.not_lt_zero_iff, NNReal.coe_image, MeasureTheory.exists_notMem_null_integral_le, schnirelmannDensity_le_of_subset, ConcaveOn.average_mem_hypograph, SzemerediRegularity.one_le_m_coe, convexHull_exists_dist_ge2, ZeroAtInftyContinuousMap.bounded, Orientation.volumeForm_apply_le, re_inner_self_nonpos, ContinuousLinearMap.norm_single_le_one, QuotientGroup.le_norm_iff, Metric.uniformContinuousOn_iff_le, BoundedContinuousFunction.norm_integral_le_mul_norm, ContinuousLinearMap.norm_compSL_le, MeasureTheory.norm_condExpInd_le, exists_norm_le_of_cauchySeq, dual_solid, CStarAlgebra.norm_negPart_le, pow_le_iff_le_log, dist_le_norm_add_norm', gauge_gaugeRescale_le, riesz_lemma_of_lt_one, InnerProductSpace.Core.cauchy_schwarz_aux', MonotoneOn.integral_le_sum, arctan_le_zero, abs_norm_sub_norm_le', CovByVAdd.nonneg, sub_le_dist, ContinuousLinearMap.opNorm_nonneg, Metric.ball_eq_empty, AntitoneOn.sum_le_integral, IsCompact.measure_eq_biInf_integral_hasCompactSupport, ModularGroup.three_le_four_mul_im_sq_of_mem_fd, neg_one_le_mulExpNegMulSq_one, PadicInt.mkUnits_eq, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, MeasureTheory.norm_Lp_toLp_restrict_le, abs_sin_le_abs, Stirling.log_stirlingSeq_diff_le_geo_sum, Complex.neg_pi_div_two_le_arg_iff, NonarchAddGroupSeminorm.le_def, PartitionOfUnity.sum_nonneg, PositiveLinearMap.norm_apply_le_of_nonneg, ContinuousLinearMap.bddAbove_rayleighQuotient, Behrend.le_sqrt_log, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, Behrend.two_div_one_sub_two_div_e_le_eight, dist_prod_prod_le, RCLike.re_sq_le_normSq, Polynomial.isGreatest_supNorm, Complex.norm_fderiv_le_one_of_mapsTo_ball, MeasureTheory.exists_le_integral, Asymptotics.IsBigO.isBoundedUnder_le, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, abs_sin_le_one, toNNReal_le_iff_le_coe, SchwartzMap.seminorm_apply, logb_nonpos_iff, norm_apply_le_norm_cfc, Complex.norm_log_one_sub_inv_sub_self_le, WithLp.norm_snd_le, norm_sup_sub_sup_le_add_norm, ConcaveOn.slope_le_rightDeriv, NNReal.mk_natCast, unitInterval.nonneg, QuotientAddGroup.norm_mk_le_norm, ProbabilityTheory.Kernel.density_nonneg, sum_div_pow_sq_le_div_sq, Bornology.IsBounded.exists_norm_le, dist_pi_const_le, MeasureTheory.L1.norm_Integral_le_one, Behrend.bound_aux, ProbabilityTheory.Kernel.mem_mutuallySingularSetSlice, ContinuousLinearMap.norm_smulRightL_le, schnirelmannDensity_le_of_notMem, spectralValue_le_one_iff, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, norm_addβ_le, Polynomial.cyclotomic_eval_le_add_one_pow_totient, Chebyshev.psi_nonneg, ENNReal.toReal_le_toReal, BoundingSieve.siftedSum_le_mainSum_errSum_of_upperMoebius, ZLattice.normBound_spec, Metric.infDist_le_infDist_add_hausdorffDist, ContDiffBump.normed_le_div_measure_closedBall_rIn, Fact.Manifold.instLeReal, NumberField.house_add_le, Metric.mem_closedBall, SchwartzMap.le_seminorm', mul_mem_closedBall_iff_norm, RCLike.re_le_neg_norm_iff_eq_neg_norm, sin_arctan_le_zero, log_natCast_le_rpow_div, ConcaveOn.continuousOn_tfae, VectorFourier.norm_fourierSMulRight_le, ConvexOn.le_slope_of_hasDerivWithinAt, abs_mulExpNegMulSq_le, ConvexOn.slope_le_derivWithin, ENNReal.dichotomy, KuratowskiEmbedding.embeddingOfSubset_dist_le, MeasureTheory.Measure.haar.addCHaar_mono, norm_commutator_units_sub_one_le, Unitization.norm_splitMul_snd_sq, Complex.norm_natCast_cpow_le_norm_natCast_cpow_iff, neg_pi_div_two_le_arcsin, intervalIntegral.norm_integral_le_abs_integral_norm, Complex.norm_exp_le_exp_norm, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Behrend.lower_bound_le_one', MeasureTheory.measure_average_le_pos, ContDiffMapSupportedIn.bounded_iteratedFDeriv, UpperHalfPlane.dist_coe_le, Tactic.ComputeAsymptotics.Seq.FriendlyOperation.dist_le, Complex.circleTransformDeriv_bound, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, Asymptotics.isLittleO_iff, HolderTriple.one_div_nonneg', HolderOnWith.dist_le, Complex.HadamardThreeLines.sSupNormIm_nonneg, MeasureTheory.measure_setAverage_le_pos, mulExpNegMulSq_one_le_one, unitInterval.one_minus_nonneg, ProbabilityTheory.measure_le_mul_measure_gt_le_of_map_rotation_eq_self, MeasureTheory.measureReal_biUnion_finset_le, exp_one_near_10, spectralValue_nonneg, VectorFourier.norm_fourierPowSMulRight_le, dist_birkhoffAverage_birkhoffAverage_le, exp_le_one_iff, riesz_lemma, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, MeasureTheory.measure_le_average_pos, PadicInt.coe_neg, Padic.norm_rat_le_one_iff_padicValuation_le_one, Cardinal.Real.Ico_countable_iff, PadicInt.norm_def, CStarAlgebra.norm_le_one_iff_of_nonneg, ContinuousMultilinearMap.norm_map_insertNth_le, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_le, ValueDistribution.logCounting_eventually_nonneg, Complex.real_le_real, norm_iteratedFDerivWithin_mul_le, Asymptotics.isBigO_iff'', PadicInt.isOpenEmbedding_coe, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, BoundedContinuousFunction.norm_const_le, Padic.norm_le_pow_iff_norm_lt_pow_add_one, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, abs_ofDigits_sub_ofDigits_le, binEntropy_le_log_two, BoxIntegral.Box.splitLower_eq_self, Complex.norm_log_natCast_le_rpow_div, WithCStarModule.max_le_prod_norm, norm_add_sub_norm_sub_le_two_mul_min, dist_midpoint_midpoint_le', sum_range_sub_log_div_le, ENNReal.toReal_ofReal_eq_iff, LinearIsometry.norm_toContinuousLinearMap_le, MeasureTheory.le_measureReal_diff, NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSet, ProbabilityTheory.Kernel.density_mono_set, UpperHalfPlane.dist_le_iff_le_sinh, ArithmeticFunction.vonMangoldt_le_log, MeasureTheory.lpNorm_expect_le, UniformSpace.Completion.dist_triangle, NNReal.tendsto_coe', NNReal.zero_le_coe, dist_dist_dist_le_left, SeminormedSpace.Core.norm_nonneg, rpow_le_rpow_iff_of_neg, EuclideanGeometry.angle_nonneg, Asymptotics.IsLittleO.eventuallyLE, BoundedContinuousFunction.coe_le_coe_add_dist, norm_apply_le_norm_cfcβ, Complex.nonneg_iff, lp.norm_const_smul_le, IsLocalMinOn.fderivWithin_nonneg, ValueDistribution.proximity_top_mul_le, ContinuousLinearMap.norm_snd_le, Seminorm.closedBall_zero_eq, range_modelWithCornersEuclideanHalfSpace, rpow_le_one_iff_of_pos, MeasureTheory.exists_upperSemicontinuous_le_integral_le, Metric.dist_le_diam_of_mem', norm_mul_le, Tactic.ComputeAsymptotics.Seq.dist_le_one, ProbabilityTheory.Fernique.logRatio_mono, Complex.arg_nonneg_iff, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, ContinuousLinearMap.opNorm_mulLeftRight_le, abs_rpow_le_exp_log_mul, ContinuousMultilinearMap.bounds_nonempty, convex_halfSpace_im_le, sqrt_nonneg, ContinuousLinearMap.norm_compLpL_le, UpperHalfPlane.mem_verticalStrip_iff, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, ruzsaSzemerediNumberNat_lower_bound, RCLike.iInter_halfSpaces_eq, inner_self_nonneg, NumberField.house_prod_le, seminormFromConst_bddBelow, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, ProperCone.hyperplane_separation, MeasureTheory.tilted_eq_withDensity_nnreal, sinh_le_sinh, ContDiffBump.nonneg', Complex.frontier_setOf_le_re_and_im_le, ArchimedeanClass.le_stdPart_of_le, PadicInt.norm_le_one, StrongDual.mem_polar_iff, Submodule.Quotient.norm_mk_le, Set.Countable.exists_pos_forall_sum_le, mem_closedBall_zero_iff, Complex.im_sq_le_normSq, AntitoneOn.integral_le_sum, PhragmenLindelof.eq_zero_on_quadrant_I, norm_iteratedFDeriv_smul_le, HolderWith.dist_le, projIcc_eq_zero, unitInterval.half_le_symm_iff, BoundedContinuousFunction.map_bounded', ExistsContDiffBumpBase.w_nonneg, RealRMK.range_cut_partition, unitary.norm_argSelfAdjoint_le_pi, le_inv_mul_exp, Complex.borelCaratheodory, Complex.le_def, ContinuousMultilinearMap.norm_map_cons_le, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, ConcaveOn.le_map_set_average, Angle.toReal_le_pi, Besicovitch.SatelliteConfig.inter, NonarchAddGroupSeminorm.coe_le_coe, ContinuousAlternatingMap.bound, gauge_add_le, Metric.Sigma.dist_triangle, NumberField.InfinitePlace.one_le_of_lt_one, IsBoundedBilinearMap.bound, Asymptotics.isBigO_iff_eventually, Polynomial.norm_root_le_one_of_mahlerMeasure_eq_one, Asymptotics.IsBigOWith.bound, Metric.isBounded_iff_exists_ge, Bornology.IsBounded.exists_pos_norm_le, norm_le_insert, posLog_nonneg, TFAE_exists_lt_isLittleO_pow, norm_inf_le_add, isSquare_iff, Cardinal.Real.Ioo_countable_iff, Unitary.norm_argSelfAdjoint_le_pi, Metric.isGLB_infDist, BoxIntegral.hasIntegral_iff, Metric.infDist_le_hausdorffDist_of_mem, Nat.ratSqrt_le_realSqrt, norm_inf_sub_inf_le_add_norm, ProbabilityTheory.gaussianPDFReal_mul, ContinuousMultilinearMap.norm_def, NormedSpace.double_dual_bound, ContDiffBump.le_one, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, IsApproximateAddSubgroup.card_add_self_le, Besicovitch.TauPackage.lastStep_nonempty, map_sub_le_max, Complex.norm_cpow_le, PiTensorProduct.injectiveSeminorm_tprod_le, ExistsContDiffBumpBase.u_nonneg, arccos_nonneg, Seminorm.mem_closedBall, rothNumberNat_le_ruzsaSzemerediNumberNat', ContinuousLinearMap.norm_holderL_le, LinearMap.polar_mem_iff, NonarchAddGroupSeminorm.add_le_max', ValueDistribution.characteristic_top_mul_eventually_le, add_one_le_exp, Complex.log_im_le_pi, Hyperreal.coe_le_coe, NormedAddGroupHom.norm_def, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, NNReal.exists, le_logb_iff_rpow_le_of_base_lt_one, norm_zpow_le_mul_norm, abs_signedDist_le_dist, NumberField.FinitePlace.norm_le_one, ENNReal.toReal_le_add', arcsin_le_iff_le_sin, norm_le_zero_iff', MeasureTheory.exists_le_average, MeasureTheory.setIntegral_le_nonneg, Complex.frontier_setOf_le_im, EuclideanGeometry.Sphere.IsTangent.radius_le_dist_center, EuclideanGeometry.Sphere.isIntTangent_self_iff, Polynomial.norm_coeff_le_choose_mul_mahlerMeasure, ConvexOn.exists_affine_le_of_lt, SmoothBumpFunction.nonneg, ContinuousLinearMap.bound, PadicInt.coe_mul, StrongDual.polar_singleton, Polynomial.finite_mahlerMeasure_le, re_inner_le_norm, ENNReal.toReal_le_add, Complex.norm_le_sqrt_two_mul_max, Polynomial.Chebyshev.abs_eval_T_real_le_one_iff, MeasureTheory.integral_norm_eq_pos_sub_neg, posLog_sum, dist_dist_dist_le_right, MeasureTheory.sum_measureReal_le_measureReal_univ, Ideal.Quotient.norm_mk_le, logb_nonneg_iff, ValueDistribution.characteristic_sum_top_eventuallyLE, ZLattice.sum_piFinset_Icc_rpow_le, IsApproximateSubgroup.one_le, ENNReal.toReal_mono, BoxIntegral.unitPartition.diam_boxIcc, norm_mul_sub_norm_div_le_two_mul_min, norm_le_norm_div_add, NormedDivisionRing.norm_le_one_of_discrete, arcsin_eq_neg_pi_div_two, LipschitzWith.diam_image_le, dist_le_pi_dist, Finset.norm_prod_le, CircleDeg1Lift.map_map_zero_le, Asymptotics.isBigOWith_inv, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, closure_halfSpace, PadicInt.coe_add, StrongDual.mem_polar_singleton, Metric.uniformity_basis_dist_le_pow, Padic.norm_lt_pow_iff_norm_le_pow_sub_one, sqrt_one_add_norm_sq_le, VectorFourier.norm_fourierIntegral_le_integral_norm, MeasureTheory.integral_abs_condExp_le, Matrix.l2_opNorm_mul, dist_smul_add_one_sub_smul_le, Complex.norm_fderiv_le_div_of_mapsTo_ball, norm_innerSL_le, MeasureTheory.norm_charFun_le, LipschitzWith.norm_compLp_le, SeminormedAddGroup.disjoint_nhds, ContinuousLinearMap.isLeast_opNorm, ofNat_le_toNNReal, CStarAlgebra.exists_sum_four_unitary, norm_sum_le, Subadditive.apply_mul_add_le, RCLike.norm_le_im_iff_eq_I_mul_norm, MeasureTheory.le_integral_rnDeriv_of_ac, PadicInt.unitCoeff_coe, norm_mul_sub_norm_div_le_two_mul, dist_sum_sum_le, MeasureTheory.Measure.haar.addPrehaar_sup_le, log_div_self_rpow_antitoneOn, dist_norm_norm_le, SmoothPartitionOfUnity.nonneg', dist_mulExpNegMulSq_le_dist, Complex.borelCaratheodory_zero, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, Module.Basis.norm_repr_le_norm, PadicInt.coe_dpow_eq, NNReal.coe_le_coe, BoundedContinuousFunction.dist_le_two_norm, Bornology.IsBounded.exists_pos_norm_le', norm_le_of_mem_closedBall', ContinuousLinearMap.dist_le_opNorm, ExistsContDiffBumpBase.y_le_one, ProbabilityTheory.poissonPMFReal_nonneg, HasLineDerivAt.le_of_lipschitz, PadicInt.coe_intCast, Complex.frontier_setOf_im_le, LinearMap.polar_mem, log_of_ne_zero, dist_pi_le_iff', Metric.hausdorffDist_nonneg, norm_nonneg, ContinuousLinearMap.norm_holder_apply_apply_le, intervalIntegral.norm_integral_le_integral_norm_uIoc, Chebyshev.theta_le_psi, Submodule.norm_subtypeL_le, ContinuousLinearMap.bound_of_antilipschitz, ENNReal.trichotomyβ, Rat.AbsoluteValue.apply_le_sum_digits, Asymptotics.isBigO_const_of_ne, SmoothPartitionOfUnity.sum_le_one, Metric.diam_union, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, ENNReal.zero_eq_ofReal, one_half_le_sum_primes_ge_one_div, ContinuousLinearMap.NonlinearRightInverse.bound', SchwartzMap.one_add_le_sup_seminorm_apply, norm_indicator_le_norm_self, sinh_nonpos_iff, dist_le_Ico_sum_dist, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos, NonUnitalStarAlgHom.norm_apply_le, ConcaveOn.slope_le_deriv, GroupSeminorm.mul_bddBelow_range_add, MeasureTheory.measureReal_diff_le_iff_le_add, ConvexOn.slope_le_of_hasDerivWithinAt_Iio, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, Chebyshev.eventually_primeCounting_le, Orthonormal.sum_inner_products_le, Padic.norm_int_le_pow_iff_dvd, MeasureTheory.JordanDecomposition.real_smul_def, ConvexOn.sSup_affine_eq, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, ContinuousMap.dist_le_iff_of_nonempty, MeasureTheory.tendsto_integral_meas_thickening_le, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, ContinuousLinearMap.norm_precompL_le, ContinuousLinearMap.norm_map_removeNth_le, mk_le, PhragmenLindelof.eq_zero_on_quadrant_III, Behrend.exists_large_sphere_aux, ENNReal.ofReal_le_natCast, sinc_le_inv_abs, Metric.uniformSpace_eq_bot, BohrMollerup.ge_logGammaSeq, norm_sup_sub_sup_le_norm, PiTensorProduct.mapLMultilinear_opNorm, exists_forall_closed_ball_dist_add_le_two_mul_sub, MeasureTheory.norm_condExpIndL1Fin_le, ContinuousMultilinearMap.norm_image_sub_le', Int.pairwise_one_le_dist, Metric.infDist_nonneg, NNReal.dist_gm_am_le, Polynomial.mahlerMeasure_le_sum_norm_coeff, dist_smul_pair, Submodule.orthogonalProjection_norm_le, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, dist_vadd_vadd_le, Valued.toNormedField.one_le_norm_iff, norm_cfcβ_le_iff, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_nonneg, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, exists_forall_closed_ball_dist_add_le_two_sub, PiNat.dist_le_one, ConcaveOn.le_slope_of_hasDerivAt, Asymptotics.IsLittleO.def, sqrt_eq_zero', MeasureTheory.norm_condExpL2_le_one, HasCompactSupport.convolution_integrand_bound_right, Complex.re_nonneg_iff_nonneg, NNReal.bddAbove_coe, posLog_nat_mul, ODE.FunSpace.dist_iterate_next_apply_le, HolderTriple.nonneg, ConvexOn.real_sSup_affine_eq, posLog_mul, dist_triangle8, sinhOrderIso_symm_apply, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, MeasureTheory.integral_coe_le_of_lintegral_coe_le, unitInterval.le_symm_comm, Set.Nontrivial.le_infsep_iff, norm_mul_le', ArchimedeanClass.stdPart_nonpos, log_nonneg_iff, zero_rpow_nonneg, log_le_sub_one_of_pos, exists_int_int_abs_mul_sub_le, HasCompactSupport.convolution_integrand_bound_right_of_subset, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_nonneg, schnirelmannDensity_mul_le_card_filter, le_iff_norm_sqrt_mul_rpow, exists_seq_norm_le_one_le_norm_sub', ContinuousLinearMap.IsPositive.re_inner_nonneg_right, balancedCore_eq_iInter, one_sub_inv_le_log_of_pos, norm_sub_le_norm_sub_add_norm_sub, LipschitzWith.norm_compLp_sub_le, antilipschitzWith_iff_exists_mul_le_norm, NumberField.house.basis_repr_norm_le_const_mul_house, HolderTriple.one_div_nonneg, mul_exp_neg_le_exp_neg_one, CauchySeq.mul_norm_bddAbove, Polynomial.derivRootWeight_nonneg, arsinh_le_arsinh, CStarAlgebra.exists_sum_four_nonneg, HasDerivAt.le_of_lipschitzOn, Urysohns.CU.lim_nonneg, cos_le_one, Metric.isBounded_range_iff, lipschitzOnWith_iff_norm_sub_le, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq, RightDerivMeasurableAux.le_of_mem_A, mul_pow_le_nat_floor_pow, ProbabilityTheory.defaultRatCDF_nonneg, posLog_norm_sum_le, norm_mulβ_le', ConvexOn.slope_le_leftDeriv_of_mem_interior, InformationTheory.mul_klFun_le_toReal_klDiv, ContinuousAlternatingMap.ratio_le_opNorm, QuotientGroup.norm_mk_le_norm, Polynomial.card_mahlerMeasure_le_prod, natCast_le_toNNReal, ContinuousLinearMap.opNorm_le_of_lipschitz, Int.Matrix.exists_ne_zero_int_vec_norm_le, seminormFromConst_seq_nonneg, Asymptotics.isBigO_iff', mulLeft_bound, ValueDistribution.characteristic_mul_top_eventuallyLE, NumberField.mixedEmbedding.convexBodySum_mem, ContinuousLinearMap.toSesqForm_apply_norm_le, dist_left_le_of_mem_uIcc, ContinuousAlternatingMap.norm_image_sub_le, MeasureTheory.exists_notMem_null_average_le, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, lipschitz_with_lipschitz_const_add, ExistsContDiffBumpBase.w_mul_Ο_nonneg, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg, MeasureTheory.condExpL2_indicator_nonneg, PadicInt.coe_pow, AkraBazziRecurrence.max_bi_le, MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_le, Complex.abs_re_div_norm_le_one, Complex.not_lt_iff, Delone.DeloneSet.exists_dist_le_coveringRadius, RCLike.im_le_norm, Asymptotics.isLittleO_iff_nat_mul_le', EReal.toReal_nonneg, norm_inner_le_norm, PowerSeries.gaussNorm_nonneg, IsUltrametricDist.norm_zpow_le, Complex.equivRealProd_apply_le, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, EisensteinSeries.div_max_sq_ge_one, coe_sinOrderIso_apply, SchwartzMap.norm_pow_mul_le_seminorm, Memβp.bddAbove, Wallis.le_W, ZLattice.exists_finsetSum_norm_rpow_le_tsum, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, le_coe_toNNReal, GromovHausdorff.HD_below_aux1, ZLattice.abs_repr_le, norm_jacobiThetaβ_term_fderiv_le, pi_norm_const_le, zero_rpow_le_one, sqrt_le_sqrt_iff', posLog_add, lp.tsum_mul_le_mul_norm, Behrend.exists_large_sphere, Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall, Orthonormal.tsum_inner_products_le, Int.Matrix.exists_ne_zero_int_vec_norm_le', ProbabilityTheory.gaussianPDFReal_nonneg, NumberField.InfinitePlace.instNonnegHomClassReal, Urysohns.CU.approx_le_lim, Archimedean.ratLt'_bddAbove, ENNReal.truncateToReal_nonneg, pi_norm_le_iff_of_nonempty', NormedRing.norm_mul_le, Asymptotics.isBigOWith_pure, WithLp.dist_fst_le, le_iff_norm_sqrt_mul_sqrt_inv, LinearMap.IsPositive.re_inner_nonneg_left, CauchySeq.norm_bddAbove, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, norm_add_sub_norm_sub_le_two_mul, norm_fst_le, MeasureTheory.BorelCantelli.process_difference_le, GromovHausdorff.HD_candidatesBDist_le, ENNReal.log_ofReal, GroupSeminorm.mul_le', ofDigits_le_one, AlgHom.norm_apply_le_self_mul_norm_one, Complex.closure_setOf_im_lt, Orientation.abs_volumeForm_apply_le, MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed, sinh_le_self_iff, PiTensorProduct.projectiveSeminormAux_add_le, one_add_norm_le_sqrt_two_mul_sqrt, expNegInvGlue.zero_iff_nonpos, BoxIntegral.Prepartition.lower_le_lower, schnirelmannDensity_nonneg, IsUltrametricDist.norm_nsmul_le, norm_iteratedFDeriv_clm_apply_const, ModularGroup.coe_truncatedFundamentalDomain
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instLT π | CompOp | 1035 mathmath: geometric_hahn_banach_open, BoundingSieve.nu_lt_one_of_dvd_prodPrimes, HurwitzZeta.isBigO_atTop_evenKernel_sub, inner_lt_one_iff_real_of_norm_eq_one, Bundle.ContMDiffRiemannianMetric.isVonNBounded, Irrational.instNoMaxOrderSubtypeReal, real_inner_div_norm_mul_norm_eq_neg_one_iff, Metric.cauchySeq_iff, RCLike.pos_iff_exists_ofReal, norm_lt_of_mem_ball', lt_norm_sub_of_not_sameRay, Angle.sign_two_zsmul_eq_sign_iff, gauge_lt_one_eq_self_of_isOpen, iInf_Ioi_eq_iInf_rat_gt, NormedCommGroup.tendsto_nhds_nhds, Seminorm.mem_ball_zero, Mathlib.Meta.Positivity.log_pos_of_isNat, RCLike.geometric_hahn_banach_point_open, toNNReal_lt_natCast', EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, Complex.UnitDisc.normSq_lt_one, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, geometric_hahn_banach_point_point, Complex.normSq_pos, PadicInt.norm_int_lt_one_iff_dvd, sqrt_eq_cases, RCLike.separate_convex_open_set, ContinuousLinearMap.exists_preimage_norm_le, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, NumberField.mixedEmbedding.convexBodyLT'_mem, ProbabilityTheory.betaPDF_eq, Metric.exists_continuous_real_forall_closedEBall_subset, Metric.uniformContinuous_iff_le, volume_iUnion_setOf_liouvilleWith, Metric.continuousWithinAt_iff', lebesgue_number_lemma_of_metric_sUnion, Metric.closedBall_eq_bInter_ball, gauge_lt_one_of_mem_of_isOpen, conformalAt_iff, UpperHalfPlane.normSq_pos, ENNReal.toReal_pos_iff, AkraBazziRecurrence.T_gt_zero', BoxIntegral.unitPartition.mem_box_iff', SmoothBumpFunction.rOut_pos, NormedCommGroup.cauchySeq_iff, geometric_hahn_banach_open_point, ENNReal.rpow_eq_zero_iff, SeminormedGroup.disjoint_nhds, norm_pos_iff, CFC.exists_pos_algebraMap_le_iff, NormedCommGroup.nhds_one_basis_norm_lt, WithSeminorms.mem_nhds_iff, eulerMascheroniConstant_lt_two_thirds, Disjoint.exists_cthickenings, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, RCLike.pos_iff, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, PadicInt.norm_intCast_lt_one_iff, Complex.not_le_iff, CircleDeg1Lift.iterate_pos_lt_iff, Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_one, Metric.equicontinuousAt_iff_pair, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Metric.eventually_prod_nhds_iff, Metric.tendsto_atTop, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, UpperHalfPlane.subset_verticalStrip_of_isCompact, UpperHalfPlane.im_pos, arctan_pos, Behrend.roth_lower_bound_explicit, CocompactMapClass.norm_le, UpperHalfPlane.specialLinearGroup_apply, artanh_pos, Bundle.RiemannianMetric.isVonNBounded, unitInterval.pos_iff_ne_zero, Module.Basis.exists_opNorm_le, summable_one_div_nat_add_rpow, UpperHalfPlane.canLift, mem_ball_iff_norm'', abs_tanh_lt_one, Subgroup.widthInfty_pos, NumberField.Units.dirichletUnitTheorem.seq_decreasing, schnirelmannDensity_le_iff_forall, StrictConcaveOn.ae_eq_const_or_lt_map_average, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, mem_ball_one_iff, UniformSpace.Completion.mem_uniformity_dist, ModularGroup.one_lt_normSq_T_zpow_smul, setOf_liouvilleWith_subset_aux, Metric.dist_lt_add_of_nonempty_ball_inter_ball, inner_lt_norm_mul_iff_real, Mathlib.Tactic.Rify.ratCast_lt, Matrix.PosDef.eigenvalues_pos, IsCompact.exists_thickening_image_subset, AkraBazziRecurrence.T_pos, ContDiffBump.pos_of_mem_ball, Metric.tendsto_nhds_nhds, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, NumberField.Units.pos_at_place, PointwiseConvergenceCLM.tendsto_nhds, geometric_hahn_banach_compact_closed, goldenRatio_lt_two, HurwitzKernelBounds.isBigO_atTop_F_int_one, Seminorm.lt_def, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAtβ, summable_nat_rpow_inv, Tactic.ComputeAsymptotics.WellFormedBasis.head_eventually_pos, ProbabilityTheory.Kernel.notMem_mutuallySingularSetSlice, Complex.neg_pi_div_two_lt_arg_iff, EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two, IsCompact.uniform_oscillation, integral_sin_pow_pos, ball_zero_eq, Seminorm.bound_of_continuous_normedSpace, RCLike.geometric_hahn_banach_closed_point, Similar.exists_pos_dist_eq, Metric.equicontinuousAt_iff, Complex.arg_le_pi_div_two_iff, SemilinearMapClass.bound_of_continuous, Metric.tendsto_nhds, ae_eq_const_or_norm_setIntegral_lt_of_norm_le_const, arccos_pos, WithSeminorms.tendsto_nhds', VitaliFamily.eventually_filterAt_iff, mfderivWithin_projIcc_one, NumberField.Units.dirichletUnitTheorem.seq_next, intervalIntegral.integral_pos_iff_support_of_nonneg_ae', abs_lt_norm_sub_of_not_sameRay, norm_sum_lt_of_strictConvexSpace, NumberField.mixedEmbedding.convexBodyLT_mem, exp_one_lt_three, neg_pi_div_two_lt_arctan, toNNReal_lt_toNNReal_iff_of_nonneg, gauge_le_eq, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, UpperHalfPlane.coe_pos_real_smul, sigmoid_lt_iff, PadicInt.norm_lt_one_iff_dvd, Absorbent.gauge_set_nonempty, Angle.sign_two_nsmul_eq_neg_sign_iff, EuclideanGeometry.angle_pos_of_not_collinear, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, ContDiffBump.one_lt_rOut_div_rIn, EuclideanGeometry.dist_lt_of_sbtw_of_inner_eq_zero, Affine.Simplex.inv_height_lt_sum_inv_height, ENNReal.top_rpow_def, pi_lt_d6, ENNReal.ofReal_lt_ofReal_iff_of_nonneg, cos_two_neg, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, Complex.interior_setOf_le_re, singleton_eq_inter_Icc, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, one_lt_goldenRatio, mfderivWithin_comp_projIcc_one, Finset.infsep_pos_iff_nontrivial, IsMIntegralCurve.periodic_xor_injective, Metric.uniformEquicontinuous_iff, Metric.tendsto_atTop', PadicInt.exists_mem_range_of_norm_rat_le_one, NormedField.exists_norm_lt_one, ProperCone.hyperplane_separation', Metric.biInter_gt_ball, Metric.measure_closedBall_pos_iff, BoxIntegral.Prepartition.mem_split_iff', Complex.frontier_setOf_im_lt, Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, Metric.continuous_iff, Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzero, NormedField.denselyOrdered_range_norm, Angle.toReal_coe_eq_self_iff, SzemerediRegularity.eps_pos, eventually_norm_mfderivWithin_symm_extChartAt_lt, CircleDeg1Lift.dist_map_map_zero_lt, MeasureTheory.Measure.haar.prehaar_pos, norm_pos_iff', neg_one_lt_goldenConj, Valued.integer.exists_norm_lt_one, antilipschitzWith_iff_exists_mul_le_norm', EisensteinSeries.r_pos, Metric.mem_thickening_iff, EisensteinSeries.r1_pos, one_lt_toNNReal, Unitary.norm_sub_one_lt_two_iff, Multipliable.eventually_bounded_finset_prod, VitaliFamily.filterAt_basis_closedBall, add_mem_ball_iff_norm, holderTriple_iff, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, NumberField.InfinitePlace.pos_iff, QuotientAddGroup.norm_lt_iff, ENNReal.ofReal_lt_iff_lt_toReal, Asymptotics.bound_of_isBigO_cofinite, HolderTriple.left_pos, ENNReal.exists_frequently_lt_of_liminf_ne_top', ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_pos_eq_zero_of_hasSubGaussianMGF_zero, Metric.mem_nhdsWithin_iff, Complex.closure_setOf_lt_im, EuclideanGeometry.Sphere.power_pos_iff_radius_lt_dist_center, Metric.eventually_nhds_iff, lt_cauchy, pi_div_two_pos, Metric.cthickening_eq_iInter_thickening, ENNReal.toReal_lt_of_lt_ofReal, edist_lt_ofReal, exists_rat_abs_sub_lt_and_lt_of_irrational, Valued.integer.norm_irreducible_lt_one, Angle.neg_pi_lt_toReal, tendsto_sub_mul_tsum_nat_cpow, log_pos_iff, Metric.ball_eq_ball, sqrt_two_lt_three_halves, cauchySeq_finset_iff_vanishing_norm, InnerProductGeometry.angle_eq_zero_iff, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, unitInterval.lt_one_iff_ne_one, lebesgue_number_lemma_of_metric, unitInterval.lt_symm_comm, Euclidean.nhds_basis_closedBall, HasFPowerSeriesOnBall.uniform_geometric_approx, summable_jacobiThetaβ_term_fderiv_iff, StieltjesFunction.iInf_rat_gt_eq, ball_eq, Metric.tendsto_nhdsWithin_nhds, Metric.exists_smooth_forall_closedBall_subset, QuotientGroup.nhds_one_hasBasis, dist_affineCombination_lt_of_strictConvexSpace, eq_zero_or_norm_pos, MeasureTheory.volume_sum_rpow_lt, EReal.toReal_neg, exists_seq_norm_le_one_le_norm_sub, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, convex_halfSpace_im_gt, Padic.norm_natCast_lt_one_iff, Rat.AbsoluteValue.equiv_on_nat_iff_equiv, eq_one_or_norm_pos, BoxIntegral.unitPartition.mem_box_iff, CircleDeg1Lift.map_map_zero_lt, NormedAddCommGroup.cauchySeq_iff, SeminormedAddGroup.disjoint_nhds_zero, Height.mulHeight_pos, Affine.Simplex.touchpointWeights_empty_pos, Set.Finite.infsep_pos_iff_nontrivial, Metric.uniformity_basis_dist, MultilinearMap.exists_bound_of_continuous, real_inner_div_norm_mul_norm_eq_one_iff, Padic.norm_p_lt_one, WeakFEPair.hk, HolderTriple.pos, exists_pos_bound_of_bound, NormedCommGroup.uniformity_basis_dist, SpectrumRestricts.nnreal_lt_iff, tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, real_sqrt_lt_nat_sqrt_succ, self_lt_sinh_iff, mk_lt, Metric.uniformity_basis_dist_rat, ball_one_eq, exists_seq_rat_strictAnti_tendsto, AkraBazziRecurrence.eventually_asympBound_pos, EisensteinSeries.div_linear_zpow_differentiableOn, Polynomial.gaussNorm_lt_one_iff_contentIdeal_le, deriv_neg_left_of_sign_deriv, sinh_lt_self_iff, exp_one_gt_d9, Complex.arg_neg_eq_arg_add_pi_iff, CircleDeg1Lift.transnumAuxSeq_dist_lt, sigmoid_pos, Metric.uniformity_basis_dist_inv_nat_succ, ContDiffBump.rIn_lt_rOut, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, Metric.isUniformInducing_iff, geometric_hahn_banach_point_closed, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left, ENNReal.mul_rpow_eq_ite, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos, Besicovitch.SatelliteConfig.rpos, Affine.Triangle.acuteAngled_iff_angle_lt, ContinuousMap.dist_lt_iff_of_nonempty, AlternatingMap.exists_bound_of_continuous, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, HasBesicovitchCovering.no_satelliteConfig, Bundle.ContMDiffRiemannianMetric.pos, HurwitzKernelBounds.isBigO_atTop_F_nat_one, Affine.Simplex.dist_lt_of_mem_interior_of_strictConvexSpace, log_two_gt_d9, Mathlib.Meta.Positivity.log_pos_of_isNNRat, AnalyticAt.exists_ball_analyticOnNhd, NumberField.FinitePlace.norm_lt_one_iff_mem, EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_pos, interior_halfSpace, Hyperreal.coe_pos, Metric.nonempty_ball, ProbabilityTheory.Kernel.rnDeriv_toReal_pos, interior_subset_gauge_lt_one, UpperHalfPlane.norm_exp_two_pi_I_lt_one, EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_center, Behrend.bound, Behrend.four_zero_nine_six_lt_exp_sixteen, Icc_chartedSpaceChartAt, ExistsContDiffBumpBase.u_int_pos, Mathlib.Meta.Positivity.log_pos_of_isRat_neg, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, pi_upper_bound_start, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, Bornology.IsBounded.exists_pos_norm_lt', pi_pos, EuclideanGeometry.angle_lt_iff_dist_lt, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', MeasureTheory.integral_pos_iff_support_of_nonneg_ae, Probability.cauchyPDF_pos, Affine.Simplex.excenterWeights_empty_lt_inv_two, summable_iff_vanishing_norm, EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius, sin_arctan_pos, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, arsinh_pos_iff, Complex.arg_lt_pi_div_two_iff, BoxIntegral.Box.mem_splitCenterBox, ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem, BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact, Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos, Complex.interior_setOf_le_im, RCLike.geometric_hahn_banach_point_point, norm_cfcβ_lt_iff, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, Metric.uniformContinuousOn_iff, Metric.exists_lt_mem_ball_of_mem_ball, arcsin_lt_iff_lt_sin, IsCoercive.bounded_below, Set.Nontrivial.infsep_lt_iff, Metric.closure_eq_iInter_cthickening, Set.infsep_pos_iff_nontrivial_of_finite, Metric.exists_ball_inter_eq_singleton_of_mem_discrete, NumberField.mixedEmbedding.neg_of_mem_negA_plusPart, ProperCone.hyperplane_separation_point, ae_eq_const_or_norm_average_lt_of_norm_le_const, integral_rpowIntegrandββ_one_pos, EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two, ofNat_lt_toNNReal, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, BoundingSieve.nu_lt_one_of_prime, RCLike.neg_iff, PowerSeries.IsRestricted.isRestricted_iff, convex_halfSpace_im_lt, ENNReal.rpow_eq_top_iff, Complex.UnitDisc.instCanLiftCoeLtRealNormOfNat, Bornology.IsBounded.subset_ball_lt, MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet, UpperHalfPlane.normSq_denom_pos, Metric.mem_closure_iff, Complex.neg_pi_lt_arg, RCLike.ofReal_mul_pos_iff, Complex.neg_iff, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, Besicovitch.TauPackage.one_lt_tau, ArithmeticFunction.vonMangoldt_pos_iff, Polynomial.mahlerMeasure_pos_of_ne_zero, Metric.tendsto_nhdsWithin_nhdsWithin, two_pi_pos, NNReal.coe_lt_one, arsinh_lt_arsinh, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, WithSeminorms.tendsto_nhds, toNNReal_pos, WithSeminorms.isOpen_iff_mem_balls, exists_lt_subset_ball, EuclideanGeometry.Sphere.power_neg_iff_dist_center_lt_radius, Metric.dist_lt_add_of_nonempty_closedBall_inter_ball, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, Metric.continuous_iff', Metric.exists_continuous_real_forall_closedBall_subset, toNNReal_lt_iff_lt_coe, Complex.arg_lt_pi_iff, closure_open_halfSpace, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', CStarModule.norm_pos, Complex.arg_eq_pi_div_two_iff, PiNat.isOpen_iff_dist, Asymptotics.IsBigO.exists_mem_basis, Bornology.IsBounded.exists_pos_norm_lt, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, AkraBazziRecurrence.bi_min_div_two_pos, mem_ball_iff_norm, UpperHalfPlane.norm_qParam_lt_one, neg_one_lt_tanh, deriv_neg_right_of_sign_deriv, Besicovitch.exists_goodΞ΄, gauge_pos, Affine.Simplex.exradius_singleton_pos, pi_gt_d2, Complex.frontier_setOf_lt_im, continuous_logb', Height.mulHeightβ_pos, Complex.slitPlane_eq_union, geometric_hahn_banach_closed_compact, QuotientAddGroup.nhds_zero_hasBasis, AddCircle.coe_real_preimage_closedBall_inter_eq, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, NormedAddGroupHom.SurjectiveOnWith.exists_pos, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_exp, QuasispectrumRestricts.lt_nnreal_iff, geometric_hahn_banach_open_open, Complex.interior_setOf_im_le, Emetric.exists_contMDiffMap_forall_closedBall_subset, Liouville.frequently_exists_num, cos_one_pos, HurwitzZeta.isBigO_atTop_oddKernel, Complex.abs_im_lt_norm, AbsoluteValue.IsEquiv.log_div_log_pos, UpperHalfPlane.ofComplex_apply_eq_ite, ENNReal.ofReal_lt_natCast, InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero, Complex.neg_pi_lt_log_im, one_lt_gold, artanh_lt_artanh_iff, Metric.exists_contMDiffMap_forall_closedBall_subset, ProbabilityTheory.gaussianPDFReal_pos, EReal.coe_neg', InnerProductGeometry.angle_add_pos_of_inner_eq_zero, Asymptotics.isBigO_atTop_iff_eventually_exists_pos, Behrend.ceil_lt_mul, pi_lt_four, ball_eq', ProbabilityTheory.mgf_pos', Metric.mem_closure_range_iff, Angle.sign_two_nsmul_eq_sign_iff, Complex.volume_sum_rpow_lt, NormedAddCommGroup.tendsto_nhds_nhds, inner_lt_one_iff_real_of_norm_one, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, toNNReal_lt_one, Metric.mem_ball, PseudoMetricSpace.uniformity_dist, Metric.continuousAt_iff', UpperHalfPlane.pos_real_smul_injective, ProbabilityTheory.IsKolmogorovProcess.q_pos, cosh_pos, MeasureTheory.Integrable.integral_eq_integral_meas_lt, Metric.hasBasis_nhdsSet_cthickening, sq_lt, NormedAddGroupHom.bound, continuous_log', sqrt_lt_sqrt_iff, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, Irrational.instDenselyOrderedSubtypeReal, Affine.Simplex.height_pos, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, Nat.realSqrt_lt_ratSqrt_add_inv_prec, ratCast_lt, ContinuousLinearEquiv.norm_symm_pos, goldenConj_neg, EuclideanGeometry.dist_lt_of_sbtw_of_mem_perpBisector, zero_lt_one, ENNReal.lt_ofReal_iff_toReal_lt, UnitAddCircle.mem_approxAddOrderOf_iff, pi_gt_sqrtTwoAddSeries, ENNReal.toReal_pos, MeasureTheory.integral_pos_iff_support_of_nonneg, NormedField.exists_lt_norm, summable_one_div_nat_rpow, Metric.continuousWithinAt_iff, Metric.mem_thickening_iff_infDist_lt, Metric.uniformity_basis_dist_le, lt_arcsin_iff_sin_lt, HolderTriple.inv_pos, VitaliFamily.mem_filterAt_iff, Complex.zero_lt_real, DirichletCharacter.LSeriesSummable_iff, lt_arcsin_iff_sin_lt', HasCompactSupport.exists_pos_le_norm, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, pi_lower_bound_start, ENNReal.zero_rpow_def, Complex.frontier_setOf_re_lt, Metric.mem_of_closed', one_half_lt_eulerMascheroniSeq_six, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, contMDiffWithinAt_comp_projIcc_iff, toNNReal_lt_ofNat, Metric.exists_isCompact_closedBall, gauge_lt_one_subset_self, cos_pos_of_mem_Ioo, Stirling.stirlingSeq'_bounded_by_pos_constant, HasFPowerSeriesOnBall.uniform_geometric_approx', one_sub_lt_exp_neg, arccos_lt_pi, IsBoundedLinearMap.bound, Valued.toNormedField.one_lt_norm_iff, Angle.sign_two_zsmul_eq_neg_sign_iff, arsinh_neg_iff, not_sameRay_iff_abs_lt_norm_sub, UpperHalfPlane.le_dist_iff_le_dist_coe_center, goldenRatio_pos, ZLattice.exists_forall_abs_repr_le_norm, SeminormedAddCommGroup.mem_closure_iff, PadicInt.norm_le_pow_iff_norm_lt_pow_add_one, Asymptotics.bound_of_isBigO_nat_atTop, InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, convex_halfSpace_re_lt, Delone.DeloneSet.packingRadius_lt_dist_of_mem_ne, Angle.toReal_neg_iff_sign_neg, Complex.closure_setOf_re_lt, arcsin_lt_zero, sinh_lt_sinh, ENNReal.ofNat_lt_ofReal, pi_lt_d2, sqrt_pos, Irrational.instNoMinOrderSubtypeReal, eulerMascheroniSeq_lt_eulerMascheroniSeq', ENNReal.ofReal_pos, one_lt_cosh, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, Metric.isOpen_iff, Euclidean.nhds_basis_ball, ENNReal.toReal_pos_iff_ne_top, EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two, EMetric.exists_continuous_real_forall_closedBall_subset, ZLattice.normBound_pos, abs_sin_lt_abs, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, ProbabilityTheory.IsKolmogorovProcess.p_pos, ContinuousMap.norm_lt_iff_of_nonempty, ENNReal.ofReal_lt_coe_iff, Padic.norm_intCast_lt_one_iff, Affine.Simplex.circumradius_pos, cosh_lt_cosh, Metric.closedBall_eq_empty, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, InnerProductGeometry.angle_sub_pos_of_inner_eq_zero, Liouville.exists_pos_real_of_irrational_root, Complex.norm_natCast_cpow_pos_of_pos, isBoundedLinearMap_iff, MeasureTheory.lintegral_eq_lintegral_meas_lt, UpperHalfPlane.pos_real_re, not_sameRay_iff_norm_add_lt, geometric_hahn_banach_point_open, Complex.interior_setOf_re_le, UpperHalfPlane.im_pos_of_dist_center_le, Complex.arg_neg_iff, ProbabilityTheory.poissonPMFReal_pos, neg_pi_div_two_lt_arcsin, re_inner_self_pos, Mathlib.Meta.Positivity.nnreal_coe_pos, ProbabilityTheory.Fernique.logRatio_pos, dist_lt_coe, ENNReal.natCast_lt_ofReal, LSeriesSummable_one_iff, separate_convex_open_set, eventually_norm_symmL_trivializationAt_lt, AkraBazziRecurrence.eventually_atTop_sumTransform_le, Metric.infDist_lt_iff, Complex.closure_setOf_lt_re, RCLike.geometric_hahn_banach_open, Metric.mem_nhds_iff, BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact, one_lt_exp_iff, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, Metric.cauchy_iff, pi_gt_d4, ProbabilityTheory.Fernique.measure_le_mul_measure_gt_normThreshold_le_of_map_rotation_eq_self, Metric.mem_uniformity_dist, Bornology.IsBounded.subset_closedBall_lt, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, dist_pos, Polynomial.sum_derivRootWeight_pos, mem_ball_iff_norm', arctan_lt_zero, one_half_lt_eulerMascheroniConstant, unitInterval.symm_lt_comm, unitInterval.coe_lt_one, LiouvilleWith.exists_pos, unitInterval.sigmoid_lt_iff, holderConjugate_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt, mdifferentiableWithinAt_comp_projIcc_iff, pi_lt_sqrtTwoAddSeries, NormedAddCommGroup.tendsto_nhds_zero, WithSeminorms.tendsto_nhds_atTop, disjoint_closedBall_closedBall_iff, Metric.cthickening_eq_iInter_cthickening, NormedAddCommGroup.uniformity_basis_dist, exists_subset_iUnion_ball_radius_lt, ENNReal.coe_rpow_def, Complex.ofReal_mem_slitPlane, MeasureTheory.measureReal_univ_pos, EuclideanSpace.ball_zero_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos, NumberField.Units.regulator_pos, AkraBazziRecurrence.eventually_atTop_sumTransform_ge, goldConj_neg, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_rpow, Complex.abs_arg_lt_pi_div_two_iff, RCLike.lt_iff_re_im, Metric.cthickening_eq_iInter_thickening'', HolderTriple.right_pos, CircleDeg1Lift.lt_iterate_pos_iff, UniformSpace.Completion.uniformity_dist, eulerMascheroniConstant_lt_eulerMascheroniSeq', ContractingWith.one_sub_K_pos, Complex.not_le_zero_iff, eulerMascheroniSeq'_six_lt_two_thirds, exp_lt_one_iff, NontriviallyNormedField.non_trivial, lt_sqrt, RCLike.normSq_pos, Complex.pos_iff, Asymptotics.isBigO_const_left_iff_pos_le_norm, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, exists_iUnion_ball_eq_radius_lt, MeasureTheory.measure_le_eq_lt, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', sign_mul_pos_of_ne_zero, interior_range_modelWithCornersEuclideanHalfSpace, Metric.hasBasis_nhdsSet_thickening, NormedField.exists_one_lt_norm, unitInterval.coe_pos, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge, PadicInt.not_isUnit_iff, NumberField.FinitePlace.pos_iff, ArithmeticFunction.LSeriesSummable_moebius_iff, mem_ball_iff_norm''', NNReal.summable_one_div_rpow, CPolynomialAt.exists_ball_cpolynomialOn, EReal.coe_pos, SmoothPartitionOfUnity.exists_pos_of_mem, MeasureTheory.Measure.haar.addPrehaar_pos, conformalFactorAt_pos, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, exp_one_lt_d9, sqrtTwoAddSeries_lt_two, rpow_lt_one_iff, CircleDeg1Lift.lt_map_map_zero, RCLike.ofReal_pos, Seminorm.mem_ball, pi_gt_three, ArithmeticFunction.LSeriesSummable_zeta_iff, one_sub_sq_div_two_lt_cos, gauge_lt_one_eq_interior, tanh_lt_one, artanh_neg, exp_lt_exp, EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two, pi_lt_d20, Absorbs.exists_pos, Metric.eventually_nhds_prod_iff, AkraBazziRecurrence.a_pos, PadicInt.norm_sub_modPart, arcsin_lt_iff_lt_sin', Asymptotics.IsBigOWith.exists_pos, arccos_lt_pi_div_two, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, Complex.mem_slitPlane_iff, IsUnifLocDoublingMeasure.scalingScaleOf_pos, Metric.mem_closure_range_iff_nat, SeminormedGroup.disjoint_nhds_one, ENNReal.toReal_lt_toReal, IsCompact.exists_cthickening_subset_open, PointwiseConvergenceCLM.tendsto_nhds_atTop, Bundle.ContinuousRiemannianMetric.pos, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Summable.norm_lt_one, integrableOn_Ioi_exp_neg_mul_sq_iff, ENNReal.exists_upcrossings_of_not_bounded_under, Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, sInf_le_iff, HasCompactMulSupport.exists_pos_le_norm, sin_pos_of_mem_Ioo, gauge_lt_eq', isConformalMap_iff, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, NormedCommGroup.nhds_basis_norm_lt, Affine.Simplex.touchpointWeights_singleton_neg, Metric.exists_ball_subset_ball, Bundle.RiemannianMetric.pos, log_two_lt_d9, summable_geometric_iff_norm_lt_one, norm_midpoint_lt_iff, cos_lt_one_div_sqrt_sq_add_one, NNReal.summable_rpow_inv, NNReal.coe_lt_coe, Metric.denseRange_iff, PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one, MeasureTheory.exists_null_frontiers_thickening, ContinuousMultilinearMap.bound, Metric.biUnion_lt_closedBall, Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, norm_cfcβ_one_sub_one_add_inv_lt_one, ZLattice.covolume_pos, Complex.summable_one_div_nat_cpow, Delone.DeloneSet.subset_ball_singleton, sinh_neg_iff, HolderTriple.lt, sinh_lt_cosh, Nat.Primes.summable_rpow, LSeriesSummable_lt_re_of_abscissaOfAbsConv_lt_re, Metric.eventually_nhds_iff_ball, SchwartzMap.decay, PadicInt.norm_sub_zmodRepr_lt_one, Rat.AbsoluteValue.one_lt_of_not_bounded, hasDerivWithinAt_forall_lt_or_forall_gt_of_forall_ne, Stirling.stirlingSeq'_pos, pi_gt_d20, ENNReal.trichotomy, ENNReal.exists_frequently_lt_of_liminf_ne_top, sin_sq_lt_sq, Complex.abs_re_lt_norm, arcsin_lt_pi_div_two, contMDiffOn_comp_projIcc_iff, MeasureTheory.integral_pos_of_integrable_nonneg_nonzero, Metric.diam_pos, AkraBazziRecurrence.b_pos, arctan_lt_pi_div_two, CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos, MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae, Metric.infDist_pos_iff_notMem_closure, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, ProperCone.hyperplane_separation_of_notMem, RCLike.ofReal_mul_neg_iff, CuspFormClass.exp_decay_atImInfty', AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le, EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_ne, Metric.uniformContinuousOn_iff_le, gold_lt_two, absolutelyContinuousOnInterval_iff, arcsin_pos, Metric.biUnion_lt_ball, NNReal.coe_pos, binEntropy_lt_log_two, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def, EulerSine.integral_cos_pow_pos, schnirelmannDensity_lt_iff, Valued.toNormedField.norm_lt_iff, Complex.UnitDisc.norm_lt_one, UnitAddCircle.mem_addWellApproximable_iff, NormedAddCommGroup.tendsto_atTop, Seminorm.closedBall_eq_biInter_ball, neg_one_lt_goldConj, dist_lt_dist_add_dist_iff, HolderTriple.pos', UpperHalfPlane.im_inv_neg_coe_pos, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty', Subgroup.strictWidthInfty_pos_iff, ENNReal.ofReal_lt_ofNat, LinearMap.toSeminorm_ball_zero, BoxIntegral.Box.lower_lt_upper, add_one_lt_exp, SzemerediRegularity.coe_m_add_one_pos, Besicovitch.BallPackage.rpos, Affine.Simplex.excenterWeights_empty_pos, HolderTriple.inv_lt_inv, BoundingSieve.nu_pos_of_dvd_prodPrimes, Metric.controlled_of_isUniformEmbedding, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def', Metric.thickening_nonempty_iff, BoundingSieve.nu_pos_of_prime, cauchySeq_bdd, Metric.isUniformEmbedding_iff, Sbtw.dist_lt_max_dist, Metric.tendstoUniformlyOnFilter_iff, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, Affine.Simplex.dist_lt_of_mem_closedInterior_of_strictConvexSpace, RCLike.neg_iff_exists_ofReal, Seminorm.preimage_metric_ball, Affine.Simplex.touchpointWeights_singleton_pos, EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_ne, EisensteinSeries.eisSummand_extension_differentiableOn, CircleDeg1Lift.map_lt_add_translationNumber_add_one, toNNReal_lt_natCast, isMIntegralCurveAt_iff', HolderTriple.one_div_pos, Metric.nhds_basis_ball, Set.infsep_pos, Subgroup.strictWidthInfty_pos, eulerMascheroniSeq_lt_eulerMascheroniConstant, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, Behrend.div_lt_floor, ENNReal.ofReal_lt_ofReal_iff', similar_iff_exists_pos_pairwise_dist_eq, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, exp_neg_one_gt_d9, ProbabilityTheory.measure_le_mul_measure_gt_le_of_map_rotation_eq_self, deriv_pos_left_of_sign_deriv, unitInterval.symm_lt_symm, integrable_exp_neg_mul_sq_iff, Emetric.exists_smooth_forall_closedBall_subset, Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, Asymptotics.isBigO_iff'', unitary.norm_sub_one_lt_two_iff, NormedAddCommGroup.nhds_zero_basis_norm_lt, Padic.norm_le_pow_iff_norm_lt_pow_add_one, Metric.continuousAt_iff, UpperHalfPlane.pos_real_im, Metric.nhds_basis_closedBall, Units.norm_pos, AbsoluteValue.isEquiv_iff_exists_rpow_eq, HolderTriple.one_div_pos', IsCompact.exists_thickening_subset_open, zero_lt_one_add_norm_sq, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, fourierCoeff_liftIoc_eq, Complex.volume_sum_rpow_lt_one, geometric_hahn_banach_closed_point, Metric.pos_of_mem_ball, ENNReal.one_lt_ofReal, sinh_pos_iff, gauge_lt_one_iff_mem_interior, Subgroup.widthInfty_pos_iff, Metric.continuousOn_iff', Polynomial.Chebyshev.node_lt, Complex.real_lt_real, le_sSup_iff, NNReal.one_lt_coe, ProperCone.hyperplane_separation, spectralNorm_zero_lt, EReal.toReal_pos, Similar.exists_pos_pairwise_dist_eq, ENNReal.toReal_strict_mono, Polynomial.instTwoPiPos, AkraBazziRecurrence.b_lt_one, sqrt_lt, RCLike.geometric_hahn_banach_compact_closed, gold_pos, Complex.neg_ofReal_mem_slitPlane, tanh_sq_lt_one, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le_nat, RCLike.geometric_hahn_banach_point_closed, cos_arctan_pos, PadicInt.mem_nonunits, ZLattice.tsumNormRPowBound_pos, CStarAlgebra.isBasis_nonneg_sections, ContinuousAlternatingMap.bound, ProbabilityTheory.mgf_pos, unitInterval.sigmoid_pos, IsBoundedBilinearMap.bound, Bornology.IsBounded.exists_pos_norm_le, deriv_pos_right_of_sign_deriv, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, TFAE_exists_lt_isLittleO_pow, InnerProductGeometry.angle_eq_pi_iff, Complex.exists_cthickening_tendstoUniformlyOn, QuotientGroup.norm_lt_iff, Affine.Simplex.inradius_pos, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, lt_toNNReal_iff_coe_lt, HurwitzZeta.isBigO_atTop_cosKernel_sub, Metric.uniformity_edist_aux, gaugeSeminorm_lt_one_of_isOpen, gauge_lt_eq, Complex.frontier_setOf_lt_re, Metric.continuousOn_iff, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, norm_div_pos_iff, ENNReal.ofReal_lt_one, NormedCommGroup.tendsto_nhds_one, Metric.cauchySeq_iff', exp_one_gt_two, zero_lt_one_add_norm_sq', WithSeminorms.isVonNBounded_iff_seminorm_bounded, eventually_norm_trivializationAt_lt, norm_lt_iff_of_nonempty_compactlySupported, convex_halfSpace_re_gt, Besicovitch.one_lt_goodΟ, PartitionOfUnity.exists_pos, Hyperreal.coe_lt_coe, NumberField.mixedEmbedding.pos_of_notMem_negAt_plusPart, HolderTriple.inv_pos', IsCompact.exists_isCompact_cthickening, ContinuousLinearMap.bound, Disjoint.exists_thickenings, UpperHalfPlane.im_pnat_div_pos, EuclideanGeometry.sin_pos_of_not_collinear, Metric.nhdsWithin_basis_ball, CStarAlgebra.hasBasis_approximateUnit, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right, SpectrumRestricts.lt_nnreal_iff, ContDiffBump.rIn_pos, Metric.biInter_gt_closedBall, NumberField.dedekindZeta_residue_pos, Padic.norm_lt_pow_iff_norm_le_pow_sub_one, Besicovitch.goodΞ΄_lt_one, LiouvilleNumber.remainder_lt, Valued.norm_pos_iff_valuation_pos, StrictConvexOn.ae_eq_const_or_map_average_lt, SeminormFamily.basisSets_iff, BoxIntegral.Box.coe_splitUpper, SeminormedAddGroup.disjoint_nhds, EuclideanGeometry.angle_lt_pi_of_not_collinear, Metric.uniformContinuous_iff, exp_neg_one_lt_half, NumberField.Units.dirichletUnitTheorem.exists_unit, Metric.exists_closedBall_inter_eq_singleton_of_discrete, Asymptotics.IsBigO.exists_pos, UpperHalfPlane.isometry_pos_mul, HolderConjugate.sub_one_pos, NumberField.mixedEmbedding.fundamentalCone.expMap_pos, mem_closure_iff, Valued.toNormedField.norm_lt_one_iff, Bornology.IsBounded.exists_pos_norm_le', one_lt_sqrt_two, Complex.upperHalfPlane_inter_integerComplement, IsCompact.uniform_oscillationWithin, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge_nat, Seminorm.ball_zero_eq, Metric.dist_lt_add_of_nonempty_ball_inter_closedBall, mul_mem_ball_iff_norm, ENNReal.trichotomyβ, NormedSpace.exists_lt_norm, unitInterval.sigmoid_lt_one, ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAux, Wallis.W_pos, Metric.uniformCauchySeqOn_iff, NormedAddCommGroup.tendsto_atTop', Hyperreal.ofSeq_lt_ofSeq, intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero, eventually_norm_mfderiv_extChartAt_lt, cos_pos_of_le_one, Gamma_three_div_two_lt_one, UpperHalfPlane.coe_im_pos, sigmoid_lt_one, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, ae_eq_const_or_norm_integral_lt_of_norm_le_const, summable_jacobiThetaβ'_term_iff, Metric.uniformSpace_eq_bot, RCLike.geometric_hahn_banach_closed_compact, smoothTransition.pos_denom, ProbabilityTheory.IsAEKolmogorovProcess.q_pos, UpperHalfPlane.mdifferentiable_iff, ModularFormClass.exp_decay_sub_atImInfty', MeasureTheory.lintegral_comp_eq_lintegral_meas_lt_mul, Complex.arg_neg_eq_arg_sub_pi_iff, WithSeminorms.hasBasis_ball, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, AkraBazziRecurrence.bi_min_div_two_lt_one, MeasureTheory.integral_exp_pos, norm_add_lt_of_not_sameRay, mk_pos, summable_nat_rpow, polarCoord_source, Complex.arg_eq_pi_iff, toNNReal_lt_toNNReal_iff', summable_exp_nat_mul_iff, real_inner_self_pos, SzemerediRegularity.eps_pow_five_pos, Metric.isOpen_singleton_iff, UniformSpace.Completion.uniformity_dist', sqrt_ne_zero', mem_ball_zero_iff, exists_seq_rat_strictMono_tendsto, norm_sub_pos_iff, MeasureTheory.volume_sum_rpow_lt_one, antilipschitzWith_iff_exists_mul_le_norm, Valued.integer.exists_norm_coe_lt_one, Metric.Sigma.isOpen_iff, ProbabilityTheory.mgf_pos_iff, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Metric.exists_real_pos_lt_infEDist_of_notMem_closure, pi_gt_d6, similar_iff_exists_pos_dist_eq, norm_lt_of_mem_ball, fourierCoeff_liftIco_eq, Metric.uniformity_basis_dist_inv_nat_pos, exp_neg_one_lt_d9, GaussianInt.normSq_div_sub_div_lt_one, Complex.arg_eq_neg_pi_div_two_iff, NormedAddCommGroup.nhds_basis_norm_lt, summable_one_div_int_add_rpow, rpow_zero_pos, Metric.ball_eq_ball', RCLike.geometric_hahn_banach_open_open, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, EMetric.exists_real_pos_lt_infEdist_of_notMem_closure, EReal.coe_lt_coe_iff, pi_lt_d4, HurwitzZeta.isBigO_atTop_sinKernel, Asymptotics.isBigO_iff', Behrend.exp_four_lt, Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two, lt_of_toNNReal_lt, conformalAt_iff', infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, Chebyshev.theta_pos, arctan_lt_arctan_iff, Affine.Simplex.ExcenterExists.exradius_pos, ENNReal.coe_lt_ofReal, SeminormedCommGroup.mem_closure_iff, Bundle.ContinuousRiemannianMetric.isVonNBounded, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, integrableAtFilter_rpow_atTop_iff, summable_jacobiThetaβ_term_iff, Complex.UnitDisc.sq_norm_lt_one, WithSeminorms.hasBasis_zero_ball, exp_pos, Metric.closure_eq_iInter_thickening, ENNReal.ofReal_ne_zero_iff, contMDiffOn_projIcc, ContDiffBump.integral_pos, NNReal.summable_rpow, Metric.exists_contMDiffMap_forall_closedEBall_subset, one_lt_rpow_iff, Mathlib.Meta.Positivity.log_pos_of_isNegNat, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Stirling.stirlingSeq_has_pos_limit_a, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, ContinuousLinearEquiv.norm_pos, Matrix.PosDef.re_dotProduct_pos, ProbabilityTheory.IsAEKolmogorovProcess.p_pos, natCast_lt_toNNReal, NumberField.Units.regOfFamily_pos, sin_arctan_lt_zero, Valued.integer.norm_irreducible_pos, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, Metric.mem_ball', Complex.lt_def, Metric.isUniformEmbedding_iff', ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, IsClosed.notMem_iff_infDist_pos, RCLike.ofReal_lt_ofReal, RCLike.geometric_hahn_banach_open_point, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Complex.closure_setOf_im_lt, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, PadicInt.norm_natCast_lt_one_iff, RCLike.ofReal_lt_zero, ContDiffBump.rOut_pos, AkraBazziRecurrence.asympBound_pos
|
instMax π | CompOp | 148 mathmath: LipschitzWith.max_const, LinearMap.mkContinuousβ_norm_le', ContinuousAlternatingMap.opNorm_prod, volume_real_Ioc, GroupSeminorm.coe_sup, Height.mulHeightβ_eq, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, ofCauchy_sup, Metric.diam_triple, MeasureTheory.Integrable.neg_part, MeasureTheory.norm_setToFun_le_mul_norm', IsUltrametricDist.norm_add_one_le_max_norm_one, Polynomial.one_le_prod_max_one_norm_roots, PadicInt.nonarchimedean, NonarchAddGroupSeminorm.coe_sup, formalMultilinearSeries_geometric_apply_norm_le, AddGroupNorm.coe_sup, PiNat.dist_triangle_nonarch, ENNReal.toReal_max, volume_real_Ioo, ContinuousAffineMap.norm_def, IsUltrametricDist.dist_triangle_max, MeasureTheory.MemLp.pos_part, ModularGroup.exists_bound_of_subgroup_invariant_of_isBigO, MultilinearMap.norm_image_sub_le_of_bound', ContinuousMultilinearMap.norm_image_sub_le, coe_toNNReal', ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, MeasureTheory.MemLp.neg_part, LocallyLipschitz.const_max, GroupNorm.coe_sup, Wbtw.dist_le_max_dist, LinearMap.norm_mkContinuousβ_aux, Prod.dist_eq, LocallyLipschitz.max, WithLp.prod_norm_eq_idemFst_sup_idemSnd, Seminorm.coe_sup, MeasureTheory.norm_setToFun_le', MeasureTheory.Lp.coeFn_negPart_eq_max, Polynomial.mahlerMeasure_C_mul_X_add_C, Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff, IsUltrametricDist.norm_mul_eq_max_of_norm_ne_norm, WithLp.prod_dist_eq_sup, NormedAddGroupHom.mkNormedAddGroupHom_norm_le', ModularFormClass.exists_petersson_le, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, dist_triangle_max, ValueDistribution.characteristic_sub_characteristic_inv_le, NumberField.FinitePlace.add_le, MeasureTheory.Lp.lipschitzWith_pos_part, Unitization.norm_eq_sup, Polynomial.mahlerMeasure_X_add_C, AlternatingMap.norm_image_sub_le_of_bound, dist_single_single, ModularFormClass.exists_bound, posLog_def, AlternatingMap.norm_image_sub_le_of_bound', MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', ENNReal.ofReal_max, MultilinearMap.mkContinuousLinear_norm_le', AddGroupSeminorm.sup_apply, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, Prod.norm_def, MultilinearMap.mkContinuousMultilinear_norm_le', Valued.norm_add_le, WithLp.prod_norm_eq_sup, MultilinearMap.norm_image_sub_le_of_bound, ContinuousAlternatingMap.norm_image_sub_le', Polynomial.mahlerMeasure_X_sub_C, NNReal.coe_sub_def, Prod.norm_mk, volume_real_Icc, LinearMap.mkContinuous_norm_le', IsUltrametricDist.norm_add_le_max, IsUltrametricDist.norm_add_eq_max_of_norm_ne_norm, Asymptotics.IsBigOWith.prod_left, AddGroupNorm.sup_apply, LipschitzWith.max, ODE.FunSpace.dist_iterate_next_le, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, NumberField.Embeddings.coeff_bdd_of_norm_le, Metric.cthickening_eq_iInter_thickening'', ModularGroup.exists_bound_of_subgroup_invariant_of_isArithmetic_of_isBigO, ModularGroup.exists_bound_of_invariant_of_isBigO, ODE.FunSpace.dist_iterate_next_iterate_next_le, LocallyLipschitz.max_const, IsMprojection.Mnorm, Padic.nonarchimedean, sq_sqrt', MeasureTheory.L1.norm_setToL1_le_mul_norm', MeasureTheory.HasFiniteIntegral.max_zero, IsUltrametricDist.norm_div_eq_max_of_norm_div_ne_norm_div, MeasureTheory.Integrable.pos_part, IsPicardLindelof.mul_max_le, MeasureTheory.L1.norm_setToL1_le', Metric.cthickening_max_zero, ProbabilityTheory.rpow_abs_le_mul_max_exp, CircleDeg1Lift.sup_apply, BoundedContinuousFunction.dist_extend_extend, ENNReal.toReal_sup, Polynomial.mahlerMeasure_of_degree_eq_one, IsUltrametricDist.norm_mul_le_max, Hyperreal.coe_max, Polynomial.coeff_bdd_of_roots_le, PadicInt.norm_add_eq_max_of_ne, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, NonarchAddGroupNorm.coe_sup, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, mk_sup, AlternatingMap.mkContinuousAlternating_norm_le_max, volume_real_Ico, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, Sbtw.dist_lt_max_dist, rpow_max, Fin.dist_insertNth_insertNth, IsUltrametricDist.dist_eq_max_of_dist_ne_dist, Seminorm.sup_apply, IsUltrametricDist.norm_sub_eq_max_of_norm_sub_ne_norm_sub, WithCStarModule.max_le_prod_norm, Padic.add_eq_max_of_ne, posLog_eq_log_max_one, MeasureTheory.Lp.coeFn_posPart, GroupNorm.sup_apply, NonarchAddGroupSeminorm.sup_apply, AddMonoidHom.mkNormedAddGroupHom_norm_le', NonarchAddGroupNorm.sup_apply, lipschitzWith_max, map_sub_le_max, NonarchAddGroupSeminorm.add_le_max', NumberField.mulHeightβ_eq, EReal.coe_ennreal_ofReal, Complex.norm_le_sqrt_two_mul_max, dist_inf_sup_pi, ContinuousMultilinearMap.opNorm_prod, intervalIntegral.norm_integral_min_max, AlternatingMap.mkContinuousLinear_norm_le_max, LipschitzWith.const_max, MultilinearMap.mkContinuous_norm_le', ContinuousMultilinearMap.norm_image_sub_le', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, ENNReal.toReal_ofReal', GroupSeminorm.sup_apply, AlternatingMap.mkContinuous_norm_le', Int.Matrix.exists_ne_zero_int_vec_norm_le, AddGroupSeminorm.coe_sup, NNReal.coe_max, ContinuousAlternatingMap.norm_image_sub_le, Asymptotics.IsBigOWith.sup'
|
instMin π | CompOp | 37 mathmath: ENNReal.toReal_min, PiCountable.min_dist_le_dist_pi, ProbabilityTheory.sub_half_inf_sub_mem_Ioo, Path.truncate_self, Metric.PiNatEmbed.dist_def, CircleDeg1Lift.inf_apply, Path.truncate_zero_zero, AddCircle.volume_closedBall, LipschitzWith.min, PiCountable.dist_summable, LipschitzWith.min_const, LipschitzWith.const_min, LocallyLipschitz.min_const, NNReal.coe_min, ProbabilityTheory.add_half_inf_sub_mem_Ioo, BoxIntegral.IntegrationParams.RCond.min, Hyperreal.coe_min, Set.infsep_triple, Path.truncate_zero_one, mk_inf, MeasureTheory.Lp.coeFn_negPart, LocallyLipschitz.const_min, Path.truncate_const_continuous_family, ENNReal.toReal_inf, Path.truncate_continuous_family, norm_add_sub_norm_sub_le_two_mul_min, MeasureTheory.HasFiniteIntegral.min_zero, PiCountable.dist_eq_tsum, ENNReal.ofReal_min, Path.truncate_one_one, norm_mul_sub_norm_div_le_two_mul_min, dist_inf_sup_pi, intervalIntegral.norm_integral_min_max, lipschitzWith_min, Path.truncate_range, LocallyLipschitz.min, ofCauchy_inf
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instMonoid π | CompOp | 1594 math, 1 bridgemath: cos_add_nat_mul_pi, range_cfcβ_nnreal, arctan_eq_arccos, MeasureTheory.Measure.integral_comp_inv_smul, isEquivalent_descFactorial, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, hasDerivAt_arccos, norm_sub_sq_real, ProbabilityTheory.variance_eq_integral, Orientation.oangle_sign_smul_add_right, MeasureTheory.setIntegral_tilted, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, Seminorm.isBounded_const, CFC.posPart_smul_of_nonpos, EuclideanGeometry.dist_smul_vadd_sq, Bundle.ContMDiffRiemannianMetric.isVonNBounded, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, real_inner_div_norm_mul_norm_eq_neg_one_iff, gold_sq, geom_le, goldenConj_mul_fib_succ_add_fib, norm_torusIntegral_le_of_norm_le_const, sqrt_eq_iff_eq_sq, MeasureTheory.Martingale.smul, mellin_eq_fourier, SchwartzMap.instLineDerivLeftSMulReal, sin_arctan, deriv_arctan, iteratedDeriv_odd_cos, MeasureTheory.charFun_eq_fourierIntegral', segment_subset_closedBall_right, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, gauge_def', bernoulliFun_eval_one_sub, MeasureTheory.hausdorffMeasure_segment, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, InnerProductSpace.volume_closedBall_of_dim_even, ZLattice.summable_norm_sub_inv_pow, Orientation.inner_rotation_pi_div_two_right_smul, intervalIntegral.intervalIntegrable_one_div_one_add_sq, tendsto_tsum_div_pow_atTop_integral, Orientation.oangle_add_left_smul_rotation_pi_div_two, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, CFC.monotoneOn_one_sub_one_add_inv, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, HurwitzZeta.hasSum_int_cosKernelβ, nnnorm_cfcβ_nnreal_le_iff, NumberField.mixedEmbedding.convexBodyLT'_mem, arctan_eq_arcsin, Complex.norm_sub_one_sq_eq_of_norm_eq_one, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, MeasureTheory.Measure.integral_comp_mul_right, intervalIntegral.inv_smul_integral_comp_div_add, taylorWithinEval_hasDerivAt_Ioo, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, rpow_add_natCast', EuclideanSpace.closedBall_zero_eq, integral_sin_mul_cosβ, EuclideanGeometry.dist_inversion_inversion, curveIntegrable_segment, Stirling.factorial_isEquivalent_stirling, norm_jacobiThetaβ_term_le, IsSelfAdjoint.norm_mul_self, norm_jacobiThetaβ_term_fderiv_ge, norm_add_eq_iff_real, Complex.integral_comp_pi_polarCoord_symm, contDiffAt_norm_smul_iff, SchwartzMap.pairing_apply_apply, log_div_le_sum_range_add, MeasureTheory.weightedSMul_apply, Commute.cfcβ_nnreal, NumberField.norm_norm_le_norm_mul_house_pow, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, hasDerivWithinAt_taylorWithinEval, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, Submodule.re_inner_starProjection_eq_normSq, dist_sq_lineMap_lineMap_of_inner_eq_zero, MeasureTheory.integral_unique, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, intervalIntegral.intervalIntegral_eq_integral_uIoc, ContinuousLinearMap.integral_apply, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, Gamma_nat_add_half, pow_le_of_le_log, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, real_inner_smul_self_left, goldConj_sq, SmoothPartitionOfUnity.contMDiffAt_finsum, Asymptotics.IsBigOWith.pow, geom_goldenRatio_isSol_fibRec, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, NumberField.dedekindZeta_residue_def, setIntegral_withDensity_eq_setIntegral_toReal_smul, le_pow_iff_log_le, Metric.nhds_basis_closedBall_pow, MeasureTheory.Measure.toSphere_apply_aux, tendsto_integral_peak_smul_of_integrable_of_tendsto, EuclideanSpace.norm_sq_eq, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, NormedRing.inverse_add_norm_diff_nth_order, bernoulliFun_two, MeasureTheory.condExpIndL1Fin_smul, add_sqrt_self_sq_sub_one_inv, InnerProductGeometry.angle_smul_right_of_pos, selfAdjoint.norm_sq_expUnitary_sub_one, SchwartzMap.decay', derivWithin_arctan, intervalIntegral.integral_comp_sub_div, PiCountable.min_dist_le_dist_pi, intervalIntegral.integral_comp_mul_left, Antitone.tendsto_alternating_series_of_tendsto_zero, BoxIntegral.unitPartition.mem_smul_span_iff, intervalIntegral.integral_comp_mul_sub, SchwartzMap.bilinLeftCLM_apply, Submodule.starProjection_singleton, Bundle.RiemannianMetric.isVonNBounded, PowerSeries.gaussNorm_monomial, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Polynomial.sub_one_pow_totient_le_cyclotomic_eval, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, tendsto_one_add_pow_exp_of_tendsto, integral_pow, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, norm_exp_sub_one_sub_id_le, tendsto_tsum_powerSeries_nhdsWithin_lt, hasSum_log_one_add_inv, combo_mem_ball_of_ne, Complex.IsExpCmpFilter.isBigO_im_pow_re, exp_nsmul, norm_add_pow_two_real, sum_geometric_two_le, summable_one_div_int_pow, norm_cexp_neg_mul_sq, Polynomial.Chebyshev.eval_T_real_node, ProbabilityTheory.cgf_gaussianReal, conformal_const_smul, ProbabilityTheory.HasSubgaussianMGF.mgf_le, NumberField.abs_discr_ge', WithCStarModule.prod_norm_sq, SchwartzMap.laplacianCLM_eq, monomial_has_deriv_aux, NumberField.abs_discr_ge, ProbabilityTheory.covarianceOperator_apply, InnerProductGeometry.angle_smul_left_of_neg, MeasureTheory.integral_tilted, deriv_arccos, MeasureTheory.average_mem_openSegment_compl_self, ProbabilityTheory.integrable_pow_abs_of_integrable_exp_mul, integral_sin_pow_three, cos_le_one_div_sqrt_sq_add_one, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, cfcβHom_nnreal_eq_restrict, Conformal.const_smul, HasFDerivAt.norm_sq, one_sub_sq_div_two_le_cos, Complex.norm_pow, AddCircle.integral_haarAddCircle, InnerProductSpace.HarmonicAt.const_smul, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, norm_pow, toNNReal_pow, Orientation.oangle_smul_left_of_neg, OrthogonalFamily.norm_sq_diff_sum, lt_pow_of_log_lt, MeasureTheory.Measure.addHaar_ball_of_pos, convexHull_union_neg_eq_absConvexHull, OrthonormalBasis.sum_sq_inner_right, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, summable_condensed_iff_of_eventually_nonneg, NumberField.prod_abs_eq_one, smul_unitClosedBall_of_nonneg, exp_bound, Polynomial.Chebyshev.integral_measureT, volume_pi_ball, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, tendsto_exp_div_pow_atTop, integral_sin_pow_pos, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, Finset.small_alternating_pow_of_small_tripling, MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', QuadraticForm.equivalent_signType_weighted_sum_squared, curveIntegralFun_segment, strictConvexOn_pow, Complex.volume_sum_rpow_le, Besicovitch.SatelliteConfig.exists_normalized_aux2, hasDerivAt_arcosh, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, Complex.norm_log_one_add_le, tendsto_self_mul_const_pow_of_lt_one, convexOn_univ_dist, HasDerivAt.arctan, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, cos_arcsin, Polynomial.le_gaussNorm, RCLike.norm_sq_eq_def_ax, setIntegral_withDensity_eq_setIntegral_toReal_smulβ, ProbabilityTheory.HasGaussianLaw.smul, tan_arccos, hasSum_sinh, sinh_arcosh, LiouvilleNumber.aux_calc, MeasureTheory.memLp_two_iff_integrable_sq_norm, sameRay_iff_inv_norm_smul_eq_of_ne, norm_sum_lt_of_strictConvexSpace, UniformConvexOn.strictConvexOn, integral_cos_pow, Orientation.oangle_sign_sub_smul_left, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', MeasureTheory.SimpleFunc.integral_eq_sum_filter, HasFDerivAt.arctan, Height.mulHeightβ_zpow, hasStrictDerivAt_arccos, Stirling.log_stirlingSeq_diff_hasSum, ProbabilityTheory.variance_of_integral_eq_zero, MeasureTheory.Measure.quasiMeasurePreserving_smul, norm_sub_pow_two_real, Polynomial.cyclotomic_eval_lt_add_one_pow_totient, intervalIntegral.intervalIntegrable_inv_one_add_sq, Complex.sin_bound, Height.mulHeightβ_pow, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, MeasureTheory.L1.setToL1_smul_left, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MeasureTheory.Measure.addHaar_ball_mul, norm_sub_sq, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, WithLp.prod_dist_eq_of_L2, WithLp.prod_norm_eq_of_nat, balancedHull_subset_convexHull_union_neg, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, stereoInvFunAux_apply, norm_curveIntegral_segment_le, HasStrictFDerivAt.arsinh, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, sin_gt_sub_cube, SchwartzMap.fourier_lineDerivOp_eq, TemperedDistribution.instLineDerivLeftSMulReal, LindemannWeierstrass.exp_polynomial_approx, tendsto_card_div_pow_atTop_volume, sin_add_nat_mul_pi, hasSum_cosh, cos_nat_mul_pi, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, EuclideanGeometry.inversion_vsub_center, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, log_two_near_10, MeasureTheory.condExpL2_indicator_ae_eq_smul, conformalAt_const_smul, NNReal.dist_agmSequences_fst_snd, CFC.negPart_smul_of_nonpos, SchwartzMap.smulLeftCLM_real_smul, MeasureTheory.Measure.integral_comp_inv_mul_left, ContDiffBump.measure_closedBall_div_le_integral, MeasureTheory.measure_smul_average, Orientation.oangle_sign_sub_smul_right, Complex.integral_comp_polarCoord_symm, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, integral_sin_sq, SchwartzMap.integral_norm_sq_fourier, Orientation.oangle_smul_left_self_of_nonneg, ProbabilityTheory.gaussianReal_map_continuousLinearMap, exp_sub_sum_range_succ_isLittleO_pow, hasDerivAt_arsinh, le_sqrt', hasSum_zeta_four, taylor_tendsto, Angle.cos_sq_add_sin_sq, Finset.small_alternating_nsmul_of_small_tripling, HasFDerivAt.curveIntegral_segment_source, mellin_hasDerivAt_of_isBigO_rpow, HasStrictDerivAt.arctan, sin_sq_arctan, strongConcaveOn_zero, Metric.PiNatEmbed.dist_def, intervalIntegral.integral_comp_add_div, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, BoxIntegral.HasIntegral.smul, sqrt_sq_eq_abs, CStarModule.inner_smul_right_real, SameRay.inv_norm_smul_eq, ProbabilityTheory.integrable_pow_mul_exp_of_integrable_exp_mul, pow_lt_iff_lt_log, norm_pow_le, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, MeasureTheory.Measure.integral_comp_smul_of_nonneg, SzemerediRegularity.hundred_lt_pow_initialBound_mul, cos_three_mul, MeasureTheory.convolution_precompR_apply, SimpleGraph.triangleRemovalBound_mul_cube_lt, Polynomial.Chebyshev.coeff_eq_iff_of_forall_abs_le_one, ZLattice.covolume.tendsto_card_div_pow, abs_exp_sub_one_sub_id_le, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, tsum_exp_neg_mul_int_sq, integral_cos_pow_aux, ContinuousMultilinearMap.norm_restr, tan_two_mul, ContinuousMultilinearMap.norm_image_sub_le, Seminorm.ball_smul, Even.strictConvexOn_pow, LiouvilleNumber.summable, hasSum_cos, isTheta_choose, affinity_unitClosedBall, ContDiffBump.normed_le_div_measure_closedBall_rOut, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, rpow_mul_natCast, MeasureTheory.integral_singleton', NumberField.mulHeight_eq, Polynomial.coeff_le_of_roots_le, pow_arith_mean_le_arith_mean_pow_of_even, one_add_tan_sq_mul_cos_sq_eq_one, Polynomial.exists_eq_gaussNorm, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, finite_integral_rpow_sub_one_pow_aux, nnnorm_cfcβ_nnreal_lt, Function.hasTemperateGrowth_iff_isBigO, Complex.sq_norm_sub_sq_re, hasSum_log_one_add, sin_sq, ProbabilityTheory.strong_law_ae, tanh_arcosh, HasDerivWithinAt.norm_sq, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, lt_geom, SmoothPartitionOfUnity.contDiffAt_finsum, Chebyshev.integral_one_div_log_sq_isBigO, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, inv_one_add_tan_sq, exp_arcosh, MeasureTheory.MemLp.integrable_norm_pow, isBigO_rpow_top_log_smul, Complex.sq_norm, Complex.norm_log_sub_logTaylor_le, SchwartzMap.smulLeftCLM_sum, le_ofDigits_cantorToTernary_sum, taylor_mean_remainder_lagrange_iteratedDeriv, two_mul_arctan, has_fderiv_at_filter_real_equiv, hasDerivWithinAt_arccos_Ici, MeasureTheory.setIntegral_condExpInd, Seminorm.gaugeSeminorm_ball, MeasureTheory.integral_comp_rpow_Ioi_of_pos, curveIntegral_segment, MultilinearMap.restr_norm_le, tan_div_sqrt_one_add_tan_sq, isEquivalent_choose, sqrt_le_iff, gauge_norm_smul, InnerProductSpace.Core.cauchy_schwarz_aux, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, convexOn_univ_norm, exists_rat_abs_sub_lt_and_lt_of_irrational, intervalIntegral.integral_deriv_comp_smul_deriv', sq_le, IsApproximateAddSubgroup.nsmul_inter_nsmul, MeasureTheory.Submartingale.smul_nonneg, openSegment_subset_ball_of_ne, NormedSpace.normalize_smul, cos_le_one_sub_mul_cos_sq, ProbabilityTheory.condVar_smul, MeasureTheory.integrable_withDensity_iff_integrable_smul', IsMIntegralCurveOn.comp_mul, ConvexBody.coe_smul, InnerProductGeometry.angle_eq_zero_iff, norm_cauchyPowerSeries_le, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, ofDigitsTerm_le, trapezoidal_error_le_of_c2, HasFPowerSeriesOnBall.uniform_geometric_approx, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_monotoneOn, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, norm_smul_of_nonneg, expNear_sub, HurwitzZeta.hasSum_int_cosKernel, fib_golden_exp', ContDiffAt.contDiffAt_norm_smul, geom_gold_isSol_fibRec, MeasureTheory.volume_sum_rpow_lt, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, EuclideanGeometry.preimage_inversion_perpBisector, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, Ioo_smul_sphere_zero, Height.mulHeight_pow, contDiffOn_stereoToFun, SchwartzMap.smulLeftCLM_fun_neg, Complex.norm_log_one_add_sub_self_le, map_pow_le_pow, norm_jacobiThetaβ_term, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, stereoInvFun_apply, AkraBazziRecurrence.GrowsPolynomially.pow, ContractingWith.apriori_dist_iterate_fixedPoint_le, MeasureTheory.integral_indicatorConstLp, integrable_rpow_neg_one_add_norm_sq, Submodule.norm_sq_eq_add_norm_sq_starProjection, SchwartzMap.pairing_apply, MeasureTheory.Measure.integral_comp_smul, UpperHalfPlane.cosh_dist, real_inner_div_norm_mul_norm_eq_one_iff, goldenRatio_pow_sub_goldenRatio_pow, Quaternion.expSeries_odd_of_imaginary, MeasureTheory.integrable_withDensity_iff_integrable_smulβ', sq_cos_pi_div_six, curveIntegral_segment_const, EuclideanGeometry.Sphere.dist_sq_eq_mul_dist_of_tangent_and_secant, MeasureTheory.memLp_two_iff_integrable_sq, BoxIntegral.BoxAdditiveMap.volume_apply, ProbabilityTheory.HasGaussianLaw.fun_smul, EuclideanGeometry.Sphere.IsTangentAt.power_eq_dist_sq, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, UpperHalfPlane.dist_coe_center, ProbabilityTheory.gaussianReal_map_linearMap, ConvexBody.convex, Stirling.le_factorial_stirling, ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mul, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, coe_fib_eq, iSup_pow, Seminorm.comp_smul, IsGreatest.nnnorm_cfcβ_nnreal, intervalIntegral.smul_integral_comp_mul_sub, MeasureTheory.hasFDerivAt_convolution_right_with_param, Complex.sq_norm_sub_sq_im, deriv_inv_log, OrthonormalBasis.sum_sq_norm_inner_right, EulerSine.sin_pi_mul_eq, CircleDeg1Lift.transnumAuxSeq_dist_lt, Chebyshev.primeCounting_eq_theta_div_log_add_integral, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, Complex.normSq_eq_norm_sq, HasCompactSupport.hasFDerivAt_convolution_right, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, bernstein.variance, tsum_geometric_of_lt_one, MeasureTheory.SimpleFunc.integral_eq_sum, bernstein_apply, LiouvilleNumber.remainder_summable, sum_div_nat_floor_pow_sq_le_div_sq, pow_arith_mean_le_arith_mean_pow, Orthonormal.inner_products_summable, Height.mulHeightβ_add_le, NormedSpace.normalize_smul_of_pos, norm_exp_mul_sq_le, intervalIntegral.integral_comp_smul_deriv'', hasStrictDerivAt_arcosh, norm_sum_neg_one_pow_le, intervalIntegral.integral_comp_smul_deriv, HurwitzKernelBounds.F_nat_one_le, Asymptotics.IsBigOWith.pow', Complex.norm_exp_sub_sum_le_norm_mul_exp, EuclideanGeometry.image_inversion_perpBisector, MeasureTheory.setIntegral_condExpIndSMul, totallyBounded_absConvexHull, inv_norm_smul_mem_unitClosedBall, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, one_div_sub_hasFPowerSeriesOnBall_zero, Polynomial.Chebyshev.leadingCoeff_le_of_forall_abs_le_one, isLittleO_pow_exp_atTop, Seminorm.bound_of_continuous, ContDiff.euclidean_dist, intervalIntegral.integral_comp_add_mul, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, exp_one_near_20, ConvexBody.ext_iff, MeasureTheory.setIntegral_rnDeriv_smul, Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, sum_le_exp_of_nonneg, integral_sin_pow_mul_cos_pow_odd, MeasureTheory.volume_sum_rpow_le, ofDigits_eq_sum_add_ofDigits, HasDerivWithinAt.arsinh, exists_natCast_add_one_lt_pow_of_one_lt, ProbabilityTheory.mgf_sum_of_identDistribβ, CFC.nnrpow_def, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, hasDerivAt_arcsin, RCLike.real_smul_eq_coe_smul, integral_comp_polarCoord_symm, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, hasDerivAt_tan, logb_pow, hasFDerivAt_integral_of_dominated_loc_of_lip', integral_id, deriv_tan_sub_id, stereoToFun_apply, arcsin_eq_arccos, MeasureTheory.MemLp.integrable_sq, ProbabilityTheory.evariance_eq_lintegral_ofReal, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', ContDiffWithinAt.norm_sq, Function.hasTemperateGrowth_norm_sq, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, Chebyshev.integrableOn_theta_div_id_mul_log_sq, IsApproximateSubgroup.pow_inter_pow, affinity_unitBall, convex_eball, sin_eq_tsum, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, abs_log_sub_add_sum_range_le, SchwartzMap.smulRightCLM_apply_apply, MeasureTheory.setToFun_smul_left, taylor_mean_remainder, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', sin_sq_eq_half_sub, Unitary.norm_sub_one_sq_eq, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, InnerProductSpace.volume_ball, cosh_sq, fderiv_norm_smul_neg, norm_inv_mul_rpow_sub_one_sub_log_le, tan_sq_div_one_add_tan_sq, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, PiNat.mem_cylinder_iff_dist_le, NumberField.mixedEmbedding.covolume_idealLattice, ContDiff.norm_sq, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, EuclideanSpace.sphere_zero_eq, setIntegral_withDensity_eq_setIntegral_toReal_smulβ', deriv_arctan, SchwartzMap.smulLeftCLM_const, NumberField.house_pow_le, MeasureTheory.integral_fintype, Asymptotics.isLittleO_pow_sub_pow_sub, OrthonormalBasis.sum_sq_inner_left, sinh_eq_tsum, integral_sin_mul_cosβ, intervalIntegral.smul_integral_comp_sub_mul, cos_eq_tsum, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, Orientation.inner_rotation_pi_div_two_left_smul, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Submodule.norm_sq_eq_add_norm_sq_projection, MeasureTheory.Measure.toSignedMeasure_smul, ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_self, arccos_eq_arcsin, goldenRatio_mul_fib_succ_add_fib, exp_arsinh, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, summable_nat_pow_inv, PowerSeries.IsRestricted.isRestricted_iff, integral_sin_pow_aux, hasDerivWithinAt_taylorWithinEval_at_Icc, integral_div_sq_add_sq, LipschitzWith.dist_iterate_succ_le_geometric, ProbabilityTheory.mgf_fun_id_gaussianReal, Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, intervalIntegral.integral_deriv_comp_smul_deriv, sq_sqrt, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, DifferentiableAt.norm_sq, tsum_geometric_two, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, ProbabilityTheory.sum_variance_truncation_le, IsApproximateAddSubgroup.card_nsmul_le, inner_eq_norm_sq_left_iff, Continuous.cfcβ_nnreal, PiCountable.dist_summable, HurwitzZeta.hasSum_int_evenKernel, intervalIntegral.integral_smul_measure, hasSum_one_div_nat_pow_mul_cos, signedDist_smul_of_pos, FormalMultilinearSeries.norm_compContinuousLinearMap_le, tendsto_pow_const_mul_const_pow_of_abs_lt_one, InnerProductSpaceable.inner_.norm_sq, sum_range_le_log_div, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, Submodule.smul_starProjection_singleton, SMulCommClass.complexToReal, Chebyshev.primeCounting_sub_theta_div_log_isBigO, ProbabilityTheory.gaussianPDFReal_def, MeasureTheory.Measure.addHaar_real_closedBall', le_sqrt, sinh_sq, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, ProbabilityTheory.variance_eq_sub, intervalIntegral.inv_smul_integral_comp_sub_div, hasDerivWithinAt_taylor_coeff_within, UniformConvexOn.convexOn, ContinuousAt.cfcβ_nnreal, integral_sin_pow_even_mul_cos_pow_even, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, Seminorm.const_isBounded, HasFDerivWithinAt.norm_sq, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, ProbabilityTheory.meas_ge_le_variance_div_sq, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, exists_taylor_mean_remainder_bound, InnerProductSpace.volume_ball_of_dim_odd, SchwartzMap.fourierInv_lineDerivOp_eq, IsOpen.smul_sphere, EuclideanGeometry.Sphere.secondInter_smul, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, strongConcaveOn_iff_convex, MeasureTheory.condExpIndL1_smul, eventually_norm_pow_le, ProbabilityTheory.Fernique.normThreshold_eq, ProbabilityTheory.moment_truncation_eq_intervalIntegral_of_nonneg, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', le_sum_ofDigitsTerm_digits, Quaternion.expSeries_even_of_imaginary, IsSelfAdjoint.norm_pow_two_pow, FormalMultilinearSeries.isLittleO_one_of_lt_radius, MeasureTheory.Measure.NullMeasurableSet.const_smul, ProbabilityTheory.Fernique.lintegral_closedBall_diff_exp_logRatio_mul_sq_le, DifferentiableOn.norm_sq, tsum_geometric_of_abs_lt_one, CircleDeg1Lift.transnumAuxSeq_def, smul_unitBall_of_pos, map_real_smul, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, Height.mulHeightβ_sum_le, circleAverage_def, hasDerivWithinAt_arcsin_Ici, HasStrictFDerivAt.arctan, NumberField.Ideal.tendsto_norm_le_div_atTopβ, cfcβ_tsub, hasSum_sq_fourierCoeffOn, ProbabilityTheory.strong_law_aux6, AlternatingMap.norm_image_sub_le_of_bound, unitary.norm_argSelfAdjoint, PMF.integral_eq_tsum, hasSum_geometric_two, ProbabilityTheory.variance_le_sq_of_bounded, intervalIntegral.integral_comp_div, contDiff_norm_sq, Orientation.oangle_sign_smul_left, ContinuousWithinAt.cfcβ_nnreal, Height.mulHeightβ_sub_le, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, ConvexBody.isBounded, PiLp.norm_sq_eq_of_L2, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, homeomorphUnitSphereProd_symm_apply_coe, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, taylorWithinEval_succ, HasDerivAt.norm_sq, abs_sin_eq_sqrt_one_sub_cos_sq, pow_rpow_inv_natCast, FormalMultilinearSeries.le_mul_pow_of_radius_pos, Polynomial.hermite_eq_deriv_gaussian', inner_vsub_vsub_right_eq_dist_sq_left_iff, isLittleO_pow_pow_of_abs_lt_left, AkraBazziRecurrence.growsPolynomially_pow, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_exp, MeasureTheory.Measure.integral_comp_mul_left, Cardinal.cantorFunctionAux_true, fderiv_arctan, HurwitzZeta.hasSum_int_sinKernel, hasStrictFDerivAt_norm_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', ContinuousWithinAt.integral_sub_linear_isLittleO_ae, sqrt_lt', ENNReal.toReal_pow, Orientation.oangle_sign_smul_sub_left, Liouville.frequently_exists_num, MeasureTheory.Measure.toSphere_apply', TemperedDistribution.instLineDerivSMulReal, range_cfcβ_nnreal_eq_image_cfcβ_real, tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, unitary.two_mul_one_sub_le_norm_sub_one_sq, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ProbabilityTheory.condVar_ae_le_condExp_sq, Filter.Tendsto.cfcβ_nnreal, mem_parallelepiped_iff, MeasureTheory.integral_biUnion_eq_sum_powerset, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, differentiableAt_norm_smul, circleAverage_eq_integral_add, intervalIntegral.inv_smul_integral_comp_div_sub, Gamma_nat_add_one_add_half, Seminorm.convex_ball, Differentiable.norm_sq, map_pow_le_pow', PartitionOfUnity.sum_finsupport_smul_eq_finsum, IsCompact.extremePoints_nonempty, Path.range_segment, HasDerivWithinAt.arctan, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, gauge_def, ProbabilityTheory.variance_mul_const, ProbabilityTheory.covarianceBilin_real_self, nnnorm_cfcβ_nnreal_lt_iff, NumberField.mixedEmbedding.norm_smul, hasStrictDerivAt_arsinh, MeasureTheory.integral_comp_rpow_Ioi, convex_closedEBall, integral_univ_inv_one_add_sq, tendsto_self_mul_const_pow_of_abs_lt_one, LinearMap.norm_extendToπ'_apply_sq, integrable_rpow_mul_exp_neg_mul_sq, tsum_geometric_two', SchwartzMap.integral_pow_mul_iteratedFDeriv_le, convex_ball, real_inner_smul_right, Orientation.oangle_sub_right_smul_rotation_pi_div_two, OrthonormalBasis.sum_sq_norm_inner_left, integrable_mul_exp_neg_mul_sq, VectorFourier.fourierSMulRight_apply, inner_self_eq_norm_sq, geom_goldConj_isSol_fibRec, StrongConcaveOn.strictConcaveOn, sq_lt, NormedRing.inverse_add_norm_diff_second_order, ProbabilityTheory.evariance_def', Seminorm.closedBall_smul, RCLike.ofReal_pow, isScalarTower, Asymptotics.isLittleO_norm_pow_norm_pow, NormedSpace.normalize_smul_of_neg, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.integral_fun_norm_addHaar, Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le, MeasureTheory.setIntegral_ge_of_const_le, imaginaryPart_apply_coe, real_inner_self_eq_norm_sq, SchwartzMap.smulLeftCLM_add, iteratedDeriv_even_cos, Complex.cos_bound, intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, segment_subset_closedBall_left, taylor_tendsto, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, iSup_pow_of_ne_zero, pi_gt_sqrtTwoAddSeries, sum_mem_ball_of_strictConvexSpace, Quaternion.normSq_exp, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, ContinuousMultilinearMap.integral_apply, cosh_le_exp_half_sq, ContDiffAt.norm_sq, ProbabilityTheory.iteratedDeriv_mgf_zero, EisensteinSeries.r1_eq, tsirelson_inequality, ProbabilityTheory.moment_truncation_eq_intervalIntegral, MeasureTheory.average_union_mem_segment, cfcβ_real_eq_nnreal, HasDerivAt.arsinh, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, ZLattice.summable_norm_pow_inv, BoxIntegral.BoxAdditiveMap.toSMul_apply, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, homeomorphSphereProd_symm_apply_coe, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Polynomial.gaussNorm_monomial, MeasureTheory.integrable_tilted_iff, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, EuclideanSpace.norm_eq, mellin_eq_fourierIntegral, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, integral_cos_pow_three, ProbabilityTheory.variance_mul, intervalIntegral.integral_comp_smul_deriv', CStarModule.norm_sq_eq, ProbabilityTheory.integrable_pow_of_mem_interior_integrableExpSet, EuclideanGeometry.inversion_def, arccos_eq_arctan, intervalIntegral.integral_comp_sub_mul, homeomorphUnitSphereProd_apply_fst_coe, CFC.posPart_smul_of_nonneg, InnerProductSpace.norm_sq_eq_re_inner, NumberField.mixedEmbedding.covolume_integerLattice, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, Polynomial.hermite_eq_deriv_gaussian, isCompact_closedAbsConvexHull_of_totallyBounded, Orientation.inner_smul_rotation_pi_div_two_right, UniformConcaveOn.concaveOn, Orientation.inner_mul_areaForm_sub', sin_pi_over_two_pow_succ, deriv_arcsin, MeasureTheory.uniformIntegrable_average, SchwartzMap.le_seminorm, cos_sq', tendsto_pow_atTop_nhds_zero_of_abs_lt_one, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, summable_one_div_pow_of_le, MeasureTheory.setIntegral_rnDeriv_smul', HasFPowerSeriesOnBall.uniform_geometric_approx', intervalIntegral.smul_integral_comp_mul_left, uniformConcaveOn_zero, mul_add_one_le_add_one_pow, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, IsApproximateSubgroup.of_small_tripling, InnerProductGeometry.angle_smul_smul, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', ModelWithCorners.convex_range, CStarAlgebra.mul_star_le_algebraMap_norm_sq, ContDiffBump.integral_normed_smul, hasSum_geometric_two', Orientation.oangle_sign_smul_right, Orientation.normSq_kahler, integral_inv_sq_add_sq, rpow_two, NNReal.smul_def, SmoothBumpFunction.contMDiff_smul, MultilinearMap.norm_image_sub_le_of_bound, PiNat.dist_eq_of_ne, sameRay_iff_inv_norm_smul_eq, cfcHom_nnreal_eq_restrict, BoxIntegral.integral_smul, Polynomial.sum_sq_norm_coeff_eq_circleAverage, ProbabilityTheory.integral_tilted_mul_eq_mgf, MeasureTheory.integral_simpleFunc_larger_space, ContDiffBump.apply, Mathlib.Meta.NormNum.IsInt.rpow_eq_inv_pow, Orientation.oangle_sign_add_smul_left, HasFDerivAt.lim_real, tsum_geometric_inv_two_ge, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, pow_div_factorial_le_exp, SimpleGraph.triangle_counting', UniformConcaveOn.strictConcaveOn, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, ContinuousOn.cfcβ_nnreal', EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, intervalIntegral.integral_const_of_cdf, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, inv_sqrt_one_add_tan_sq, dist_sq_of_inner_eq_zero, Metric.uniformity_basis_dist_pow, intervalIntegral.integral_const', RCLike.normSq_eq_def', sin_sq_le_sq, goldenConj_sq, Orientation.oangle_sub_left_smul_rotation_pi_div_two, sin_sq_le_one, tangentConeAt_real_subset_isRCLikeNormedField, Liouville.exists_pos_real_of_irrational_root, integral_withDensity_eq_integral_toReal_smul, ProbabilityTheory.HasSubgaussianMGF.cgf_le, ZLattice.covolume.tendsto_card_div_pow', PiLp.dist_sq_eq_of_L2, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, Unitization.nnreal_cfcβ_eq_cfc_inr, integral_sqrt_one_sub_sq, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, integrable_inv_one_add_sq, CStarModule.inner_smul_left_real, InnerProductSpace.HarmonicOnNhd.const_smul, MeasureTheory.setIntegral_indicatorConstLp, EuclideanGeometry.inversion_mul, cos_nat_mul_pi_sub, Complex.norm_add_mul_I, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, signedDist_smul, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_pos, HasFDerivWithinAt.arsinh, Orientation.oangle_add_right_smul_rotation_pi_div_two, hasStrictDerivAt_arctan, sin_bound, ContinuousMultilinearMap.norm_iteratedFDeriv_le, Orientation.inner_smul_rotation_pi_div_two_left, taylor_isLittleO, MeasureTheory.Supermartingale.smul_nonpos, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, ContDiffOn.norm_sq, isConformalMap_complex_linear_conj, trapezoidal_error_le, mellin_comp_rpow, MeasureTheory.Submartingale.sum_smul_sub', ContinuousMultilinearMap.norm_iteratedFDeriv_le', convex_RCLike_iff_convex_real, cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, intervalIntegral.smul_integral_comp_mul_add, EulerSine.integral_cos_pow_eq, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, SchwartzMap.tsupport_smulLeftCLM_subset, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, Probability.cauchyPDFReal_def', MeasureTheory.Measure.addHaar_smul_of_nonneg, Orientation.oangle_smul_right_of_neg, WithLp.prod_norm_sq_eq_of_L2, Complex.ofReal_comp_pow, sin_sq_add_cos_sq, ConvexBody.nonempty, MeasureTheory.integral_rnDeriv_smul, fourierCoeff_eq_intervalIntegral, CStarAlgebra.conjugate_le_norm_smul', ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, inner_sum_smul_sum_smul_of_sum_eq_zero, Complex.exp_bound, MeasureTheory.Measure.map_addHaar_smul, ContinuousLinearMap.intervalIntegral_apply, PMF.integral_eq_sum, MeasureTheory.average_add_measure, ProbabilityTheory.variance_le_expectation_sq, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, PiLp.norm_eq_of_nat, Continuous.cfcβ_nnreal_of_mem_nhdsSet, pi_lt_sqrtTwoAddSeries, FormalMultilinearSeries.isLittleO_of_lt_radius, aemeasurable_withDensity_iff, Complex.IsExpCmpFilter.isLittleO_im_pow_exp_re, Orientation.inner_sq_add_areaForm_sq, coe_fib_eq', signedDist_smul_of_neg, bernoulliFun_mul, ContinuousLinearMap.rotation_apply, norm_add_sq_real, hasFPowerSeriesOnBall_linear_zero, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, ODE.FunSpace.dist_iterate_next_le, CStarAlgebra.star_mul_le_algebraMap_norm_sq, HasStrictDerivAt.arsinh, fderiv_norm_smul, isMIntegralCurveAt_comp_mul_ne_zero, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, EuclideanSpace.ball_zero_eq, HasFDerivAt.hasFDerivAt_norm_smul, rpow_inv_natCast_pow, HurwitzZeta.hasSum_int_oddKernel, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, StarModule.complexToReal, IsMIntegralCurve.comp_mul, Complex.norm_sub_one_sq_eqOn_sphere, sum_mul_le_sqrt_mul_sqrt, MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, NumberField.Embeddings.coeff_bdd_of_norm_le, convex_parallelepiped, summable_geometric_of_abs_lt_one, cos_sq_le_one, SchwartzMap.pairing_continuous_left, integral_sin_pow_odd_mul_cos_pow, NumberField.exists_ideal_in_class_of_norm_le, SchwartzMap.integralCLM_apply, EulerSine.tendsto_integral_cos_pow_mul_div, ConvexBody.isClosed, cos_sq_add_sin_sq, summable_pow_div_factorial, norm_add_sq, RCLike.norm_sq_re_conj_add, summable_condensed_iff_of_nonneg, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, norm_jacobiThetaβ'_term_le, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.strong_law_Lp, geom_lt, lt_sqrt, ProbabilityTheory.moment_def, MeasureTheory.integral_const, tsum_geometric_inv_two, cos_pi_over_two_pow, CStarAlgebra.star_left_conjugate_le_norm_smul, one_sub_div_pow_le_exp_neg, sin_arccos, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, SchwartzMap.lineDerivOp_fourierInv_eq, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', EuclideanSpace.volume_ball, sqrt_le_left, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, Unitary.two_mul_one_sub_le_norm_sub_one_sq, ProbabilityTheory.condVar_bot', sq_sqrt', gaugeRescale_def, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, abs_cos_eq_sqrt_one_sub_sin_sq, ConvexBody.isCompact, Complex.coe_smul, AkraBazziRecurrence.deriv_smoothingFn, inner_vsub_vsub_left_eq_dist_sq_right_iff, OpenPartialHomeomorph.univUnitBall_apply, ProbabilityTheory.condVar_of_sigmaFinite, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, RCLike.inv_def, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, BoxIntegral.integralSum_smul, HasFDerivWithinAt.arctan, MeasureTheory.setIntegral_tilted', Complex.normSq_add_mul_I, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, tsum_sq_fourierCoeffOn, ProbabilityTheory.iteratedDeriv_two_cgf, ContinuousOn.integral_sub_linear_isLittleO_ae, exp_neg_mul_sq_isLittleO_exp_neg, integral_sin_mul_cos_sq, Nonneg.instNonUnitalContinuousFunctionalCalculus, Orientation.oangle_smul_smul_self_of_nonneg, quadratic_root_cos_pi_div_five, NNReal.coe_pow, rpow_sub_natCast', Complex.integrable_pow_mul_norm_one_add_mul_inv, MeasureTheory.Measure.addHaar_ball_mul_of_pos, iteratedDeriv_even_sin, AkraBazziRecurrence.dist_r_b, integrableOn_peak_smul_of_integrableOn_of_tendsto, cosh_arsinh, cosh_three_mul, ModelWithCorners.convex_range', isLittleO_pow_exp_pos_mul_atTop, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, parallelepiped_eq_sum_segment, ContDiffBump.convolution_eq_right, ExistsContDiffBumpBase.w_def, MeasureTheory.Measure.setIntegral_comp_smul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, lt_sq_of_sqrt_lt, isLittleO_pow_pow_of_lt_left, quadratic_le_exp_of_nonneg, one_sub_sq_div_two_lt_cos, summable_pow_mul_exp_neg_nat_mul, Monotone.tendsto_alternating_series_of_tendsto_zero, EuclideanGeometry.hasFDerivAt_inversion, dist_div_norm_sq_smul, cos_sub_nat_mul_pi, FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, two_mul_arctan_sub_pi, isLittleO_coe_const_pow_of_one_lt, sin_three_mul, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, ProbabilityTheory.IsGaussianProcess.smul, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, Orientation.two_zsmul_oangle_smul_right_self, HasFDerivAt.curveIntegral_segment_source', RCLike.norm_sq_eq_def, fib_golden_conj_exp, rexp_neg_quadratic_isLittleO_rpow_atTop, hasSum_one_div_nat_pow_mul_sin, SchwartzMap.fderivCLM_fourier_eq, two_mul_arctan_add_pi, CStarModule.inner_mul_inner_swap_le, ProbabilityTheory.strong_law_aux4, SchwartzMap.derivCLM_apply, Seminorm.gauge_ball, iteratedDeriv_exp_const_mul, integrableOn_Ioi_exp_neg_mul_sq_iff, MeasureTheory.integral_fun_fst, SmoothPartitionOfUnity.contMDiff_finsum_smul, MeasureTheory.pdf.integrable_pdf_smul_iff, ProbabilityTheory.mgf_sum_of_identDistrib, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, hasDerivAt_arctan', Complex.GammaSeq_eq_approx_Gamma_integral, SimpleGraph.triangleRemovalBound_le, Wallis.W_eq_factorial_ratio, ProbabilityTheory.condVar_bot_ae_eq, hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, le_pow_of_log_le, Seminorm.finset_sup_smul, CStarAlgebra.conjugate_le_norm_smul, Complex.exp_bound', hasSum_zeta_two, Seminorm.isBounded_sup, norm_midpoint_lt_iff, MeasureTheory.integral_comp_mul_right_Ioi, HasFDerivAt.arsinh, cos_lt_one_div_sqrt_sq_add_one, MeasureTheory.Submartingale.sum_smul_sub, IsApproximateSubgroup.card_pow_le, integral_one_div_one_add_sq, EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_mem, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, MeasureTheory.integrable_withDensity_iff_integrable_coe_smulβ, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, intervalIntegral.intervalIntegrable_pow, MeasureTheory.integral_countable, NumberField.abs_discr_ge_of_isTotallyComplex, CompactlySupportedContinuousMap.toReal_smul, tendsto_sum_pi_div_four, norm_cfcβ_one_sub_one_add_inv_lt_one, rpow_neg_one_add_norm_sq_le, Complex.dist_mk, continuousOn_cfcβ_nnreal, DifferentiableWithinAt.norm_sq, surjOn_extremePoints_image, BoxIntegral.Integrable.smul, isMIntegralCurveOn_comp_mul_ne_zero, integral_sin_pow_succ_le, ProbabilityTheory.integrable_pow_abs_mul_exp_of_integrable_exp_mul, tendsto_mul_exp_add_div_pow_atTop, cos_two_mul, LiouvilleNumber.partialSum_succ, rpow_ofNat, tendsto_div_pow_mul_exp_add_atTop, hasFDerivAt_integral_of_dominated_of_fderiv_le, IsScalarTower.complexToReal, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, Polynomial.coeff_bdd_of_roots_le, tendsto_pow_const_mul_const_pow_of_lt_one, VectorFourier.fourierPowSMulRight_apply, inner_eq_norm_mul_iff_real, MeasureTheory.Submartingale.smul_nonpos, polarCoord_apply, SchwartzMap.decay, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, SzemerediRegularity.pow_mul_m_le_card_part, Asymptotics.isLittleO_norm_pow_id, EuclideanSpace.dist_eq, Chebyshev.integral_theta_div_log_sq_isBigO, sin_sub_nat_mul_pi, norm_pow_le', Filter.Tendsto.integral_sub_linear_isLittleO_ae, Complex.isometryOfOrthonormal_apply, intervalIntegral.smul_integral_comp_mul_right, sin_sq_lt_sq, intervalIntegral.integral_comp_div_add, cosh_sq', integral_gaussian, hasDerivAt_tan_of_mem_Ioo, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, dimH_segment, HasFDerivAt.hasFDerivAt_norm_smul_neg, ModularForm.prod_fintype_slash, integral_sin_sq_mul_cos, RCLike.re_ofReal_pow, hasSum_sin, RCLike.norm_sq_re_add_conj, sqrt_sq, pow_le_iff_le_log, rpow_sub_natCast, hasSum_geometric_of_abs_lt_one, MeasureTheory.integrable_comp_smul_iff, Chebyshev.integral_theta_div_log_sq_isLittleO, cfcβ_nnreal_eq_real, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, EulerSine.integral_cos_pow_pos, IsMIntegralCurveAt.comp_mul_ne_zero, sin_sq_pi_over_two_pow, sq_sin_pi_div_three, stereographic_apply, ModularGroup.three_le_four_mul_im_sq_of_mem_fd, OrthogonalFamily.norm_sum, Orientation.rotation_apply, SameRay.norm_smul_eq, tendsto_pow_logb_div_mul_add_atTop, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Stirling.log_stirlingSeq_diff_le_geo_sum, hasSum_sq_fourierCoeff, ProbabilityTheory.strong_law_aux1, MeasureTheory.withDensityα΅₯_rnDeriv_smul, StrongConvexOn.strictConvexOn, ProbabilityTheory.mgf_gaussianReal, PiLp.dist_eq_of_L2, ContinuousLinearMap.reApplyInnerSelf_smul, MeasureTheory.integral_indicator_const, EReal.coe_pow, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, MeasureTheory.integrable_rnDeriv_smul_iff, ProbabilityTheory.strong_law_ae_simpleFunc_comp, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, log_pow, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, ProbabilityTheory.variance_linearMap_gaussianReal, Complex.norm_log_one_sub_inv_sub_self_le, MeasureTheory.Measure.addHaar_closedBall, ProbabilityTheory.mgf_id_gaussianReal, exp_bound', sum_div_pow_sq_le_div_sq, Behrend.bound_aux, sin_nat_mul_pi_sub, Polynomial.cyclotomic_eval_le_add_one_pow_totient, SchwartzMap.tsupport_derivCLM_subset, Filter.Tendsto.cesaro_smul, setOf_liouville_eq_iInter_iUnion, hasSum_arctan, ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul, SchwartzMap.le_seminorm', imaginaryPart_smul, NumberField.mixedEmbedding.norm_real, rpow_add_natCast, integral_inv_one_add_sq, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, iteratedDeriv_odd_sin, EuclideanSpace.dist_sq_eq, summable_geometric_two', Orientation.two_zsmul_oangle_smul_left_self, Finset.small_pow_of_small_tripling, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, Antitone.cauchySeq_alternating_series_of_tendsto_zero, ProbabilityTheory.strong_law_aux2, one_div_sub_pow_hasFPowerSeriesOnBall_zero, Complex.norm_exp_sub_one_sub_id_le, Unitization.norm_splitMul_snd_sq, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Unitary.norm_argSelfAdjoint, UnitAddTorus.hasSum_sq_mFourierCoeff, fourierCoeffOn_eq_integral, HurwitzKernelBounds.F_nat_zero_le, MeasureTheory.SimpleFunc.integral_const, rpow_pow_comm, tendsto_pow_const_div_const_pow_of_one_lt, integral_sin_pow_odd, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, Orientation.oangle_sign_smul_add_smul_right, realPart_apply_coe, intervalIntegral.integral_comp_mul_right, exp_one_near_10, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, VectorFourier.norm_fourierPowSMulRight_le, EuclideanGeometry.dist_smul_vadd_eq_dist, MeasureTheory.integral_singleton, summable_pow_mul_jacobiThetaβ_term_bound, intervalIntegral.integral_comp_div_sub, circleMap_zero_pow, integrable_exp_neg_mul_sq_iff, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, ConvexBody.hausdorffDist_coe, cos_sq, AffineSubspace.mem_perpBisector_iff_inner_eq, InnerProductSpace.volume_closedBall, cantorSequence_eq_self_sub_sum_cantorToTernary, ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, WithCStarModule.pi_norm_sq, NormedSpace.norm_smul_normalize, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, LinearMap.mem_span_iff_bound, homeomorphSphereProd_apply_fst_coe, MeasureTheory.Measure.volumeIoiPow_apply_Iio, ContinuousOn.cfcβ_nnreal, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, taylor_mean_remainder_cauchy, abs_ofDigits_sub_ofDigits_le, SchwartzMap.smulLeftCLM_sub, summable_geometric_two, MeasureTheory.Egorov.exists_notConvergentSeq_lt, SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, tendsto_card_div_pow_atTop_volume', strongConvexOn_zero, SchwartzMap.fourier_fderivCLM_eq, ProbabilityTheory.evariance_mul, ConvexBody.hausdorffEDist_coe, sum_range_sub_log_div_le, exp_one_pow, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MeasureTheory.SimpleFunc.integral_eq, exp_approx_end, integrableOn_rpow_mul_exp_neg_mul_sq, le_geom, integral_withDensity_eq_integral_toReal_smulβ, summable_one_div_nat_pow, hasStrictDerivAt_tan, InnerProductSpace.volume_closedBall_of_dim_odd, real_inner_smul_left, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, Polynomial.sub_one_pow_totient_lt_cyclotomic_eval, tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Irreducible.maximalIdeal_pow_eq_closedBall_pow, zero_lt_one_add_norm_sq, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, ConvexBody.hausdorffEdist_coe, fderiv_norm_smul_pos, integral_Ioi_inv_one_add_sq, hasDerivAt_arctan, MeasureTheory.Measure.addHaar_closedBall_mul, Complex.volume_sum_rpow_lt_one, taylor_mean_remainder_bound, Mathlib.Meta.NormNum.IsNat.rpow_eq_pow, CStarAlgebra.star_right_conjugate_le_norm_smul, NNReal.instContinuousMapZero.UniqueHom, MeasureTheory.integral_comp_mul_left_Ioi, ContinuousMapZero.toNNReal_neg_smul, ProbabilityTheory.integrable_pow_abs_mul_exp_add_of_integrable_exp_mul, UpperHalfPlane.dist_coe_center_sq, MeasureTheory.SimpleFunc.map_integral, FormalMultilinearSeries.summable_norm_mul_pow, IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, norm_add_pow_two, setOf_liouville_eq_irrational_inter_iInter_iUnion, MeasureTheory.measure_smul_setAverage, MeasureTheory.Integrable.comp_smul, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, unitary.norm_sub_one_sq_eq, deriv_arcsin_aux, exp_approx_end', MeasureTheory.Measure.setIntegral_comp_smul_of_pos, intervalIntegral.integral_comp_mul_add, tsum_sq_fourierCoeff, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, MeasureTheory.Measure.addHaar_ball, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, sqrt_lt, integral_gaussian_Ioi, MeasureTheory.condExp_bot', Polynomial.Chebyshev.coeff_le_of_forall_abs_le_one, SchwartzMap.smulLeftCLM_ofReal, Orientation.oangle_smul_right_of_pos, realPart_smul, PiCountable.dist_eq_tsum, abs_real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivAt.hasFDerivAt_norm_smul_pos, integrable_exp_neg_mul_sq, Complex.norm_eq_sqrt_sq_add_sq, UpperHalfPlane.cosh_dist', EuclideanGeometry.dist_center_inversion, hasSum_pow_div_log_of_abs_lt_one, MeasureTheory.integral_finset, tanh_sq_lt_one, Orientation.inner_smul_rotation_pi_div_two_smul_right, GaussianFourier.verticalIntegral_norm_le, ContinuousAt.integral_sub_linear_isLittleO_ae, SchwartzMap.integrable_pow_mul, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, cosh_sq_sub_sinh_sq, ContinuousMapZero.toNNReal_smul, integral_sin_sq_mul_cos_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, fderivWithin_arctan, TFAE_exists_lt_isLittleO_pow, integral_mul_rpow_one_add_sq, MeasureTheory.measureReal_biUnion_eq_sum_powerset, ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, inner_vsub_vsub_left_eq_dist_sq_left_iff, summable_geometric_of_lt_one, ConvexBody.coe_add, ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp, norm_sub_pow_two, isConformalMap_complex_linear, SchwartzMap.smulLeftCLM_apply, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, ProbabilityTheory.integrable_pow_of_integrable_exp_mul, Chebyshev.intervalIntegrable_one_div_log_sq, MeasureTheory.condExpIndSMul_ae_eq_smul, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, NumberField.InfinitePlace.prod_eq_abs_norm, integral_Iic_inv_one_add_sq, pow_lt_of_lt_log, Monotone.cauchySeq_alternating_series_of_tendsto_zero, tendsto_pow_log_div_mul_add_atTop, SmoothPartitionOfUnity.contMDiff_smul, isLittleO_pow_const_const_pow_of_one_lt, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, interval_average_eq, IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq, NumberField.mulHeightβ_eq, TemperedDistribution.derivCLM_apply_apply, integral_cos_sq, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, MeasureTheory.Supermartingale.smul_nonneg, arcsin_eq_arctan, ruzsaSzemerediNumberNat_asymptotic_lower_bound, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, cos_eq_sqrt_one_sub_sin_sq, MeasureTheory.weightedSMul_smul_measure, tanh_arsinh, cosh_eq_tsum, posLog_pow, PiLp.norm_eq_of_L2, sinh_three_mul, zero_lt_one_add_norm_sq', MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Finset.small_nsmul_of_small_tripling, isLittleO_pow_log_id_atTop, Asymptotics.IsBigO.pow_of_le_right, EuclideanGeometry.dist_inversion_center, Orientation.oangle_smul_right_self_of_nonneg, Complex.ofReal_pow, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', tendsto_const_div_pow, Asymptotics.isLittleO_pow_sub_sub, MeasureTheory.integrable_fun_norm_addHaar, hasSum_zeta_nat, CFC.abs_smul, ZLattice.sum_piFinset_Icc_rpow_le, fib_succ_sub_goldenConj_mul_fib, tan_arcsin, Orientation.oangle_sign_smul_add_smul_left, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, MeasureTheory.average_union_mem_openSegment, MeasureTheory.MemLp.integrable_norm_pow', ConvexBody.coe_nsmul, CFC.negPart_smul_of_nonneg, Metric.uniformity_basis_dist_le_pow, sqrt_one_add_norm_sq_le, MeasureTheory.integral_fun_snd, ZLattice.covolume.tendsto_card_div_pow'', LiouvilleNumber.remainder_lt, real_inner_smul_self_right, dist_smul_add_one_sub_smul_le, integral_cos_sq_sub_sin_sq, exists_extension_norm_eq, Seminorm.convex_closedBall, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, nnnorm_cfcβ_nnreal_le, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, MeasureTheory.average_union, OpenPartialHomeomorph.univUnitBall_symm_apply, SmoothBumpCovering.embeddingPiTangent_coe, ENNReal.ofReal_pow, isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt, volume_pi_closedBall, apply_le_nnnorm_cfcβ_nnreal, taylor_mean_remainder_lagrange, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Function.hasTemperateGrowth_one_add_norm_sq_rpow, Orientation.two_zsmul_oangle_smul_smul_self, SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, Orientation.rotation_symm_apply, HurwitzZeta.hasSum_nat_cosKernelβ, uniformity_basis_dist_pow_of_lt_one, fib_succ_sub_goldenRatio_mul_fib, continuousOn_cfcβ_nnreal_setProd, tendsto_factorial_div_pow_self_atTop, EuclideanGeometry.inversion_eq_lineMap, inner_eq_norm_sq_right_iff, Complex.norm_sub_one_sq_eq_of_norm_one, WithLp.prod_norm_eq_of_L2, cos_sq_arctan, dist_sq_lineMap_of_inner_eq_zero, Rat.AbsoluteValue.apply_le_sum_digits, Orientation.oangle_sign_smul_sub_right, MonotoneOn.nnnorm_cfcβ, seminormFromConst_seq_def, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, exp_sub_sum_range_isBigO_pow, SchwartzMap.one_add_le_sup_seminorm_apply, gaugeRescale_smul, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, padicNorm_two_harmonic, taylor_within_apply, exp_nat_mul, hasDerivWithinAt_arccos_Iic, Complex.approx_Gamma_integral_tendsto_Gamma_integral, cosh_two_mul, Orthonormal.sum_inner_products_le, ProbabilityTheory.variance_smul, Affine.Simplex.ninePointCircle_center, MeasureTheory.integral_smul_measure, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, sinh_artanh, Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_one, SchwartzMap.integrable_pow_mul_iteratedFDeriv, deriv_tan, gold_pow_sub_gold_pow, OrthogonalFamily.summable_iff_norm_sq_summable, isLittleO_pow_logb_id_atTop, Stirling.second_wallis_limit, integral_sin_pow_antitone, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, Function.HasTemperateGrowth.isBigO_uniform, InnerProductSpace.volume_ball_of_dim_even, integral_pow_abs_sub_uIoc, ProbabilityTheory.variance_const_mul, EuclideanSpace.volume_closedBall, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, Orientation.rotationAux_apply, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, sin_eq_sqrt_one_sub_cos_sq, integral_comp_pi_polarCoord_symm, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, ODE.FunSpace.dist_iterate_next_apply_le, MeasureTheory.charFun_map_smul, convex_closedBall, one_div_sub_sq_hasFPowerSeriesOnBall_zero, sameRay_iff_norm_smul_eq, cos_two_mul', rpow_natCast, SimpleGraph.triangle_counting, sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, MeasureTheory.volume_sum_rpow_lt_one, MeasureTheory.integral_countable', cantorSequence_get_succ, isBigO_rpow_zero_log_smul, unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, ConvexBody.coe_smul', MeasureTheory.SignedMeasure.toJordanDecomposition_smul, cosh_artanh, Metric.nhds_basis_ball_pow, CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, rpow_natCast_mul, geom_goldenConj_isSol_fibRec, hasSum_log_sub_log_of_abs_lt_one, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, fderiv_norm_sq_apply, RightDerivMeasurableAux.le_of_mem_A, mul_pow_le_nat_floor_pow, aestronglyMeasurable_withDensity_iff, integral_sin_pow_even, Affine.Simplex.points_vsub_eulerPoint, bernoulliFun_eval_half, InnerProductGeometry.angle_smul_left_of_pos, cos_bound, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, fderiv_norm_sq, Seminorm.smul_le_smul, Complex.ofReal_choose, inner_vsub_vsub_right_eq_dist_sq_right_iff, MeasureTheory.condExp_bot_ae_eq, Function.HasTemperateGrowth.isBigO, LiouvilleNumber.remainder_lt', Orientation.inner_mul_inner_add_areaForm_mul_areaForm', hasSum_L_function_mod_four_eval_three, hasDerivWithinAt_arcsin_Iic, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, NumberField.IsCMField.regOfFamily_realFunSystem, Orientation.oangle_smul_left_of_pos, ContinuousAlternatingMap.norm_image_sub_le, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', hasSum_geometric_of_lt_one, summable_geometric_two_encode, HasCompactSupport.hasFDerivAt_convolution_left, Bundle.ContinuousRiemannianMetric.isVonNBounded, TemperedDistribution.smulLeftCLM_apply_apply, isBigO_pow_pow_of_le_left, Complex.UnitDisc.sq_norm_lt_one, tendsto_one_add_div_pow_exp, tendsto_pow_mul_exp_neg_atTop_nhds_zero, Orientation.inner_mul_areaForm_sub, MeasureTheory.Measure.addHaar_closedBall', ofDigits_digits_sum_eq, uniformConvexOn_zero, lt_pow_iff_log_lt, NumberField.mixedEmbedding.norm_apply, deriv2_sqrt_mul_log, EisensteinSeries.div_max_sq_ge_one, BoxIntegral.unitPartition.tag_mem_smul_span, SchwartzMap.norm_pow_mul_le_seminorm, Continuous.cfcβ_nnreal', intervalIntegral.inv_smul_integral_comp_add_div, hasFDerivAt_integral_of_dominated_loc_of_lip, norm_jacobiThetaβ_term_fderiv_le, GaussianFourier.integral_rexp_neg_mul_sq_norm, Complex.exp_bound_sq, bernsteinApproximation.apply, HurwitzZeta.hasSum_int_evenKernelβ, sin_sq_pi_over_two_pow_succ, MeasureTheory.Measure.addHaar_real_closedBall, Orthonormal.tsum_inner_products_le, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, Complex.dist_eq_re_im, cos_arctan, goldenRatio_sq, MeasureTheory.average_eq, AkraBazziRecurrence.isLittleO_self_div_log_id, MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOn, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, intervalIntegral.smul_integral_comp_add_mul, MeasureTheory.Measure.integral_comp_inv_mul_right, Besicovitch.SatelliteConfig.exists_normalized_aux3, Probability.cauchyPDFReal_def, IsApproximateAddSubgroup.of_small_tripling, ProbabilityTheory.integral_tilted_mul_eq_cgf, MeasureTheory.Measure.addHaar_smul, one_add_norm_le_sqrt_two_mul_sqrt, MeasureTheory.Measure.addHaar_image_homothety, Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, MeasureTheory.setIntegral_const, norm_combo_lt_of_ne, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq
bridge: BoxIntegral.hasIntegralIndicatorConst
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instMonoidWithZero π | CompOp | 1 mathmath: BoundingSieve.nu_mult
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instMul π | CompOp | 2318 mathmath: List.norm_prod_le, cos_add_nat_mul_pi, SchwartzMap.norm_toLp_le_seminorm, Behrend.roth_lower_bound, EuclideanGeometry.Sphere.mul_dist_eq_abs_power, Convex.norm_image_sub_le_of_norm_derivWithin_le, Polynomial.Chebyshev.isExtrOn_T_real_iff, HurwitzZeta.isBigO_atTop_evenKernel_sub, norm_sub_sq_real, BoundedContinuousFunction.tietze_extension_step, Circle.periodic_exp, norm_smul_le, le_log_one_add_of_nonneg, abs_exp_sub_one_le, PiLp.norm_toLp_const', EuclideanGeometry.dist_smul_vadd_sq, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, real_inner_div_norm_mul_norm_eq_neg_one_iff, isBigO_log_mul_const_log_atTop, EuclideanGeometry.sin_oangle_right_mul_dist_of_oangle_eq_pi_div_two, rpow_add_of_nonneg, Polynomial.mahlerMeasure_def_of_ne_zero, Height.logHeightβ_pow, deriv_exp, Complex.mul_im, AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound, ContinuousLinearMap.le_of_opNorm_le_of_le, sin_add_sin, Complex.norm_circleTransformBoundingFunction_le, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, Complex.re_mul_ofReal, HasDerivAt.const_rpow, expNear_succ, goldenConj_mul_fib_succ_add_fib, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, ProbabilityTheory.gaussianReal_map_const_mul, InformationTheory.integral_llr_add_mul_log_nonneg, norm_torusIntegral_le_of_norm_le_const, HasCompactSupport.convolution_integrand_bound_left, Besicovitch.SatelliteConfig.hlast', mellin_eq_fourier, HasDerivWithinAt.liminf_right_slope_norm_le, LipschitzOnWith.norm_sub_le, Complex.isTheta_exp_arg_mul_im, RCLike.normSq_to_real, MeasureTheory.norm_indicatorConstLp_le, ProbabilityTheory.gammaPDF_of_nonneg, deriv_arctan, iteratedDeriv_odd_cos, MeasureTheory.charFun_eq_fourierIntegral', MeasureTheory.Integrable.comp_mul_left', real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, norm_zsmul, HasStrictDerivAt.rpow, bernoulliFun_eval_one_sub, dist_midpoint_right, sqrt_eq_cases, TsirelsonInequality.sqrt_two_inv_mul_self, ContinuousLinearMap.exists_preimage_norm_le, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, Convex.norm_image_sub_le_of_norm_fderivWithin_le', ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, smul_map_volume_mul_right, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, hasDerivAt_sqrt_mul_log, HurwitzZeta.hasSum_int_cosKernelβ, ProbabilityTheory.aemeasurable_exp_mul, Complex.norm_sub_one_sq_eq_of_norm_eq_one, MeasureTheory.Measure.integral_comp_mul_right, ProbabilityTheory.betaPDF_eq, hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, HurwitzZeta.LSeriesHasSum_cos, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, rpow_add_natCast', Complex.normSq_natCast, fourierIntegralInv_eq', ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_le, sin_add_two_pi, Height.mulHeightβ_eq, ProbabilityTheory.gaussianReal_const_mul, ProbabilityTheory.condIndep_iff, integral_sin_mul_cosβ, EuclideanGeometry.dist_inversion_inversion, Stirling.factorial_isEquivalent_stirling, MeasureTheory.Submartingale.sum_mul_sub', AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, ProbabilityTheory.covarianceBilinDual_apply', sinh_add, spectrum.subset_closedBall_norm_mul, norm_jacobiThetaβ_term_le, RightDerivMeasurableAux.norm_sub_le_of_mem_A, ProbabilityTheory.mgf_const_add, InnerProductSpace.Core.inner_mul_inner_self_le, Complex.norm_sub_mem_Icc_angle, cos_eq_zero_iff, Angle.cos_add, conformalAt_iff, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, rpow_eq_nhds_of_neg, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, young_inequality, norm_jacobiThetaβ_term_fderiv_ge, NormedAddGroupHom.norm_comp_le, le_log_of_zpow_le, CFC.tendsto_cfc_rpow_sub_one_log, integrableOn_exp_mul_Iic, dist_mulExpNegMulSq_le_two_mul_sqrt, Complex.norm_mul_self_eq_normSq, intervalIntegral.mul_integral_comp_mul_sub, BoxIntegral.unitPartition.mem_box_iff', log_div_le_sum_range_add, norm_iteratedFDerivWithin_smul_le, BumpCovering.toPartitionOfUnity_apply, ENNReal.rpow_mul, tan_int_mul_pi, ContinuousMultilinearMap.norm_map_snoc_le, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, NumberField.norm_norm_le_norm_mul_house_pow, countingFunction_finsum_eq_finsum_add, HasDerivWithinAt.cosh, AddCircle.homeomorphCircle'_apply_mk, hasStrictDerivAt_rpow_const_of_ne, UpperHalfPlane.image_coe_sphere, dist_smul_le, norm_natCast_eq_mul_norm_one, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, hasDerivWithinAt_taylorWithinEval, toNNReal_mul, Matrix.l2_opNorm_mulVec, sin_periodic, ENNReal.rpow_intCast_mul, Complex.locally_lipschitz_exp, dist_sq_lineMap_lineMap_of_inner_eq_zero, InformationTheory.mul_log_le_klDiv, circleIntegral_def_Icc, integral_exp_mul_Iic, EuclideanGeometry.law_sin, Orientation.sin_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two, Seminorm.ball_smul_closedBall, Gamma_nat_add_half, circleIntegrable_iff, ProbabilityTheory.covarianceBilinDual_apply, Complex.exp_re, CircleDeg1Lift.iterate_pos_le_iff, LipschitzWith.dist_le_mul, PiLp.norm_toLp_one, norm_iteratedFDeriv_comp_le', real_inner_smul_self_left, norm_iteratedFDeriv_mul_le, Irrational.ratCast_mul, CircleDeg1Lift.iterate_eq_of_map_eq_add_int, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, exp_mul, ContinuousLinearMap.norm_compLp_le, one_add_mul_le_cos, Affine.Simplex.dist_point_faceOppositeCentroid, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, Circle.exp_natCast_mul, cos_int_mul_two_pi, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, SeparationQuotient.norm_liftNormedAddGroupHom_apply_le, Orientation.areaForm_le, diam_smulβ, NumberField.dedekindZeta_residue_def, CircleDeg1Lift.iterate_pos_lt_iff, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero, EisensteinSeries.summand_bound_of_mem_verticalStrip, MeasureTheory.norm_setToFun_le_mul_norm', InnerProductGeometry.sin_angle, le_pow_iff_log_le, MeasureTheory.norm_indicatorConstLp, norm_iteratedFDerivWithin_clm_apply, mul_log_nonneg, dist_left_midpoint, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, UpperHalfPlane.dist_le_iff_dist_coe_center_le, Complex.angle_exp_one, AkraBazziRecurrence.tendsto_atTop_sumCoeffsExp, hasDerivAt_bernoulliFun, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, continuous_mul_log, norm_iteratedFDerivWithin_comp_le_aux, ContinuousMap.dist_le_two_norm, MeasureTheory.pdf.integral_mul_eq_integral, ProbabilityTheory.uncenteredCovarianceBilin_apply, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, selfAdjoint.norm_sq_expUnitary_sub_one, SchwartzMap.decay', Complex.mul_re, derivWithin_arctan, Behrend.roth_lower_bound_explicit, ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, goldenRatio_mul_goldenConj, intervalIntegral.integral_comp_mul_left, Antitone.tendsto_alternating_series_of_tendsto_zero, UpperHalfPlane.im_smul_eq_div_normSq, BoxIntegral.unitPartition.mem_smul_span_iff, intervalIntegral.integral_comp_mul_sub, exists_eq_const_mul_intervalIntegral_of_nonneg, AkraBazziRecurrence.isBigO_apply_r_sub_b, NumberField.Units.regOfFamily_eq_det, Affine.Triangle.dist_point_faceOppositeCentroid, OrderedFinpartition.norm_applyOrderedFinpartition_le, rpow_eq_const_mul_integral, MeasureTheory.pdf.IsUniform.mul_pdf_integrable, HasDerivWithinAt.liminf_right_norm_slope_le, ProbabilityTheory.mgf_dirac, isIntegral_two_mul_sin_rat_mul_pi, MeasureTheory.toReal_rnDeriv_tilted_left, PowerSeries.gaussNorm_monomial, LipschitzWith.norm_sub_le_of_le, MeasureTheory.Integrable.simpleFunc_mul', LiouvilleWith.mul_int_iff, Module.Basis.exists_opNorm_le, Height.logHeightβ_sum_le, Orientation.sin_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, Height.logHeightβ_add_le, tendsto_tsum_powerSeries_nhdsWithin_lt, hasSum_log_one_add_inv, Differentiable.fderiv_norm_rpow, integral_log_sin_zero_pi_div_two, FDerivMeasurableAux.le_of_mem_A, mulRight_bound, MeasureTheory.Submartingale.mul_integral_upcrossingsBefore_le_integral_pos_part, sin_two_pi, HasConstantSpeedOnWith.ratio, norm_add_pow_two_real, Besicovitch.SatelliteConfig.hlast, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, BohrMollerup.le_logGammaSeq, tan_sub', NNReal.rpow_intCast_mul, norm_cexp_neg_mul_sq, norm_smul, ProbabilityTheory.cgf_gaussianReal, MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul, rpow_def_of_pos, UpperHalfPlane.moebius_im, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, ProbabilityTheory.HasSubgaussianMGF.mgf_le, norm_sub_mul_self, NumberField.abs_discr_ge', ProbabilityTheory.covariance_mul_right, Metric.diam_le_of_subset_closedBall, monomial_has_deriv_aux, vector_fourierIntegral_eq_integral_exp_smul, MeasureTheory.Integrable.comp_mul_right', PiTensorProduct.projectiveSeminormAux_smul, hasDerivAt_mul_log, iInf_mul_of_nonneg, fourier_real_eq_integral_exp_smul, Dilation.mapsTo_sphere, NumberField.abs_discr_ge, derivWithin_cosh, inner_lt_norm_mul_iff_real, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, AddCircle.homeomorphCircle'_symm_apply, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, Complex.normSq_ratCast, MeasureTheory.Measure.toSphere_real_apply_univ, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, log_mul_self_monotoneOn, unitInterval.mul_mem, Height.logHeightβ_sub_le, norm_iteratedFDeriv_clm_apply, AntilipschitzWith.mul_le_dist, deriv_sqrt_mul_log, ProbabilityTheory.cdf_expMeasure_eq, volume_closedBall, Function.Periodic.norm_qParam_lt_iff, InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero, mulExpNegSq_apply, Circle.isAddQuotientCoveringMap_exp, ProbabilityTheory.covariance_mul_left, MeasureTheory.Submartingale.sum_upcrossingStrat_mul, Convex.image_sub_le_mul_sub_of_deriv_le, hasStrictFDerivAt_rpow_of_pos, rpow_sum_le_const_mul_sum_rpow_of_nonneg, Asymptotics.IsBigOWith_def, integrable_prod_sub, abs_setIntegral_mulExpNegMulSq_comp_sub_le_mul_measure, Complex.normSq_mk, RCLike.smul_re, mellin_convergent_zero_of_isBigO, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, integral_exp_neg_mul_rpow, HurwitzKernelBounds.isBigO_atTop_F_int_one, RCLike.realRingEquiv_symm_apply, summable_condensed_iff_of_eventually_nonneg, NumberField.prod_abs_eq_one, Stirling.log_stirlingSeq_formula, exp_bound, cos_add_int_mul_two_pi, Polynomial.Chebyshev.integral_measureT, volume_pi_ball, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, list_prod_map_rpow', ProbabilityTheory.HasSubgaussianMGF.const_mul, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, parallelogram_law_with_norm, List.norm_prod_le', Seminorm.closedBall_smul_ball, InformationTheory.klFun_apply, Complex.integral_rpow_mul_exp_neg_rpow, IsBoundedBilinearMap.isBigO_comp, Behrend.log_two_mul_two_le_sqrt_log_eight, logb_mul, Circle.exp_eq_exp, Seminorm.bound_of_continuous_normedSpace, Complex.volume_sum_rpow_le, HasDerivWithinAt.sin, Similar.exists_pos_dist_eq, Besicovitch.SatelliteConfig.h, zpow_le_iff_le_log, LipschitzWith.dist_le_mul_of_le, Complex.norm_log_one_add_le, dist_inv_invβ, Complex.mul_angle_le_norm_sub, tendsto_self_mul_const_pow_of_lt_one, AkraBazziRecurrence.GrowsPolynomially.const_mul, Polynomial.Chebyshev.isLocalMin_T_real, Complex.integral_circleTransform, NormedField.norm_mul, norm_pow_le_mul_norm, HasDerivAt.arctan, Polynomial.toAddCircle_X_pow_eq_fourier, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, MeasureTheory.Integrable.simpleFunc_mul, NNReal.rpow_mul_intCast, HasDerivAt.sqrt, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, Angle.toReal_coe, Polynomial.le_gaussNorm, RCLike.norm_sq_eq_def_ax, rpow_mul_intCast, MeromorphicOn.extract_zeros_poles_log, Circle.exp_two_pi_mul_int, SemilinearMapClass.bound_of_continuous, integral_rpow_mul_exp_neg_rpow, AddCircle.scaled_exp_map_periodic, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, ae_eq_const_or_norm_setIntegral_lt_of_norm_le_const, GammaIntegral_convergent, CStarRing.norm_mul_self_le, Affine.Simplex.dist_circumcenter_sq_eq_sq_sub_circumradius, LiouvilleNumber.aux_calc, AlgebraNormClass.map_smul_eq_mul, sin_add_int_mul_pi, antilipschitzWith_iff_le_mul_dist, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, image_circleMap_Ioc, inner_mul_inner_self_le, gold_mul_goldConj, integral_cos_pow, cos_nat_mul_two_pi_sub_pi, NumberField.mixedEmbedding.convexBodySumFun_apply', Stirling.log_stirlingSeq_diff_hasSum, AntilipschitzWith.le_mul_norm, log_list_prod, norm_sub_pow_two_real, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, zpow_lt_iff_lt_log, ContinuousLinearMap.le_opNorm, RCLike.mul_im_ax, artanh_eq_half_log, LipschitzWith.le_add_mul, Complex.sin_bound, MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, tan_int_mul_pi_div_two, cos_add_two_pi, ofCauchy_mul, isIntegral_two_mul_cos_rat_mul_pi, MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae', MeasureTheory.L1.setToL1_smul_left, HurwitzZeta.hasSum_nat_sinZeta, norm_sub_le_mul_volume_of_norm_lineDeriv_le, MeasureTheory.Measure.addHaar_ball_mul, EisensteinSeries.r1_aux_bound, norm_sub_sq, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le, rpowIntegrandββ_le_rpow_sub_two_mul_self, norm_curveIntegral_segment_le, irrational_mul_natCast_iff, Complex.log_exp_eq_re_add_toIocMod, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, not_continuousAt_deriv_mul_log_zero, ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, Gamma_mul_Gamma_add_half, CovByVAdd.trans, spectrum.norm_le_norm_mul_of_mem, two_mul_arctan_inv_2_sub_arctan_inv_7, AntilipschitzWith.le_mul_dist, norm_iteratedFDerivWithin_clm_apply_const, blimsup_thickening_mul_ae_eq_aux, EuclideanGeometry.Sphere.mul_dist_eq_neg_power_of_dist_center_le_radius, Complex.normSq_mul, sin_add_nat_mul_pi, cos_nat_mul_pi, set_smul_sphere_zero, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, IsBoundedBilinearMap.isBigO', Irrational.mul_intCast, ProbabilityTheory.mgf_const, Irrational.intCast_mul, ProbabilityTheory.centralMoment_one', CircleDeg1Lift.le_iterate_of_add_int_le_map, LipschitzWith.norm_div_le, similar_iff_exists_dist_eq, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero, Asymptotics.isLittleO_iff_nat_mul_le, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, LiouvilleWith.mul_nat, AddCircle.norm_div_natCast, Stirling.le_log_factorial_stirling, ProbabilityTheory.variance_le_sub_mul_sub, abs_real_inner_le_norm, MeasureTheory.Measure.integral_comp_inv_mul_left, curveIntegralFun_trans_aeeq_right, UpperHalfPlane.dist_eq_iff_eq_sinh, Module.Basis.norm_mul_le_const_mul_norm, ZLattice.tsum_norm_rpow_le, smul_closedBall', integral_sin_sq, norm_add_eq_sqrt_iff_real_inner_eq_zero, EuclideanSpace.volume_closedBall_fin_three, norm_lineDeriv_le_of_lipschitz, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, real_inner_mul_inner_self_le, Polynomial.Chebyshev.T_real_cos, rescale_to_shell_semi_normed_zpow, HasDerivWithinAt.cos, arith_mean_weighted_of_constant, uniformContinuous_const_mul, volume_preimage_mul_left, InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_norm, HasStrictDerivAt.arctan, dist_pair_smul, FDerivMeasurableAux.norm_sub_le_of_mem_A, ENNReal.ofReal_mul, deriv_norm_ofReal_cpow, Asymptotics.isBigO_iff, gronwallBound_of_K_ne_0, exp_list_sum, NonUnitalSeminormedRing.norm_mul_le, MeasureTheory.integral_mul_upcrossingsBefore_le_integral, deriv_sqrt_aux, norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, ContinuousMap.HomotopyRel.trans_apply, Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, tan_nat_mul_pi_sub, LinearEquiv.toSpanNonzeroSingleton_homothety, NumberField.house_mul_le, cos_add_cos, deriv_rpow_const, Complex.ofReal_mul', exists_dist_eq, ProbabilityTheory.covariance_mul_const_left, pow_lt_iff_lt_log, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, ModularGroup.exists_bound_of_subgroup_invariant_of_isBigO, AkraBazziRecurrence.sumTransform_def, Path.extend_trans_of_le_half, EuclideanGeometry.tan_oangle_left_mul_dist_of_oangle_eq_pi_div_two, UpperHalfPlane.im_le_im_mul_exp_dist, Gamma_mul_Gamma_one_sub, SzemerediRegularity.hundred_lt_pow_initialBound_mul, Tactic.ComputeAsymptotics.Majorized.mul, AntilipschitzWith.le_mul_norm', Seminorm.ball_norm_mul_subset, sin_sub, exists_ratio_deriv_eq_ratio_slope, ContinuousMultilinearMap.opNorm_smul_le, cos_three_mul, cos_two_pi, LipschitzOnWith.norm_sub_le_of_le, SimpleGraph.triangleRemovalBound_mul_cube_lt, ProbabilityTheory.condIndepSets_singleton_iff, log_rpow, mul_le_sin, norm_image_sub_le_of_norm_deriv_le_segment, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, tsum_exp_neg_mul_int_sq, integral_cos_pow_aux, ContinuousMultilinearMap.norm_restr, tan_two_mul, antilipschitzWith_iff_exists_mul_le_norm', ContinuousMultilinearMap.norm_image_sub_le, negMulLog_mul, Convex.image_sub_lt_mul_sub_of_deriv_lt, inner_le_Lp_mul_Lq_hasSum_of_nonneg, hasSum_cos, sqrt_mul_self, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical, Asymptotics.IsBigOWith.trans, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, rpow_mul_natCast, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, MeasureTheory.lpNorm_mul_natCast, lp.summable_mul, NumberField.mulHeight_eq, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', Polynomial.coeff_le_of_roots_le, Metric.diam_closedBall_eq, pow_arith_mean_le_arith_mean_pow_of_even, one_add_tan_sq_mul_cos_sq_eq_one, PseudoMetricSpace.le_two_mul_dist_ofPreNNDist, norm_inner_eq_norm_iff, Complex.norm_exp_I_mul_ofReal_sub_one, Polynomial.exists_eq_gaussNorm, CircleDeg1Lift.translate_iterate, smul_map_volume_mul_left, cos_two_pi_sub, MeasureTheory.Submartingale.sum_mul_sub, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, ProbabilityTheory.covariance_smul_left, Irrational.mul_natCast, Complex.arg_cos_add_sin_mul_I_sub, hasSum_log_one_add, BohrMollerup.f_add_nat_ge, Complex.GammaIntegral_ofReal, HasDerivWithinAt.norm_sq, strictConcaveOn_sqrt_mul_log_Ioi, Complex.norm_cpow_of_ne_zero, InnerProductGeometry.norm_toLp_symm_crossProduct, ZSpan.measureReal_fundamentalDomain, Orientation.tan_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Module.Basis.norm_smul, Similar.exists_dist_eq, LiouvilleWith.nat_mul, Asymptotics.bound_of_isBigO_cofinite, Complex.integral_exp_neg_rpow, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, Complex.norm_mul_cos_arg, Complex.norm_log_sub_logTaylor_le, taylor_mean_remainder_lagrange_iteratedDeriv, UpperHalfPlane.image_coe_ball, le_zpow_iff_log_le, two_mul_arctan, has_fderiv_at_filter_real_equiv, NumberField.Units.regulator_eq_det, integral_le_sum_mul_Ico_of_antitone_monotone, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Orientation.sin_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, Complex.dist_self_conj, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, summable_schlomilch_iff_of_nonneg, InnerProductSpace.Core.cauchy_schwarz_aux, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero, Asymptotics.IsBigOWith.const_smul_left, Asymptotics.IsLittleO.bound, ZLattice.tsumNormRPowBound_spec, LipschitzWith.mapsTo_ball, lp.norm_const_smul, HurwitzZeta.hasSum_nat_completedCosZeta, Polynomial.toAddCircle.integrable, IsApproximateAddSubgroup.nsmul_inter_nsmul, ContinuousLinearMap.exists_approx_preimage_norm_le, cos_le_one_sub_mul_cos_sq, IsMIntegralCurveOn.comp_mul, Complex.norm_cpow_of_imp, ContinuousMultilinearMap.le_opNorm, approxOrderOf.image_pow_subset_of_coprime, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, norm_cauchyPowerSeries_le, log_nat_eq_sum_factorization, RCLike.div_im, HasDerivWithinAt.const_rpow, hasFDerivAt_norm_rpow, ofDigitsTerm_le, trapezoidal_error_le_of_c2, volume_ball, NormSMulClass.norm_smul, HasFPowerSeriesOnBall.uniform_geometric_approx, norm_sub_le_mul_volume_of_norm_deriv_le_of_le, AddCircle.norm_coe_mul, RCLike.ofReal_mul, Path.Homotopy.hcomp_apply, NormedAddGroupHom.norm_comp_le_of_le, norm_smul_of_nonneg, NumberField.Units.finrank_mul_regOfFamily_eq_det, InnerProductGeometry.cos_angle, expNear_sub, dist_lineMap_left, HurwitzZeta.hasSum_int_cosKernel, fib_golden_exp', fourier_real_eq, ContinuousAlternatingMap.le_opNorm, Asymptotics.isBigO_top, Seminorm.rescale_to_shell_zpow, mul_rpow, MeasureTheory.volume_sum_rpow_lt, hasDerivAt_abs_rpow, Angle.coe_eq_zero_iff, Seminorm.smul_closedBall_zero, iSup_mul_of_nonpos, norm_commutator_sub_one_le, NumberField.mixedEmbedding.convexBodySumFun_apply, logb_rpow_eq_mul_logb_of_pos, Ioo_smul_sphere_zero, ZetaAsymptotics.term_tsum_of_lt, rpow_arith_mean_le_arith_mean_rpow, smul_sphere', Polynomial.Chebyshev.isLocalMax_T_real, Complex.norm_log_one_add_sub_self_le, Convex.norm_image_sub_le_of_norm_fderivWithin_le, norm_jacobiThetaβ_term, deriv_Gamma_nat, trapezoidal_integral_ext, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, inner_le_Lp_mul_Lq_tsum_of_nonneg', AkraBazziRecurrence.isTheta_smoothingFn_sub_self, CStarRing.norm_star_mul_self', Circle.exp_two_pi, NNReal.rpow_mul, Complex.normSq_add, Polynomial.Chebyshev.S_two_mul_real_cos, UpperHalfPlane.center_im, InnerProductGeometry.cos_angle_mul_norm_mul_norm, ContractingWith.apriori_dist_iterate_fixedPoint_le, HasStrictDerivAt.sin, NormedAddGroupHom.le_of_opNorm_le, hasDerivAt_gronwallBound_shift, exp_one_mul_le_exp, HasDerivWithinAt.sqrt, Complex.cpow_ofReal_re, spectralAlgNorm_mul, UpperHalfPlane.cosh_dist, MultilinearMap.exists_bound_of_continuous, real_inner_div_norm_mul_norm_eq_one_iff, le_rpow_add, Filter.Tendsto.cesaro, UpperHalfPlane.image_coe_closedBall, Asymptotics.isBigO_nat_atTop_iff, LinearGrowth.Real.eventually_atTop_exists_int_between, Behrend.lower_bound_le_one, Complex.re_sq_le_normSq, Hyperreal.st_mul, irrational_ratCast_mul_iff, Quaternion.expSeries_odd_of_imaginary, norm_mulβ_le, Complex.div_im, sigmoid_mul_rexp_neg, Cardinal.cantorFunctionAux_succ, Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, MeasureTheory.norm_integral_sub_setIntegral_le, abs_cos_int_mul_pi, EuclideanGeometry.Sphere.dist_sq_eq_mul_dist_of_tangent_and_secant, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, intervalIntegral.integral_deriv_comp_mul_deriv', UpperHalfPlane.dist_coe_center, RCLike.ofNat_mul_re, norm_sub_eq_sqrt_iff_real_inner_eq_zero, Subgroup.two_mul_withInfty_mem_strictPeriods, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, Stirling.le_factorial_stirling, ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mul, dist_right_midpoint, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Complex.equivRealProd_apply_le', intervalIntegral.smul_integral_comp_mul_sub, mellin_convergent_of_isBigO_scalar, mul_self_sqrt, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, LSeriesSummable.le_const_mul_rpow, Chebyshev.primeCounting_eq_theta_div_log_add_integral, dist_center_homothety, Seminorm.smul', Convex.norm_image_sub_le_of_norm_hasDerivWithin_le, irrational_mul_ratCast_iff, ProbabilityTheory.exponentialPDF_eq, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_mul, HasStrictDerivAt.exp, bernstein.variance, bernstein_apply, logb_nat_eq_sum_factorization, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left, sum_div_nat_floor_pow_sq_le_div_sq, NumberField.mixedEmbedding.convexBodySumFun_smul, pow_arith_mean_le_arith_mean_pow, HasDerivAt.cosh, Height.mulHeightβ_add_le, sin_nat_mul_two_pi_sub, Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gamma, norm_exp_mul_sq_le, isLittleO_exp_mul_rpow_of_lt, mul_sub_le_image_sub_of_le_deriv, Metric.diam_thickening_le, irrational_mul_intCast_iff, ProbabilityTheory.condIndepSet_iff, NormedAddGroupHom.le_opNorm_of_le, Complex.log_exp_eq_sub_toIocDiv, rpowIntegrandββ_apply_mul_eqOn_Ici, Dilation.mapsTo_closedBall, HurwitzKernelBounds.F_nat_one_le, Matrix.l2_opNorm_conjTranspose_mul_self, ProbabilityTheory.variance_sub, isAlgebraic_tan_rat_mul_pi, Orientation.cos_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, isBigO_log_const_mul_log_atTop, Complex.norm_exp_sub_sum_le_norm_mul_exp, dist_integral_mulExpNegMulSq_comp_le, lipschitz_with_lipschitz_const_mul, Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO, Polynomial.intervalIntegrable_mahlerMeasure, ProbabilityTheory.betaPDF_of_pos_lt_one, irrational_natCast_mul_iff, lipschitzOnWith_iff_norm_div_le, volume_real_closedBall, Complex.HadamardThreeLines.norm_invInterpStrip, ENNReal.rpow_mul_natCast, BumpCovering.toPartitionOfUnity_eq_mul_prod, FormalMultilinearSeries.compAlongComposition_bound, AlternatingMap.exists_bound_of_continuous, Convex.mul_sub_le_image_sub_of_le_deriv, log_zpow, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, intervalIntegral.integral_comp_add_mul, two_mul_le_exp, MeasureTheory.norm_setToFun_le', MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, HasStrictFDerivAt.sqrt, HurwitzKernelBounds.isBigO_atTop_F_nat_one, circleIntegral.norm_integral_le_of_norm_le_const, AlgebraNorm.smul', integral_sin_pow_mul_cos_pow_odd, MeasureTheory.Lp.norm_const_le, MeasureTheory.volume_sum_rpow_le, geom_mean_eq_arith_mean_weighted_iff', ofDigits_eq_sum_add_ofDigits, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul', isAlgebraic_cos_rat_mul_pi, deriv2_binEntropy, MeasureTheory.integrableOn_Ioi_comp_mul_left_iff, ProbabilityTheory.exponentialPDF_of_nonneg, integral_rpow_mul_exp_neg_mul_rpow, HasDerivAt.exp, LiouvilleWith.mul_rat, ProbabilityTheory.paretoPDF_of_le, gronwallBound_K0, HasStrictFDerivAt.rpow, rpow_def_of_neg, RingSeminorm.exists_index_pow_le, Complex.normSq_sub, Function.Periodic.im_invQParam, LiouvilleWith.mul_int, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, lt_log_of_rpow_lt, spectralNorm_mul, logb_pow, Complex.arg_exp_mul_I, AddCircle.volume_closedBall, mul_gauge_le_norm, leftDeriv_mul_log, inner_le_weight_mul_Lp_of_nonneg, circleIntegrable_log_norm_factorizedRational, ENNReal.rpow_natCast_mul, PiTensorProduct.norm_eval_le_injectiveSeminorm, rpow_sum_le_const_mul_sum_rpow, MeasureTheory.lpNorm_fun_mul_natCast, HasDerivAt.cos, exists_nat_abs_mul_sub_round_le, ContinuousLinearMap.norm_smulRight_apply, Set.Icc.coe_convexCombo, similar_iff_exists_pairwise_dist_eq, Orientation.tan_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, CFC.rpow_rpow, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', strictConvexOn_mul_log, HasStrictDerivAt.cosh, Complex.sub_conj, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, Chebyshev.integrableOn_theta_div_id_mul_log_sq, IsApproximateSubgroup.pow_inter_pow, BohrMollerup.f_add_nat_le, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, sin_eq_tsum, tendsto_rpow_div_mul_add, AffineIsometryEquiv.dist_pointReflection_self, BoxIntegral.Box.dist_le_distortion_mul, cos_int_mul_pi_sub, ContinuousMultilinearMap.norm_map_init_le, IsApproximateSubgroup.card_mul_self_le, AffineIsometryEquiv.dist_pointReflection_self_real, NumberField.house.exists_ne_zero_int_vec_house_le, IsUnifLocDoublingMeasure.measure_mul_le_scalingConstantOf_mul, differentiableOn_mul_log, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_aux, MeasureTheory.setToFun_smul_left, taylor_mean_remainder, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', sin_sq_eq_half_sub, Unitary.norm_sub_one_sq_eq, sin_add, Angle.sin_two_nsmul, sqrt_mul, RCLike.im_mul_ofReal, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, PositiveLinearMap.exists_norm_apply_le, fourierIntegral_real_eq_integral_exp_smul, deriv_mulExpNegMulSq, dist_right_pointReflection, InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi, norm_jacobiTheta_sub_one_le, goldenConj_mul_goldenRatio, ProbabilityTheory.cgf_const, isLittleO_rpow_exp_pos_mul_atTop, Orientation.inner_eq_norm_mul_norm_mul_cos_oangle, IsCoercive.bounded_below, HurwitzZeta.hasSum_nat_cosZeta, NumberField.mixedEmbedding.covolume_idealLattice, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContractingWith.dist_le_mul, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, mellin_convergent_top_of_isBigO, HasDerivWithinAt.rpow, Circle.exp_inj, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, mk_mul, UpperHalfPlane.dist_self_center, integral_sin_mul_cosβ, intervalIntegral.smul_integral_comp_sub_mul, cos_eq_tsum, MeasureTheory.Lp.norm_const', HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, MeasureTheory.norm_condExpIndL1_le, AkraBazziRecurrence.p_def, smul_sphere, InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi, ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_self, goldenRatio_mul_fib_succ_add_fib, ProbabilityTheory.tilted_mul_apply_mgf', Quaternion.re_exp, dist_lineMap_right, MeasureTheory.lpNorm_fun_natCast_mul, PowerSeries.IsRestricted.isRestricted_iff, integral_sin_pow_aux, hasDerivWithinAt_taylorWithinEval_at_Icc, RingSeminorm.mul_le', Convex.norm_image_sub_le_of_norm_fderiv_le, integral_comp_abs, Circle.exp_add_two_pi, ContinuousMap.HomotopyWith.trans_apply, isBigO_logb_mul_const_log_atTop, tendsto_rpow_sub_one_log, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, LipschitzWith.dist_iterate_succ_le_geometric, ProbabilityTheory.mgf_fun_id_gaussianReal, Polynomial.Chebyshev.S_two_mul_real_cosh, Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, NormedAddGroupHom.bound', MeasureTheory.norm_condExpInd_apply_le, norm_iteratedFDerivWithin_prod_le, Metric.diam_ball, CStarModule.norm_inner_le, rescale_to_shell, hasFDerivAt_iff_tendsto, LiouvilleWith.rat_mul_iff, exp_mul_le_cosh_add_mul_sinh, arith_mean_le_rpow_mean, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, Angle.two_zsmul_toReal_eq_two_mul, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, ProbabilityTheory.sum_variance_truncation_le, IsApproximateAddSubgroup.card_nsmul_le, MeasureTheory.condExp_stronglyMeasurable_mul_of_bound, HurwitzZeta.hasSum_int_evenKernel, sin_nat_mul_pi, BoxIntegral.Box.volume_face_mul, hasSum_one_div_nat_pow_mul_cos, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Quaternion.normSq_eq_norm_mul_self, Orientation.sin_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two, hasStrictDerivAt_const_rpow_of_neg, tendsto_pow_const_mul_const_pow_of_abs_lt_one, Orientation.cos_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two, norm_zsmul_le, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ModularFormClass.exp_decay_sub_atImInfty, EuclideanGeometry.cos_oangle_left_mul_dist_of_oangle_eq_pi_div_two, HasDerivAt.sinh, HasDerivWithinAt.limsup_norm_slope_le, sum_range_le_log_div, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, ModularFormClass.exists_petersson_le, ContinuousLinearMap.opNorm_comp_le, two_pi_pos, norm_mul, ProbabilityTheory.gaussianPDFReal_def, LipschitzWith.dist_lt_mul_of_lt, MeasureTheory.Measure.addHaar_real_closedBall', HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, MeasureTheory.Lp.norm_smul_le, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, cos_eq_cos_iff, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty, signedDist_lineMap_lineMap, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, hasDerivWithinAt_taylor_coeff_within, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, lipschitzWith_iff_norm_div_le, Behrend.exp_neg_two_mul_le, AkraBazziRecurrence.strictAnti_sumCoeffsExp, intervalIntegral.inv_mul_integral_comp_add_div, mul_iInf_of_nonneg, sinh_sub, tendsto_integral_mul_one_add_inv_smul_sq_pow, derivWithin_cos, expNegInvGlue.tendsto_polynomial_inv_mul_zero, le_rpow_iff_log_le, rescale_to_shell_semi_normed, integral_sin_pow_even_mul_cos_pow_even, isLittleO_exp_neg_mul_rpow_atTop, Metric.diam_closedBall, sin_two_pi_sub, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, Complex.normSq_ofNat, sum_mul_Ico_le_integral_of_monotone_antitone, derivWithin_const_rpow, norm_fderiv_norm_rpow_le, mul_log_nonpos, MellinConvergent.comp_mul_left, Angle.angle_eq_iff_two_pi_dvd_sub, exists_taylor_mean_remainder_bound, LinearMap.bound_of_ball_bound', sin_two_mul, InnerProductGeometry.norm_ofLp_crossProduct, BoundingSieve.siftedSum_eq_sum_support_mul_ite, InnerProductSpace.volume_ball_of_dim_odd, Asymptotics.isBigOWith_iff, le_limsup_mul, le_log_of_pow_le, curveIntegralFun_trans_of_half_lt, cos_int_mul_two_pi_add_pi, MeasureTheory.integral_charFun_Icc, dist_homothety_self, OneHomClass.bound_of_antilipschitz, strongConcaveOn_iff_convex, Complex.dist_le_div_mul_dist_of_mapsTo_ball, lt_zpow_iff_log_lt, NNReal.rpow_natCast_mul, ProbabilityTheory.Fernique.normThreshold_eq, deriv_rpow_const, Quaternion.expSeries_even_of_imaginary, sin_eq_sin_iff, ContinuousLinearMap.le_of_opNorm_le, MeasureTheory.mul_le_integral_rnDeriv_of_ac, intervalIntegral.inv_mul_integral_comp_sub_div, ProbabilityTheory.gaussianReal_mul_const, UpperHalfPlane.dist_eq, MeasureTheory.Submartingale.sum_mul_upcrossingStrat_le, FormalMultilinearSeries.isLittleO_one_of_lt_radius, circleIntegral.norm_integral_lt_of_norm_le_const_of_lt, isBigO_at_im_infty_jacobiTheta_sub_one, AddCircle.exists_norm_eq_of_isOfFinAddOrder, Asymptotics.IsBigO.exists_mem_basis, geom_mean_le_arith_mean4_weighted, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, norm_nsmul_le, ProbabilityTheory.Fernique.lintegral_closedBall_diff_exp_logRatio_mul_sq_le, sign_mul_nonneg, HasDerivWithinAt.limsup_slope_norm_le, MeasureTheory.DominatedFinMeasAdditive.of_smul_measure, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, Asymptotics.IsBigOWith.smul, lipschitzWith_iff_norm_sub_le, Height.mulHeightβ_sum_le, ContinuousLinearMap.le_opNorm_of_le, norm_inner_eq_norm_tfae, circleAverage_def, Polynomial.mahlerMeasure_mul, ProbabilityTheory.covariance_eq_sub, derivWithin_exp, NumberField.Ideal.tendsto_norm_le_div_atTopβ, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, unitInterval.qRight_zero_right, Irrational.natCast_mul, MeasureTheory.DominatedFinMeasAdditive.smul, NumberField.mixedEmbedding.logMap_apply_of_norm_eq_one, RCLike.smul_im, polarCoord_symm_apply, Gamma_add_one, lt_log_of_zpow_lt, dist_self_homothety, ModularFormClass.exists_bound, BoxIntegral.norm_integral_le_of_le_const, derivWithin_rpow_const, Height.mulHeightβ_sub_le, Complex.integral_exp_neg_mul_rpow, ContinuousLinearMap.NonlinearRightInverse.bound, Angle.intCast_mul_eq_zsmul, two_mul_cos_mul_cos, tendsto_mul_log_one_add_div_atTop, AkraBazziRecurrence.GrowsPolynomially.mul, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, taylorWithinEval_succ, HasDerivAt.norm_sq, mul_logb, MeasureTheory.norm_setIntegral_le_of_norm_le_const, iInf_mul_of_nonpos, nnnorm_mul_toNNReal, FormalMultilinearSeries.le_mul_pow_of_radius_pos, InnerProductSpace.Core.norm_inner_le_norm, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, seminormFromConst_const_mul, rpow_one_add', ProbabilityTheory.condIndepSets_iff, Polynomial.hermite_eq_deriv_gaussian', Orientation.oangle_sign_smul_add_smul_smul_add_smul, AntilipschitzWith.le_mul_norm_div, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_exp, MeasureTheory.Measure.integral_comp_mul_left, Hyperreal.IsSt.mul, HurwitzZeta.hasSum_int_sinKernel, Affine.Simplex.dist_point_centroid, Path.Homotopy.trans_apply, inner_self_eq_norm_mul_norm, HurwitzZeta.oddKernel_functional_equation, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', cos_add, CovBySMul.trans, Complex.ofReal_comp_mul, norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, sin_int_mul_two_pi_sub, deriv_sinh, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, HurwitzZeta.isBigO_atTop_oddKernel, unitary.two_mul_one_sub_le_norm_sub_one_sq, Height.mulHeight_eq, InformationTheory.mul_log_le_toReal_klDiv, intervalIntegral.integral_comp_mul_deriv, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul, InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero, hasDerivAt_rpow_const, toNNReal_mul_nnnorm, real_inner_le_norm, RCLike.normSq_mul, ContinuousLinearMap.norm_map_tail_le, circleAverage_eq_integral_add, LipschitzOnWith.norm_div_le_of_le, rpowIntegrandββ_apply_mul, Gamma_nat_add_one_add_half, ContinuousMap.Homotopy.trans_apply, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, BoundedContinuousFunction.Lp_norm_le, Behrend.ceil_lt_mul, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, Polynomial.Chebyshev.rootMultiplicity_T_real, periodic_circleMap, conformalFactorAt_inner_eq_mul_inner', HasDerivWithinAt.arctan, MeasurableEmbedding.gaussianReal_comap_apply, intervalIntegral.mul_integral_comp_add_mul, Complex.add_conj, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, signedDist_lineMap_left, ProbabilityTheory.variance_mul_const, ProbabilityTheory.covarianceBilin_real_self, BoundingSieve.siftedSum_le_sum_of_upperMoebius, tendsto_rightDeriv_mul_log_atTop, NumberField.mixedEmbedding.norm_smul, Complex.normSq_intCast, MeasureTheory.integral_comp_rpow_Ioi, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, sin_int_mul_pi_sub, ProbabilityTheory.covariance_const_mul_right, tendsto_self_mul_const_pow_of_abs_lt_one, InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm, integrable_rpow_mul_exp_neg_mul_sq, HolderConjugate.mul_eq_add, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, RCLike.realLinearIsometryEquiv_symm_apply, Polynomial.Chebyshev.U_real_cos, real_inner_smul_right, Asymptotics.isBigOWith_top, mul_sub_lt_image_sub_of_lt_deriv, infDist_smulβ, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, abs_real_inner_div_norm_mul_norm_le_one, integrable_mul_exp_neg_mul_sq, ENNReal.toReal_ofReal_mul, rpow_add_one, cos_sub_nat_mul_two_pi, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, Angle.sin_add, NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply, NormedAddGroupHom.bound, MeasureTheory.norm_integral_le_of_norm_le_const, LinearGrowth.Real.eventually_atTop_exists_nat_between, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le, iteratedDeriv_even_cos, Complex.cos_bound, MeasureTheory.Lp.norm_const, ProbabilityTheory.mgf_add_const, sinh_two_mul, geom_mean_le_arith_mean3_weighted, ZetaAsymptotics.zeta_limit_aux1, ContinuousLinearMap.norm_extendToπ'_bound, pi_gt_sqrtTwoAddSeries, CStarRing.norm_star_mul_self, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, rpow_intCast_mul, spectralNorm_smul, list_prod_map_rpow, RCLike.I_im, Complex.div_re, ProbabilityTheory.integrable_exp_mul_gaussianReal, hasGradientAt_iff_tendsto, image_sub_le_mul_sub_of_deriv_le, inv_logb_mul_base, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, MeasureTheory.integrable_comp_mul_left_iff, ProbabilityTheory.gaussianReal_map_mul_const, rightDeriv_mul_log, AkraBazziRecurrence.asympBound_def', LinearMap.toSpanSingleton_homothety, UpperHalfPlane.le_dist_coe, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Polynomial.gaussNorm_monomial, ContinuousLinearMap.le_opNormβ, one_sub_mul_le_cos, Nat.roughNumbersUpTo_card_le', Polynomial.Chebyshev.isMinOn_T_real, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.covarianceOperator_inner, tan_nat_mul_pi, mellin_eq_fourierIntegral, unitInterval.mul_pos_mem_iff, HurwitzZeta.hasSum_nat_completedSinZeta, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, ProbabilityTheory.variance_mul, fourierIntegral_eq', HasDerivAt.rpow, Polynomial.Chebyshev.isLocalExtr_T_real_iff, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, RCLike.ofNat_mul_im, Quaternion.im_exp, Metric.diam_ball_eq, LiouvilleWith.int_mul, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, InnerProductSpaceable.parallelogram_identity, ProbabilityTheory.covarianceBilin_apply_pi, ProbabilityTheory.exp_neg_integrableOn_Ioc, EuclideanGeometry.Sphere.mul_dist_eq_power_of_radius_le_dist_center, ZLattice.covolume_eq_det_mul_measureReal, FormalMultilinearSeries.compAlongComposition_norm, intervalIntegral.integral_comp_sub_mul, AddCircle.toCircle_apply_mk, NumberField.mixedEmbedding.covolume_integerLattice, ModularGroup.exists_bound_fundamental_domain_of_isBigO, Polynomial.hermite_eq_deriv_gaussian, LipschitzOnWith.le_add_mul, isLittleO_zpow_exp_pos_mul_atTop, MeasureTheory.dist_convolution_le', trapezoidal_integral_one, Dilation.mapsTo_ball, IsBoundedSMul.dist_pair_smul', MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul, MeasureTheory.measureReal_ennreal_smul_apply, HasFDerivWithinAt.rpow_const, CircleDeg1Lift.translate_zpow, dist_homothety_center, EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, SchwartzMap.le_seminorm, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, LipschitzWith.norm_sub_le, summable_exp_nat_mul_of_ge, circleMap_zero_mul, tan_add_int_mul_pi, LipschitzOnWith.norm_div_le, ProbabilityTheory.variance_fun_sub, NormedAddGroupHom.le_opNorm, HasFPowerSeriesOnBall.uniform_geometric_approx', mul_abs_le_abs_sin, intervalIntegral.smul_integral_comp_mul_left, IsBoundedLinearMap.bound, derivWithin_sin, Complex.angle_le_mul_norm_sub, ZetaAsymptotics.term_sum_of_lt, deriv_const_rpow, EuclideanSpace.volume_ball_fin_three, UpperHalfPlane.le_dist_iff_le_dist_coe_center, LipschitzWith.norm_le_mul, Orientation.abs_areaForm_le, mul_add_one_le_add_one_pow, deriv_mul_log, ZLattice.exists_forall_abs_repr_le_norm, MeasureTheory.Lp.norm_le_of_ae_bound, rpowIntegrandββ_eq_pow_div, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, MeasureTheory.integral_rnDeriv_mul_log, EisensteinSeries.r_mul_max_le, cos_sub_int_mul_pi, integral_log_sin_zero_pi, integrableOn_rpow_mul_exp_neg_rpow, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, Asymptotics.bound_of_isBigO_nat_atTop, Asymptotics.IsBigO.bound, InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero, norm_lineDeriv_le_of_lipschitzOn, norm_sub_sq_eq_norm_sq_add_norm_sq_real, integrableOn_exp_mul_Ioi, Orientation.normSq_kahler, ProbabilityTheory.integrable_of_mem_integrableExpSet, integral_inv_sq_add_sq, QuotientAddGroup.norm_lift_apply_le, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, ProbabilityTheory.paretoPDF_eq, ContinuousAlternatingMap.norm_image_sub_le', EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, Polynomial.toAddCircle_monomial_eq_smul_fourier, HasDerivWithinAt.sinh, sin_sub_int_mul_pi, ProbabilityTheory.integral_tilted_mul_eq_mgf, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp, rpow_add', RCLike.mul_im_I_ax, EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle, tsum_geometric_inv_two_ge, norm_algebraMap, approxAddOrderOf.image_nsmul_subset, HasFDerivAt.rpow_const, exists_rat_abs_sub_le_and_den_le, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, geom_mean_lt_arith_mean_weighted_iff_of_pos, MeasureTheory.measureReal_abs_gt_le_integral_charFun, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, UpperHalfPlane.dist_center_dist, EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, Complex.normSq_ofReal, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, Vitali.exists_disjoint_subfamily_covering_enlargement, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, cosh_sub, HasStrictFDerivAt.const_rpow, NumberField.Units.abs_det_eq_abs_det, AbsolutelyContinuousOnInterval.const_mul, BoxIntegral.unitPartition.index_apply, StrongDual.norm_toLpβ_le, Liouville.exists_pos_real_of_irrational_root, EuclideanGeometry.tan_oangle_right_mul_dist_of_oangle_eq_pi_div_two, Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.HasSubgaussianMGF.cgf_le, RCLike.re_mul_ofReal, sqrt_eq_iff_mul_self_eq, ProbabilityTheory.cgf_const', UpperHalfPlane.dist_le_dist_coe_div_sqrt, Polynomial.Chebyshev.isMaxOn_T_real, LiouvilleWith.mul_rat_iff, integral_log, hasDerivAtFilter_iff_tendsto, Tactic.ComputeAsymptotics.Majorized.mul_bounded, deriv_cos, ProbabilityTheory.exponentialCDFReal_eq, Gamma_eq_integral, isBoundedLinearMap_iff, EuclideanGeometry.inversion_mul, cos_nat_mul_pi_sub, UpperHalfPlane.pos_real_re, Polynomial.Chebyshev.rootMultiplicity_U_real, signedDist_smul, ContinuousAlternatingMap.le_of_opNorm_le, MeromorphicOn.circleAverage_log_norm, ProbabilityTheory.gaussianPDFReal_inv_mul, abs_log_mul_self_rpow_lt, sin_bound, ContinuousMultilinearMap.norm_iteratedFDeriv_le, LipschitzOnWith.iff_le_add_mul, Height.logHeightβ_zpow, intervalIntegral.inv_mul_integral_comp_div_sub, BoxIntegral.Box.diam_Icc_le_of_distortion_le, trapezoidal_error_le, lipschitzWith_iff_dist_le_mul, mulExpNegMulSq_eq_sqrt_mul_mulExpNegMulSq_one, ContinuousMultilinearMap.norm_iteratedFDeriv_le', MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, MulAlgebraNormClass.map_smul_eq_mul, 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, integral_log_from_zero_of_pos, EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two, sqrt_eq_iff_mul_self_eq_of_pos, EulerSine.integral_cos_pow_eq, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, hasDerivAt_mulExpNegMulSq, tendstoLocallyUniformlyOn_rpow_sub_one_log, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, LiouvilleWith.int_mul_iff, Probability.cauchyPDFReal_def', dist_pointReflection_right, ContinuousLinearMap.opNorm_le_iff, NormedDivisionRing.norm_mul, EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two, Seminorm.ball_smul_ball, CStarRing.norm_self_mul_star, Summable.mul_of_nonneg, ZeroHomClass.bound_of_antilipschitz, tendsto_deriv_mul_log_atTop, Orientation.abs_areaForm_of_orthogonal, EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two, ProbabilityTheory.mgf_smul_left, NumberField.mixedEmbedding.unitSMul_smul, doublingGamma_add_one, exists_eq_const_mul_intervalIntegral_of_ae_nonneg, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, inner_sum_smul_sum_smul_of_sum_eq_zero, Complex.exp_bound, MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae, sqrt_mul_self_eq_abs, tan_add', le_integral_rpowIntegrandββ_one, EuclideanGeometry.inner_weightedVSub, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, ProbabilityTheory.variance_add, ProbabilityTheory.mgf_const', Asymptotics.IsBigOWith.of_const_mul_right, pi_lt_sqrtTwoAddSeries, FormalMultilinearSeries.isLittleO_of_lt_radius, MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles, iSup_mul_of_nonneg, Orientation.inner_sq_add_areaForm_sq, PiLp.norm_toLp_const, MeasureTheory.lpNorm_const_smul, bernoulliFun_mul, Seminorm.smul_closedBall_subset, Complex.toIocMod_arg, lp.tsum_mul_le_mul_norm', intervalIntegral.norm_integral_le_of_norm_le_const_ae, norm_add_sq_real, hasFPowerSeriesOnBall_linear_zero, Convex.norm_image_sub_le_of_norm_deriv_le, Angle.coe_toIocMod, norm_iteratedFDerivWithin_comp_le, NumberField.mixedEmbedding.fundamentalCone.expMap_single_symm_apply, sin_sub_sin, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, ODE.FunSpace.dist_iterate_next_le, hasDerivAt_Gamma_one_half, SeminormClass.map_smul_eq_mul, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, expNegInvGlue.continuous_polynomial_eval_inv_mul, isMIntegralCurveAt_comp_mul_ne_zero, liminf_mul_le, HurwitzZeta.hasSum_int_oddKernel, Gamma_mul_Gamma_add_half_of_pos, rpow_def_of_nonneg, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, Cardinal.cantorFunction_succ, IsMIntegralCurve.comp_mul, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, Complex.norm_sub_one_sq_eqOn_sphere, exists_ratio_hasDerivAt_eq_ratio_slope, sum_mul_le_sqrt_mul_sqrt, MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, NumberField.Embeddings.coeff_bdd_of_norm_le, MeasureTheory.setIntegral_gt_gt, HasFDerivWithinAt.sqrt, Asymptotics.isBigO_principal, lt_sin_mul, integral_sin_pow_odd_mul_cos_pow, NumberField.exists_ideal_in_class_of_norm_le, inner_le_Lp_mul_Lq_tsum_of_nonneg, CircleDeg1Lift.lt_iterate_pos_iff, Polynomial.fourierCoeff_toAddCircle_natCast, image_sub_lt_mul_sub_of_deriv_lt, norm_add_sq, fderivWithin_sqrt, AbsolutelyContinuousOnInterval.mul, SeminormedRing.norm_mul_le, cos_sub_cos, summable_condensed_iff_of_nonneg, not_DifferentiableAt_log_mul_zero, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, cos_nat_mul_two_pi_sub, norm_jacobiThetaβ'_term_le, norm_iteratedFDeriv_comp_le, ProbabilityTheory.covarianceBilin_real, ModularGroup.exists_bound_of_subgroup_invariant_of_isArithmetic_of_isBigO, bernoulliFun_eq_integral, ModularGroup.exists_bound_of_invariant_of_isBigO, Angle.natCast_mul_eq_nsmul, ENNReal.toReal_mul, norm_iteratedFDeriv_prod_le, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_apply, Angle.toIocMod_toReal, UpperHalfPlane.cosh_half_dist, norm_add_mul_self, EuclideanGeometry.Sphere.mul_dist_eq_zero_of_mem_sphere, ProbabilityTheory.tilted_mul_apply_mgf, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, tan_int_mul_pi_sub, sign_mul_pos_of_ne_zero, fourierChar_apply, AntilipschitzWith.le_mul_norm_sub, Unitary.two_mul_one_sub_le_norm_sub_one_sq, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, LipschitzWith.iff_le_add_mul, MeasureTheory.L1.norm_setToL1_le_mul_norm', LipschitzOnWith.dist_le_mul, Seminorm.rescale_to_shell, Angle.zsmul_eq_iff, Polynomial.Chebyshev.T_real_cosh, lt_log_of_pow_lt, Matrix.frobenius_norm_mul, Circle.exp_int_mul_two_pi, Orientation.cos_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two, NonUnitalNormedRing.norm_mul_le, rpow_le_iff_le_log, Path.trans_apply, MeasureTheory.mul_meas_ge_le_integral_of_nonneg, tendsto_integral_exp_smul_cocompact, exp_neg_mul_rpow_isLittleO_exp_neg, mellin_convergent_iff_norm, UpperHalfPlane.exp_half_dist, TensorProduct.dist_tmul_le, Metric.diam_sphere_eq, ArithmeticFunction.sum_moebius_mul_log_eq, exp_neg_mul_sq_isLittleO_exp_neg, isAlgebraic_sin_rat_mul_pi, IsPicardLindelof.mul_max_le, integral_exp_mul_Ioi, integral_sin_mul_cos_sq, HasFDerivWithinAt.rpow, ProbabilityTheory.covariance_smul_right, real_inner_sub_sub_self, Complex.norm_exp_sub_one_le, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, HurwitzKernelBounds.F_nat_zero_zero_sub_le, deriv_sigmoid, exists_ratio_deriv_eq_ratio_slope', Algebra.trace_complex_apply, IsBoundedSMul.dist_smul_pair', negMulLog_eq_neg, quadratic_root_cos_pi_div_five, geom_mean_eq_arith_mean_weighted_iff, cos_periodic, geom_mean_le_arith_mean, LipschitzWith.norm_div_le_of_le, Complex.im_mul_ofReal, rescale_to_shell_zpow, Complex.integrable_pow_mul_norm_one_add_mul_inv, MeasureTheory.Measure.addHaar_ball_mul_of_pos, iteratedDeriv_even_sin, Padic.padicNormE.mul, Matrix.linfty_opNorm_mul, AkraBazziRecurrence.dist_r_b, cosh_three_mul, dist_left_lineMap, real_inner_self_eq_norm_mul_norm, MeasureTheory.setIntegral_ge_of_const_le_real, isLittleO_pow_exp_pos_mul_atTop, ApproximatesLinearOn.closedBall_subset_target, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, NormedAlgebra.norm_smul_le, HasLineDerivAt.le_of_lipschitzOn, ExistsContDiffBumpBase.w_def, EReal.toReal_mul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, tendsto_mul_add_inv_atTop_nhds_zero, expNegInvGlue.contDiff_polynomial_eval_inv_mul, circleAverage_log_norm_factorizedRational, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, ProbabilityTheory.memLp_tilted_mul, summable_pow_mul_exp_neg_nat_mul, NormedSpace.norm_smul_le, HasDerivWithinAt.rpow_const, ProbabilityTheory.covarianceBilin_apply, Monotone.tendsto_alternating_series_of_tendsto_zero, ProbabilityTheory.gammaPDF_eq, Chebyshev.theta_le_log4_mul_x, ContinuousLinearMap.opNorm_smul_le, hasDerivAt_gronwallBound, NumberField.mixedEmbedding.logMap_apply, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, dist_div_norm_sq_smul, Asymptotics.IsBigOWith.const_mul_right', cos_sub_nat_mul_pi, FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, hasDerivAt_norm_rpow, lipschitzOnWith_iff_dist_le_mul, two_mul_arctan_sub_pi, MeasureTheory.integrable_comp_mul_right_iff, ProbabilityTheory.rpow_abs_le_mul_max_exp, sin_three_mul, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, sin_add_nat_mul_two_pi, tan_eq_zero_iff, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, volume_real_ball, RCLike.norm_sq_eq_def, fib_golden_conj_exp, Complex.circleTransformDeriv_periodic, rexp_neg_quadratic_isLittleO_rpow_atTop, hasSum_one_div_nat_pow_mul_sin, NumberField.mixedEmbedding.logMap_apply_of_norm_one, HasFDerivAt.const_rpow, intervalIntegral.mul_integral_comp_mul_add, Polynomial.Chebyshev.roots_T_real, mul_lt_sin, two_mul_arctan_add_pi, ProbabilityTheory.strong_law_aux4, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, Circle.exp_intCast_mul, iteratedDeriv_exp_const_mul, integrableOn_Ioi_exp_neg_mul_sq_iff, abs_sin_eq_one_iff, Continuous.mul_log, circleIntegral.norm_integral_le_of_norm_le_const', SimpleGraph.triangleRemovalBound_le, deriv_bernoulliFun, PiTensorProduct.norm_eval_le_projectiveSeminorm, isConformalMap_iff, Wallis.W_eq_factorial_ratio, deriv2_qaryEntropy, negMulLog_def, Chebyshev.psi_le, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, intervalIntegral.integral_deriv_comp_mul_deriv, logb_mul_base, Complex.cpow_ofReal_im, Angle.coe_toIcoMod, tendsto_sub_mul_tsum_nat_rpow, Complex.exp_bound', InnerProductGeometry.inner_eq_mul_norm_of_angle_eq_zero, MeasureTheory.integral_comp_mul_right_Ioi, sin_eq_neg_one_iff, rpow_lt_iff_lt_log, IsApproximateSubgroup.card_pow_le, RCLike.mul_self_norm, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, UpperHalfPlane.sinh_half_dist_add_dist, ProbabilityTheory.lintegral_betaPDF, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, two_mul_arctan_inv_3_add_arctan_inv_7, MeasureTheory.charFun_map_mul, Similar.exists_pairwise_dist_eq, ContDiffMapSupportedIn.seminorm_postcompLM_le, circleAverage_eq_intervalAverage, EReal.coe_mul, ContinuousMultilinearMap.bound, mul_log_eq_log_iff, NumberField.abs_discr_ge_of_isTotallyComplex, ProbabilityTheory.rpow_abs_le_mul_exp_abs, lt_log_one_add_of_pos, tendsto_sum_pi_div_four, Nat.norm_cast_le, rpow_neg_one_add_norm_sq_le, derivWithin_sqrt, fourierChar_apply', EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi, cos_sub_two_pi, isMIntegralCurveOn_comp_mul_ne_zero, MeasureTheory.norm_setToFun_le_mul_norm, ZLattice.le_norm_of_le_abs_repr, ContinuousAlternatingMap.opNorm_le_iff, Complex.im_ofReal_mul, tendsto_mul_exp_add_div_pow_atTop, ContinuousAffineMap.norm_comp_le, cos_two_mul, tan_mul_cos, signedDist_right_lineMap, tendsto_div_pow_mul_exp_add_atTop, cos_int_mul_two_pi_sub_pi, RCLike.realRingEquiv_apply, circleIntegrable_def, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, Asymptotics.isBigOWith_principal, Polynomial.coeff_bdd_of_roots_le, smul_ball, tendsto_pow_const_mul_const_pow_of_lt_one, RCLike.mul_im, ProbabilityTheory.mgf_dirac', rpow_add, inner_eq_norm_mul_iff_real, intervalIntegral.norm_integral_le_of_norm_le_const, SchwartzMap.decay, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, RCLike.im_sq_le_normSq, CFC.rpow_rpow_of_exponent_nonneg, SzemerediRegularity.pow_mul_m_le_card_part, deriv_rpow_const', Convex.mul_sub_lt_image_sub_of_lt_deriv, Dilation.diam_range, dist_smulβ, Asymptotics.isLittleO_iff_nat_mul_le_aux, MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg, Chebyshev.integral_theta_div_log_sq_isBigO, sin_sub_nat_mul_pi, MeasureTheory.L1.norm_setToL1_le_mul_norm, Dilation.diam_image, HasDerivAt.rpow_const, LipschitzWith.norm_le_mul', CircleDeg1Lift.le_iterate_pos_iff, intervalIntegral.smul_integral_comp_mul_right, LinearMap.bound_of_sphere_bound, hasStrictDerivAt_sqrt, conformalFactorAt_inner_eq_mul_inner, integral_gaussian, NumberField.mixedEmbedding.normAtPlace_smul, BumpCovering.exists_finset_toPOUFun_eventuallyEq, intervalIntegral.mul_integral_comp_sub_mul, IsBoundedBilinearMap.isBigO, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, ContinuousMultilinearMap.le_of_opNorm_le, tan_sub_nat_mul_pi, Function.Periodic.norm_qParam, inner_le_Lp_mul_Lq, iter_deriv_rpow_const, map_volume_mul_right, norm_intCast_eq_abs_mul_norm_one, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul', ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, fderiv_sqrt, Polynomial.Chebyshev.eval_T_real_eq_one_iff, HolderConjugate.sub_one_mul_conj, CuspFormClass.exp_decay_atImInfty', integral_sin_sq_mul_cos, NumberField.house_nat_mul, Affine.Simplex.ExcenterExists.signedInfDist_excenter, hasSum_sin, cos_eq_one_iff, Polynomial.Chebyshev.U_real_cosh, BoundedContinuousFunction.norm_integral_le_mul_norm, curveIntegralFun_trans_aeeq_left, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, Complex.integral_rpow_mul_exp_neg_mul_rpow, pow_le_iff_le_log, hasFDerivAtFilter_iff_tendsto, Chebyshev.integral_theta_div_log_sq_isLittleO, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, InnerProductSpace.Core.cauchy_schwarz_aux', SlashInvariantForm.vAdd_width_periodic, MeasureTheory.pdf.IsUniform.integral_eq, IsMIntegralCurveAt.comp_mul_ne_zero, CircleDeg1Lift.iterate_le_of_map_le_add_int, ModularGroup.three_le_four_mul_im_sq_of_mem_fd, tendsto_pow_logb_div_mul_add_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_add, HasStrictDerivAt.sinh, HurwitzKernelBounds.isBigO_exp_neg_mul_of_le, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty', rpow_eq_nhds_of_pos, Stirling.log_stirlingSeq_diff_le_geo_sum, ProbabilityTheory.strong_law_aux1, PositiveLinearMap.norm_apply_le_of_nonneg, Behrend.le_sqrt_log, norm_sub_le_mul_volume_of_norm_fderiv_le, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ProbabilityTheory.mgf_gaussianReal, RCLike.re_sq_le_normSq, ContinuousLinearMap.reApplyInnerSelf_smul, SimpleGraph.regularityReduced_edges_card_aux, cos_nat_mul_two_pi_add_pi, MeasureTheory.lpNorm_natCast_mul, rpow_one_add_lt_one_add_mul_self, Angle.coe_two_pi, log_pow, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, ProbabilityTheory.variance_linearMap_gaussianReal, MeasureTheory.condExp_stronglyMeasurable_mul_of_boundβ, Complex.norm_log_one_sub_inv_sub_self_le, ProbabilityTheory.mgf_id_gaussianReal, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le', exists_ratio_hasDerivAt_eq_ratio_slope', ProbabilityTheory.integrable_exp_mul_of_le, exp_bound', sum_div_pow_sq_le_div_sq, RCLike.mul_re, TensorProduct.norm_tmul, sin_nat_mul_pi_sub, ENNReal.rpow_mul_intCast, signedDist_lineMap_right, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, integral_rpow_mul_exp_neg_mul_Ioi, MeasureTheory.measureReal_prod_prod, NNReal.coe_mul, hasSum_arctan, BoundingSieve.siftedSum_le_mainSum_errSum_of_upperMoebius, sin_eq_zero_iff, ZLattice.normBound_spec, ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul, tendsto_abs_tan_atTop, SchwartzMap.le_seminorm', cos_sub_int_mul_two_pi, rpow_add_natCast, VectorFourier.norm_fourierSMulRight_le, blimsup_thickening_mul_ae_eq, Irrational.mul_ratCast, iteratedDeriv_odd_sin, AkraBazziRecurrence.h_rec, ContinuousLinearMap.le_of_opNormβ_le_of_le, norm_commutator_units_sub_one_le, EuclideanGeometry.law_cos, BoundingSieve.multSum_eq_main_err, Affine.Simplex.signedInfDist_affineCombination, Antitone.cauchySeq_alternating_series_of_tendsto_zero, irrational_cos_rat_mul_pi, Gamma_integrand_isLittleO, SeminormedSpace.Core.norm_smul, intervalIntegral.mul_integral_comp_mul_right, EuclideanGeometry.sin_oangle_left_mul_dist_of_oangle_eq_pi_div_two, one_div_sub_pow_hasFPowerSeriesOnBall_zero, AddCircle.norm_eq, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Behrend.lower_bound_le_one', RCLike.im_ofReal_mul, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, HurwitzKernelBounds.F_nat_zero_le, UpperHalfPlane.dist_coe_le, integral_sin_pow_odd, EuclideanGeometry.dist_affineCombination, similar_iff_exists_pos_pairwise_dist_eq, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, Asymptotics.isLittleO_iff, Angle.nsmul_toReal_eq_mul, HolderOnWith.dist_le, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, HasFDerivWithinAt.const_rpow, BohrMollerup.logGammaSeq_add_one, Submodule.orthogonalProjectionFn_norm_sq, exp_neg_integrableOn_Ioi, Complex.norm_exp_mul_exp_add_exp_neg_le_of_abs_im_le, intervalIntegral.integral_comp_mul_right, CliffordAlgebraComplex.Q_apply, le_liminf_mul, geom_mean_eq_arith_mean_weighted_of_constant, VectorFourier.norm_fourierPowSMulRight_le, EuclideanGeometry.dist_smul_vadd_eq_dist, summable_pow_mul_jacobiThetaβ_term_bound, riesz_lemma, circleMap_zero_pow, integrable_exp_neg_mul_sq_iff, young_inequality_of_nonneg, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, cos_sq, intervalIntegral.inv_mul_integral_comp_div, ContinuousMultilinearMap.norm_map_insertNth_le, ProbabilityTheory.strong_law_aux3, norm_iteratedFDerivWithin_mul_le, VectorFourier.norm_fourierSMulRight, LiouvilleWith.mul_nat_iff, Asymptotics.isBigO_iff'', cos_int_mul_two_pi_sub, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, cantorSequence_eq_self_sub_sum_cantorToTernary, ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, HolderWith.dist_le_of_le, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, dist_le_of_trajectories_ODE, taylor_mean_remainder_cauchy, UpperHalfPlane.pos_real_im, MeasureTheory.Egorov.exists_notConvergentSeq_lt, HurwitzZeta.evenKernel_functional_equation, strongConvexOn_iff_convex, norm_add_sub_norm_sub_le_two_mul_min, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip', ProbabilityTheory.mgf_const_mul, ProbabilityTheory.evariance_mul, sum_range_sub_log_div_le, goldConj_mul_gold, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, exp_approx_end, integrableOn_rpow_mul_exp_neg_mul_sq, dist_algebraMap, UpperHalfPlane.sinh_half_dist, Seminorm.smul_ball_zero, EuclideanGeometry.cos_oangle_right_mul_dist_of_oangle_eq_pi_div_two, InnerProductSpace.volume_closedBall_of_dim_odd, real_inner_smul_left, norm_add_mul_self_real, UpperHalfPlane.dist_le_iff_le_sinh, SimpleGraph.isEquivalent_extremalNumber, Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_real, tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, List.norm_prod, intervalIntegral.integral_comp_mul_deriv', InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq', Dilation.dist_eq, gauge_smul, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, Bertrand.real_main_inequality, MeasureTheory.Measure.addHaar_closedBall_mul, dist_right_lineMap, Complex.volume_sum_rpow_lt_one, taylor_mean_remainder_bound, rpow_def_of_nonpos, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, MeasureTheory.Measure.integral_isAddLeftInvariant_isAddRightInvariant_combo, EuclideanGeometry.dist_inversion_mul_dist_center_eq, Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero, MeasureTheory.norm_indicatorConstLp', ArchimedeanClass.stdPart_mul, ContinuousLinearMap.exists_mul_lt_of_lt_opNorm, lp.norm_const_smul_le, MeasureTheory.integral_comp_mul_left_Ioi, AkraBazziRecurrence.one_mem_range_sumCoeffsExp, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Orientation.tan_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, ContinuousMap.norm_smul_const, UpperHalfPlane.dist_coe_center_sq, Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, blimsup_cthickening_mul_ae_eq, FormalMultilinearSeries.summable_norm_mul_pow, norm_mul_le, ProbabilityTheory.covariance_const_mul_left, 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', IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq, Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_real, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, Complex.normSq_apply, abs_rpow_le_exp_log_mul, NNReal.rpow_mul_natCast, RCLike.re_ofReal_mul, Polynomial.Chebyshev.isLocalExtr_T_real, norm_add_pow_two, HasFDerivAt.sqrt, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, half_mul_log_add_log_abs, ruzsaSzemerediNumberNat_lower_bound, hasGradientWithinAt_iff_tendsto, real_inner_add_add_self, unitary.norm_sub_one_sq_eq, deriv_sin, MeasurableEquiv.gaussianReal_map_symm_apply, Complex.arg_exp, hofer, tan_add_nat_mul_pi, Similar.exists_pos_pairwise_dist_eq, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq', IsPrimitiveRoot.arg, Complex.norm_log_one_add_half_le_self, ProbabilityTheory.indepFun_iff_integral_comp_mul, ContinuousMultilinearMap.opNorm_le_iff, intervalIntegral.integral_comp_mul_add, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, RCLike.normSq_add, Polynomial.Chebyshev.isExtrOn_T_real, RCLike.div_re, integral_sin_pow, hasDerivAt_iff_tendsto, Polynomial.instTwoPiPos, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, Complex.im_sq_le_normSq, isBigO_logb_const_mul_log_atTop, norm_image_sub_le_of_norm_deriv_right_le_segment, integral_gaussian_Ioi, Circle.exp_eq_one, norm_iteratedFDeriv_smul_le, HolderWith.dist_le, abs_real_inner_div_norm_mul_norm_eq_one_iff, integrable_exp_neg_mul_sq, cauchy_mul, fderiv_norm_rpow, UpperHalfPlane.cosh_dist', Polynomial.toAddCircle_X_eq_fourier_one, MeasureTheory.GridLines.T_univ, hasStrictDerivAt_const_rpow, HasStrictDerivAt.cos, InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero, ContinuousLinearMap.norm_adjoint_comp_self, GaussianFourier.verticalIntegral_norm_le, CircleIntegrable.out, le_inv_mul_exp, SchwartzMap.integrable_pow_mul, Complex.borelCaratheodory, LipschitzWith.mapsTo_closedBall, ContinuousMultilinearMap.norm_map_cons_le, ContinuousMultilinearMap.norm_smulRight, rpow_mul, BumpCovering.toPOUFun_eq_mul_prod, zpow_arith_mean_le_arith_mean_zpow, AkraBazziRecurrence.continuous_sumCoeffsExp, MeasureTheory.rnDeriv_tilted_right, LiouvilleWith.rat_mul, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, ProbabilityTheory.IndepFun.exp_mul, cos_add_nat_mul_two_pi, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, ContinuousAlternatingMap.bound, IsBoundedBilinearMap.bound, Asymptotics.isBigO_iff_eventually, Asymptotics.IsBigOWith.bound, Hyperreal.coe_mul, CircleDeg1Lift.translationNumber_pow, ringEquivCauchy_apply, CuspFormClass.exp_decay_atImInfty, mul_iSup_of_nonpos, approxOrderOf.image_pow_subset, integral_sin_sq_mul_cos_sq, le_log_of_rpow_le, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, integral_mul_rpow_one_add_sq, sqrt_mul', MeasureTheory.measureReal_biUnion_eq_sum_powerset, isSquare_iff, ModularGroup.lcRow0_apply, ProbabilityTheory.gaussianPDFReal_mul, rpow_of_add_eq, MeasureTheory.integrable_withDensity_iff, curveIntegralFun_trans_of_lt_half, norm_sub_pow_two, Module.Basis.opNorm_le, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, Angle.toReal_coe_eq_self_add_two_pi_iff, rpow_add_intCast, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, uniformContinuous_mul, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, MeasureTheory.integrableOn_Ioi_comp_mul_right_iff, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, AddCircle.norm_eq', NumberField.Units.finrank_mul_regulator_eq_det, IsApproximateAddSubgroup.card_add_self_le, Besicovitch.TauPackage.lastStep_nonempty, Complex.norm_cpow_le, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, MeasureTheory.lpNorm_const, isIntegral_two_mul_cos_rat_mul_pi, HurwitzZeta.isBigO_atTop_cosKernel_sub, Monotone.cauchySeq_alternating_series_of_tendsto_zero, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, tendsto_pow_log_div_mul_add_atTop, approxAddOrderOf.image_nsmul_subset_of_coprime, one_add_mul_self_lt_rpow_one_add, rothNumberNat_le_ruzsaSzemerediNumberNat', ProbabilityTheory.condIndepFun_iff, compact_inner_le_weight_mul_Lp_of_nonneg, cos_eq_neg_one_iff, abs_cos_eq_one_iff, IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq, Asymptotics.IsBigOWith.const_mul_left, NumberField.mulHeightβ_eq, Seminorm.comp_smul_apply, sin_sub_two_pi, cos_sub, Wallis.W_succ, integral_cos_sq, TorusIntegrable.function_integrable, NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral, ProbabilityTheory.mgf_smul_measure, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, norm_zpow_le_mul_norm, Orientation.norm_kahler, dist_midpoint_left, HurwitzZeta.LSeriesHasSum_sin, ruzsaSzemerediNumberNat_asymptotic_lower_bound, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, NumberField.Units.sum_mult_mul_log, hasStrictFDerivAt_rpow_of_neg, hasStrictDerivAt_rpow_const, Complex.arg_mul_cos_add_sin_mul_I_sub, integral_rpowIntegrandββ_eq_rpow_mul_const, RCLike.normSq_apply, posLog_pow, sinh_three_mul, smul_closedBall, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, ENNReal.ofReal_mul', ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, le_sin_mul, Polynomial.norm_coeff_le_choose_mul_mahlerMeasure, rpowIntegrandββ_apply_mul', sum_sqrt_mul_sqrt_le, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, ContinuousLinearMap.bound, hasDerivAt_Gamma_nat, ordinaryHypergeometricSeries_norm_div_succ_norm, Height.AdmissibleAbsValues.product_formula, re_inner_le_norm, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', Complex.norm_le_sqrt_two_mul_max, unitInterval.two_mul_sub_one_mem_iff, hasSum_zeta_nat, cos_add_int_mul_pi, ZLattice.sum_piFinset_Icc_rpow_le, derivWithin_sinh, Angle.toReal_coe_eq_self_sub_two_pi_iff, fib_succ_sub_goldenConj_mul_fib, AddChar.zmod_intCast, HasDerivAt.sin, norm_mul_sub_norm_div_le_two_mul_min, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right, cosh_add, LipschitzWith.diam_image_le, EuclideanGeometry.Sphere.secondInter_eq_lineMap, RCLike.mul_re_ax, MeasureTheory.mul_upcrossingsBefore_le, sin_sub_int_mul_two_pi, HasDerivWithinAt.exp, hasFDerivWithinAt_iff_tendsto, NormMulClass.norm_mul, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, fourierInv_eq', tendsto_log_mul_rpow_nhdsGT_zero, Asymptotics.isBigOWith_inv, AkraBazziRecurrence.injective_sumCoeffsExp, norm_sub_mul_self_real, integral_log_from_zero, Polynomial.toAddCircle_C_eq_smul_fourier_zero, MeasureTheory.DominatedFinMeasAdditive.of_measure_le_smul, real_inner_smul_self_right, Matrix.l2_opNorm_mul, InnerProductGeometry.sin_angle_add, MeasureTheory.eLpNorm'_norm_rpow, LipschitzWith.norm_compLp_le, fourierIntegral_real_eq, mul_iInf_of_nonpos, integral_cos_sq_sub_sin_sq, ProbabilityTheory.variance_tilted_mul, Subadditive.apply_mul_add_le, HolderOnWith.hausdorffMeasure_image_le, InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero, ZetaAsymptotics.term_of_lt, hasConstantSpeedOnWith_iff_ordered, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, norm_mul_sub_norm_div_le_two_mul, AddCircle.homeomorphCircle'_apply, volume_pi_closedBall, Complex.norm_mul, taylor_mean_remainder_lagrange, Complex.borelCaratheodory_zero, sin_eq_one_iff, HurwitzZeta.hasSum_nat_cosKernelβ, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, rpow_add_intCast', intervalIntegral.inv_mul_integral_comp_div_add, fib_succ_sub_goldenRatio_mul_fib, expNegInvGlue.differentiable_polynomial_eval_inv_mul, AkraBazziRecurrence.sumCoeffsExp_p_eq_one, Asymptotics.IsBigOWith.mul, ProbabilityTheory.Fernique.normThreshold_add_one, rpow_one_add_le_one_add_mul_self, CircleDeg1Lift.iterate_pos_eq_iff, cos_nat_mul_two_pi, BoundedContinuousFunction.dist_le_two_norm, ContinuousLinearMap.dist_le_opNorm, Circle.exp_sub_two_pi, HasLineDerivAt.le_of_lipschitz, RCLike.I_im', Complex.norm_sub_one_sq_eq_of_norm_one, norm_fderiv_norm_id_rpow, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, ContinuousLinearMap.norm_holder_apply_apply_le, ProbabilityTheory.variance_fun_add, ProbabilityTheory.covariance_mul_const_right, CircleDeg1Lift.translate_pow, dist_sq_lineMap_of_inner_eq_zero, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, ContinuousLinearMap.bound_of_antilipschitz, deriv_mul_log_zero, Rat.AbsoluteValue.apply_le_sum_digits, norm_mul_le_of_le, rpowIntegrandββ_one_ge_rpow_sub_two, intervalIntegral.integral_comp_mul_deriv'', log_mul, sin_add_int_mul_two_pi, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, tendsto_prod_pi_div_two, hasDerivAt_sqrt, norm_image_sub_le_of_norm_deriv_le_segment', ContinuousLinearMap.NonlinearRightInverse.bound', SchwartzMap.one_add_le_sup_seminorm_apply, Polynomial.Chebyshev.roots_U_real_nodup, taylor_within_apply, exp_nat_mul, cosh_two_mul, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, convexOn_mul_log, Chebyshev.eventually_primeCounting_le, exp_add, Complex.IsExpCmpFilter.isTheta_cpow_exp_re_mul_log, ProbabilityTheory.variance_smul, tan_sub_int_mul_pi, deriv_sqrt_mul_log', UpperHalfPlane.c_mul_im_sq_le_normSq_denom, isMIntegralCurve_comp_mul_ne_zero, MeasureTheory.lpNorm_const', Chebyshev.psi_le_const_mul_self, SchwartzMap.integrable_pow_mul_iteratedFDeriv, norm_add_sq_eq_norm_sq_add_norm_sq_real, ae_eq_const_or_norm_integral_lt_of_norm_le_const, tendsto_log_mul_self_nhdsLT_zero, rpow_add_one', cos_int_mul_pi, ContinuousLinearMap.norm_map_removeNth_le, Polynomial.Chebyshev.roots_T_real_nodup, exists_forall_closed_ball_dist_add_le_two_mul_sub, abs_log_mul_self_lt, MeasureTheory.norm_condExpIndL1Fin_le, ContinuousMultilinearMap.norm_image_sub_le', InnerProductGeometry.sin_angle_mul_norm_mul_norm, volume_preimage_mul_right, fourier_eq', NNReal.coe_list_prod, EisensteinSeries.summand_bound, dist_smul_pair, ringEquivCauchy_symm_apply_cauchy, ModularFormClass.exp_decay_sub_atImInfty', UpperHalfPlane.smulAux'_im, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStripββ', ProbabilityTheory.variance_const_mul, tendsto_exp_mul_div_rpow_atTop, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, limsup_mul_le, Asymptotics.IsLittleO.def, two_mul_sin_mul_sin, Height.logHeight_pow, Orientation.cos_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, HasCompactSupport.convolution_integrand_bound_right, Orientation.cos_oangle_eq_inner_div_norm_mul_norm, Metric.diam_cthickening_le, posLog_nat_mul, ODE.FunSpace.dist_iterate_next_apply_le, sin_le_mul, one_add_mul_self_le_rpow_one_add, dist_le_of_trajectories_ODE_of_mem, posLog_mul, FormalMultilinearSeries.ofScalars_norm_eq_mul, one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, summable_exp_nat_mul_iff, rpowIntegrandββ_eqOn_mul_rpowIntegrandββ_one, HasFDerivAt.rpow, ProbabilityTheory.integral_tilted_mul_self, cos_two_mul', Path.extend_trans_of_half_le, MeasureTheory.toReal_rnDeriv_tilted_right, RCLike.normSq_sub, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, inner_le_Lp_mul_Lq_of_nonneg, exists_int_int_abs_mul_sub_le, four_mul_arctan_inv_5_sub_arctan_inv_239, HasCompactSupport.convolution_integrand_bound_right_of_subset, schnirelmannDensity_mul_le_card_filter, sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, Complex.ofReal_mul, LipschitzWith.norm_compLp_sub_le, hasDerivWithinAt_iff_tendsto, MeasureTheory.volume_sum_rpow_lt_one, antilipschitzWith_iff_exists_mul_le_norm, Complex.exp_im, Polynomial.Chebyshev.C_two_mul_real_cos, NumberField.house.basis_repr_norm_le_const_mul_house, Complex.dist_conj_self, RCLike.realLinearIsometryEquiv_apply, cantorSequence_get_succ, unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, mul_exp_neg_le_exp_neg_one, ZMod.toCircle_eq_circleExp, Polynomial.Chebyshev.roots_U_real, LinearMap.bound_of_ball_bound, ProbabilityTheory.mgf_pos_iff, ContinuousLinearMap.norm_smulRightL_apply, BoundedContinuousFunction.dist_le_two_norm', rpow_natCast_mul, similar_iff_exists_pos_dist_eq, hasSum_log_sub_log_of_abs_lt_one, AbsolutelyContinuousOnInterval.fun_mul, lipschitzOnWith_iff_norm_sub_le, MeasureTheory.eLpNorm'_enorm_rpow, RightDerivMeasurableAux.le_of_mem_A, tan_eq_zero_iff', mul_pow_le_nat_floor_pow, lt_rpow_iff_log_lt, CircleDeg1Lift.translationNumber_zpow, NumberField.mixedEmbedding.logMap_mul, InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero, integral_sin_pow_even, InformationTheory.mul_klFun_le_toReal_klDiv, bernoulliFun_eval_half, MeasureTheory.norm_setToFun_le, MulAlgebraNorm.smul', Angle.two_nsmul_toReal_eq_two_mul, cos_bound, hasConstantSpeedOnWith_iff_variationOnFromTo_eq, summable_mul_of_Lp_Lq_of_nonneg, Int.Matrix.exists_ne_zero_int_vec_norm_le, HasStrictDerivAt.sqrt, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.isBigO_atTop_sinKernel, Asymptotics.isBigO_iff', mulLeft_bound, LiouvilleNumber.remainder_lt', NumberField.mixedEmbedding.convexBodySum_mem, hasSum_L_function_mod_four_eval_three, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, deriv_cosh, conformalAt_iff', ContinuousLinearMap.toSesqForm_apply_norm_le, Function.Periodic.exp_decay_sub_of_bounded_at_inf, sin_int_mul_pi, NumberField.IsCMField.regOfFamily_realFunSystem, ContinuousAlternatingMap.norm_image_sub_le, LipschitzWith.integral_lineDeriv_mul_eq, dist_lineMap_lineMap, lipschitz_with_lipschitz_const_add, ExistsContDiffBumpBase.w_mul_Ο_nonneg, Affine.Triangle.dist_point_centroid, log_doublingGamma_eq, geom_mean_le_arith_mean2_weighted, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, MeasureTheory.integrable_rnDeriv_mul_log_iff, two_mul_sin_mul_cos, deriv_sqrt, Asymptotics.isLittleO_iff_nat_mul_le', tendsto_pow_mul_exp_neg_atTop_nhds_zero, Orientation.inner_mul_areaForm_sub, norm_inner_le_norm, ofDigits_digits_sum_eq, MeasureTheory.measureReal_nnreal_smul_apply, Function.Periodic.exp_decay_of_zero_at_inf, lt_pow_iff_log_lt, deriv2_sqrt_mul_log, mellin_comp_mul_left, ConvexOn.lipschitzOnWith_of_abs_le, rpowIntegrandββ_eqOn_pow_div, sum_trapezoidal_integral_adjacent_intervals, Complex.cpow_ofReal, AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T, MeasureTheory.pdf.hasFiniteIntegral_mul, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, SchwartzMap.norm_pow_mul_le_seminorm, gronwallBound_Ξ΅0, Stirling.tendsto_self_div_two_mul_self_add_one, HolderOnWith.dist_le_of_le, Wallis.le_W, InnerProductSpace.norm_rankOne, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Angle.nsmul_eq_iff, ZLattice.abs_repr_le, norm_jacobiThetaβ_term_fderiv_le, norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero, ProbabilityTheory.IndepFun.mgf_add', Seminorm.closedBall_smul_closedBall, mellin_comp_mul_right, GaussianFourier.integral_rexp_neg_mul_sq_norm, irrational_intCast_mul_iff, lp.tsum_mul_le_mul_norm, Complex.exp_bound_sq, HurwitzZeta.hasSum_int_evenKernelβ, integrableOn_rpow_mul_exp_neg_mul_rpow, Complex.norm_mul_sin_arg, MeasureTheory.Measure.addHaar_real_closedBall, Int.Matrix.exists_ne_zero_int_vec_norm_le', HasStrictFDerivAt.rpow_const, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, NormedRing.norm_mul_le, Asymptotics.isBigOWith_pure, LiouvilleWith.nat_mul_iff, Complex.angle_exp_exp, mul_iSup_of_nonneg, Polynomial.Chebyshev.C_two_mul_real_cosh, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, intervalIntegral.smul_integral_comp_add_mul, norm_add_sub_norm_sub_le_two_mul, circleMap_zero_zpow, Complex.re_ofReal_mul, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, MeasureTheory.Measure.integral_comp_inv_mul_right, Probability.cauchyPDFReal_def, deriv2_mul_log, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, geom_mean_le_arith_mean_weighted, ConcaveOn.lipschitzOnWith_of_abs_le, Asymptotics.IsBigOWith.const_mul_right, AlgHom.norm_apply_le_self_mul_norm_one, intervalIntegral.mul_integral_comp_mul_left, sin_sub_nat_mul_two_pi, map_volume_mul_left, one_add_norm_le_sqrt_two_mul_sqrt, Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, ProbabilityTheory.integrable_rpow_mul_exp_of_mem_interior_integrableExpSet, norm_iteratedFDeriv_clm_apply_const
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instNNRatCast π | CompOp | 25 mathmath: pi_lt_d6, ofCauchy_nnratCast, nnnorm_nnratCast, Complex.norm_nnratCast, exp_one_gt_d9, log_two_gt_d9, Complex.ofReal_nnratCast, cauchy_nnratCast, pi_gt_d2, Behrend.ceil_lt_mul, NNReal.coe_ofScientific, pi_lt_d2, pi_gt_d4, exp_one_lt_d9, RCLike.norm_nnratCast, RCLike.ofReal_nnratCast, pi_lt_d20, log_two_lt_d9, pi_gt_d20, exp_neg_one_gt_d9, norm_nnratCast, Complex.re_nnratCast, pi_gt_d6, exp_neg_one_lt_d9, pi_lt_d4
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instNatCast π | CompOp | 1693 mathmath: cos_add_nat_mul_pi, Unitary.openPartialHomeomorph_source, Behrend.roth_lower_bound, MeasureTheory.exists_pos_preimage_ball, CuspFormClass.qExpansion_isBigO, pi_div_four_le_arcsin, isEquivalent_descFactorial, Polynomial.Chebyshev.isExtrOn_T_real_iff, norm_sub_sq_real, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, BoundedContinuousFunction.tietze_extension_step, Circle.periodic_exp, le_log_one_add_of_nonneg, abs_exp_sub_one_le, tan_pi_div_four, EuclideanGeometry.dist_smul_vadd_sq, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, cos_pi_div_five, Polynomial.mahlerMeasure_def_of_ne_zero, EulerSine.integral_cos_mul_cos_pow, Height.logHeightβ_pow, AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound, sin_add_sin, Complex.norm_circleTransformBoundingFunction_le, LiouvilleWith.nat_sub_iff, expNear_succ, Angle.sign_two_zsmul_eq_sign_iff, goldenConj_mul_fib_succ_add_fib, NNReal.rpow_sub_intCast, norm_torusIntegral_le_of_norm_le_const, EuclideanGeometry.Sphere.thales_theorem, sinh_eq, toNNReal_lt_natCast', sinh_log, mellin_eq_fourier, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, pi_le_four, MeasureTheory.charFun_eq_fourierIntegral', arcsin_eq_pi_div_two_sub_arccos, InnerProductSpace.volume_closedBall_of_dim_even, TsirelsonInequality.sqrt_two_inv_mul_self, Orientation.inner_rotation_pi_div_two_right_smul, tendsto_tsum_div_pow_atTop_integral, Orientation.oangle_add_left_smul_rotation_pi_div_two, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, hasDerivAt_sqrt_mul_log, Complex.norm_sub_one_sq_eq_of_norm_eq_one, sin_pi_div_two, Chebyshev.theta_eq_theta_coe_floor, taylorWithinEval_hasDerivAt_Ioo, HurwitzZeta.LSeriesHasSum_cos, rpow_add_natCast', Complex.normSq_natCast, fourierIntegralInv_eq', Angle.two_zsmul_eq_pi_iff, CircleDeg1Lift.map_add_nat, sqrt_one_add_le, volume_iUnion_setOf_liouvilleWith, sin_add_two_pi, integral_sin_mul_cosβ, Angle.sin_add_pi_div_two, Stirling.factorial_isEquivalent_stirling, norm_jacobiThetaβ_term_le, RightDerivMeasurableAux.norm_sub_le_of_mem_A, Complex.norm_sub_mem_Icc_angle, cos_eq_zero_iff, MeasureTheory.lpNorm_fun_div_natCast, dist_mulExpNegMulSq_le_two_mul_sqrt, BoxIntegral.unitPartition.mem_box_iff', log_div_le_sum_range_add, norm_iteratedFDerivWithin_smul_le, real_sqrt_le_nat_sqrt_succ, AddCircle.homeomorphCircle'_apply_mk, neg_pi_div_two_eq_arcsin, log2_le_logb, norm_natCast_eq_mul_norm_one, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, hasDerivWithinAt_taylorWithinEval, sin_periodic, log_sqrt, circleIntegral_def_Icc, Complex.natCast_re, Nat.isUniformEmbedding_coe_real, CircleDeg1Lift.commute_nat_add, Complex.arg_neg_I, Gamma_nat_add_half, circleIntegrable_iff, posLog_norm_add_le, LiouvilleWith.sub_nat, CircleDeg1Lift.iterate_pos_le_iff, eulerMascheroniConstant_lt_two_thirds, Nat.dist_cast_real, norm_iteratedFDeriv_comp_le', norm_iteratedFDeriv_mul_le, CircleDeg1Lift.iterate_eq_of_map_eq_add_int, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, Affine.Simplex.dist_point_faceOppositeCentroid, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, bernoulliFun_eval_half_eq_zero, Circle.exp_natCast_mul, cos_int_mul_two_pi, natFloor_logb_natCast, ProbabilityTheory.Fernique.lt_normThreshold_zero, log_neg_natCast_nonneg, NumberField.dedekindZeta_residue_def, nat_floor_real_sqrt_eq_nat_sqrt, CircleDeg1Lift.iterate_pos_lt_iff, Ioo_eq_ball, le_pow_iff_log_le, norm_iteratedFDerivWithin_clm_apply, circleMap_neg_pi_div_two, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, EReal.coe_coe_eq_natCast, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Complex.angle_exp_one, hasDerivAt_bernoulliFun, Unitary.continuousOn_argSelfAdjoint, norm_two, bernoulliFun_two, ProbabilityTheory.sum_prob_mem_Ioc_le, norm_iteratedFDerivWithin_comp_le_aux, BoxIntegral.unitPartition.box_upper, ContinuousMap.dist_le_two_norm, selfAdjoint.norm_sq_expUnitary_sub_one, Behrend.roth_lower_bound_explicit, PiCountable.min_dist_le_dist_pi, BoxIntegral.unitPartition.mem_smul_span_iff, tendsto_cos_pi_div_two, AkraBazziRecurrence.isBigO_apply_r_sub_b, NumberField.Units.regOfFamily_eq_det, Affine.Triangle.dist_point_faceOppositeCentroid, isIntegral_two_mul_sin_rat_mul_pi, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, CFC.sqrt_rpow, integral_pow, summable_one_div_nat_add_rpow, Height.logHeightβ_sum_le, Height.logHeightβ_add_le, Complex.sqrt_I, PadicInt.norm_p_pow, hasSum_log_one_add_inv, Differentiable.fderiv_norm_rpow, Behrend.sphere_subset_preimage_metric_sphere, integral_log_sin_zero_pi_div_two, toNNReal_le_ofNat, LiouvilleNumber.partialSum_eq_rat, MeasureTheory.Submartingale.mul_integral_upcrossingsBefore_le_integral_pos_part, MeasureTheory.isAddHaarMeasure_hausdorffMeasure, sin_two_pi, schnirelmannDensity_le_iff_forall, ProbabilityTheory.sub_half_inf_sub_mem_Ioo, norm_add_pow_two_real, sum_geometric_two_le, EuclideanGeometry.pi_div_three_le_angle_of_le_of_le, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, BohrMollerup.le_logGammaSeq, PNat.dist_eq, ProbabilityTheory.cgf_gaussianReal, le_schnirelmannDensity_iff, ProbabilityTheory.HasSubgaussianMGF.mgf_le, norm_sub_mul_self, NumberField.abs_discr_ge', log_add_one_le_harmonic, Metric.diam_le_of_subset_closedBall, NNReal.pow_rpow_inv_natCast, monomial_has_deriv_aux, vector_fourierIntegral_eq_integral_exp_smul, range_arctan, IsLowerSet.exists_subset_ball, fourier_real_eq_integral_exp_smul, NumberField.abs_discr_ge, setOf_liouvilleWith_subset_aux, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, AddCircle.homeomorphCircle'_symm_apply, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, integral_sin_pow_three, MeasureTheory.Measure.toSphere_real_apply_univ, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, CStarAlgebra.norm_le_natCast_iff_of_nonneg, Height.logHeightβ_sub_le, norm_iteratedFDeriv_clm_apply, NNReal.rpow_natCast, deriv_sqrt_mul_log, volume_closedBall, Function.Periodic.norm_qParam_lt_iff, Wallis.W_le, ENNReal.ofReal_eq_ofNat, Circle.isAddQuotientCoveringMap_exp, one_sub_sq_div_two_le_cos, antideriv_bernoulliFun, rpow_sum_le_const_mul_sum_rpow_of_nonneg, goldenRatio_lt_two, CircleDeg1Lift.translationNumber_eq_rat_iff, SimpleGraph.antitoneOn_extremalNumber_div_choose_two, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, Mathlib.Meta.NormNum.rpow_isRat_eq_inv_rpow, summable_condensed_iff_of_eventually_nonneg, Angle.abs_toReal_eq_pi_div_two_iff, Stirling.log_stirlingSeq_formula, summable_nat_rpow_inv, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, Complex.neg_pi_div_two_lt_arg_iff, exp_bound, cos_add_int_mul_two_pi, volume_pi_ball, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, Behrend.bound_aux', BoxIntegral.Box.upper_sub_lower_splitCenterBox, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, Chebyshev.psi_eq_psi_coe_floor, parallelogram_law_with_norm, MeasureTheory.Measure.haar.prehaar_le_index, NNReal.sqrt_eq_rpow, sin_pi_div_three, Behrend.log_two_mul_two_le_sqrt_log_eight, Circle.exp_eq_exp, Complex.volume_sum_rpow_le, Irrational.natCast_add, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, Complex.norm_log_one_add_le, Complex.mul_angle_le_norm_sub, tendsto_self_mul_const_pow_of_lt_one, Metric.iUnion_ball_nat_succ, Polynomial.Chebyshev.isLocalMin_T_real, Complex.integral_circleTransform, norm_pow_le_mul_norm, Polynomial.toAddCircle_X_pow_eq_fourier, Complex.arg_le_pi_div_two_iff, HasDerivAt.sqrt, Angle.toReal_coe, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, Circle.exp_two_pi_mul_int, arctan_mem_Ioo, Angle.two_zsmul_coe_div_two, AddCircle.scaled_exp_map_periodic, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, MeasureTheory.measure_lt_one_eq_integral_div_gamma, Orientation.neg_rotation_neg_pi_div_two, hasSum_sinh, exists_of_schnirelmannDensity_eq_zero, Polynomial.isRoot_cos_pi_div_five, image_circleMap_Ioc, exp_one_lt_three, integral_cos_pow, neg_pi_div_two_lt_arctan, cos_nat_mul_two_pi_sub_pi, AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const, NumberField.mixedEmbedding.convexBodySumFun_apply', Chebyshev.psi_eq_sum_theta, Stirling.log_stirlingSeq_diff_hasSum, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, norm_sub_pow_two_real, HolderConjugate.two_two, Gamma_two, artanh_eq_half_log, Complex.sin_bound, sin_sub_pi_div_two, ENNReal.pow_rpow_inv_natCast, tan_int_mul_pi_div_two, Wallis.tendsto_W_nhds_pi_div_two, Angle.sign_two_nsmul_eq_neg_sign_iff, cos_add_two_pi, NNReal.eventually_pow_one_div_le, isIntegral_two_mul_cos_rat_mul_pi, HurwitzZeta.hasSum_nat_sinZeta, BoxIntegral.unitPartition.integralSum_eq_tsum_div, norm_sub_sq, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, EuclideanGeometry.angle_orthogonalProjection_self, PiLp.dist_eq_card, WithLp.prod_norm_eq_of_nat, rpowIntegrandββ_le_rpow_sub_two_mul_self, stereoInvFunAux_apply, irrational_mul_natCast_iff, Complex.log_exp_eq_re_add_toIocMod, Gamma_mul_Gamma_add_half, sin_gt_sub_cube, two_mul_arctan_inv_2_sub_arctan_inv_7, EulerSine.integral_cos_mul_cos_pow_aux, Affine.Simplex.ninePointCircle_radius, Angle.toReal_neg_pi_div_two, LindemannWeierstrass.exp_polynomial_approx, norm_natCast, tendsto_card_div_pow_atTop_volume, cos_two_neg, sin_add_nat_mul_pi, hasSum_cosh, cos_nat_mul_pi, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, log_two_near_10, InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two, CircleDeg1Lift.le_iterate_of_add_int_le_map, enorm_natCast, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, pi_div_two_le_two, Asymptotics.isLittleO_iff_nat_mul_le, NNReal.dist_agmSequences_fst_snd, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, LiouvilleWith.mul_nat, AddCircle.norm_div_natCast, Stirling.le_log_factorial_stirling, curveIntegralFun_trans_aeeq_right, not_summable_indicator_one_div_natCast, EuclideanGeometry.Sphere.IsTangentAt.angle_eq_pi_div_two, UpperHalfPlane.dist_eq_iff_eq_sinh, integral_sin_sq, arcsin_eq_pi_div_two, exp_sub_sum_range_succ_isLittleO_pow, EuclideanSpace.volume_closedBall_fin_three, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, hasSum_zeta_four, cos_pi_div_four, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, FDerivMeasurableAux.norm_sub_le_of_mem_A, MeasureTheory.integral_mul_upcrossingsBefore_le_integral, Metric.PiNatEmbed.dist_def, deriv_sqrt_aux, ContinuousMap.HomotopyRel.trans_apply, Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, tan_nat_mul_pi_sub, arccos_eq_pi_div_two_sub_arcsin, cos_add_cos, Nat.closedBall_eq_Icc, pow_lt_iff_lt_log, tendsto_smoothingFun_comp, AkraBazziRecurrence.sumTransform_def, SzemerediRegularity.hundred_lt_pow_initialBound_mul, Padic.norm_eq_zpow_log_mulValuation, arcsin_le_pi_div_two, cos_three_mul, cos_two_pi, SimpleGraph.triangleRemovalBound_mul_cube_lt, Polynomial.Chebyshev.coeff_eq_iff_of_forall_abs_le_one, ZLattice.covolume.tendsto_card_div_pow, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, niven_sin, tsum_exp_neg_mul_int_sq, integral_cos_pow_aux, tan_two_mul, ContinuousMultilinearMap.norm_image_sub_le, Complex.norm_natCast, hasSum_cos, isTheta_choose, ENNReal.rpow_natCast, InnerProductGeometry.angle_zero_right, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, rpow_mul_natCast, MeasureTheory.lpNorm_mul_natCast, Unitary.norm_sub_one_lt_two_iff, Polynomial.coeff_le_of_roots_le, cos_pi_div_sixteen, Metric.diam_closedBall_eq, Nat.preimage_closedBall, BohrMollerup.f_nat_eq, UniformConvexSpace.uniform_convex, PseudoMetricSpace.le_two_mul_dist_ofPreNNDist, LSeries.summable_real_of_abscissaOfAbsConv_lt, Complex.norm_exp_I_mul_ofReal_sub_one, CircleDeg1Lift.translate_iterate, Angle.cos_add_pi_div_two, cos_two_pi_sub, arctan_add_arctan_lt_pi_div_two, CFC.sqrt_eq_rpow, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, Irrational.mul_natCast, InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two, Complex.arg_cos_add_sin_mul_I_sub, hasSum_log_one_add, BohrMollerup.f_add_nat_ge, Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, ProbabilityTheory.strong_law_ae, HasDerivWithinAt.norm_sq, Gamma_one_half_eq, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, pi_div_two_eq_arcsin, two_le_pi, Chebyshev.integral_one_div_log_sq_isBigO, Complex.natCast_log, LiouvilleWith.nat_mul, Complex.integral_exp_neg_rpow, irrational_sqrt_natCast_iff, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, Complex.norm_log_sub_logTaylor_le, NNReal.rpow_sub_natCast, EReal.coe_natCast, le_ofDigits_cantorToTernary_sum, taylor_mean_remainder_lagrange_iteratedDeriv, two_mul_arctan, RCLike.ofReal_natCast, NumberField.Units.regulator_eq_det, ENNReal.ofNat_le_ofReal, pi_div_two_pos, Complex.dist_self_conj, AddCircle.exists_norm_nsmul_le, arctan_eq_neg_pi_div_four, isEquivalent_choose, summable_schlomilch_iff_of_nonneg, exists_isMinOn_Gamma_Ioi, InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, circleMap_pi_div_two, exists_rat_abs_sub_lt_and_lt_of_irrational, ZLattice.covolume_div_covolume_eq_relIndex, MeasureTheory.Measure.haar.mem_prehaar_empty, HurwitzZeta.hasSum_nat_completedCosZeta, Polynomial.toAddCircle.integrable, ContinuousLinearMap.exists_approx_preimage_norm_le, sqrt_two_lt_three_halves, cos_le_one_sub_mul_cos_sq, approxOrderOf.image_pow_subset_of_coprime, norm_cauchyPowerSeries_le, log_nat_eq_sum_factorization, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, hasFDerivAt_norm_rpow, ofDigitsTerm_le, trapezoidal_error_le_of_c2, dist_birkhoffAverage_apply_birkhoffAverage, volume_ball, ENNReal.eventually_pow_one_div_le, AkraBazziRecurrence.one_add_smoothingFn_le_two, Path.Homotopy.hcomp_half, Stirling.stirlingSeq_one, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Path.Homotopy.hcomp_apply, HurwitzZeta.hasSum_nat_hurwitzZetaEven, NumberField.Units.finrank_mul_regOfFamily_eq_det, expNear_sub, PadicInt.norm_eq_zpow_neg_valuation, fib_golden_exp', norm_natCast, quarters_mem_preCantorSet, MeasureTheory.volume_sum_rpow_lt, cos_one_le, hasDerivAt_abs_rpow, Angle.coe_eq_zero_iff, norm_commutator_sub_one_le, NumberField.mixedEmbedding.convexBodySumFun_apply, Irrational.add_natCast, EuclideanGeometry.angle_le_pi_div_three_of_le_of_le, ZetaAsymptotics.term_tsum_of_lt, MeasureTheory.Measure.haar.add_prehaar_le_addIndex, AddCircle.norm_half_period_eq, Polynomial.Chebyshev.isLocalMax_T_real, Complex.norm_log_one_add_sub_self_le, tendsto_cos_neg_pi_div_two, norm_jacobiThetaβ_term, dist_midpoint_midpoint_le, deriv_Gamma_nat, trapezoidal_integral_ext, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, BoxIntegral.unitPartition.mem_box_iff, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, stereoInvFun_apply, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, tan_pi_div_two, Circle.exp_two_pi, Complex.normSq_add, Polynomial.Chebyshev.S_two_mul_real_cos, MeasureTheory.hausdorffMeasure_pi_real, arccos_le_pi_div_two, HasDerivWithinAt.sqrt, NNReal.rpow_add_natCast', WithLp.prod_edist_eq_of_L2, hasDerivAt_qaryEntropy, Metric.iUnion_ball_nat, UpperHalfPlane.cosh_dist, Padic.norm_p_pow, Filter.Tendsto.cesaro, Chebyshev.sum_PrimePow_eq_sum_sum, Behrend.lower_bound_le_one, Quaternion.expSeries_odd_of_imaginary, sq_cos_pi_div_six, spectrum.gelfand_formula, ProbabilityTheory.tsum_prob_mem_Ioi_lt_top, Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, AkraBazziRecurrence.tendsto_atTop_r_real, real_sqrt_lt_nat_sqrt_succ, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, Behrend.norm_of_mem_sphere, UpperHalfPlane.dist_coe_center, Subgroup.two_mul_withInfty_mem_strictPeriods, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, tendsto_sin_neg_pi_div_two, sqrtTwoAddSeries_two, Stirling.le_factorial_stirling, EuclideanGeometry.angle_self_right, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mul, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, coe_fib_eq, Int.norm_natCast, Gamma_strictMonoOn_Ici, LSeriesSummable.le_const_mul_rpow, EulerSine.sin_pi_mul_eq, CircleDeg1Lift.transnumAuxSeq_dist_lt, HurwitzZeta.hasSum_nat_sinKernel, Metric.uniformity_basis_dist_inv_nat_succ, bernstein.variance, arcsin_neg_one, bernstein_apply, logb_nat_eq_sum_factorization, sum_div_nat_floor_pow_sq_le_div_sq, tendsto_harmonic_sub_log, Height.mulHeightβ_add_le, sin_nat_mul_two_pi_sub, Metric.diam_thickening_le, ValueDistribution.proximity_sum_top_le, ENNReal.rpow_two, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos, Nat.realSqrt_mem_Ico, Complex.log_exp_eq_sub_toIocDiv, ProbabilityTheory.variance_sub, dist_integral_mulExpNegMulSq_comp_le, CircleDeg1Lift.tendsto_translation_number', Affine.Triangle.acuteAngled_iff_angle_lt, Polynomial.intervalIntegrable_mahlerMeasure, irrational_natCast_mul_iff, volume_real_closedBall, ENNReal.rpow_mul_natCast, sin_pi_div_two_sub, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, Polynomial.Chebyshev.leadingCoeff_le_of_forall_abs_le_one, two_mul_le_exp, exp_one_near_20, irrational_div_natCast_iff, arccos_eq_pi_div_two, HasStrictFDerivAt.sqrt, Gamma_eq_zero_iff, sum_le_exp_of_nonneg, circleIntegral.norm_integral_le_of_norm_le_const, arcsin_mem_Icc, log_two_gt_d9, MeasureTheory.volume_sum_rpow_le, toNNReal_le_natCast, ofDigits_eq_sum_add_ofDigits, natCeil_logb_natCast, exists_natCast_add_one_lt_pow_of_one_lt, MeasureTheory.tendsto_indicator_ge, cos_pi_div_two, Convex.taylor_approx_two_segment, CircleDeg1Lift.map_nat_add, Matrix.frobenius_norm_def, Orientation.inner_rotation_pi_div_two_right, gold_sub_goldConj, RingSeminorm.exists_index_pow_le, Complex.arg_one_add_mem_Ioo, Complex.normSq_sub, Function.Periodic.im_invQParam, ENNReal.ofReal_le_ofNat, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, ENNReal.toReal_natCast, logb_pow, CircleDeg1Lift.translationNumber_of_map_pow_eq_add_int, integral_id, Behrend.bound, Complex.arg_exp_mul_I, Behrend.four_zero_nine_six_lt_exp_sixteen, AddCircle.volume_closedBall, ArchimedeanClass.stdPart_ofNat, ENNReal.rpow_natCast_mul, stereoToFun_apply, rpow_sum_le_const_mul_sum_rpow, MeasureTheory.lpNorm_fun_mul_natCast, exists_nat_abs_mul_sub_round_le, pow_mul_norm_iteratedFDeriv_fourier_le, Angle.toReal_pi_div_two, dist_birkhoffAverage_birkhoffAverage, AkraBazziRecurrence.asympBound_def, arctan_inv_of_neg, Orientation.inner_rotation_pi_div_two_left, Complex.sub_conj, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, Affine.Simplex.excenterWeights_empty_lt_inv_two, Chebyshev.integrableOn_theta_div_id_mul_log_sq, FormalMultilinearSeries.radius_inv_eq_limsup, BohrMollerup.f_add_nat_le, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, sin_eq_tsum, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, arccos_le_pi_div_four, IsApproximateSubgroup.card_mul_self_le, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, AffineIsometryEquiv.dist_pointReflection_self_real, Padic.norm_eq_zpow_neg_valuation, NumberField.house.exists_ne_zero_int_vec_house_le, abs_log_sub_add_sum_range_le, MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_aux, SlashInvariantForm.exists_one_half_le_im_and_norm_le, Complex.arg_lt_pi_div_two_iff, Nat.dist_eq, taylor_mean_remainder, BoxIntegral.Box.mem_splitCenterBox, sin_sq_eq_half_sub, Unitary.norm_sub_one_sq_eq, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, InnerProductSpace.volume_ball, fourierIntegral_real_eq_integral_exp_smul, deriv_mulExpNegMulSq, cos_pi_div_eight, EisensteinSeries.norm_eq_max_natAbs, norm_jacobiTheta_sub_one_le, Nat.Primes.not_summable_one_div, PiNat.mem_cylinder_iff_dist_le, HurwitzZeta.hasSum_nat_cosZeta, NumberField.mixedEmbedding.covolume_idealLattice, injOn_tan, ValueDistribution.proximity_add_top_le, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, deriv_qaryEntropy, Asymptotics.isLittleO_sum_range_of_tendsto_zero, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, monotoneOn_deriv_descPochhammer_eval, Circle.exp_inj, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, sinh_eq_tsum, MeasureTheory.uniformIntegrable_average_real, integral_sin_mul_cosβ, cos_eq_tsum, Angle.two_zsmul_neg_pi_div_two, CFC.rpow_natCast, Orientation.inner_rotation_pi_div_two_left_smul, EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two, goldenRatio_mul_fib_succ_add_fib, InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero, ofNat_lt_toNNReal, RingSeminorm.isBoundedUnder, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, MeasureTheory.lpNorm_fun_natCast_mul, summable_nat_pow_inv, integral_sin_pow_aux, hasDerivWithinAt_taylorWithinEval_at_Icc, integral_comp_abs, MeasureTheory.hausdorffMeasure_prod_real, Circle.exp_add_two_pi, ContinuousMap.HomotopyWith.trans_apply, harmonic_le_one_add_log, RCLike.sqrt_eq_real_add_ite, PadicInt.norm_int_le_pow_iff_dvd, ProbabilityTheory.mgf_fun_id_gaussianReal, Polynomial.Chebyshev.S_two_mul_real_cosh, Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, norm_iteratedFDerivWithin_prod_le, Metric.diam_ball, tsum_geometric_two, Angle.two_zsmul_toReal_eq_two_mul, ProbabilityTheory.sum_variance_truncation_le, IsApproximateAddSubgroup.card_nsmul_le, PiCountable.dist_summable, summable_exp_neg_nat, sin_nat_mul_pi, ArithmeticFunction.log_apply, hasSum_one_div_nat_pow_mul_cos, EuclideanGeometry.oangle_orthogonalProjection_self, tendsto_pow_const_mul_const_pow_of_abs_lt_one, ModularFormClass.exp_decay_sub_atImInfty, NNReal.rpow_two, CircleDeg1Lift.commute_add_nat, Irrational.natCast_sub, sum_range_le_log_div, Chebyshev.primeCounting_sub_theta_div_log_isBigO, two_pi_pos, ProbabilityTheory.gaussianPDFReal_def, RCLike.natCast_re, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, cos_eq_cos_iff, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty, ENNReal.ofReal_eq_natCast, hasDerivWithinAt_taylor_coeff_within, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, ArithmeticFunction.vonMangoldt_sum, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Behrend.exp_neg_two_mul_le, InnerProductGeometry.angle_zero_left, tendsto_integral_mul_one_add_inv_smul_sq_pow, NumberField.Units.regOfFamily_div_regulator, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two, integral_sin_pow_even_mul_cos_pow_even, Metric.diam_closedBall, sin_two_pi_sub, qaryEntropy_strictAntiOn, sinOrderIso_apply, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, ValueDistribution.characteristic_add_top_eventuallyLE, Angle.cos_eq_zero_iff, floor_real_sqrt_eq_nat_sqrt, Angle.angle_eq_iff_two_pi_dvd_sub, sin_two_mul, InnerProductSpace.volume_ball_of_dim_odd, Irrational.natCast_div, le_log_of_pow_le, MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le, cos_int_mul_two_pi_add_pi, smoothingFun_le, strongConcaveOn_iff_convex, NNReal.rpow_natCast_mul, ProbabilityTheory.Fernique.normThreshold_eq, le_sum_ofDigitsTerm_digits, Quaternion.expSeries_even_of_imaginary, sin_eq_sin_iff, Complex.arg_eq_pi_div_two_iff, CircleDeg1Lift.map_sub_nat, ZMod.toAddCircle_natCast, UpperHalfPlane.dist_eq, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, circleIntegral.norm_integral_lt_of_norm_le_const_of_lt, AddCircle.exists_norm_eq_of_isOfFinAddOrder, AkraBazziRecurrence.bi_min_div_two_pos, norm_nsmul_le, CircleDeg1Lift.transnumAuxSeq_def, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, Height.mulHeightβ_sum_le, circleAverage_def, toNNReal_eq_natCast, Chebyshev.theta_eq_log_primorial, UpperHalfPlane.norm_qParam_lt_one, NumberField.Ideal.tendsto_norm_le_div_atTopβ, unitInterval.qRight_zero_right, Irrational.natCast_mul, NumberField.mixedEmbedding.logMap_apply_of_norm_eq_one, ProbabilityTheory.strong_law_aux6, AlternatingMap.norm_image_sub_le_of_bound, convexOn_descPochhammer_eval, NNReal.rpow_add_natCast, hasSum_geometric_two, NNReal.coe_natCast, LSeries.norm_term_eq, ProbabilityTheory.variance_le_sq_of_bounded, Height.mulHeightβ_sub_le, ProbabilityTheory.hasFPowerSeriesAt_mgf, Complex.integral_exp_neg_mul_rpow, lp.norm_eq_card_dsupport, abs_sin_half, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, two_mul_cos_mul_cos, sqrtTwoAddSeries_succ, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, taylorWithinEval_succ, HasDerivAt.norm_sq, MeasureTheory.Measure.haar.mem_addPrehaar_empty, ZLattice.covolume.tendsto_card_le_div', EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, pow_rpow_inv_natCast, ZetaAsymptotics.term_one, Polynomial.hermite_eq_deriv_gaussian', BoxIntegral.unitPartition.box_lower, ENNReal.natCast_le_ofReal, Affine.Simplex.dist_point_centroid, Path.Homotopy.trans_apply, HurwitzZeta.oddKernel_functional_equation, tan_pi_div_two_sub, MeasureTheory.exists_pos_ball, arcsin_of_le_neg_one, Liouville.frequently_exists_num, sin_int_mul_two_pi_sub, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, unitary.two_mul_one_sub_le_norm_sub_one_sq, ofCauchy_natCast, Int.toNat_add_toNat_neg_eq_norm, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, cos_pi_div_six, ENNReal.ofReal_lt_natCast, range_arcsin, nnnorm_two, InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero, rothNumberNat_isLittleO_id, MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countable, coe_intFib_eq, circleAverage_eq_integral_add, Gamma_nat_add_one_add_half, ContinuousMap.Homotopy.trans_apply, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, ENNReal.toNNReal_natCast_eq_toNNReal, pi_lt_four, Polynomial.Chebyshev.rootMultiplicity_T_real, periodic_circleMap, Angle.sign_two_nsmul_eq_sign_iff, Complex.add_conj, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, LiouvilleWith.add_nat, ProbabilityTheory.add_half_inf_sub_mem_Ioo, tendsto_self_mul_const_pow_of_abs_lt_one, tsum_geometric_two', arcsin_le_neg_pi_div_two, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, inv_sqrt_two_sub_one, Orientation.oangle_sub_right_smul_rotation_pi_div_two, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, Angle.sin_pi_div_two_sub, sin_add_pi_div_two, tendsto_fib_div_fib_succ_atTop, cos_sub_nat_mul_two_pi, NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply, LinearGrowth.Real.eventually_atTop_exists_nat_between, NNReal.coe_two, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le, imaginaryPart_apply_coe, Nat.realSqrt_lt_ratSqrt_add_inv_prec, Complex.cos_bound, Complex.cpow_inv_two_im_eq_sqrt, sinh_two_mul, Complex.cpow_inv_two_re, one_le_pi_div_two, cauchy_natCast, UnitAddCircle.mem_approxAddOrderOf_iff, ZetaAsymptotics.zeta_limit_aux1, pi_gt_sqrtTwoAddSeries, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, cosh_le_exp_half_sq, tsirelson_inequality, Gamma_ofNat_eq_factorial, Complex.abs_arg_le_pi_div_two_iff, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, NumberField.Units.regOfFamily_div_regOfFamily, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, summable_one_div_nat_rpow, LiouvilleWith.frequently_lt_rpow_neg, AkraBazziRecurrence.asympBound_def', ValueDistribution.characteristic_sum_top_le, Nat.roughNumbersUpTo_card_le', Polynomial.Chebyshev.isMinOn_T_real, schnirelmannDensity_le_div, Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, tan_nat_mul_pi, log_div_sqrt_antitoneOn, irrational_natCast_sub_iff, mellin_eq_fourierIntegral, HurwitzZeta.hasSum_nat_completedSinZeta, integral_cos_pow_three, fourierIntegral_eq', AddCircle.norm_coe_eq_abs_iff, ModularGroup.exists_one_half_le_im_smul, Polynomial.Chebyshev.isLocalExtr_T_real_iff, Complex.norm_natCast_cpow_of_pos, Metric.diam_ball_eq, arctan_inv_2_add_arctan_inv_3, arctan_one, InnerProductSpaceable.parallelogram_identity, ValueDistribution.characteristic_add_top_le, Metric.iUnion_inter_closedBall_nat, AddCircle.toCircle_apply_mk, CFC.rpow_sqrt_nnreal, Angle.two_nsmul_eq_pi_iff, NumberField.mixedEmbedding.covolume_integerLattice, Polynomial.hermite_eq_deriv_gaussian, one_half_lt_eulerMascheroniSeq_six, exp_half, Orientation.inner_smul_rotation_pi_div_two_right, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, sin_pi_over_two_pow_succ, trapezoidal_integral_one, bijOn_sin, toNNReal_lt_ofNat, MeasureTheory.uniformIntegrable_average, qaryEntropy_strictMonoOn, tan_pi_div_six, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ArchimedeanClass.stdPart_natCast, ProbabilityTheory.variance_fun_sub, Rat.AbsoluteValue.exists_pos_eq_pow_neg, natLog_le_logb, Complex.angle_le_mul_norm_sub, Angle.sign_two_zsmul_eq_neg_sign_iff, ZetaAsymptotics.term_sum_of_lt, EuclideanSpace.volume_ball_fin_three, arctan_inv_sqrt_three, mul_add_one_le_add_one_pow, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, PadicInt.norm_le_pow_iff_norm_lt_pow_add_one, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, integral_log_sin_zero_pi, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero, hasSum_geometric_two', arcsin_of_one_le, Complex.norm_prime_cpow_le_one_half, log_natCast_nonneg, AkraBazziRecurrence.eventually_one_sub_smoothingFn_nonneg, rpow_two, MultilinearMap.norm_image_sub_le_of_bound, ENNReal.ofNat_lt_ofReal, PiNat.dist_eq_of_ne, PadicInt.norm_le_pow_iff_le_valuation, Complex.norm_ofNat, Polynomial.toAddCircle_monomial_eq_smul_fourier, preCantorSet_succ, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp, tsum_geometric_inv_two_ge, tendsto_tan_pi_div_two, Orientation.neg_rotation_pi_div_two, approxAddOrderOf.image_nsmul_subset, exists_rat_abs_sub_le_and_den_le, RCLike.norm_natCast, PadicInt.norm_le_pow_iff_mem_span_pow, pow_div_factorial_le_exp, MeasureTheory.measureReal_abs_gt_le_integral_charFun, cos_pi_div_thirty_two, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, bernoulliFun_one, NumberField.Units.abs_det_eq_abs_det, BoxIntegral.unitPartition.index_apply, niven_angle_eq, Orientation.oangle_sub_left_smul_rotation_pi_div_two, Liouville.exists_pos_real_of_irrational_root, Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.HasSubgaussianMGF.cgf_le, ZLattice.covolume.tendsto_card_div_pow', binEntropy_eq_log_two, pow_mul_le_of_le_of_pow_mul_le, Polynomial.Chebyshev.isMaxOn_T_real, CuspFormClass.exists_bound, integral_sqrt_one_sub_sq, cos_nat_mul_pi_sub, Polynomial.Chebyshev.rootMultiplicity_U_real, Orientation.oangle_add_right_smul_rotation_pi_div_two, sin_bound, ContinuousMultilinearMap.norm_iteratedFDeriv_le, Orientation.inner_smul_rotation_pi_div_two_left, surjOn_sin, sin_pi_div_thirty_two, Height.logHeightβ_zpow, sqrtTwoAddSeries_one, neg_pi_div_two_lt_arcsin, trapezoidal_error_le, ContinuousMultilinearMap.norm_iteratedFDeriv_le', Chebyshev.theta_eq_sum_Icc, cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, sin_pi_div_six, EulerSine.integral_cos_pow_eq, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, ENNReal.natCast_lt_ofReal, hasDerivAt_mulExpNegMulSq, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, image_tan_Ioo, CongruenceSubgroup.strictWidthInfty_Gamma, irrational_add_natCast_iff, tendsto_mod_div_atTop_nhds_zero_nat, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, inner_sum_smul_sum_smul_of_sum_eq_zero, Complex.exp_bound, one_half_lt_eulerMascheroniConstant, numDerangements_tendsto_inv_e, le_integral_rpowIntegrandββ_one, MeasureTheory.norm_one_sub_charFun_le_two, EuclideanGeometry.inner_weightedVSub, transcendental_liouvilleNumber, LiouvilleWith.exists_pos, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, ProbabilityTheory.variance_add, Hamming.norm_eq_hammingNorm, PiLp.norm_eq_of_nat, pi_lt_sqrtTwoAddSeries, ZLattice.covolume.tendsto_card_le_div, UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStrip, coe_fib_eq', injOn_sin, bernoulliFun_mul, Complex.toIocMod_arg, norm_add_sq_real, hasFPowerSeriesOnBall_linear_zero, Angle.coe_toIocMod, norm_iteratedFDerivWithin_comp_le, NumberField.mixedEmbedding.fundamentalCone.expMap_single_symm_apply, sin_sub_sin, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, ODE.FunSpace.dist_iterate_next_le, hasDerivAt_Gamma_one_half, quarter_mem_preCantorSet, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, rpow_inv_natCast_pow, Gamma_mul_Gamma_add_half_of_pos, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, sigmoid_zero, ProbabilityTheory.strong_law_aux7, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, Complex.norm_sub_one_sq_eqOn_sphere, Complex.sqrt_neg_I, ZMod.toAddCircle_intCast, Complex.abs_arg_lt_pi_div_two_iff, NumberField.Embeddings.coeff_bdd_of_norm_le, HasFDerivWithinAt.sqrt, lt_sin_mul, NumberField.exists_ideal_in_class_of_norm_le, Complex.sqrt_eq_real_add_ite, RCLike.norm_two, CircleDeg1Lift.lt_iterate_pos_iff, Polynomial.fourierCoeff_toAddCircle_natCast, summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, SimpleGraph.tendsto_turanDensity, norm_add_sq, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, fderivWithin_sqrt, eulerMascheroniSeq'_six_lt_two_thirds, cos_sub_cos, summable_condensed_iff_of_nonneg, tendsto_sum_range_one_div_nat_succ_atTop, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, cos_nat_mul_two_pi_sub, norm_jacobiThetaβ'_term_le, CircleDeg1Lift.tendsto_translation_numberβ, RCLike.sqrt_neg_I, norm_iteratedFDeriv_comp_le, ZMod.toAddCircle_apply, ceil_logb_natCast, ProbabilityTheory.strong_law_Lp, tendsto_tan_neg_pi_div_two, bernoulliFun_eq_integral, Angle.natCast_mul_eq_nsmul, tsum_geometric_inv_two, cos_pi_over_two_pow, not_summable_one_div_natCast, binEntropy_two_inv_add, norm_iteratedFDeriv_prod_le, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_apply, Angle.toIocMod_toReal, UpperHalfPlane.cosh_half_dist, norm_add_mul_self, EuclideanSpace.volume_ball, fourierChar_apply, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, Unitary.two_mul_one_sub_le_norm_sub_one_sq, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, Angle.sign_coe_pi_div_two, Irrational.sub_natCast, Angle.zsmul_eq_iff, lt_log_of_pow_lt, Circle.exp_int_mul_two_pi, cos_half, RCLike.sqrt_I, Path.trans_apply, natCastle_toNNReal', UpperHalfPlane.exp_half_dist, Metric.diam_sphere_eq, tendsto_arctan_atTop, NumberField.InfinitePlace.one_le_mult, integral_sin_mul_cos_sq, real_inner_sub_sub_self, Complex.norm_exp_sub_one_le, Algebra.trace_complex_apply, quadratic_root_cos_pi_div_five, cos_periodic, rpow_sub_natCast', ArithmeticFunction.vonMangoldt_apply, MeasureTheory.lpNorm_div_natCast, AkraBazziRecurrence.dist_r_b, sqrtTwoAddSeries_lt_two, cosh_three_mul, CongruenceSubgroup.strictPeriods_Gamma, Complex.div_natCast_im, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, Complex.ofReal_natCast, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, NNReal.rpow_sub_natCast', OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, pi_gt_three, quadratic_le_exp_of_nonneg, MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finite, one_sub_sq_div_two_lt_cos, summable_pow_mul_exp_neg_nat_mul, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, Chebyshev.theta_le_log4_mul_x, NumberField.mixedEmbedding.logMap_apply, PadicInt.exists_pow_neg_lt, cos_sub_nat_mul_pi, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, hasDerivAt_norm_rpow, PadicInt.norm_p, two_mul_arctan_sub_pi, GromovHausdorff.ghDist_le_of_approx_subsets, tan_pi_div_three, pi_div_two_le_arcsin, LiouvilleWith.sub_nat_iff, sin_three_mul, arccos_lt_pi_div_two, sin_add_nat_mul_two_pi, tan_eq_zero_iff, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, Metric.mem_closure_range_iff_nat, volume_real_ball, fib_golden_conj_exp, zero_mem_lowerBounds_smoothingSeminormSeq_range, Complex.circleTransformDeriv_periodic, hasSum_one_div_nat_pow_mul_sin, NumberField.mixedEmbedding.fundamentalCone.intNorm_coe, NumberField.mixedEmbedding.logMap_apply_of_norm_one, Polynomial.Chebyshev.roots_T_real, tendsto_arctan_atBot, two_mul_arctan_add_pi, ProbabilityTheory.strong_law_aux4, nat_sqrt_le_real_sqrt, Angle.two_nsmul_coe_div_two, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, pow_mul_norm_iteratedFDeriv_fourierIntegral_le, abs_sin_eq_one_iff, Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, mapsTo_sin_Ioo, exists_nat_pos_inv_lt, circleIntegral.norm_integral_le_of_norm_le_const', BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter, Complex.GammaSeq_eq_approx_Gamma_integral, SimpleGraph.triangleRemovalBound_le, floor_logb_natCast, deriv_bernoulliFun, LSeriesSummable.isBigO_rpow, Wallis.W_eq_factorial_ratio, Chebyshev.psi_le, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, smoothingSeminormSeq_bddBelow, Angle.coe_toIcoMod, log_two_lt_d9, tendsto_sub_mul_tsum_nat_rpow, hasSum_zeta_two, norm_midpoint_lt_iff, sin_eq_neg_one_iff, sin_pi_div_sixteen, IsApproximateSubgroup.card_pow_le, UpperHalfPlane.sinh_half_dist_add_dist, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one, two_mul_arctan_inv_3_add_arctan_inv_7, circleAverage_eq_intervalAverage, Nat.preimage_ball, NumberField.abs_discr_ge_of_isTotallyComplex, Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, cos_add_pi_div_two, arctan_inv_of_pos, lt_log_one_add_of_pos, tendsto_sum_pi_div_four, Nat.norm_cast_le, rpow_neg_one_add_norm_sq_le, derivWithin_sqrt, ModularFormClass.qExpansion_isBigO, fourierChar_apply', cos_sub_two_pi, Angle.cos_pi_div_two_sub, ZLattice.le_norm_of_le_abs_repr, EuclideanGeometry.oangle_self_orthogonalProjection, cos_two_mul, Nat.isClosedEmbedding_coe_real, cos_int_mul_two_pi_sub_pi, circleIntegrable_def, Polynomial.coeff_bdd_of_roots_le, tendsto_pow_const_mul_const_pow_of_lt_one, Nat.Primes.summable_rpow, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, not_summable_natCast_inv, SzemerediRegularity.pow_mul_m_le_card_part, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, Asymptotics.isLittleO_iff_nat_mul_le_aux, Chebyshev.integral_theta_div_log_sq_isBigO, sin_sub_nat_mul_pi, exists_forall_sphere_dist_add_le_two_sub, IsUpperSet.exists_subset_ball, CircleDeg1Lift.le_iterate_pos_iff, AddCircle.norm_le_half_period, hasStrictDerivAt_sqrt, toNNReal_coe_nat, arcsin_lt_pi_div_two, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, tan_sub_nat_mul_pi, Function.Periodic.norm_qParam, iter_deriv_rpow_const, HurwitzZeta.hurwitzOddFEPair_k, cosh_log, arctan_lt_pi_div_two, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, fderiv_sqrt, Polynomial.Chebyshev.eval_T_real_eq_one_iff, SzemerediRegularity.one_le_m_coe, integral_sin_sq_mul_cos, arctan_sqrt_three, NumberField.house_nat_mul, hasSum_sin, EisensteinSeries.abs_norm_eq_max_natAbs, Complex.norm_cpow_inv_nat, EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_ne, cos_eq_one_iff, gold_lt_two, curveIntegralFun_trans_aeeq_left, pow_le_iff_le_log, rpow_sub_natCast, Chebyshev.integral_theta_div_log_sq_isLittleO, binEntropy_lt_log_two, InnerProductSpace.Core.cauchy_schwarz_aux', EulerSine.integral_cos_pow_pos, SlashInvariantForm.vAdd_width_periodic, schnirelmannDensity_lt_iff, CircleDeg1Lift.iterate_le_of_map_le_add_int, sin_sq_pi_over_two_pow, sq_sin_pi_div_three, UnitAddCircle.mem_addWellApproximable_iff, BohrMollerup.f_add_nat_eq, stereographic_apply, ModularGroup.three_le_four_mul_im_sq_of_mem_fd, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, integral_pow_mul_le_of_le_of_pow_mul_le, Stirling.log_stirlingSeq_diff_le_geo_sum, ProbabilityTheory.strong_law_aux1, nnnorm_natCast, Complex.neg_pi_div_two_le_arg_iff, ENNReal.ofReal_lt_ofNat, Behrend.le_sqrt_log, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, Behrend.two_div_one_sub_two_div_e_le_eight, ProbabilityTheory.mgf_gaussianReal, monotoneOn_sin, SzemerediRegularity.coe_m_add_one_pos, cos_nat_mul_two_pi_add_pi, MeasureTheory.lpNorm_natCast_mul, Irrational.div_natCast, Angle.coe_two_pi, ProbabilityTheory.strong_law_ae_simpleFunc_comp, log_pow, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, schnirelmannDensity_setOf_modeq_one, Complex.norm_log_one_sub_inv_sub_self_le, ProbabilityTheory.mgf_id_gaussianReal, NNReal.mk_natCast, exp_bound', tendsto_fib_succ_div_fib_atTop, Behrend.bound_aux, sin_nat_mul_pi_sub, arcsin_image_Icc, schnirelmannDensity_le_of_notMem, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, Metric.nhds_basis_ball_inv_nat_succ, CFC.sqrt_rpow_nnreal, Filter.Tendsto.cesaro_smul, Hamming.dist_eq_hammingDist, hasSum_arctan, Complex.cpow_inv_two_im_eq_neg_sqrt, tendsto_abs_tan_atTop, cos_sub_int_mul_two_pi, rpow_add_natCast, log_natCast_le_rpow_div, VectorFourier.norm_fourierSMulRight_le, EisensteinSeries.abs_norm_eq_max_natAbs_neg, EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_ne, AkraBazziRecurrence.h_rec, summable_geometric_two', norm_commutator_units_sub_one_le, toNNReal_lt_natCast, EuclideanGeometry.law_cos, Gamma_integrand_isLittleO, ProbabilityTheory.strong_law_aux2, one_div_sub_pow_hasFPowerSeriesOnBall_zero, goldenRatio_sub_goldenConj, neg_pi_div_two_le_arcsin, EuclideanGeometry.angle_self_orthogonalProjection, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Behrend.lower_bound_le_one', ZLattice.covolume.tendsto_card_le_div'', Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, tendsto_pow_const_div_const_pow_of_one_lt, integral_sin_pow_odd, EuclideanGeometry.dist_affineCombination, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, Angle.nsmul_toReal_eq_mul, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, realPart_apply_coe, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, BohrMollerup.logGammaSeq_add_one, ZetaAsymptotics.term_welldef, irrational_sub_natCast_iff, exp_one_near_10, rpow_div_two_eq_sqrt, VectorFourier.norm_fourierPowSMulRight_le, EuclideanGeometry.dist_smul_vadd_eq_dist, dist_birkhoffAverage_birkhoffAverage_le, summable_pow_mul_jacobiThetaβ_term_bound, circleMap_zero_pow, ZetaAsymptotics.term_sum_one, cos_sq, AffineSubspace.mem_perpBisector_iff_inner_eq, not_summable_one_div_on_primes, Orientation.rotation_pi_div_two, ProbabilityTheory.strong_law_aux3, norm_iteratedFDerivWithin_mul_le, VectorFourier.norm_fourierSMulRight, LiouvilleWith.mul_nat_iff, InnerProductSpace.volume_closedBall, cos_int_mul_two_pi_sub, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, unitary.norm_sub_one_lt_two_iff, cantorSequence_eq_self_sub_sum_cantorToTernary, Matrix.frobenius_nnnorm_def, LiouvilleWith.nat_sub, Padic.norm_le_pow_iff_norm_lt_pow_add_one, MeasureTheory.Measure.volumeIoiPow_apply_Iio, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, taylor_mean_remainder_cauchy, abs_ofDigits_sub_ofDigits_le, binEntropy_le_log_two, summable_geometric_two, MeasureTheory.Egorov.exists_notConvergentSeq_lt, HurwitzZeta.evenKernel_functional_equation, strongConvexOn_iff_convex, Complex.norm_log_natCast_le_rpow_div, norm_add_sub_norm_sub_le_two_mul_min, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, tendsto_card_div_pow_atTop_volume', sum_range_sub_log_div_le, exp_one_pow, exp_approx_end, CircleDeg1Lift.tendsto_translationNumber, UpperHalfPlane.sinh_half_dist, ProbabilityTheory.strong_law_ae_real, summable_one_div_nat_pow, InnerProductSpace.volume_closedBall_of_dim_odd, ProbabilityTheory.strong_law_aux5, norm_add_mul_self_real, liouville_liouvilleNumber, UpperHalfPlane.dist_le_iff_le_sinh, SimpleGraph.isEquivalent_extremalNumber, ArithmeticFunction.vonMangoldt_le_log, tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, sin_pi_div_eight, binEntropy_strictAntiOn, arctan_eq_pi_div_four, MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore, integral_Ioi_inv_one_add_sq, Complex.volume_sum_rpow_lt_one, taylor_mean_remainder_bound, Complex.betaIntegral_convergent_left, Nat.ratSqrt_mem_Ioc, schnirelmannDensity_setOf_Odd, UpperHalfPlane.dist_coe_center_sq, Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle, DiffContOnCl.ball_subset_image_closedBall, Padic.norm_p, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, binEntropy_two_inv, NNReal.rpow_mul_natCast, Polynomial.Chebyshev.isLocalExtr_T_real, norm_add_pow_two, HasFDerivAt.sqrt, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, half_mul_log_add_log_abs, ruzsaSzemerediNumberNat_lower_bound, sum_mul_eq_sub_integral_mul, real_inner_add_add_self, unitary.norm_sub_one_sq_eq, Complex.arg_exp, hofer, Nat.not_irrational, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter, tan_add_nat_mul_pi, LiouvilleWith.nat_add_iff, unitInterval.eq_closedBall, BoxIntegral.unitPartition.tag_apply, IsPrimitiveRoot.arg, tendsto_sin_pi_div_two, Angle.cos_sub_pi_div_two, RCLike.normSq_add, arccos_zero, Polynomial.Chebyshev.isExtrOn_T_real, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, Polynomial.instTwoPiPos, integral_gaussian_Ioi, Polynomial.Chebyshev.coeff_le_of_forall_abs_le_one, Circle.exp_eq_one, norm_iteratedFDeriv_smul_le, cosh_eq, PiCountable.dist_eq_tsum, strictMonoOn_sin, fderiv_norm_rpow, unitInterval.half_le_symm_iff, UpperHalfPlane.cosh_dist', Polynomial.toAddCircle_X_eq_fourier_one, MeasureTheory.GridLines.T_univ, hasSum_pow_div_log_of_abs_lt_one, Orientation.inner_smul_rotation_pi_div_two_smul_right, GaussianFourier.verticalIntegral_norm_le, CircleIntegrable.out, NNReal.rpow_inv_natCast_pow, Complex.borelCaratheodory, Complex.div_natCast, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, fourier_add_half_inv_index, cos_add_nat_mul_two_pi, Affine.Simplex.Equilateral.angle_eq_pi_div_three, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, Angle.two_nsmul_neg_pi_div_two, CircleDeg1Lift.translationNumber_pow, CuspFormClass.exp_decay_atImInfty, approxOrderOf.image_pow_subset, integral_sin_sq_mul_cos_sq, integral_mul_rpow_one_add_sq, ProbabilityTheory.strong_law_ae_of_measurable, Nat.ratSqrt_le_realSqrt, tendsto_log_nat_add_one_sub_log, norm_sub_pow_two, UpperHalfPlane.tanh_half_dist, Angle.toReal_coe_eq_self_add_two_pi_iff, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, NumberField.Units.finrank_mul_regulator_eq_det, IsApproximateAddSubgroup.card_add_self_le, Complex.norm_two, ENNReal.rpow_inv_natCast_pow, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, strictMonoOn_tan, integral_Iic_inv_one_add_sq, isIntegral_two_mul_cos_rat_mul_pi, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, approxAddOrderOf.image_nsmul_subset_of_coprime, rothNumberNat_le_ruzsaSzemerediNumberNat', cantorSet_eq_union_halves, cos_eq_neg_one_iff, BoxIntegral.unitPartition.box.upper_sub_lower, sin_sub_two_pi, Wallis.W_succ, integral_cos_sq, TorusIntegrable.function_integrable, NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral, log_of_nat_eq_posLog, HurwitzZeta.LSeriesHasSum_sin, ruzsaSzemerediNumberNat_asymptotic_lower_bound, NumberField.InfinitePlace.map_natCast, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, NumberField.Units.sum_mult_mul_log, Complex.arg_mul_cos_add_sin_mul_I_sub, rpow_neg_natCast, cosh_eq_tsum, posLog_pow, sinh_three_mul, exp_one_gt_two, cos_pi_div_three, Icc_eq_closedBall, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, le_sin_mul, Polynomial.norm_coeff_le_choose_mul_mahlerMeasure, Gamma_nat_eq_factorial, spectralValueTerms_of_lt_natDegree, Angle.toReal_eq_pi_div_two_iff, hasDerivAt_Gamma_nat, Complex.abs_cpow_inv_two_im, tendsto_const_div_pow, Nat.Prime.irrational_sqrt, Complex.norm_le_sqrt_two_mul_max, unitInterval.two_mul_sub_one_mem_iff, posLog_sum, hasSum_zeta_nat, ValueDistribution.characteristic_sum_top_eventuallyLE, Angle.toReal_coe_eq_self_sub_two_pi_iff, fib_succ_sub_goldenConj_mul_fib, AddChar.zmod_intCast, BoxIntegral.unitPartition.diam_boxIcc, norm_mul_sub_norm_div_le_two_mul_min, surjOn_tan, arcsin_eq_neg_pi_div_two, Metric.nhds_basis_ball_inv_nat_pos, EuclideanGeometry.Sphere.secondInter_eq_lineMap, MeasureTheory.mul_upcrossingsBefore_le, sum_mul_eq_sub_integral_mulβ, sin_sub_int_mul_two_pi, irrational_natCast_add_iff, ArithmeticFunction.vonMangoldt_apply_prime, fourierInv_eq', norm_sub_mul_self_real, Padic.norm_lt_pow_iff_norm_le_pow_sub_one, ZLattice.covolume.tendsto_card_div_pow'', Polynomial.toAddCircle_C_eq_smul_fourier_zero, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter, cos_sub_pi_div_two, strictConcaveOn_cos_Icc, ofNat_le_toNNReal, MeasureTheory.measure_unitBall_eq_integral_div_gamma, CStarAlgebra.exists_sum_four_unitary, Subadditive.apply_mul_add_le, exp_neg_one_lt_half, ENNReal.ofReal_natCast, ZetaAsymptotics.term_of_lt, norm_mul_sub_norm_div_le_two_mul, Metric.iUnion_closedBall_nat, Gamma_neg_nat_eq_zero, AddCircle.homeomorphCircle'_apply, schnirelmannDensity_setOf_mod_eq_one, volume_pi_closedBall, EuclideanGeometry.angle_self_left, taylor_mean_remainder_lagrange, Complex.borelCaratheodory_zero, sin_eq_one_iff, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, HurwitzZeta.hasSum_nat_cosKernelβ, InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, fib_succ_sub_goldenRatio_mul_fib, tendsto_factorial_div_pow_self_atTop, ProbabilityTheory.Fernique.normThreshold_add_one, Angle.sin_sub_pi_div_two, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, CircleDeg1Lift.iterate_pos_eq_iff, cos_nat_mul_two_pi, BoundedContinuousFunction.dist_le_two_norm, one_lt_sqrt_two, Circle.exp_sub_two_pi, EuclideanSpace.edist_eq, Complex.norm_sub_one_sq_eq_of_norm_one, ProbabilityTheory.variance_fun_add, CircleDeg1Lift.translate_pow, sum_mul_eq_sub_sub_integral_mul, Polynomial.fourierCoeff_toAddCircle, Rat.AbsoluteValue.apply_le_sum_digits, rpowIntegrandββ_one_ge_rpow_sub_two, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, sin_add_int_mul_two_pi, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, tendsto_prod_pi_div_two, one_half_le_sum_primes_ge_one_div, exp_sub_sum_range_isBigO_pow, hasDerivAt_sqrt, SchwartzMap.one_add_le_sup_seminorm_apply, qExpansion_coeff_isBigO_of_norm_isBigO, padicNorm_two_harmonic, Polynomial.Chebyshev.roots_U_real_nodup, taylor_within_apply, exp_nat_mul, Complex.approx_Gamma_integral_tendsto_Gamma_integral, cosh_two_mul, Chebyshev.eventually_primeCounting_le, Padic.norm_int_le_pow_iff_dvd, Affine.Simplex.ninePointCircle_center, Gamma_three_div_two_lt_one, deriv_sqrt_mul_log', Padic.norm_p_zpow, Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_one, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Chebyshev.psi_le_const_mul_self, FormalMultilinearSeries.radius_eq_liminf, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, Polynomial.Chebyshev.roots_T_real_nodup, Behrend.exists_large_sphere_aux, cos_pi_div_two_sub, ENNReal.ofReal_le_natCast, exists_forall_closed_ball_dist_add_le_two_mul_sub, NNReal.dist_gm_am_le, fourier_eq', Stirling.second_wallis_limit, InnerProductSpace.volume_ball_of_dim_even, integral_pow_abs_sub_uIoc, EuclideanSpace.volume_closedBall, sqrt_eq_rpow, Angle.toReal_eq_neg_pi_div_two_iff, exists_forall_closed_ball_dist_add_le_two_sub, two_mul_sin_mul_sin, Height.logHeight_pow, toNNReal_eq_ofNat, AkraBazziRecurrence.bi_min_div_two_lt_one, CFC.conjugate_rpow_neg_one_half, CircleDeg1Lift.commute_sub_nat, tendsto_harmonic_sub_log_add_one, Complex.arg_I, Metric.diam_cthickening_le, posLog_nat_mul, summable_nat_rpow, ODE.FunSpace.dist_iterate_next_apply_le, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, Complex.div_natCast_re, summable_exp_nat_mul_iff, LiouvilleWith.add_nat_iff, irrational_natCast_div_iff, cos_two_mul', irrational_sqrt_two, RCLike.normSq_sub, rpow_natCast, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, exists_int_int_abs_mul_sub_le, four_mul_arctan_inv_5_sub_arctan_inv_239, schnirelmannDensity_mul_le_card_filter, LiouvilleWith.nat_add, sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, le_iff_norm_sqrt_mul_rpow, Mathlib.Meta.NormNum.nnreal_rpow_isRat_eq_inv_nnreal_rpow, MeasureTheory.volume_sum_rpow_lt_one, Polynomial.Chebyshev.C_two_mul_real_cos, Complex.dist_conj_self, CircleDeg1Lift.tendsto_translation_numberβ', cantorSequence_get_succ, ZMod.toCircle_eq_circleExp, Polynomial.Chebyshev.roots_U_real, BoundedContinuousFunction.dist_le_two_norm', ZLattice.covolume_div_covolume_eq_relIndex', CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux, rpow_natCast_mul, Metric.uniformity_basis_dist_inv_nat_pos, hasSum_log_sub_log_of_abs_lt_one, mul_pow_le_nat_floor_pow, Complex.arg_eq_neg_pi_div_two_iff, posLog_norm_sum_le, EulerSine.integral_cos_mul_cos_pow_even, integral_sin_pow_even, Affine.Simplex.points_vsub_eulerPoint, bernoulliFun_eval_half, natCast_le_toNNReal, Angle.two_nsmul_toReal_eq_two_mul, Complex.norm_natCast_cpow_of_re_ne_zero, cos_bound, Angle.sign_coe_neg_pi_div_two, Int.Matrix.exists_ne_zero_int_vec_norm_le, HasStrictDerivAt.sqrt, Behrend.exp_four_lt, NumberField.mixedEmbedding.convexBodySum_mem, niven, hasSum_L_function_mod_four_eval_three, Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, Function.Periodic.exp_decay_sub_of_bounded_at_inf, PiLp.edist_eq_of_L2, quarter_mem_cantorSet, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, NumberField.IsCMField.regOfFamily_realFunSystem, ContinuousAlternatingMap.norm_image_sub_le, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, Affine.Triangle.dist_point_centroid, summable_geometric_two_encode, log_doublingGamma_eq, two_mul_sin_mul_cos, deriv_sqrt, tendsto_one_add_div_pow_exp, Asymptotics.isLittleO_iff_nat_mul_le', arcsin_one, ofDigits_digits_sum_eq, Function.Periodic.exp_decay_of_zero_at_inf, lt_pow_iff_log_lt, deriv2_sqrt_mul_log, ConvexOn.lipschitzOnWith_of_abs_le, sum_trapezoidal_integral_adjacent_intervals, AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T, coe_sinOrderIso_apply, BoxIntegral.unitPartition.tag_mem_smul_span, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, Stirling.tendsto_self_div_two_mul_self_add_one, PiLp.norm_eq_card, Wallis.le_W, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Angle.nsmul_eq_iff, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, MeasureTheory.Measure.integrable_pow_neg_integrablePower, sin_pi_div_four, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, norm_jacobiThetaβ_term_fderiv_le, natCast_lt_toNNReal, posLog_add, GaussianFourier.integral_rexp_neg_mul_sq_norm, Behrend.exists_large_sphere, sin_sq_pi_over_two_pow_succ, Int.Matrix.exists_ne_zero_int_vec_norm_le', binEntropy_strictMonoOn, LiouvilleWith.nat_mul_iff, Complex.angle_exp_exp, AkraBazziRecurrence.isLittleO_self_div_log_id, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, Polynomial.Chebyshev.C_two_mul_real_cosh, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, continuousOn_tan_Ioo, norm_add_sub_norm_sub_le_two_mul, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, unitary.continuousOn_argSelfAdjoint, Rat.AbsoluteValue.le_pow_log, exists_cos_eq_zero, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, CFC.rpow_sqrt, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, ConcaveOn.lipschitzOnWith_of_abs_le, sin_sub_nat_mul_two_pi, one_add_norm_le_sqrt_two_mul_sqrt, tendsto_logb_nat_add_one_sub_logb, ModularGroup.coe_truncatedFundamentalDomain
|
instNeg π | CompOp | 795 mathmath: cos_add_nat_mul_pi, Behrend.roth_lower_bound, hasDerivAt_arccos, HurwitzZeta.isBigO_atTop_evenKernel_sub, range_sin, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, CFC.posPart_smul_of_nonpos, real_inner_div_norm_mul_norm_eq_neg_one_iff, ValueDistribution.characteristic_even, MeasureTheory.SimpleFunc.posPart_sub_negPart, sinh_eq, not_continuousAt_inv_log_neg_one, mellin_eq_fourier, Quaternion.coeComplex_re, sin_eq_zero_iff_cos_eq, ProbabilityTheory.gammaPDF_of_nonneg, iteratedDeriv_odd_cos, MeasureTheory.charFun_eq_fourierIntegral', hasFDerivAt_fourierChar_neg_bilinear_left, tan_pi_sub, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, CircleDeg1Lift.translate_inv_apply, bernoulliFun_eval_one_sub, ProbabilityTheory.measure_ge_le_exp_cgf, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, HurwitzZeta.hasSum_int_cosKernelβ, cos_add_pi, ProbabilityTheory.covariance_neg_left, deriv_negMulLog, Angle.two_zsmul_eq_pi_iff, deriv_abs, norm_jacobiThetaβ_term_le, cos_sub_pi, Complex.GammaIntegral_eq_mellin, neg_pi_div_two_eq_arcsin, mapsTo_cos, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, ContinuousMap.attachBound_apply_coe, mapsTo_cos_Ioo, fourierIntegral_eq, ProbabilityTheory.gaussianReal_map_neg, intervalIntegral.intervalIntegral_eq_integral_uIoc, Complex.arg_neg_I, fderiv_fourierChar_neg_bilinear_right_apply, Quaternion.continuous_imI, Quaternion.coeComplex_mul, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, ProbabilityTheory.mgf_neg, log_neg_natCast_nonneg, MeasureTheory.Integrable.neg_part, tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero, EisensteinSeries.summand_bound_of_mem_verticalStrip, circleMap_neg_pi_div_two, Function.Periodic.norm_qParam_le_of_one_half_le_im, Complex.angle_exp_one, CStarAlgebra.norm_or_neg_norm_mem_spectrum, rpow_neg_one, Behrend.roth_lower_bound_explicit, goldenRatio_mul_goldenConj, Antitone.tendsto_alternating_series_of_tendsto_zero, Complex.norm_eq_one_iff', MeasureTheory.tilted_neg_same', Circle.starRingEnd_addChar, neg_sqrt_lt_of_sq_lt, Quaternion.imI_coeComplex, variationOnFromTo.eq_of_ge, strictAntiOn_arccos, integral_log_sin_zero_pi_div_two, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, ContinuousMap.toNNReal_neg_algebraMap, differentiableOn_arcsin, norm_cexp_neg_mul_sq, Polynomial.Chebyshev.eval_T_real_node, LiouvilleWith.neg_iff, monomial_has_deriv_aux, Angle.toReal_coe_eq_self_iff_mem_Ioc, vector_fourierIntegral_eq_integral_exp_smul, CompactlySupportedContinuousMap.nnrealPart_smul_neg, range_arctan, fourier_real_eq_integral_exp_smul, deriv_arccos, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, ProbabilityTheory.cdf_expMeasure_eq, Function.Periodic.norm_qParam_lt_iff, mulExpNegSq_apply, artanh_bijOn, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, circleMap_zero_inv, logb_inv, WeakFEPair.hf_zero', one_sub_le_exp_neg, sigmoid_neg, deriv_abs_neg, integral_exp_neg_mul_rpow, HurwitzKernelBounds.isBigO_atTop_F_int_one, Angle.abs_toReal_eq_pi_div_two_iff, Complex.neg_pi_div_two_lt_arg_iff, Polynomial.Chebyshev.integral_measureT, log_neg_eq_log, Orientation.inner_rightAngleRotation_swap', ProbabilityTheory.variance_fun_neg, QuadraticForm.equivalent_signType_weighted_sum_squared, Complex.arg_mul_eq_add_arg_iff, MeasureTheory.withDensityα΅₯_eq_withDensity_pos_part_sub_withDensity_neg_part, Complex.UnitDisc.im_neg, inv_goldenConj, Complex.UnitDisc.im_star, Angle.toReal_coe, arctan_mem_Ioo, MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_part, GammaIntegral_convergent, MeasureTheory.measure_lt_one_eq_integral_div_gamma, logb_eq_zero, Orientation.neg_rotation_neg_pi_div_two, MeasureTheory.SignedMeasure.toJordanDecomposition_eq_of_eq_add_withDensity, Quaternion.instCStarRingReal, sin_add_int_mul_pi, strictMonoOn_artanh, gold_mul_goldConj, neg_pi_div_two_lt_arctan, cos_nat_mul_two_pi_sub_pi, cosPartialEquiv_target, hasStrictDerivAt_arccos, inv_goldenRatio, sin_antiperiodic, arsinh_neg, HasStrictFDerivAt.abs, NumberField.mixedEmbedding.convexBodySum_neg_mem, sin_sub_pi_div_two, Complex.hasDerivAt_GammaIntegral, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, Quaternion.linearIsometryEquivTuple_symm_apply, Complex.log_exp_eq_re_add_toIocMod, integrable_one_add_norm, Angle.toReal_mem_Ioc, Angle.toReal_neg_pi_div_two, EuclideanGeometry.Sphere.mul_dist_eq_neg_power_of_dist_center_le_radius, sin_add_nat_mul_pi, cos_nat_mul_pi, EReal.coe_neg, CFC.negPart_smul_of_nonpos, tan_neg, Orientation.areaForm_swap, HasDerivWithinAt.cos, integrableOn_Ioi_cpow_iff, summable_abs_int_rpow, PeriodPair.weierstrassP_bound, hasDerivAt_abs_neg, tan_nat_mul_pi_sub, range_cos, tendsto_exp_neg_atTop_nhds_zero, hasDerivWithinAt_abs, ProbabilityTheory.covariance_fun_neg_right, Angle.sin_add_pi, Angle.toReal_coe_eq_self_iff, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Angle.sin_neg, neg_one_lt_goldenConj, Irrational.neg, ModularGroup.lcRow0Extend_symm_apply, integrableOn_Ioi_norm_cpow_iff, niven_sin, tsum_exp_neg_mul_int_sq, MeasureTheory.JordanDecomposition.real_smul_neg, hasSum_cos, arccos_image_Icc, Angle.cos_add_pi, MeasureTheory.llr_tilted_right, CFC.rpow_neg, logb_neg_base_eq_logb, Quaternion.nnnorm_star, Angle.cos_add_pi_div_two, finite_integral_rpow_sub_one_pow_aux, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, Complex.GammaIntegral_ofReal, mellinInv_eq_fourierIntegralInv, Complex.integral_exp_neg_rpow, polarCoord_target, orthonormalBasis_one_dim, hasDerivWithinAt_arccos_Ici, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, tendsto_integral_exp_smul_cocompact, StarAlgHom.realContinuousMapOfNNReal_apply, Complex.ofReal_neg, arctan_eq_neg_pi_div_four, Angle.neg_pi_lt_toReal, Quaternion.coeComplex_add, sq_le, Complex.partialGamma_add_one, NormedSpace.normalize_smul, NNReal.rpow_neg_one, MeasureTheory.MemLp.neg_part, sigmoid_def, mellinInv_eq_fourierInv, intervalIntegral.integrableOn_Ioo_rpow_iff, HurwitzZeta.hasSum_int_cosKernel, fourier_real_eq, tendsto_cos_neg_pi_div_two, norm_jacobiThetaβ_term, Angle.toReal_neg_eq_neg_toReal_iff, ProbabilityTheory.integral_truncation_eq_intervalIntegral, deriv_Gamma_nat, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, HurwitzZeta.sinKernel_neg, fourierIntegral_convergent_iff', integrable_rpow_neg_one_add_norm_sq, artanh_surjOn, Behrend.lower_bound_le_one, sigmoid_mul_rexp_neg, HasFDerivAt.abs, Quaternion.continuous_imJ, HasFDerivWithinAt.abs, tendsto_sin_neg_pi_div_two, Angle.cos_sub_pi, deriv_inv_log, InnerProductSpace.Core.inner_im_symm, ProbabilityTheory.exponentialPDF_eq, HurwitzZeta.hasSum_nat_sinKernel, Quaternion.coeComplex_zero, arcsin_neg_one, Quaternion.instCompleteSpaceReal, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left, sin_nat_mul_two_pi_sub, fderivWithin_cos, norm_exp_mul_sq_le, Complex.log_exp_eq_sub_toIocDiv, norm_sum_neg_one_pow_le, HurwitzKernelBounds.F_nat_one_le, ProbabilityTheory.Kernel.HasSubgaussianMGF.neg, ModularGroup.lcRow0Extend_apply, Complex.HadamardThreeLines.norm_invInterpStrip, Circle.exp_neg, Gamma_eq_zero_iff, HurwitzKernelBounds.isBigO_atTop_F_nat_one, arcsin_mem_Icc, arccos_neg, deriv2_binEntropy, ProbabilityTheory.exponentialPDF_of_nonneg, ProbabilityTheory.paretoPDF_of_le, posLog_neg, le_rpow_one_add_norm_iff_norm_le, integral_exp_mul_I_eq_sinc, circleAverage_neg_radius, MeasureTheory.Lp.coeFn_negPart_eq_max, Complex.arg_one_add_mem_Ioo, Polynomial.Chebyshev.node_eq_neg_one, Function.Periodic.im_invQParam, Complex.arg_exp_mul_I, arctan_neg, RCLike.conj_im_ax, HasDerivAt.cos, arctan_inv_of_neg, BoundedContinuousFunction.neg_norm_le_apply, Complex.det_conjAe, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, ProbabilityTheory.covariance_neg_right, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, iteratedDeriv_add_one_cos, Complex.conj_im, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, sin_eq_tsum, exp_abs_le, cos_int_mul_pi_sub, intervalIntegral.integrableOn_Ioo_cpow_iff, RCLike.ofReal_neg, Complex.arg_mem_Ioc, Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, fourierIntegral_real_eq_integral_exp_smul, deriv_mulExpNegMulSq, sin_neg, integral_exp_mul_I_eq_sin, InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi, norm_jacobiTheta_sub_one_le, ProbabilityTheory.covariance_fun_neg_left, goldenConj_mul_goldenRatio, injOn_tan, MeasureTheory.lintegral_deriv_eq_volume_image_of_antitoneOn, cos_eq_tsum, sinh_neg, Angle.two_zsmul_neg_pi_div_two, MeasureTheory.tilted_neg_same, InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi, fourierIntegral_eq_half_sub_half_period_translate, artanh_eq_zero_iff, Quaternion.re_exp, RCLike.inv_im, uniformContinuous_neg, Angle.two_zsmul_toReal_eq_two_mul, log_eq_zero, Complex.neg_pi_lt_arg, HurwitzZeta.hasSum_int_evenKernel, summable_exp_neg_nat, hasSum_one_div_nat_pow_mul_cos, neg_inv_le_log, Quaternion.normSq_eq_norm_mul_self, EuclideanGeometry.oangle_orthogonalProjection_self, AkraBazziRecurrence.GrowsPolynomially.neg, ModularFormClass.exp_decay_sub_atImInfty, ProbabilityTheory.gaussianReal_neg, Circle.invOn_arg_exp, ProbabilityTheory.gaussianPDFReal_def, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty, MeasureTheory.SimpleFunc.negPart_map_norm, Behrend.exp_neg_two_mul_le, Complex.arg_conj, derivWithin_cos, Complex.arg_eq_nhds_of_im_neg, isLittleO_exp_neg_mul_rpow_atTop, sin_two_pi_sub, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, sInf_neg, Complex.UnitDisc.re_neg, sinOrderIso_apply, NumberField.mixedEmbedding.convexBodySumFun_neg, Angle.cos_eq_zero_iff, InnerProductGeometry.cos_eq_neg_one_iff_angle_eq_pi, hasStrictDerivAt_abs, cos_int_mul_two_pi_add_pi, MeasureTheory.integral_charFun_Icc, norm_of_nonpos, hasDerivAt_cos, Circle.star_addChar, fderiv_cos, isBigO_at_im_infty_jacobiTheta_sub_one, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, arcsin_neg, exp_log_of_neg, Complex.range_arg, neg_one_lt_tanh, CFC.rpow_neg_one_eq_cfc_inv, unitInterval.sigmoid_neg, Complex.log_mul_eq_add_log_iff, Complex.UnitDisc.im_conj, EReal.toReal_neg_eq, injOn_arcsin, Quaternion.coeComplex_imK, Complex.integral_exp_neg_mul_rpow, Complex.mul_I_re, UniformConcaveOn.neg, fourier_eq, closedBall_zero_eq_Icc, EReal.coe_coe_sign, Polynomial.hermite_eq_deriv_gaussian', HurwitzZeta.hasSum_int_sinKernel, finite_integral_one_add_norm, spectralRadius_mem_spectrum_or, cos_pi_sub, sin_int_mul_two_pi_sub, ball_zero_eq_Ioo, HurwitzZeta.isBigO_atTop_oddKernel, EisensteinSeries.summable_one_div_norm_rpow, range_arcsin, tendsto_integral_exp_smul_cocompact_of_inner_product, MeasureTheory.integral_biUnion_eq_sum_powerset, Complex.neg_pi_lt_log_im, arccos_eq_pi, MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part, LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re, Units.val_inv_cfcRpow, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, CFC.rpow_neg_one_eq_inv, signedDist_lineMap_left, sin_int_mul_pi_sub, ProbabilityTheory.cgf_neg, trapezoidal_error_symm, arcsin_le_neg_pi_div_two, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, integral_exp_neg_rpow, WeakFEPair.hf_zero, ProbabilityTheory.HasSubgaussianMGF.neg, integrable_mul_exp_neg_mul_sq, tendsto_fib_div_fib_succ_atTop, rpow_neg_eq_inv_rpow, sq_lt, signedDist_anticomm, iteratedDeriv_even_cos, Quaternion.normSq_exp, ArchimedeanClass.stdPart_neg, EuclideanGeometry.cos_eq_neg_one_iff_angle_eq_pi, ProbabilityTheory.moment_truncation_eq_intervalIntegral, logb_inv_base, ArchimedeanClass.stdPart_sub_eq_right, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, LiouvilleWith.frequently_lt_rpow_neg, UpperHalfPlane.le_dist_coe, Polynomial.Chebyshev.isMinOn_T_real, circleMap_neg_radius, Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, mellin_eq_fourierIntegral, hasStrictDerivAt_abs_neg, fourierIntegral_eq', HurwitzZeta.oddKernel_neg, Quaternion.im_exp, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, Algebra.leftMulMatrix_complex, ProbabilityTheory.exp_neg_integrableOn_Ioc, Quaternion.re_coeComplex, Circle.argEquiv_symm_apply, Angle.two_nsmul_eq_pi_iff, Polynomial.hermite_eq_deriv_gaussian, neg_sqrt_le_of_sq_le, neg_one_le_sinc, bijOn_sin, sign_neg, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, bijOn_cos, strictMonoOn_arcsin, one_sub_lt_exp_neg, Rat.AbsoluteValue.exists_pos_eq_pow_neg, arccos_lt_pi, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, integrableOn_Ioi_rpow_iff, eulerMascheroniConstant_eq_neg_deriv, MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply, NumberField.mixedEmbedding.convexBodyLT_neg_mem, cos_sub_int_mul_pi, integral_log_sin_zero_pi, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_antitoneOn, signedDist_neg, ProbabilityTheory.paretoPDF_eq, neg_one_le_real_inner_of_norm_eq_one, rpow_logb_of_neg, sin_sub_int_mul_pi, MeasureTheory.withDensity_ofReal_mutuallySingular, signedDist_vsub_self_rev, Orientation.neg_rotation_pi_div_two, MeasureTheory.measureReal_abs_gt_le_integral_charFun, MeasureTheory.exp_neg_llr, integral_exp_neg_Ioi, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Orientation.rotation_eq_matrix_toLin, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, Orientation.inner_rightAngleRotation_swap, NumberField.mixedEmbedding.polarSpaceCoord_target', MeasureTheory.exp_neg_llr', integral_comp_neg_Iic, neg_one_le_cos, sinh_sub_cosh, Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, pow_mul_le_of_le_of_pow_mul_le, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Polynomial.Chebyshev.isMaxOn_T_real, HasStrictFDerivAt.cos, integral_sqrt_one_sub_sq, deriv_cos, ProbabilityTheory.exponentialCDFReal_eq, Gamma_eq_integral, cos_nat_mul_pi_sub, signedDist_smul, surjOn_sin, neg_pi_div_two_lt_arcsin, Quaternion.continuous_im, AddCircle.norm_neg_period, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, hasDerivAt_mulExpNegMulSq, image_tan_Ioo, sin_sub_pi, NumberField.mixedEmbedding.normAtPlace_neg, differentiableOn_arccos, fourierIntegral_convergent_iff, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, inner_sum_smul_sum_smul_of_sum_eq_zero, numDerangements_tendsto_inv_e, le_integral_rpowIntegrandββ_one, EuclideanGeometry.inner_weightedVSub, Quaternion.imK_coeComplex, cauchy_neg, signedDist_smul_of_neg, injOn_sin, ContinuousLinearMap.rotation_apply, Complex.toIocMod_arg, integrableOn_exp_neg_Ioi, contDiffOn_arccos, hasDerivAt_Gamma_one_half, Complex.I_mul, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, HurwitzZeta.hasSum_int_oddKernel, Complex.arg_of_im_neg, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, Complex.I_mul_re, Quaternion.inner_def, ContinuousMap.neg_norm_le_apply, MeasureTheory.SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingular, cos_sub_cos, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, norm_jacobiThetaβ'_term_le, tendsto_tan_neg_pi_div_two, one_sub_div_pow_le_exp_neg, Angle.toIocMod_toReal, hasDerivAt_abs, RCLike.conj_im, cos_eq_zero_iff_sin_eq, tan_int_mul_pi_sub, hasDerivAt_Gamma_one, fourier_bilin_convolution_eq_integral, hasStrictDerivAt_cos, mapsTo_sin, AkraBazziRecurrence.deriv_smoothingFn, Complex.re_eq_neg_norm, tendsto_integral_exp_smul_cocompact, exp_neg_mul_rpow_isLittleO_exp_neg, cos_neg, ArithmeticFunction.sum_moebius_mul_log_eq, exp_neg_mul_sq_isLittleO_exp_neg, integral_exp_mul_Ioi, Complex.neg_re, surjOn_cos, NNReal.rpow_neg, HurwitzKernelBounds.F_nat_zero_zero_sub_le, negMulLog_eq_neg, cos_antiperiodic, Complex.arg_inv, iteratedDeriv_even_sin, Quaternion.inner_self, CStarAlgebra.rpow_neg_one_le_one, sign_apply_eq, signedDist_vadd_left, strictMonoOn_one_add_div_one_sub, MeasureTheory.JordanDecomposition.real_smul_posPart_neg, summable_pow_mul_exp_neg_nat_mul, fourierIntegral_half_period_translate, Monotone.tendsto_alternating_series_of_tendsto_zero, HasFDerivAt.cos, ProbabilityTheory.gammaPDF_eq, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, Quaternion.norm_exp, ContinuousMap.comp_attachBound_mem_closure, ofCauchy_neg, cos_sub_nat_mul_pi, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, inv_gold, ProbabilityTheory.rpow_abs_le_mul_max_exp, tendsto_rpow_neg_div, neg_mulExpNegMulSq_neg, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, arccos_neg_one, AkraBazziRecurrence.GrowsPolynomially.neg_iff, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, Circle.surjOn_exp_neg_pi_pi, UniformConvexOn.neg, tendsto_rpow_neg_atTop, hasSum_one_div_nat_pow_mul_sin, tendsto_arctan_atBot, ProbabilityTheory.variance_neg, neg_one_le_sin, ProbabilityTheory.condVar_neg, deriv_cos, integrableOn_Ioi_exp_neg_mul_sq_iff, mapsTo_sin_Ioo, RCLike.I_mul_re, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, ProbabilityTheory.covariance_const_sub_left, deriv2_qaryEntropy, negMulLog_def, sin_eq_neg_one_iff, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, IntervalIntegrable.iff_comp_neg, MeasureTheory.Lp.coeFn_negPart, cos_add_pi_div_two, Orientation.inner_rightAngleRotationAuxβ_right, tendsto_sum_pi_div_four, rpow_neg_one_add_norm_sq_le, MeasureTheory.SignedMeasure.toMeasureOfLEZero_real_apply, EuclideanGeometry.oangle_self_orthogonalProjection, cos_int_mul_two_pi_sub_pi, integral_comp_neg_Ioi, Nat.Primes.summable_rpow, Complex.inv_im, MeasureTheory.JordanDecomposition.real_smul_negPart_neg, deriv_cos', sin_sub_nat_mul_pi, integral_gaussian, Function.Periodic.norm_qParam, LiouvilleWith.neg, Circle.argPartialEquiv_target, Orientation.inner_rightAngleRotation_right, ValueDistribution.proximity_even, CuspFormClass.exp_decay_atImInfty', Affine.Simplex.ExcenterExists.signedInfDist_excenter, hasSum_sin, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, Complex.toMatrix_conjAe, neg_one_le_mulExpNegMulSq_one, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, integral_pow_mul_le_of_le_of_pow_mul_le, neg_one_lt_goldConj, HurwitzKernelBounds.isBigO_exp_neg_mul_of_le, hasDerivWithinAt_abs_neg, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty', Complex.neg_pi_div_two_le_arg_iff, UpperHalfPlane.val_J, monotoneOn_sin, ENNReal.rpow_neg_one, cos_nat_mul_two_pi_add_pi, cosh_sub_sinh, differentiable_fourierChar_neg_bilinear_right, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, MeasureTheory.SignedMeasure.rnDeriv_neg, closedBall_rpow_sub_one_eq_empty_aux, tanh_eq, ProbabilityTheory.measure_le_le_exp_mul_mgf, sin_nat_mul_pi_sub, nnreal_trichotomy, arcsin_image_Icc, integral_rpow_mul_exp_neg_mul_Ioi, tendsto_integral_exp_inner_smul_cocompact, hasSum_arctan, Complex.cpow_inv_two_im_eq_neg_sqrt, ProbabilityTheory.measure_ge_le_exp_mul_mgf, RCLike.re_le_neg_norm_iff_eq_neg_norm, ContinuousMap.polynomial_comp_attachBound, iteratedDeriv_odd_sin, Antitone.cauchySeq_alternating_series_of_tendsto_zero, nnreal_dichotomy, Gamma_integrand_isLittleO, neg_pi_div_two_le_arcsin, Quaternion.coeComplex_imJ, Behrend.lower_bound_le_one', exists_isMIntegralCurve_iff_exists_isMIntegralCurveOn_Ioo, HurwitzKernelBounds.F_nat_zero_le, ContinuousMap.toNNReal_neg_one, EuclideanGeometry.dist_affineCombination, Angle.nsmul_toReal_eq_mul, exp_neg_one_gt_d9, exp_neg_integrableOn_Ioi, EReal.coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal, Quaternion.imJ_coeComplex, CliffordAlgebraComplex.Q_apply, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, EuclideanGeometry.dist_smul_vadd_eq_dist, summable_pow_mul_jacobiThetaβ_term_bound, integrable_exp_neg_mul_sq_iff, hasFDerivAt_fourierChar_neg_bilinear_right, WeakFEPair.f_modif_aux1, trapezoidal_integral_symm, Quaternion.coeComplex_imI, Polynomial.Chebyshev.node_mem_Icc, irrational_neg_iff, goldConj_mul_gold, differentiable_fourierChar_neg_bilinear_left, Quaternion.coe_ofComplex, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, ENNReal.rpow_neg, CircleDeg1Lift.translationNumber_units_inv, ContinuousMap.polynomial_comp_attachBound_mem, integral_exp_neg_Ioi_zero, ruzsaSzemerediNumberNat_lower_bound, Hyperreal.coe_neg, Complex.arg_exp, log_inv, variationOnFromTo.eq_neg_swap, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Polynomial.Chebyshev.isExtrOn_T_real, integral_gaussian_Ioi, cosh_eq, strictMonoOn_sin, integrable_exp_neg_mul_sq, hasSum_pow_div_log_of_abs_lt_one, HasStrictDerivAt.cos, GaussianFourier.verticalIntegral_norm_le, Quaternion.instNormOneClassReal, Complex.ofReal_comp_neg, MeasureTheory.rnDeriv_tilted_right, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, Angle.two_nsmul_neg_pi_div_two, Complex.image_exp_Ioc_eq_sphere, CuspFormClass.exp_decay_atImInfty, TFAE_exists_lt_isLittleO_pow, MeasureTheory.measureReal_biUnion_eq_sum_powerset, mk_neg, Angle.toReal_coe_eq_self_add_two_pi_iff, Angle.sin_antiperiodic, Quaternion.linearIsometryEquivTuple_apply, artanh_injOn, strictMonoOn_tan, HurwitzZeta.isBigO_atTop_cosKernel_sub, Monotone.cauchySeq_alternating_series_of_tendsto_zero, cos_eq_neg_one_iff, HolderConjugate.inv_sub_one, sign_apply_eq_of_ne_zero, ruzsaSzemerediNumberNat_asymptotic_lower_bound, rpow_neg_natCast, Complex.GammaIntegral_convergent, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, NumberField.mixedEmbedding.convexBodyLT'_neg_mem, hasDerivAt_Gamma_nat, logb_neg_eq_logb, NumberField.mixedEmbedding.polarCoordReal_target, hasSum_zeta_nat, logDeriv_cos, sin_add_pi, cos_add_int_mul_pi, Complex.polarCoord_target, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right, surjOn_tan, arcsin_eq_neg_pi_div_two, EuclideanGeometry.Sphere.secondInter_eq_lineMap, Quaternion.coeComplex_one, Affine.Simplex.excenterWeightsUnnorm_compl, parallelepiped_orthonormalBasis_one_dim, exp_neg, sign_of_neg, intervalIntegral.integral_comp_neg, Angle.cos_antiperiodic, VectorFourier.hasFDerivAt_fourierChar_smul, Hyperreal.IsSt.neg, cosh_neg, strictConcaveOn_cos_Icc, fourierIntegral_real_eq, HasFDerivWithinAt.cos, Quaternion.continuous_imK, MeasureTheory.measure_unitBall_eq_integral_div_gamma, exp_neg_one_lt_half, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, Gamma_neg_nat_eq_zero, rpow_neg, ProbabilityTheory.measure_le_le_exp_cgf, HurwitzZeta.hasSum_nat_cosKernelβ, Angle.sin_sub_pi_div_two, CFC.rpow_neg_mul_rpow, sSup_neg, sin_mem_Icc, Quaternion.coe_real_complex_mul, tanh_surjOn, sinc_neg, hasDerivWithinAt_arccos_Iic, cos_pi, contDiffOn_arcsin, MeasureTheory.JordanDecomposition.real_smul_def, Hyperreal.st_neg, fderiv_fourierChar_neg_bilinear_left_apply, Function.locallyFinsuppWithin.logCounting_even, cos_int_mul_pi, tanh_neg, CFC.rpow_mul_rpow_neg, sInf_def, fourier_eq', EisensteinSeries.summand_bound, ModularFormClass.exp_decay_sub_atImInfty', Complex.neg_re_eq_norm, cos_mem_Icc, Angle.toReal_eq_neg_pi_div_two_iff, Quaternion.continuous_re, ProbabilityTheory.covariance_const_sub_right, CFC.conjugate_rpow_neg_one_half, summable_nat_rpow, inner_im_symm, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, Complex.neg_im, Circle.argEquiv_apply_coe, MeasureTheory.toReal_rnDeriv_tilted_right, le_iff_norm_sqrt_mul_rpow, Complex.det_conjLIE, mul_exp_neg_le_exp_neg_one, Orientation.areaForm_rightAngleRotation_left, tanh_bijOn, exp_neg_one_lt_d9, Complex.arg_eq_neg_pi_div_two_iff, Quaternion.norm_toLp_equivTuple, Quaternion.exp_eq, Angle.two_nsmul_toReal_eq_two_mul, Angle.sign_coe_neg_pi_div_two, HurwitzZeta.isBigO_atTop_sinKernel, real_inner_mem_Icc_of_norm_eq_one, niven, Function.Periodic.exp_decay_sub_of_bounded_at_inf, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, integrableAtFilter_rpow_atTop_iff, tendsto_pow_mul_exp_neg_atTop_nhds_zero, Function.Periodic.exp_decay_of_zero_at_inf, deriv2_sqrt_mul_log, rpow_neg_ofNat, NNReal.summable_rpow, coe_sinOrderIso_apply, deriv2_negMulLog, MeasureTheory.Measure.integrable_pow_neg_integrablePower, GaussianFourier.integral_rexp_neg_mul_sq_norm, HurwitzZeta.hasSum_int_evenKernelβ, Angle.sin_sub_pi, MeasureTheory.neg_llr, ValueDistribution.logCounting_even, Angle.coe_neg, Complex.angle_exp_exp, Angle.cos_coe_pi, continuousOn_tan_Ioo, inv_goldConj, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, Quaternion.norm_star, hasDerivAt_negMulLog, arccos_injOn
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instOne π | CompOp | 2182 mathmath: List.norm_prod_le, cos_add_nat_mul_pi, withSeminorms_iff_mem_nhds_isVonNBounded, arctan_eq_arccos, BoundingSieve.nu_lt_one_of_dvd_prodPrimes, differentiableOn_arcosh, hasDerivAt_arccos, HurwitzZeta.isBigO_atTop_evenKernel_sub, CStarAlgebra.preimage_inr_Icc_zero_one, HurwitzZeta.expZeta_zero, range_sin, continuousSMul_sphere_ball, RCLike.sqrt_eq_ite, smoothTransition.eq_one_iff_one_le, le_log_one_add_of_nonneg, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, tan_pi_div_four, ofDigits_const_last_eq_one, Bundle.ContMDiffRiemannianMetric.isVonNBounded, cos_pi_div_five, real_inner_div_norm_mul_norm_eq_neg_one_iff, Polynomial.mahlerMeasure_def_of_ne_zero, exists_continuous_sum_one_of_isOpen_isCompact, one_le_sqrt, PiLp.nndist_eq_sum, gold_sq, AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound, PadicInt.coe_sub, RCLike.one_re, continuousOn_stereoToFun, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, expNear_succ, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, gauge_lt_one_eq_self_of_isOpen, GroupSeminorm.apply_one, NormedAddGroupHom.norm_id_of_nontrivial_seminorm, exists_contMDiffMap_zero_one_of_isClosed, arcosh_bijOn, InformationTheory.integral_llr_add_mul_log_nonneg, one_le_cosh, not_continuousAt_inv_log_neg_one, NumberField.mixedEmbedding.logMap_one, BumpCovering.eventuallyEq_one, Quaternion.coeComplex_re, ContinuousLinearMap.norm_inr_le_one, Complex.isTheta_exp_arg_mul_im, Complex.UnitDisc.normSq_lt_one, sin_arctan, sin_eq_zero_iff_cos_eq, MeasureTheory.norm_indicatorConstLp_le, ProbabilityTheory.gammaPDF_of_nonneg, ProbabilityTheory.condDistrib_ae_eq_condExp, deriv_arctan, iteratedDeriv_odd_cos, isApproximateAddSubgroup_zero, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, NormedRing.inverse_one_sub_norm, HasStrictDerivAt.rpow, PadicInt.norm_int_lt_one_iff_dvd, bernoulliFun_eval_one_sub, MeasureTheory.hausdorffMeasure_segment, abs_sinc_le_one, fourierCoeff_tsum_comp_add, intervalIntegral.intervalIntegrable_one_div_one_add_sq, RCLike.separate_convex_open_set, ProbabilityTheory.tendsto_defaultRatCDF_atTop, ExistsContDiffBumpBase.u_support, gauge_le_one_of_mem, HurwitzZeta.hasSum_int_cosKernelβ, NumberField.mixedEmbedding.convexBodyLT'_mem, arctan_eq_arcsin, ContractingWith.dist_fixedPoint_le, PadicInt.mem_subring_iff, ProbabilityTheory.IsCondKernelCDF.le_one, sin_pi_div_two, rpow_lt_one_iff_of_pos, ContinuousLinearMap.sSup_unit_ball_eq_norm, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, ProbabilityTheory.betaPDF_eq, tsum_eq_tsum_fourier, deriv_negMulLog, hasDerivAt_sigmoid, UnitAddCircle.lintegral_preimage, gold_add_goldConj, Complex.ofReal_eq_one, Metric.unitSphere.coe_one, MeasureTheory.eLpNorm'_const', PadicInt.coe_zero, Height.mulHeightβ_eq, Padic.norm_intCast_eq_one_iff, ProbabilityTheory.condIndep_iff, deriv_abs, curveIntegrable_segment, ZMod.LFunction_stdAddChar_eq_expZeta, Stirling.factorial_isEquivalent_stirling, abs_cos_le_one, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, continuousSMul_sphere_sphere, logb_one, deriv_binEntropy, gauge_lt_one_of_mem_of_isOpen, cos_eq_zero_iff, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, ContinuousLinearMap.norm_inl_le_one, CFC.tendsto_cfc_rpow_sub_one_log, UnitAddCircle.intervalIntegral_preimage, BoxIntegral.unitPartition.mem_box_iff', ProbabilityTheory.Kernel.density_fst_univ, BumpCovering.toPartitionOfUnity_apply, real_sqrt_le_nat_sqrt_succ, MeasureTheory.probReal_compl_eq_one_subβ, Padic.withValUniformEquiv_norm_le_one_iff, Valued.toNormedField.norm_le_one_iff, Orthonormal.norm_eq_one, hasStrictDerivAt_rpow_const_of_ne, neg_pi_div_two_eq_arcsin, sign_one, mapsTo_cos, mapsTo_cos_Ioo, AddSubgroup.norm_normedMk_le, Angle.cos_zero, RCLike.conjCLE_norm, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, CStarAlgebra.inr_mem_Icc_iff_norm_le, integral_const_on_unit_interval, intervalIntegral.intervalIntegral_eq_integral_uIoc, Gamma_nat_add_half, LinearMap.polar_eq_iInter, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_one_of_monotone, PMF.bernoulli_expectation, ContDiffBumpBase.smooth, goldConj_sq, NormedSpace.isBounded_iff_subset_smul_ball, Quaternion.continuous_imI, RCLike.norm_I_of_ne_zero, one_add_mul_le_cos, Affine.Simplex.dist_point_faceOppositeCentroid, Quaternion.coeComplex_mul, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, ContDiffBump.eventuallyEq_one, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, cos_int_mul_two_pi, AkraBazziRecurrence.exists_eventually_const_mul_le_r, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, ProbabilityTheory.Fernique.lt_normThreshold_zero, schnirelmannDensity_le_one, PadicInt.norm_intCast_lt_one_iff, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, seminormFromConst_seq_one, ProbabilityTheory.Kernel.densityProcess_le_one, exists_smooth_one_nhds_of_subset_interior, indicator_indepFun_pi_of_prod_bcf, MeasureTheory.norm_indicatorConstLp, MeasureTheory.Measure.toSphere_apply_aux, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, Topology.CWComplex.continuousOn, MeasureTheory.Integrable.hasSum_intervalIntegral, summable_log_one_add_of_summable, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, ProbabilityTheory.sum_prob_mem_Ioc_le, IsUltrametricDist.norm_intCast_le_one, BoxIntegral.unitPartition.box_upper, Set.instTietzeExtensionUnitBall, NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_one, Tactic.ComputeAsymptotics.Seq.dist_cons_nil, NormedAddGroupHom.norm_id_le, Complex.UnitDisc.instSMulCommClass_closedBall_circle, selfAdjoint.norm_sq_expUnitary_sub_one, rpow_neg_one, derivWithin_arctan, Complex.ofRealCLM_norm, Complex.UnitDisc.instSMulCommClass_closedBall_left, contMDiff_neg_sphere, goldenRatio_mul_goldenConj, IsUltrametricDist.norm_add_one_le_max_norm_one, Antitone.tendsto_alternating_series_of_tendsto_zero, Besicovitch.SatelliteConfig.centerAndRescale_radius, Polynomial.one_le_prod_max_one_norm_roots, TopologicalSpace.Opens.CompleteCopy.dist_eq, ContDiffBump.integral_normed, Complex.norm_eq_one_iff', OrthonormalBasis.det_to_matrix_orthonormalBasis_of_same_orientation, IsOpen.exists_smooth_support_eq, isUltrametricDist_iff_forall_norm_natCast_le_one, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, instSMulCommClass_sphere_sphere_sphere, Bundle.RiemannianMetric.isVonNBounded, BoundedContinuousFunction.indicator_apply, MeasureTheory.le_eLpNorm_of_bddBelow, NumberField.FinitePlace.mulSupport_finite, one_mem_posTangentConeAt_iff_frequently, tendsto_one_add_pow_exp_of_tendsto, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, integral_pow, Quaternion.imI_coeComplex, summable_one_div_nat_add_rpow, tendsto_tsum_powerSeries_nhdsWithin_lt, round_exp_one_eq_three, hasSum_log_one_add_inv, strictAntiOn_arccos, abs_tanh_lt_one, lintegral_fderiv_lineMap_eq_edist, UnitAddTorus.mFourierSubalgebra_coe, CStarAlgebra.mem_Icc_iff_norm_le_one, Path.range_subpathAux, PadicInt.coe_eq_zero, sum_geometric_two_le, InnerProductSpace.gramSchmidtNormed_unit_length_coe, PadicInt.padic_norm_e_of_padicInt, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, tan_sub', NNReal.coe_le_one, summable_one_div_int_pow, differentiableOn_arcsin, Polynomial.Chebyshev.eval_T_real_node, MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul, RCLike.abs_im_div_norm_le_one, one_le_exp_iff, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, Topology.RelCWComplex.pairwiseDisjoint', MeasureTheory.lintegral_prod_lintegral_pow_le, Height.fun_mulHeight_zero, monomial_has_deriv_aux, HurwitzZeta.evenKernel_def, UnitAddTorus.mFourierSubalgebra_closure_eq_top, hasDerivAt_mul_log, ModularGroup.one_lt_normSq_T_zpow_smul, WithLp.prod_nnnorm_eq_add, setOf_liouvilleWith_subset_aux, PadicInt.coe_sum, tendsto_sigmoid_atTop, CStarAlgebra.span_nonneg_inter_unitBall, deriv_arccos, smul_unitClosedBall, CongruenceSubgroup.strictPeriods_Gamma0, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, entry_norm_bound_of_unitary, MeasureTheory.Measure.toSphere_real_apply_univ, Gamma_strictAntiOn_Ioc, cos_le_one_div_sqrt_sq_add_one, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, log_mul_self_monotoneOn, CircleDeg1Lift.dist_map_zero_translationNumber_le, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, Metric.unitBall.instContinuousMul, sin_le_one, SmoothBumpFunction.le_one, PadicInt.norm_units, hasStrictDerivAt_abs_pos, CStarRing.norm_of_mem_unitary, Complex.norm_cos_add_sin_mul_I, ProbabilityTheory.cdf_expMeasure_eq, hasDerivWithinAt_abs_pos, InformationTheory.klFun_eq_zero_iff, tendsto_mul_log_one_add_of_tendsto, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, artanh_bijOn, one_sub_sq_div_two_le_cos, antideriv_bernoulliFun, hasStrictFDerivAt_rpow_of_pos, ProbabilityTheory.Kernel.density_le_one, DirichletCharacter.norm_LSeries_product_ge_one, norm_smul_inv_norm, HolderTriple.one_div_eq, MeasureTheory.Measure.addHaar_ball_of_pos, one_sub_le_exp_neg, mellin_convergent_zero_of_isBigO, sigmoid_neg, deriv_abs_neg, integral_exp_neg_mul_rpow, Asymptotics.isBigOWith_refl, MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, Homeomorph.contDiff_unitBall, LinearMap.polar_singleton, arcosh_zero, HurwitzZeta.hurwitzZetaEven_zero, NumberField.prod_abs_eq_one, Stirling.log_stirlingSeq_formula, summable_nat_rpow_inv, ProbabilityTheory.Kernel.notMem_mutuallySingularSetSlice, smul_unitClosedBall_of_nonneg, Polynomial.Chebyshev.integral_measureT, stereographic'_source, list_prod_map_rpow', Affine.Simplex.sum_mongePointWeightsWithCircumcenter, ContinuousMultilinearMap.norm_smulRightL_le, WeakFEPair.h_feq, ENNReal.lintegral_mul_rpow_le_lintegral_rpow_mul_lintegral_rpow, List.norm_prod_le', InformationTheory.klFun_apply, NNReal.sqrt_eq_rpow, QuadraticForm.equivalent_signType_weighted_sum_squared, InformationTheory.leftDeriv_klFun_one, ZMod.completedLFunction_def_even, ContinuousMultilinearMap.norm_mkPiAlgebra_le, exists_smooth_tsupport_subset, RCLike.reCLM_norm, integral_bernoulliFun, Metric.iUnion_ball_nat_succ, rpow_inv_log, enorm_fderiv_norm_rpow_le, formalMultilinearSeries_geometric_apply_norm_le, Padic.norm_int_le_one, Path.extend_symm_apply, HasDerivAt.arctan, Icc_mem_vitaliFamily_at_left, instZeroLEOneClass, NormedSpace.isBounded_iff_subset_smul_closedBall, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, one_sub_gold, cos_arcsin, Orientation.abs_volumeForm_apply_of_orthonormal, HurwitzZeta.oddKernel_def', IsApproximateAddSubgroup.one_le, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, BoxIntegral.hasIntegral_GP_pderiv, ProbabilityTheory.Kernel.measurable_singularPart_fun_right, Topology.RelCWComplex.source_eq, GammaIntegral_convergent, MeasureTheory.measure_lt_one_eq_integral_div_gamma, logb_eq_zero, tan_arccos, one_add_rpow_hasFPowerSeriesOnBall_zero, arccos_pos, ContinuousLinearMap.sSup_sphere_eq_nnnorm, Height.one_le_mulHeight, MeasureTheory.charFunDual_eq_charFun_map_one, Quaternion.instCStarRingReal, fourier_norm, ContinuousLinearMap.opNorm_mul, LiouvilleNumber.aux_calc, sin_add_int_mul_pi, Polynomial.isRoot_cos_pi_div_five, ENNReal.toReal_one, strictMonoOn_artanh, MulRingSeminorm.apply_one, exp_one_lt_three, gold_mul_goldConj, integral_cos_pow, cos_nat_mul_two_pi_sub_pi, HasFDerivAt.arctan, cosPartialEquiv_target, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, hasStrictDerivAt_arccos, ContinuousLinearMap.norm_fst_le, Chebyshev.psi_eq_sum_theta, Stirling.log_stirlingSeq_diff_hasSum, MeasureTheory.dominatedFinMeasAdditive_condExpInd, log_list_prod, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, HasStrictFDerivAt.abs, isScalarTower_closedBall_closedBall_closedBall, Gamma_two, intervalIntegral.intervalIntegrable_inv_one_add_sq, Topology.RelCWComplex.continuousOn, isScalarTower_sphere_closedBall_closedBall, PadicInt.norm_lt_one_iff_dvd, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, exists_continuous_zero_one_of_isClosed, NNReal.eventually_pow_one_div_le, stdSimplex_subset_closedBall, RCLike.abs_re_div_norm_le_one, norm_sub_le_mul_volume_of_norm_lineDeriv_le, norm_deriv_mulExpNegMulSq_le_one, Quaternion.linearIsometryEquivTuple_symm_apply, Probability.integral_cauchyPDFReal, WithLp.prod_norm_eq_of_nat, Topology.RelCWComplex.union', fourierCoeff_bernoulli_eq, PadicInt.algebraMap_apply, cosh_surjOn, integrable_one_add_norm, Gamma_mul_Gamma_add_half, HasStrictFDerivAt.arsinh, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, ContDiffBump.one_lt_rOut_div_rIn, ZMod.LFunction_def_odd, IsPowMul.map_one_le_one, arccos_one, entrywise_sup_norm_bound_of_unitary, DirichletCharacter.norm_le_one, sin_add_nat_mul_pi, cos_nat_mul_pi, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atTop, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, one_lt_goldenRatio, log_two_near_10, ProbabilityTheory.iCondIndep_iff, ProbabilityTheory.centralMoment_one', MeasureTheory.condExpL2_indicator_ae_eq_smul, ContinuousLinearMap.exists_lt_apply_of_lt_opNorm, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, PartitionOfUnity.sum_eq_one', Metric.Sum.one_le_dist_inr_inl, CircleDeg1Lift.map_one_add, SmoothPartitionOfUnity.sum_finsupport', MeasureTheory.probReal_add_probReal_compl, curveIntegralFun_trans_aeeq_right, not_summable_indicator_one_div_natCast, ZLattice.tsum_norm_rpow_le, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, arcsin_eq_pi_div_two, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, NumberField.exists_conjugate_one_le_norm, Metric.unitSphere.coe_mul, seminormFromBounded_one_le, isTheta_exp_comp_one, hasDerivAt_arsinh, NormedField.exists_norm_lt_one, hasSum_zeta_four, Angle.cos_sq_add_sin_sq, integrableOn_Ioi_cpow_iff, Polynomial.supNorm_X, HasStrictDerivAt.arctan, deriv_norm_ofReal_cpow, mk_one, arccos_eq_zero, HurwitzZeta.completedSinZeta_neg, gronwallBound_of_K_ne_0, exp_list_sum, ProbabilityTheory.stieltjesOfMeasurableRat_le_one, sin_sq_arctan, hasDerivAt_abs_neg, Orientation.det_rotation, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, deriv_sqrt_aux, smoothTransition.one, ContinuousMap.HomotopyRel.trans_apply, curveIntegralFun_symm_apply, SeparationQuotient.norm_normedMk_eq_one, range_cos, SeparationQuotient.norm_normedMk_le, deriv_rpow_const, hasDerivWithinAt_abs, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, HurwitzZeta.evenKernel_eq_cosKernel_of_zero, PartitionOfUnity.exists_finset_nhds, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ModularGroup.exists_bound_of_subgroup_invariant_of_isBigO, AkraBazziRecurrence.sumTransform_def, Gamma_mul_Gamma_one_sub, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, CircleDeg1Lift.dist_map_map_zero_lt, HurwitzZeta.hurwitzZetaEven_apply_zero, MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, neg_one_lt_goldenConj, DirichletCharacter.unit_norm_eq_one, Valued.integer.exists_norm_lt_one, cos_two_pi, MeasureTheory.upcrossingStrat_le_one, SimpleGraph.triangleRemovalBound_mul_cube_lt, ProbabilityTheory.condIndepSets_singleton_iff, ProbabilityTheory.Kernel.rnDeriv_def', MeasureTheory.setIntegral_condExpL2_indicator, MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd, integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, niven_sin, tsum_exp_neg_mul_int_sq, integral_cos_pow_aux, HurwitzZeta.expZeta_one_sub, tan_two_mul, diam_stdSimplex, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, Gamma_one, NNReal.isGreatest_Lp, hasSum_cos, IsOpen.exists_contMDiff_support_eq_aux, one_lt_toNNReal, ENNReal.rpow_one, IsApproximateSubgroup.subgroup, arccos_image_Icc, affinity_unitClosedBall, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, Orientation.volumeForm_zero_pos, HolderConjugate.one_sub_inv, CFC.rpow_one, one_add_tan_sq_mul_cos_sq_eq_one, Quaternion.nnnorm_star, finite_integral_rpow_sub_one_pow_aux, CFC.sqrt_eq_rpow, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two, Function.hasTemperateGrowth_iff_isBigO, hasSum_log_one_add, sin_sq, Complex.GammaIntegral_ofReal, Gamma_one_half_eq, strictConcaveOn_sqrt_mul_log_Ioi, pi_div_two_eq_arcsin, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, Chebyshev.integral_one_div_log_sq_isBigO, ENNReal.lintegral_rpow_add_le_add_eLpNorm_mul_lintegral_rpow_add, inv_one_add_tan_sq, PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne, CovByVAdd.of_subset, MeasureTheory.Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, BoundingSieve.one_le_y, bernoulliFun_eval_one, Complex.exists_norm_eq_mul_self, one_sub_goldConj, orthonormalBasis_one_dim, hasDerivWithinAt_arccos_Ici, unitInterval.symm_projIcc, Seminorm.gaugeSeminorm_ball, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, toNNReal_le_one, integral_bernoulliFun_eq_zero, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Complex.HadamardThreeLines.mem_verticalClosedStrip_of_scale_id_mem_verticalClosedStrip, curveIntegral_segment, tan_div_sqrt_one_add_tan_sq, arctan_eq_neg_pi_div_four, PadicInt.mk_coe, ExistsContDiffBumpBase.u_le_one, Homeomorph.coe_unitBall_apply_zero, eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo, exists_isMinOn_Gamma_Ioi, AkraBazziRecurrence.strictMonoOn_one_sub_smoothingFn, ValueDistribution.isBigO_characteristic_sub_characteristic_shift, unitSphereToUnits_apply_coe, ZLattice.tsumNormRPowBound_spec, exists_rat_abs_sub_lt_and_lt_of_irrational, Valued.integer.norm_irreducible_lt_one, Quaternion.coeComplex_add, tendsto_sub_mul_tsum_nat_cpow, log_pos_iff, arcosh_injOn, Complex.normSq_I, PiLp.edist_eq_sum, ContinuousLinearMap.exists_approx_preimage_norm_le, NormedSpace.normalize_smul, cos_le_one_sub_mul_cos_sq, NNReal.rpow_neg_one, sigmoid_def, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, ofDigitsTerm_le, curveIntegral_def, ENNReal.eventually_pow_one_div_le, MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul, intervalIntegral.integrableOn_Ioo_rpow_iff, Path.Homotopy.hcomp_half, HasFPowerSeriesOnBall.uniform_geometric_approx, Stirling.stirlingSeq_one, isBigO_one_exp_comp, ZMod.toAddCircle_inj, Path.Homotopy.hcomp_apply, Complex.norm_eq_one_iff, Filter.IsIncreasingApproximateUnit.eventually_norm, HurwitzZeta.hasSum_int_cosKernel, ZMod.completedLFunction_def_odd, OrthonormalBasis.norm_eq_one, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, quarters_mem_preCantorSet, ProbabilityTheory.defaultRatCDF_le_one, cos_one_le, Subgroup.strictWidthInfty_eq_one_of_T_mem, Tactic.ComputeAsymptotics.Seq.dist_cons_cons_eq_one, unitInterval.volume_uIcc, isBigO_exp_comp_one, contDiffOn_stereoToFun, Hyperreal.coe_eq_one, exists_seq_norm_le_one_le_norm_sub, unitInterval.volume_Ici, Padic.norm_natCast_lt_one_iff, ProbabilityTheory.condExpKernel_ae_eq_condExp', deriv_Gamma_nat, trapezoidal_integral_ext, inner_le_Lp_mul_Lq_tsum_of_nonneg', BoxIntegral.unitPartition.mem_box_iff, LogDeriv_exp, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, CircleDeg1Lift.map_map_zero_lt, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, HurwitzZeta.sinKernel_neg, NormOneClass.norm_one, Polynomial.Chebyshev.S_two_mul_real_cos, ContractingWith.apriori_dist_iterate_fixedPoint_le, integrable_rpow_neg_one_add_norm_sq, MeasureTheory.Measure.toSphere_apply_univ, hasDerivAt_binEntropy, PartitionOfUnity.sum_le_one', rpow_zero, exp_one_mul_le_exp, UnitAddTorus.mFourier_add, WithLp.prod_edist_eq_of_L2, hasDerivAt_qaryEntropy, artanh_surjOn, NNReal.one_le_coe, UpperHalfPlane.cosh_dist, LSeries_eq_mul_integral_of_nonneg, ContDiffBumpBase.mem_Icc, real_inner_div_norm_mul_norm_eq_one_iff, SmoothPartitionOfUnity.le_one, Chebyshev.sum_PrimePow_eq_sum_sum, Padic.norm_p_lt_one, Behrend.lower_bound_le_one, Tactic.ComputeAsymptotics.Seq.dist_eq_one_of_head, HurwitzZeta.oddKernel_def, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, one_mem_posTangentConeAt_iff_mem_closure, BumpCovering.le_one, unitSphereToUnits_injective, gaugeSeminorm_ball_one, spectrum.gelfand_formula, tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, MeasureTheory.enorm_indicatorConstLp_le, ModularFormClass.one_mem_strictPeriods_SL2Z, NormedSpace.inclusionInDoubleDual_norm_le, stereographic'_target, abs_cos_int_mul_pi, real_sqrt_lt_nat_sqrt_succ, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, HasFDerivAt.abs, MeasureTheory.L1.integral_eq_setToL1, Quaternion.continuous_imJ, abs_iteratedDeriv_cos_le_one, exists_contMDiffMap_zero_one_nhds_of_isClosed, one_div_one_sub_hasFPowerSeriesOnBall_zero, HasFDerivWithinAt.abs, continuousSMul_closedBall_ball, ProbabilityTheory.gaussianReal_map_linearMap, projIcc_eq_one, tendsto_sin_neg_pi_div_two, bernoulliFun_endpoints_eq_of_ne_one, Polynomial.gaussNorm_intAdicAbv_le_one, Stirling.le_factorial_stirling, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, Complex.equivRealProd_apply_le', UnitAddTorus.mFourier_zero, tendsto_exp_nhds_zero_nhds_one, Urysohns.CU.lim_le_one, isScalarTower_sphere_sphere_sphere, Polynomial.gaussNorm_lt_one_iff_contentIdeal_le, CStarAlgebra.span_nonneg_inter_unitClosedBall, mellin_convergent_of_isBigO_scalar, exp_one_gt_d9, CircleDeg1Lift.transnumAuxSeq_dist_lt, UnitAddCircle.measure_univ, PartitionOfUnity.sum_eq_one, exists_bounded_zero_one_of_closed, exp_eq_one_iff, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, Metric.uniformity_basis_dist_inv_nat_succ, Quaternion.coeComplex_zero, bernstein.variance, ModularGroup.re_T_smul, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, EuclideanSpace.instIsManifoldSphere, CongruenceSubgroup.strictWidthInfty_Gamma0, RCLike.I_eq_zero_or_im_I_eq_one, arcsin_neg_one, bernstein_apply, Quaternion.instCompleteSpaceReal, ProbabilityTheory.condIndepSet_iff, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos, Nat.realSqrt_mem_Ico, HurwitzZeta.hurwitzEvenFEPair_zero_symm, CliffordAlgebraComplex.ofComplex_I, UnitAddTorus.coeFn_mFourierLp, norm_sum_neg_one_pow_le, HurwitzKernelBounds.F_nat_one_le, MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere, CircleDeg1Lift.tendsto_translation_number', inv_norm_smul_mem_unitClosedBall, Polynomial.intervalIntegrable_mahlerMeasure, exists_continuous_one_zero_of_isCompact, Complex.HadamardThreeLines.norm_invInterpStrip, MeasureTheory.lintegral_rpow_eq_lintegral_meas_lt_mul, BumpCovering.toPartitionOfUnity_eq_mul_prod, exp_one_rpow, one_div_sub_hasFPowerSeriesOnBall_zero, WithLp.prod_norm_eq_add, exp_one_near_20, HasBesicovitchCovering.no_satelliteConfig, Complex.UnitDisc.coe_closedBall_smul, HasStrictFDerivAt.sqrt, Metric.unitClosedBall.coe_mul, integral_sin_pow_mul_cos_pow_odd, MeasureTheory.Lp.norm_const_le, HasDerivWithinAt.arsinh, Path.Homotopy.transAssocReparamAux_one, NumberField.FinitePlace.norm_lt_one_iff_mem, Complex.imCLM_norm, deriv2_binEntropy, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, UnitAddTorus.mFourier_neg, ProbabilityTheory.paretoPDF_of_le, ProbabilityTheory.integral_gaussianPDFReal_eq_one, Height.one_le_mulHeightβ, HasStrictFDerivAt.rpow, RCLike.exists_norm_eq_mul_self, le_rpow_one_add_norm_iff_norm_le, Matrix.frobenius_norm_def, hasDerivAt_arcsin, RingSeminorm.exists_index_pow_le, Polynomial.Chebyshev.node_eq_neg_one, HurwitzZeta.cosZeta_eq, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, Path.Homotopy.transReflReparamAux_one, MeasureTheory.eLpNorm'_smul_measure, interior_subset_gauge_lt_one, UpperHalfPlane.norm_exp_two_pi_I_lt_one, MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ, hasDerivAt_tan, Behrend.bound, PiLp.norm_eq_sum, deriv_tan_sub_id, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, leftDeriv_mul_log, Finset.norm_prod_one_add_sub_one_le, WeakFEPair.h_feq', stereoToFun_apply, arcsin_eq_arccos, unitInterval.one_minus_le_one, exists_nat_abs_mul_sub_round_le, Set.Icc.coe_convexCombo, PadicInt.coe_one, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', log_one, UniformSpace.Completion.norm_toComplL, instSMulCommClass_sphere_closedBall_closedBall, ProbabilityTheory.cdf_le_one, ofDigits_SurjOn, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, MeasureTheory.integral_indicator_one, Complex.det_conjAe, gauge_eq_one_iff_mem_frontier, ZetaAsymptotics.continuousOn_term, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ModularGroup.re_T_inv_smul, logb_self_eq_one_iff, FormalMultilinearSeries.radius_inv_eq_limsup, affinity_unitBall, sin_eq_tsum, tendsto_rpow_div_mul_add, cos_int_mul_pi_sub, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, intervalIntegral.integrableOn_Ioo_cpow_iff, SlashInvariantForm.exists_one_half_le_im_and_norm_le, WithLp.prod_norm_eq_add_idemFst, sin_sq_eq_half_sub, Unitary.norm_sub_one_sq_eq, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, InnerProductSpace.volume_ball, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, cosh_sq, ExistsContDiffBumpBase.u_exists, norm_jacobiTheta_sub_one_le, tan_sq_div_one_add_tan_sq, Nat.Primes.not_summable_one_div, periodizedBernoulli.continuous, goldenConj_mul_goldenRatio, PiNat.mem_cylinder_iff_dist_le, Metric.unitBall.coe_eq_zero, preCantorSet_subset_unitInterval, one_rpow, Submodule.norm_subtypeL, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, deriv_qaryEntropy, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, deriv_arctan, continuousSMul_sphere_closedBall, HurwitzZeta.completedHurwitzZetaEven_eq, monotoneOn_deriv_descPochhammer_eval, RingNorm.apply_one, one_le_gauge_of_notMem, mellin_convergent_top_of_isBigO, HasDerivWithinAt.rpow, SmoothPartitionOfUnity.sum_eq_one', NormedDivisionRing.norm_eq_one_iff_ne_zero_of_discrete, UpperHalfPlane.dist_self_center, Matrix.permMatrix_l2_opNorm_le, cos_eq_tsum, MeasureTheory.Lp.norm_const', SmoothBumpFunction.mem_Icc, RCLike.wInner_one_eq_inner, ProbabilityTheory.iCondIndepSets_singleton_iff, AkraBazziRecurrence.p_def, ProbabilityTheory.mgf_zero, Complex.ofReal_one, arccos_eq_arcsin, exp_arsinh, artanh_eq_zero_iff, Topology.CWComplex.union', Quaternion.re_exp, PadicInt.coe_natCast, BoundingSieve.nu_lt_one_of_prime, isScalarTower_closedBall_ball_ball, integral_sin_pow_aux, ContinuousMap.HomotopyWith.trans_apply, harmonic_le_one_add_log, tendsto_rpow_sub_one_log, Polynomial.Chebyshev.S_two_mul_real_cosh, PadicInt.valuation_coe_nonneg, Set.Icc.eq_convexCombo, ArchimedeanClass.stdPart_one, OpenPartialHomeomorph.univUnitBall_target, UnitAddTorus.mFourier_norm, posLog_eq_zero_iff, Complex.UnitDisc.instCanLiftCoeLtRealNormOfNat, Height.mulHeight_zero, tsum_geometric_two, MeasureTheory.hausdorffMeasure_lineMap_image, log_eq_zero, Polynomial.one_le_mahlerMeasure_of_ne_zero, HurwitzZeta.hasSum_int_evenKernel, unitInterval.one_mem, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, Quaternion.normSq_eq_norm_mul_self, one_lt_rpow_iff_of_pos, eq_one_of_pos_of_log_eq_zero, Besicovitch.TauPackage.one_lt_tau, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, log_lt_sub_one_of_pos, ProbabilityTheory.Kernel.densityProcess_fst_univ_ae, ModularFormClass.exists_petersson_le, NumberField.Units.mem_torsion, ProbabilityTheory.condExp_set_generateFrom_singleton, MeasureTheory.Measure.addHaar_real_closedBall', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, NNReal.coe_lt_one, Valued.integer.norm_le_one, sinh_sq, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, Asymptotics.IsLittleO.isBigOWith, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, sum_trapezoidal_error_adjacent_intervals, mfderiv_coe_sphere_injective, exists_continuous_zero_one_of_isCompact', hasDerivWithinAt_taylor_coeff_within, schnirelmannDensity_eq_one_iff, AkraBazziRecurrence.strictAntiOn_one_add_smoothingFn, HurwitzZeta.completedCosZetaβ_neg, tendsto_integral_mul_one_add_inv_smul_sq_pow, Submodule.starProjection_norm_le, EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two, integral_sin_pow_even_mul_cos_pow_even, tendsto_nat_mul_log_one_add_of_tendsto, SimpleGraph.UnitDistEmbedding.unit_dist, qaryEntropy_strictAntiOn, diam_stdSimplex_le, Asymptotics.isBigOWith_of_le, OpenPartialHomeomorph.contDiffOn_univUnitBall_symm, sinOrderIso_apply, ProbabilityTheory.IsMeasurableRatCDF.le_one, NNReal.mk_one, Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, InnerProductGeometry.cos_eq_neg_one_iff_angle_eq_pi, hasStrictDerivAt_abs, BoundingSieve.siftedSum_eq_sum_support_mul_ite, cos_int_mul_two_pi_add_pi, smoothingFun_le, ContinuousMap.toNNReal_one, ProbabilityTheory.Fernique.normThreshold_eq, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', Topology.CWComplex.source_eq, Topology.CWComplex.pairwiseDisjoint', toNNReal_one, sin_eq_sin_iff, PadicInt.coe_adicCompletionIntegersEquiv_apply, ZMod.toAddCircle_natCast, Submodule.norm_starProjection, indicator_indepFun_pi_of_bcf, sqrt_div_self', FormalMultilinearSeries.isLittleO_one_of_lt_radius, Tactic.ComputeAsymptotics.Seq.dist_nil_cons, zero_rpow_eq_iff, Polynomial.mahlerMeasure_X_add_C, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, exists_dual_vector, OrthonormalBasis.det_to_matrix_orthonormalBasis, mem_balancedHull_iff, smul_unitBall_of_pos, eq_zero_rpow_iff, Padic.norm_natCast_eq_one_iff, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, hasDerivWithinAt_arcsin_Ici, UpperHalfPlane.norm_qParam_lt_one, HasStrictFDerivAt.arctan, unitInterval.coe_symm_eq, smoothTransition.le_one, neg_one_lt_tanh, unitInterval.qRight_zero_right, CFC.rpow_neg_one_eq_cfc_inv, CFC.monotoneOn_one_sub_one_add_inv_real, convexOn_descPochhammer_eval, MeasureTheory.tendsto_sum_indicator_atTop_iff', ProbabilityTheory.Kernel.rnDerivAux_le_one, Gamma_add_one, unitary.norm_argSelfAdjoint, Besicovitch.exists_goodΞ΄, hasSum_geometric_two, injOn_arcsin, cosh_zero, ModularFormClass.exists_bound, unitary.spectrum_subset_circle, ProbabilityTheory.Kernel.measurable_singularPart_fun, ContinuousLinearMap.sSup_sphere_eq_norm, Polynomial.logMahlerMeasure_def, HurwitzZeta.sinKernel_zero, deriv_abs_pos, indicator_indepFun_process_of_bcf, Quaternion.coeComplex_imK, ContinuousLinearMap.norm_inr, abs_sin_half, HurwitzZeta.completedCosZetaβ_zero, HurwitzZeta.oddKernel_zero, tendsto_mul_log_one_add_div_atTop, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae, Path.range_subpath, homeomorphUnitSphereProd_symm_apply_coe, WithLp.prod_nndist_eq_add, taylorWithinEval_succ, abs_sin_eq_sqrt_one_sub_cos_sq, exists_msmooth_support_eq_eq_one_iff, nonunits.subset_compl_ball, ZetaAsymptotics.term_one, rpow_one_add', MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, ProbabilityTheory.condIndepSets_iff, EReal.coe_coe_sign, Polynomial.hermite_eq_deriv_gaussian', fderiv_arctan, HurwitzZeta.hasSum_int_sinKernel, ProbabilityTheory.iCondIndepSet_iff, Path.Homotopy.trans_apply, MeasureTheory.eLpNorm_indicator_const_le, HurwitzZeta.oddKernel_functional_equation, ProbabilityTheory.Kernel.withDensity_one_sub_rnDerivAux, finite_integral_one_add_norm, NumberField.one_le_house_of_isIntegral, ENNReal.ofReal_le_one, ContinuousMultilinearMap.norm_mkPiAlgebra, hasMellin_one_Ioc, NumberField.FinitePlace.mulSupport_finite_int, Liouville.frequently_exists_num, cos_one_pos, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, PadicInt.one_le_norm_iff, tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, unitary.two_mul_one_sub_le_norm_sub_one_sq, Topology.CWComplex.mapsTo', SmoothBumpCovering.eventuallyEq_one, NormedRing.inverse_add_norm, ENNReal.one_le_ofReal, Nat.pairwise_one_le_dist, PadicInt.norm_natCast_zmodRepr_eq_one_iff, sin_half_eq_neg_sqrt, Metric.unitBall.instIsLeftCancelMulZero, sqrt_le_one, mem_parallelepiped_iff, MeasureTheory.integral_biUnion_eq_sum_powerset, seminormFromBounded_one, one_lt_gold, arccos_eq_pi, Complex.I_im, Gamma_nat_add_one_add_half, 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, rpow_one, exists_dual_vector'', exists_msmooth_zero_iff_one_iff_of_isClosed, Homeomorph.unitBall_apply_coe, schnirelmannDensity_univ, ZetaAsymptotics.term_tsum_one, MeasureTheory.Lp.norm_constL_le, Polynomial.Chebyshev.rootMultiplicity_T_real, isTheta_deriv_rpow_const_atTop, Metric.Sum.one_le_dist_inl_inr, HasDerivWithinAt.arctan, PadicInt.isUnit_iff, log_div_self_antitoneOn, ENNReal.ofReal_one, logb_one_left, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, ProbabilityTheory.IsRatCondKernelCDFAux.le_one', CFC.rpow_neg_one_eq_inv, toNNReal_lt_one, hasStrictDerivAt_arsinh, MeasureTheory.integral_comp_rpow_Ioi, integral_univ_inv_one_add_sq, sin_int_mul_pi_sub, multipliable_one_add_of_summable, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, SmoothPartitionOfUnity.sum_le_one', logb_one_left_eq_zero, MeasureTheory.Lp.eLpNorm'_lim_eq_lintegral_liminf, Height.AdmissibleAbsValues.mulSupport_finite, arcsin_le_neg_pi_div_two, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, integral_exp_neg_rpow, Polynomial.Chebyshev.U_real_cos, inv_sqrt_two_sub_one, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, Urysohns.CU.approx_le_one, abs_real_inner_div_norm_mul_norm_le_one, RCLike.exists_norm_mul_eq_self, rpow_add_one, stereographic_neg_apply, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, HolderConjugate.conjugate_eq, binEntropy_one, CongruenceSubgroup.strictWidthInfty_Gamma1, MeasureTheory.eLpNorm_const', circleAverage_eq_circleAverage_zero_one, Manifold.riemannianEDist_def, MeasureTheory.norm_charFun_le_one, unitInterval.le_one, WithLp.prod_dist_eq_add, spectralNorm_one, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.integral_fun_norm_addHaar, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae', isScalarTower_sphere_sphere_closedBall, Complex.UnitDisc.instSMulCommClass_closedBall_right, IsOpen.measure_eq_biSup_integral_continuous, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, Nat.realSqrt_lt_ratSqrt_add_inv_prec, iteratedDeriv_even_cos, MeasureTheory.Lp.norm_const, zero_lt_one, uniqueDiffOn_Icc_zero_one, ValueDistribution.isBigO_characteristic_sub_characteristic_inv, one_le_pi_div_two, MeasureTheory.Measure.haar.chaar_self, UnitAddCircle.mem_approxAddOrderOf_iff, Quaternion.normSq_exp, NNReal.rpow_inv_rpow_self, list_prod_map_rpow, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, EuclideanGeometry.cos_eq_neg_one_iff_angle_eq_pi, Affine.Simplex.sum_circumcenterWeightsWithCircumcenter, Chebyshev.psi_eq_theta_add_sum_theta, EisensteinSeries.r1_eq, MeasureTheory.GridLines.T_empty, Submonoid.coe_unitSphere, NNReal.rpow_add_rpow_le, HasDerivAt.arsinh, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, Circle.norm_coe, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, HurwitzZeta.completedHurwitzZetaOdd_neg, Complex.UnitDisc.instIsScalarTower_closedBall, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, summable_one_div_nat_rpow, ceil_exp_one_eq_three, rpow_sub_one, Metric.sphere.instContinuousMul, rightDeriv_mul_log, AkraBazziRecurrence.asympBound_def', ZMod.LFunction_def_even, UpperHalfPlane.le_dist_coe, one_sub_mul_le_cos, Nat.roughNumbersUpTo_card_le', Polynomial.Chebyshev.isMinOn_T_real, goldenRatio_add_goldenConj, Complex.HadamardThreeLines.diffContOnCl_interpStrip, ContinuousLinearMap.opNorm_mul_le, unitInterval.mul_pos_mem_iff, hasStrictDerivAt_abs_neg, isScalarTower_sphere_sphere_ball, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, LSeries_eq_mul_integral, AddGroupSeminorm.apply_one, HurwitzZeta.oddKernel_neg, ModularGroup.exists_one_half_le_im_smul, HasDerivAt.rpow, DirichletCharacter.LSeriesSummable_iff, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, ENNReal.rpow_add_rpow_le, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Quaternion.im_exp, HurwitzZeta.evenKernel_neg, arctan_one, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, integral_one_div_of_pos, arccos_eq_arctan, Affine.Simplex.sum_excenterWeights_eq_one_iff, self_subset_gauge_le_one, NonarchAddGroupSeminorm.apply_one, Quaternion.re_coeComplex, ProbabilityTheory.condExpKernel_ae_eq_condExp, binEntropy_eq_negMulLog_add_negMulLog_one_sub', HurwitzZeta.cosZeta_zero, homeomorphUnitSphereProd_apply_fst_coe, NNReal.rpow_sub_one, Polynomial.hermite_eq_deriv_gaussian, one_half_lt_eulerMascheroniSeq_six, negMulLog_one, formalMultilinearSeries_geometric_apply_norm, neg_one_le_sinc, sign_of_pos, MeasureTheory.eLpNorm_nnreal_eq_lintegral, bijOn_sin, cosh_bijOn, deriv_arcsin, Metric.unitSphere.coe_inv, InnerProductSpace.innerSL_norm, NNReal.rpow_one_sub', bijOn_cos, gauge_lt_one_subset_self, cos_sq', qaryEntropy_strictMonoOn, tan_pi_div_six, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, strictMonoOn_arcsin, WithLp.prod_dist_eq_card, HasFPowerSeriesOnBall.uniform_geometric_approx', one_sub_lt_exp_neg, arccos_lt_pi, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, Valued.toNormedField.one_lt_norm_iff, integrableOn_Ioi_rpow_iff, eulerMascheroniConstant_eq_neg_deriv, mul_add_one_le_add_one_pow, deriv_mul_log, IsOpen.exists_msmooth_support_eq_aux, isScalarTower_sphere_closedBall_ball, ContinuousLinearMap.norm_single, cos_sub_int_mul_pi, logDeriv_exp, AddChar.norm_apply, PadicInt.norm_intCast_eq_one_iff, exists_contMDiff_zero_iff_one_iff_of_isClosed, Complex.ball_one_subset_slitPlane, rpow_sub_one', NormedDivisionRing.unitClosedBall_eq_univ_of_discrete, AkraBazziRecurrence.eventually_one_sub_smoothingFn_nonneg, unitInterval.image_coe_preimage_symm, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, sigmoid_le_one, ENNReal.orderIsoUnitIntervalBirational_apply_coe, Complex.stolzCone_subset_stolzSet_aux, MeasureTheory.nnnorm_indicatorConstLp_le, ProbabilityTheory.paretoPDF_eq, gauge_unit_ball, PiNat.dist_eq_of_ne, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, MeasureTheory.count_real_singleton', AddGroupNorm.apply_one, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, one_lt_cosh, ContractingWith.dist_inequality, sin_sub_int_mul_pi, Polynomial.sum_sq_norm_coeff_eq_circleAverage, one_sub_goldenConj, Polynomial.mahlerMeasure_X_sub_C, ProbabilityTheory.iCondIndepSets_iff, one_le_toNNReal, BumpCovering.ind_apply, rpow_inv_log_le_exp_one, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, exists_rat_abs_sub_le_and_den_le, coord_norm', Int.Matrix.one_le_norm_A_of_ne_zero, bernoulliFun_zero, norm_fderiv_norm, SimpleGraph.triangle_counting', FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, UnitAddCircle.measurePreserving_mk, binEntropy_one_sub, smul_unitBall, Padic.norm_le_one_iff_val_nonneg, Padic.norm_intCast_lt_one_iff, inv_sqrt_one_add_tan_sq, bernoulliFun_one, Metric.unitSphere.coe_zpow, MeasureTheory.ofReal_setIntegral_one, CongruenceSubgroup.strictPeriods_Gamma1, cantorSet_subset_unitInterval, neg_one_le_cos, PadicInt.norm_natCast_zmodRepr_eq, goldenConj_sq, sin_sq_le_one, Liouville.exists_pos_real_of_irrational_root, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff, InnerProductSpace.gramSchmidtNormed_unit_length, SmoothPartitionOfUnity.sum_eq_one, HolderConjugate.inv_add_inv_eq_one, pow_mul_le_of_le_of_pow_mul_le, AkraBazziRecurrence.growsPolynomially_one_add_smoothingFn, exists_continuous_zero_one_of_isCompact, Asymptotics.isBigO_one_nat_atTop_iff, Polynomial.Chebyshev.isMaxOn_T_real, Complex.abs_im_div_norm_le_one, LinearMap.mem_polar_singleton, RCLike.ofRealCLM_norm, integral_sqrt_one_sub_sq, integrable_inv_one_add_sq, circleAverage_log_norm_add_const_eq_posLog, Complex.UnitDisc.coe_smul_closedBall, ProbabilityTheory.exponentialCDFReal_eq, Gamma_eq_integral, spectralAlgNorm_one, cos_nat_mul_pi_sub, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, Metric.unitClosedBall.coe_eq_zero, Polynomial.Chebyshev.rootMultiplicity_U_real, MeasureTheory.hausdorffMeasure_smul_right_image, signedDist_smul, HasFDerivWithinAt.arsinh, hasStrictDerivAt_arctan, one_le_norm_one, ENNReal.lintegral_mul_le_Lp_mul_Lq, sub_isBigO_norm_rpow_add_one_of_fderiv, InformationTheory.klFun_zero, surjOn_sin, NNReal.rpow_add_one, CStarModule.norm_eq_csSup, GroupNorm.apply_one, neg_pi_div_two_lt_arcsin, Quaternion.continuous_im, mulExpNegMulSq_eq_sqrt_mul_mulExpNegMulSq_one, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, Valued.integer.norm_unit, cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, DirichletCharacter.norm_LFunction_product_ge_one, WithLp.prod_norm_eq_card, sin_pi_div_six, EulerSine.integral_cos_pow_eq, abs_mulExpNegMulSq_one_le_one, exists_dual_vector', LSeriesSummable_one_iff, tendstoLocallyUniformlyOn_rpow_sub_one_log, MeasureTheory.integral_condExp_indicator, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, separate_convex_open_set, UnitAddTorus.mFourierSubalgebra_separatesPoints, NNReal.rpow_add_one', Probability.cauchyPDFReal_def', Complex.betaIntegral_convergent, differentiableOn_arccos, one_lt_exp_iff, UnitAddCircle.norm_eq, sin_sq_add_cos_sq, LinearMap.polar_eq_biInter_preimage, NumberField.InfinitePlace.eq_one_of_rpow_eq, fourierCoeff_eq_intervalIntegral, doublingGamma_add_one, one_half_lt_eulerMascheroniConstant, numDerangements_tendsto_inv_e, tan_add', LindemannWeierstrass.integral_exp_mul_eval, isBigO_norm_rpow_add_one_of_fderiv_of_apply_eq_zero, unitInterval.coe_lt_one, MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ, InformationTheory.isMinOn_klFun, Rat.AbsoluteValue.padic_le_one, NormedField.completeSpace_iff_isComplete_closedBall, Complex.exists_norm_mul_eq_self, PiLp.norm_eq_of_nat, Quaternion.imK_coeComplex, holderConjugate_iff, RCLike.ofReal_one, pi_lt_sqrtTwoAddSeries, FormalMultilinearSeries.isLittleO_of_lt_radius, MeasureTheory.integral_eq_setToFun, ContractingWith.dist_le_of_fixedPoint, nnnorm_fderiv_norm_rpow_le, hasFPowerSeriesOnBall_linear_zero, HurwitzZeta.completedHurwitzZetaEven_zero, Polynomial.mahlerMeasure_one, spectrum.norm_eq_one_of_unitary, contDiffOn_arccos, CovByVAdd.rfl, Set.instTietzeExtensionUnitClosedBall, HurwitzZeta.cosKernel_def, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, hasDerivAt_Gamma_one_half, HasStrictDerivAt.arsinh, quarter_mem_preCantorSet, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, HurwitzZeta.hasSum_int_oddKernel, Gamma_mul_Gamma_add_half_of_pos, rpow_def_of_nonneg, range_mfderiv_coe_sphere, AkraBazziRecurrence.exists_eventually_r_le_const_mul, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Hyperreal.coe_one, Complex.norm_sub_one_sq_eqOn_sphere, Quaternion.inner_def, ZMod.toAddCircle_intCast, RCLike.wInner_one_const_right, NumberField.Embeddings.coeff_bdd_of_norm_le, HasFDerivWithinAt.sqrt, ContinuousLinearMap.norm_id_le, cos_sq_le_one, one_add_rpow_hasFPowerSeriesAt_zero, integral_sin_pow_odd_mul_cos_pow, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atTop_one, inner_le_Lp_mul_Lq_tsum_of_nonneg, ProbabilityTheory.condCDF_le_one, cos_sq_add_sin_sq, ContractingWith.one_sub_K_pos, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, fderivWithin_sqrt, Affine.Simplex.sum_reflectionCircumcenterWeightsWithCircumcenter, tendsto_sum_range_one_div_nat_succ_atTop, exp_lt_one_iff, ZMod.toAddCircle_apply, NontriviallyNormedField.non_trivial, ModularGroup.exists_bound_of_subgroup_invariant_of_isArithmetic_of_isBigO, MeasureTheory.SimpleFunc.eLpNorm'_eq, ModularGroup.exists_bound_of_invariant_of_isBigO, not_summable_one_div_natCast, preCantorSet_zero, one_sub_div_pow_le_exp_neg, sin_arccos, HurwitzZeta.hurwitzZetaOdd_eq, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, cos_eq_zero_iff_sin_eq, Path.truncate_zero_one, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', ContinuousLinearMap.opNorm_lsmul_le, EuclideanSpace.volume_ball, BumpCovering.sum_toPartitionOfUnity_eq, Unitary.two_mul_one_sub_le_norm_sub_one_sq, Path.extend_one, ExistsContDiffBumpBase.y_smooth, Affine.Simplex.ExcenterExists.sum_excenterWeights_eq_one, ValueDistribution.abs_characteristic_sub_characteristic_shift_eqO, sinc_le_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, NormedField.exists_one_lt_norm, PartitionOfUnity.sum_le_one, abs_cos_eq_sqrt_one_sub_sin_sq, HurwitzZeta.hurwitzZeta_zero, hasDerivAt_Gamma_one, mapsTo_sin, OpenPartialHomeomorph.unitBallBall_source, OpenPartialHomeomorph.univUnitBall_apply, ContinuousLinearMap.norm_compL_le, cos_half, InformationTheory.klFun_one, curveIntegral_eq_intervalIntegral_deriv, InnerProductSpace.gramSchmidtNormed_unit_length', Path.trans_apply, PadicInt.not_isUnit_iff, ZetaAsymptotics.continuousOn_term_tsum, HasFDerivWithinAt.arctan, MeasureTheory.Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, mellin_convergent_iff_norm, ArithmeticFunction.LSeriesSummable_moebius_iff, Metric.Sum.dist_eq_glueDist, NNReal.summable_one_div_rpow, AkraBazziRecurrence.isLittleO_smoothingFn_one, NumberField.InfinitePlace.one_le_mult, tendsto_rpow_div, ContinuousLinearMap.norm_fst, HasFDerivWithinAt.rpow, surjOn_cos, CovBySMul.rfl, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, HurwitzKernelBounds.F_nat_zero_zero_sub_le, deriv_sigmoid, NNReal.rpow_sub_one', Height.fun_mulHeight_one, Topology.RelCWComplex.mapsTo, quadratic_root_cos_pi_div_five, exp_one_lt_d9, one_add_rpow_hasFPowerSeriesAt_zero, ProbabilityTheory.iCondIndepFun_iff, circleAverage_log_norm_sub_const_eq_posLog, MeasureTheory.probReal_univ, iteratedDeriv_even_sin, exists_smooth_zero_one_of_isClosed, cosh_arsinh, instSMulCommClass_sphere_ball_ball, Metric.unitSphere.coe_pow, Quaternion.inner_self, CStarAlgebra.rpow_neg_one_le_one, Complex.norm_deriv_le_one_of_mapsTo_ball, sign_apply_eq, rpow_lt_one_iff, MeasureTheory.ae_mem_limsup_atTop_iff, CircleDeg1Lift.lt_map_map_zero, strictMonoOn_one_add_div_one_sub, HurwitzZeta.hurwitzZeta_one_sub, WeakFEPair.hf_modif_FE, rpow_add_rpow_le, PadicInt.valuation_coe, SmoothBumpCovering.eventuallyEq_one', quadratic_le_exp_of_nonneg, ArithmeticFunction.LSeriesSummable_zeta_iff, one_sub_sq_div_two_lt_cos, gauge_lt_one_eq_interior, exists_contMDiff_support_eq_eq_one_iff, tanh_lt_one, Monotone.tendsto_alternating_series_of_tendsto_zero, ProbabilityTheory.gammaPDF_eq, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, Quaternion.norm_exp, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, isBigO_deriv_ofReal_cpow_const_atTop, Metric.unitBall.coe_mul, cos_sub_nat_mul_pi, isApproximateSubgroup_one, pi_div_two_le_arcsin, sinc_zero, tendsto_rpow_neg_div, Asymptotics.isBigOWith_snd_prod, Path.extend_symm, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, ContinuousLinearMap.norm_inl, arccos_neg_one, MeasureTheory.hausdorffMeasure_real, EReal.toReal_one, Metric.mem_closure_range_iff_nat, zero_mem_lowerBounds_smoothingSeminormSeq_range, IsOfFinOrder.norm_eq_one, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_ae_of_monotone, Polynomial.Chebyshev.roots_T_real, MeasureTheory.setIntegral_one_eq_measureReal, HurwitzZeta.completedHurwitzZetaEvenβ_neg, NNReal.coe_mulIndicator, Metric.unitBall.instIsRightCancelMulZero, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, neg_one_le_sin, Seminorm.gauge_ball, SelbergSieve.one_le_level, NumberField.FinitePlace.norm_eq_one_iff_notMem, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, HurwitzZeta.completedHurwitzZetaEvenβ_zero, Summable.norm_lt_one, Orientation.volumeForm_zero_neg, abs_sin_eq_one_iff, mapsTo_sin_Ioo, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, SmoothPartitionOfUnity.sum_finsupport, hasDerivAt_arctan', Complex.GammaSeq_eq_approx_Gamma_integral, indicator_indepFun_of_bcf, Wallis.W_eq_factorial_ratio, deriv2_qaryEntropy, Topology.RelCWComplex.disjointBase', hasStrictDerivAt_arcsin, Metric.unitClosedBall.coe_one, NumberField.mixedEmbedding.logMap_real, liouvilleWith_one, ZSpan.fundamentalDomain_pi_basisFun, ConvexBody.iInter_smul_eq_self, BumpCovering.eventuallyEq_one', SmoothBumpFunction.one_of_dist_le, abs_iteratedDeriv_sin_le_one, smoothingSeminormSeq_bddBelow, MeasureTheory.measureReal_le_one, IsOpen.exists_contDiff_support_eq, integral_zpow, tendsto_sub_mul_tsum_nat_rpow, hasSum_zeta_two, not_irrational_one, summable_geometric_iff_norm_lt_one, norm_midpoint_lt_iff, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, exists_continuousMap_one_of_isCompact_subset_isOpen, contDiffOn_arcosh, isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo, sin_eq_neg_one_iff, HasFDerivAt.arsinh, cos_lt_one_div_sqrt_sq_add_one, Complex.HadamardThreeLines.scale_bddAbove, ZMod.toAddCircle_injective, integral_one_div_one_add_sq, Complex.log_eq_integral, ContinuousAlternatingMap.norm_ofSubsingleton_id, NNReal.summable_rpow_inv, integral_one, gauge_le_one_iff_mem_closure, Complex.norm_I, ProbabilityTheory.tendsto_cdf_atTop, ProbabilityTheory.lintegral_betaPDF, Padic.norm_rat_le_one, IsUltrametricDist.norm_natCast_le_one, IsPrimitiveRoot.norm'_eq_one, Subgroup.strictPeriods_SL2Z, one_le_exp, HurwitzZeta.sinZeta_neg, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, tendsto_one_add_rpow_exp_of_tendsto, lt_log_one_add_of_pos, tendsto_sum_pi_div_four, norm_cfcβ_one_sub_one_add_inv_lt_one, rpow_neg_one_add_norm_sq_le, Metric.Sigma.one_le_dist_of_ne, HurwitzZeta.completedCosZeta_eq, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm_toReal, Complex.summable_one_div_nat_cpow, cos_two_mul, PartitionOfUnity.le_one, signedDist_right_lineMap, LiouvilleNumber.partialSum_succ, Complex.norm_eq_one_of_mem_rootsOfUnity, MeasureTheory.eLpNorm_indicator_const', cos_int_mul_two_pi_sub_pi, MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top, Affine.Simplex.sum_touchpointWeights, Valued.integer.mem_iff, Affine.Simplex.sum_pointWeightsWithCircumcenter, SmoothBumpCovering.apply_ind, Polynomial.coeff_bdd_of_roots_le, Nat.Primes.summable_rpow, HurwitzZeta.hurwitzEvenFEPair_neg, isBigO_deriv_rpow_const_atTop, PadicInt.norm_sub_zmodRepr_lt_one, deriv_rpow_const', ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg, sin_sub_nat_mul_pi, MeasureTheory.Measure.haar.prehaar_self, Matrix.l2_opNorm_le_one_of_mem_doublyStochastic, continuousSMul_closedBall_closedBall, SmoothBumpFunction.eventuallyEq_one_of_dist_lt, CStarAlgebra.directedOn_nonneg_ball, tendsto_Icc_vitaliFamily_left, Circle.normSq_coe, hasStrictDerivAt_sqrt, cosh_sq', BumpCovering.exists_finset_toPOUFun_eventuallyEq, HurwitzZeta.completedHurwitzZetaEven_neg, ofCauchy_one, hasDerivAt_tan_of_mem_Ioo, arcsin_lt_pi_div_two, integral_one_div, inner_le_Lp_mul_Lq, AlgHom.toContinuousLinearMap_norm, exists_continuous_one_zero_of_isCompact_of_isGΞ΄, fderiv_sqrt, Polynomial.Chebyshev.eval_T_real_eq_one_iff, HolderConjugate.sub_one_mul_conj, RCLike.wInner_one_const_left, HurwitzZeta.cosKernel_neg, MeasureTheory.pow_mul_meas_ge_le_eLpNorm, SzemerediRegularity.one_le_m_coe, NNReal.inner_le_Lp_mul_Lq_tsum', Affine.Simplex.ExcenterExists.signedInfDist_excenter, hasSum_sin, EisensteinSeries.abs_norm_eq_max_natAbs, MeasureTheory.eLpNorm_const, ContDiffBump.eventuallyEq_one_of_mem_ball, ContinuousLinearMap.norm_single_le_one, rpow_one_sub', cos_eq_one_iff, Polynomial.Chebyshev.U_real_cosh, ContinuousLinearMap.norm_compSL_le, curveIntegralFun_trans_aeeq_left, NNReal.rpow_one_add', Valued.integer.isUnit_iff_norm_eq_one, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Metric.unitSphere.coe_div, InnerProductSpace.isIdempotentElem_rankOne_self_iff, MeasureTheory.hausdorffMeasure_affineSegment, Complex.UnitDisc.norm_lt_one, sin_sq_pi_over_two_pow, IsCompact.measure_eq_biInf_integral_hasCompactSupport, UnitAddCircle.mem_addWellApproximable_iff, Complex.toMatrix_conjAe, Cardinal.cantorFunctionAux_zero, neg_one_le_mulExpNegMulSq_one, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, integral_pow_mul_le_of_le_of_pow_mul_le, neg_one_lt_goldConj, hasDerivWithinAt_abs_neg, instSMulCommClass_closedBall_closedBall_ball, Stirling.log_stirlingSeq_diff_le_geo_sum, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBot, Behrend.le_sqrt_log, Complex.UnitDisc.instSMulCommClass_circle_closedBall, norm_sub_le_mul_volume_of_norm_fderiv_le, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, Behrend.two_div_one_sub_two_div_e_le_eight, UpperHalfPlane.val_J, MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ, add_one_lt_exp, ProbabilityTheory.Kernel.densityProcess_fst_univ, SzemerediRegularity.coe_m_add_one_pos, Path.extend_extends', ENNReal.rpow_neg_one, Complex.norm_fderiv_le_one_of_mapsTo_ball, EReal.coe_one, cos_nat_mul_two_pi_add_pi, abs_sin_le_one, InnerProductGeometry.cos_eq_one_iff_angle_eq_zero, Complex.conjCLE_norm, ProbabilityTheory.variance_linearMap_gaussianReal, HurwitzZeta.completedCosZeta_zero, isScalarTower_sphere_ball_ball, MeasureTheory.Measure.addHaar_closedBall, ContinuousLinearMap.norm_id, HurwitzZeta.completedCosZeta_neg, posLog_one, MeasureTheory.L1.norm_Integral_le_one, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm, ProbabilityTheory.Kernel.mem_mutuallySingularSetSlice, sin_nat_mul_pi_sub, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, arcsin_image_Icc, ContinuousLinearMap.norm_smulRightL_le, schnirelmannDensity_le_of_notMem, spectralValue_le_one_iff, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, MeasureTheory.eLpNorm_indicator_constβ, MeasureTheory.Measure.haar.addCHaar_self, Metric.nhds_basis_ball_inv_nat_succ, integral_rpow_mul_exp_neg_mul_Ioi, setOf_liouville_eq_iInter_iUnion, det_rotation, PadicInt.norm_mahler_eq, strictConcave_binEntropy, tendsto_abs_tan_atTop, Int.norm_coe_units, ContDiffBump.normed_le_div_measure_closedBall_rIn, HurwitzZeta.cosZeta_neg, integral_inv_one_add_sq, EisensteinSeries.abs_norm_eq_max_natAbs_neg, RCLike.wInner_one_eq_sum, EReal.coe_eq_one, ENNReal.dichotomy, iteratedDeriv_odd_sin, CircleDeg1Lift.map_lt_add_translationNumber_add_one, HurwitzZeta.sinKernel_def, exp_zero, HolderTriple.one_div_pos, Complex.HadamardThreeLines.scale_diffContOnCl, Antitone.cauchySeq_alternating_series_of_tendsto_zero, Gamma_integrand_isLittleO, Complex.HadamardThreeLines.diffContOnCl_invInterpStrip, one_div_sub_pow_hasFPowerSeriesOnBall_zero, MeasureTheory.measureReal_univ_eq_one, Valued.toNormedField.setOf_mem_integer_eq_closedBall, Quaternion.coeComplex_imJ, le_egauge_ball_one, Behrend.lower_bound_le_one', Unitary.norm_argSelfAdjoint, CircleDeg1Lift.map_add_one', fourierCoeffOn_eq_integral, HurwitzKernelBounds.F_nat_zero_le, sphere_ext_iff, ContinuousMap.toNNReal_neg_one, HolderTriple.one_div_add_one_div, UpperHalfPlane.dist_coe_le, homeomorphUnitSphereProd_apply_snd_coe, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atTop_one, sinc_apply, ContractingWith.fixedPoint_lipschitz_in_map, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, ContDiffBump.one_of_mem_closedBall, HolderTriple.one_div_nonneg', curveIntegralFun_symm, BohrMollerup.logGammaSeq_add_one, exp_neg_one_gt_d9, ZetaAsymptotics.term_welldef, mulExpNegMulSq_one_le_one, Quaternion.imJ_coeComplex, PiLp.nnnorm_eq_sum, unitInterval.one_minus_nonneg, exp_one_near_10, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, exp_le_one_iff, ProbabilityTheory.Kernel.singularPart_def, ZetaAsymptotics.term_sum_one, UnitAddTorus.mFourier_single, cos_sq, ModularFormClass.differentiableOn_cuspFunction_ball, PadicInt.coe_neg, Padic.norm_rat_le_one_iff_padicValuation_le_one, PadicInt.norm_def, PadicInt.norm_natCast_eq_one_iff, lp.norm_eq_tsum_rpow, not_summable_one_div_on_primes, WeakFEPair.f_modif_aux1, CStarAlgebra.norm_le_one_iff_of_nonneg, cauchy_one, Metric.unitClosedBall.coe_pow, ENNReal.ofReal_eq_one, PadicInt.isOpenEmbedding_coe, InnerProductSpace.volume_closedBall, ContinuousLinearEquiv.coord_norm', stereographic'_symm_apply, Matrix.frobenius_nnnorm_def, Metric.unitClosedBall.instIsCancelMulZero, smoothTransition.projIcc, indicator_indepFun_process_of_prod_bcf, MeasureTheory.Measure.volumeIoiPow_apply_Iio, Quaternion.coeComplex_imI, summable_geometric_two, HurwitzZeta.evenKernel_functional_equation, not_continuousAt_inv_log_one, Polynomial.Chebyshev.node_mem_Icc, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip', goldConj_mul_gold, exp_one_pow, posLog_eq_log_max_one, HolderTriple.one_div_pos', summable_one_div_nat_pow, HurwitzZeta.hurwitzZetaOdd_neg, LinearIsometry.norm_toContinuousLinearMap_le, hasStrictDerivAt_tan, MeasureTheory.eLpNorm'_eq_lintegral_enorm, circleAverage_zero_one_congr_inv, ExistsContDiffBumpBase.w_integral, NNReal.coe_one, Metric.unitClosedBall.instContinuousMul, tendsto_euler_sin_prod, List.norm_prod, zero_lt_one_add_norm_sq, binEntropy_strictAntiOn, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, Metric.unitClosedBall.coe_eq_one, arctan_eq_pi_div_four, DilationEquiv.smulTorsor_preimage_ball, integral_Ioi_inv_one_add_sq, Quaternion.coe_ofComplex, hasDerivAt_arctan, NonarchAddGroupNorm.apply_one, rpow_def_of_nonpos, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, ZMod.toAddCircle_eq_zero, Complex.betaIntegral_convergent_left, Nat.ratSqrt_mem_Ioc, polynomialFunctions_closure_eq_top', schnirelmannDensity_eq_one_iff_of_zero_mem, ENNReal.one_lt_ofReal, MeasureTheory.norm_indicatorConstLp', sqrt_one, AddSubgroup.norm_normedMk, gauge_lt_one_iff_mem_interior, bernstein.probability, AkraBazziRecurrence.one_mem_range_sumCoeffsExp, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, ContinuousLinearMap.norm_snd_le, NNReal.coe_mulSingle, rpow_le_one_iff_of_pos, floor_exp_one_eq_two, Tactic.ComputeAsymptotics.Seq.dist_le_one, toNNReal_eq_one, integral_exp_neg_Ioi_zero, ContinuousLinearMap.opNorm_mulLeftRight_le, Complex.norm_exp_ofReal_mul_I, setOf_liouville_eq_irrational_inter_iInter_iUnion, HasFDerivAt.sqrt, Padic.norm_natCast_p_sub_one, Affine.Simplex.sum_excenterWeights, UpperHalfPlane.I_im, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTop, NNReal.one_lt_coe, unitary.norm_sub_one_sq_eq, deriv_arcsin_aux, exists_contDiff_tsupport_subset, BoxIntegral.unitPartition.tag_apply, tendsto_sin_pi_div_two, hasMellin_cpow_Ioc, PadicInt.norm_le_one, StrongDual.mem_polar_iff, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Polynomial.Chebyshev.isExtrOn_T_real, Complex.HadamardThreeLines.sSupNormIm_scale_right, integral_sin_pow, Polynomial.cyclotomic_mahlerMeasure_eq_one, MeasureTheory.Measure.addHaar_ball, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, AkraBazziRecurrence.b_lt_one, MeasureTheory.eLpNorm_sub_le_of_dist_bdd, AkraBazziRecurrence.growsPolynomially_one_sub_smoothingFn, abs_real_inner_div_norm_mul_norm_eq_one_iff, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, Height.mulHeightβ_zero, projIcc_eq_zero, unitInterval.half_le_symm_iff, NNReal.inner_le_Lp_mul_Lq_tsum, MeasureTheory.GridLines.T_univ, isTheta_deriv_ofReal_cpow_const_atTop, RealRMK.range_cut_partition, Metric.unitBall.instIsCancelMulZero, tanh_sq_lt_one, PadicInt.mem_nonunits, Quaternion.instNormOneClassReal, Icc_mem_vitaliFamily_at_right, BumpCovering.toPOUFun_eq_mul_prod, instSMulCommClass_sphere_closedBall_ball, curveIntegral_def', ModularGroup.det_coe, CStarAlgebra.isBasis_nonneg_sections, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, cosh_sq_sub_sinh_sq, Submodule.norm_orthogonalProjection, RingSeminorm.apply_one, Complex.image_exp_Ioc_eq_sphere, ContinuousLinearMap.opNorm_lsmul, HurwitzZeta.completedHurwitzZetaEven_residue_zero, fderivWithin_arctan, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, integral_mul_rpow_one_add_sq, isScalarTower_closedBall_closedBall_ball, MeasureTheory.measureReal_biUnion_eq_sum_powerset, tendsto_log_nat_add_one_sub_log, exists_tsupport_one_of_isOpen_isClosed, log_nonpos_iff, MulRingNorm.apply_one, Archimedean.embedReal_one, tsum_eq_tsum_fourierIntegral, ENNReal.fun_eq_funMulInvSnorm_mul_eLpNorm, ContDiffBump.le_one, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, SchwartzMap.tsum_eq_tsum_fourierIntegral, NNReal.rpow_self_rpow_inv, Polynomial.Chebyshev.node_eq_one, ContinuousLinearMap.norm_snd, MeasureTheory.condExpIndSMul_ae_eq_smul, Quaternion.linearIsometryEquivTuple_apply, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, artanh_injOn, integral_Iic_inv_one_add_sq, NNReal.rpow_one, HurwitzZeta.isBigO_atTop_cosKernel_sub, Monotone.cauchySeq_alternating_series_of_tendsto_zero, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ProbabilityTheory.condIndepFun_iff, gaugeSeminorm_lt_one_of_isOpen, Topology.CWComplex.mapsTo, LinearMap.polar_mem_iff, cos_eq_neg_one_iff, abs_cos_eq_one_iff, ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le', gaugeSeminormFamily_ball, add_one_le_exp, HolderConjugate.inv_sub_one, BoxIntegral.unitPartition.box.upper_sub_lower, sign_apply_eq_of_ne_zero, NumberField.mulHeightβ_eq, Wallis.W_succ, Complex.Gamma_def, NormedSpace.norm_normalize, NumberField.FinitePlace.norm_le_one, cos_eq_sqrt_one_sub_sin_sq, hasStrictFDerivAt_rpow_of_neg, ContinuousMap.Homotopy.extend_one, ENNReal.ofReal_lt_one, tanh_arsinh, PartitionOfUnity.exists_finset_nhds', continuousOn_arcosh, exp_one_gt_two, IsApproximateAddSubgroup.addSubgroup, cos_pi_div_three, Valued.integer.norm_coe_unit, zero_lt_one_add_norm_sq', HurwitzZeta.sinZeta_eq, cos_zero, PadicInt.norm_natCast_zmodRepr_eq_iff, BumpCovering.le_one', Besicovitch.one_lt_goodΟ, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Metric.unitClosedBall.coe_zero, Complex.one_re, PadicInt.coe_mul, Gamma_nat_eq_factorial, StrongDual.polar_singleton, spectralValueTerms_of_lt_natDegree, hasDerivAt_Gamma_nat, EuclideanGeometry.cos_eq_one_iff_angle_eq_zero, Path.truncate_one_one, Height.AdmissibleAbsValues.product_formula, Polynomial.Chebyshev.abs_eval_T_real_le_one_iff, unitInterval.two_mul_sub_one_mem_iff, hasSum_zeta_nat, MeasureTheory.dominatedFinMeasAdditive_weightedSMul, arcosh_surjOn, cos_add_int_mul_pi, doublingGamma_one, exists_smooth_zero_one_nhds_of_isClosed, ZLattice.sum_piFinset_Icc_rpow_le, CStarAlgebra.hasBasis_approximateUnit, not_continuousAt_deriv_qaryEntropy_one, IsApproximateSubgroup.one_le, integral_exp_Iic_zero, SmoothBumpFunction.eventuallyEq_one, tan_arcsin, BoxIntegral.unitPartition.diam_boxIcc, NormedDivisionRing.norm_le_one_of_discrete, arcsin_eq_neg_pi_div_two, ENNReal.inner_le_Lp_mul_Lq, Metric.nhds_basis_ball_inv_nat_pos, instSMulCommClass_sphere_sphere_closedBall, Quaternion.coeComplex_one, parallelepiped_orthonormalBasis_one_dim, pi_rpow_zero, PadicInt.coe_add, StrongDual.mem_polar_singleton, sign_of_neg, sqrt_one_add_norm_sq_le, MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int, Complex.norm_exp_I_mul_ofReal, Besicovitch.goodΞ΄_lt_one, LiouvilleNumber.remainder_lt, Manifold.exists_lt_of_riemannianEDist_lt, norm_innerSL_le, Quaternion.continuous_imK, Urysohns.CU.lim_of_notMem_U, MeasureTheory.measure_unitBall_eq_integral_div_gamma, exp_neg_one_lt_half, PadicInt.unitCoeff_coe, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, RCLike.normSq_one, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, OpenPartialHomeomorph.univUnitBall_symm_apply, orthonormal_vecCons_iff, log_div_self_rpow_antitoneOn, MeasureTheory.eLpNorm'_const, HolderConjugate.sub_one_pos, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, Function.hasTemperateGrowth_one_add_norm_sq_rpow, instIsAddHaarMeasureUnitAddCircleVolume, sin_eq_one_iff, Complex.log_inv_eq_integral, ZMod.LFunction_dft, HurwitzZeta.hasSum_nat_cosKernelβ, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, PadicInt.coe_dpow_eq, instSMulCommClass_closedBall_closedBall_closedBall, Valued.toNormedField.norm_lt_one_iff, ProbabilityTheory.poissonPMFRealSum, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, AkraBazziRecurrence.sumCoeffsExp_p_eq_one, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, cos_nat_mul_two_pi, one_lt_sqrt_two, ExistsContDiffBumpBase.y_le_one, EuclideanSpace.edist_eq, MeasureTheory.isProbabilityMeasure_iff_real, ofDigits_const_last_eq_one', intervalIntegral.intervalIntegrable_one_div, PadicInt.coe_intCast, PadicInt.norm_natCast_p_sub_one, Complex.range_exp_mul_I, LinearMap.polar_mem, MeasureTheory.Lp.pow_mul_meas_ge_le_enorm, sin_mem_Icc, sqrt_eq_one, Subgroup.strictWidthInfty_SL2Z, qaryEntropy_one, SmoothBumpFunction.eq_one, Submodule.norm_subtypeL_le, cos_sq_arctan, exists_contMDiffMap_one_nhds_of_subset_interior, Complex.norm_eq_one_of_pow_eq_one, NormedSpace.norm_normalize_eq_one_iff, CovBySMul.of_subset, SmoothPartitionOfUnity.sum_le_one, CStarRing.norm_one, ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAux, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, NumberField.mixedEmbedding.norm_unit, MeasureTheory.exp_llr, tendsto_prod_pi_div_two, one_half_le_sum_primes_ge_one_div, Quaternion.coe_real_complex_mul, hasDerivAt_sqrt, SchwartzMap.one_add_le_sup_seminorm_apply, UnitAddCircle.integral_preimage, tanh_surjOn, integral_one_div_of_neg, Polynomial.Chebyshev.roots_U_real_nodup, hasDerivWithinAt_arccos_Iic, Complex.approx_Gamma_integral_tendsto_Gamma_integral, Polynomial.isPrimitive_iff_forall_gaussNorm_eq_one, cos_pi, contDiffOn_arcsin, PartitionOfUnity.sum_finsupport', Affine.Simplex.ninePointCircle_center, Gamma_three_div_two_lt_one, spectrum.subset_circle_of_unitary, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, ProbabilityTheory.Kernel.rnDeriv_def, range_sigmoid, FormalMultilinearSeries.radius_eq_liminf, deriv_tan, sigmoid_lt_one, tendsto_one_add_div_rpow_exp, NNReal.coe_eq_one, Metric.unitBall.coe_zero, rpow_add_one', cos_int_mul_pi, Polynomial.Chebyshev.roots_T_real_nodup, Behrend.exists_large_sphere_aux, one_sub_goldenRatio, instSMulCommClass_sphere_sphere_ball, PiTensorProduct.mapLMultilinear_opNorm, Int.pairwise_one_le_dist, CircleDeg1Lift.map_add_one, smoothTransition.pos_denom, NNReal.coe_list_prod, MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, Submodule.orthogonalProjection_norm_le, Function.HasTemperateGrowth.isBigO_uniform, MeasureTheory.Measure.haar.addPrehaar_self, integral_pow_abs_sub_uIoc, Valued.toNormedField.one_le_norm_iff, EuclideanSpace.volume_closedBall, cos_mem_Icc, CStarRing.norm_coe_unitary, BumpCovering.sum_toPOUFun_eq, sqrt_eq_rpow, PiNat.dist_le_one, sin_half_eq_sqrt, sin_eq_sqrt_one_sub_cos_sq, le_egauge_closedBall_one, AkraBazziRecurrence.bi_min_div_two_lt_one, Quaternion.continuous_re, one_add_rpow_hasFPowerSeriesOnBall_zero, CFC.conjugate_rpow_neg_one_half, WithLp.prod_edist_eq_add, MeasureTheory.norm_condExpL2_le_one, tendsto_harmonic_sub_log_add_one, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, BumpCovering.coe_single, summable_nat_rpow, ProbabilityTheory.tendsto_condCDF_atTop, balanced_iff_closedBall_smul, one_div_sub_sq_hasFPowerSeriesOnBall_zero, rpowIntegrandββ_eqOn_mul_rpowIntegrandββ_one, HasFDerivAt.rpow, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, LSeries_eq_mul_integral', log_nonneg_iff, SimpleGraph.triangle_counting, inner_le_Lp_mul_Lq_of_nonneg, log_le_sub_one_of_pos, exists_int_int_abs_mul_sub_le, sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, le_iff_norm_sqrt_mul_rpow, balancedCore_eq_iInter, RCLike.wInner_cWeight_eq_smul_wInner_one, one_sub_inv_le_log_of_pos, Complex.det_conjLIE, Height.mulHeightβ_one, HolderTriple.one_div_nonneg, CircleDeg1Lift.tendsto_translation_numberβ', Valued.integer.exists_norm_coe_lt_one, strictConcaveOn_qaryEntropy, unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, mul_exp_neg_le_exp_neg_one, Unitary.spectrum_subset_circle, Polynomial.Chebyshev.roots_U_real, MeasureTheory.count_real_singleton, HurwitzZeta.hurwitzZetaEven_neg, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, tanh_bijOn, Metric.uniformity_basis_dist_inv_nat_pos, exp_neg_one_lt_d9, cos_le_one, GaussianInt.normSq_div_sub_div_lt_one, NNReal.inner_le_Lp_mul_Lq, ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone, MeasureTheory.probReal_compl_eq_one_sub, Quaternion.norm_toLp_equivTuple, integral_sin_pow_even, arcsin_projIcc, ContinuousMultilinearMap.norm_mkPiAlgebraFin, Affine.Simplex.points_vsub_eulerPoint, bernoulliFun_eval_half, summable_one_div_int_add_rpow, UpperHalfPlane.modular_T_smul, Quaternion.exp_eq, RCLike.inner_eq_wInner_one, isLittleO_one_exp_comp, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div, MeasureTheory.Measure.toSphere_apply_univ', Int.Matrix.exists_ne_zero_int_vec_norm_le, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Function.HasTemperateGrowth.isBigO, PiLp.dist_eq_sum, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, niven, hasSum_L_function_mod_four_eval_three, Urysohns.CU.approx_of_notMem_U, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, Asymptotics.isBigOWith_fst_prod, NNReal.lintegral_mul_le_Lp_mul_Lq, Complex.tendsto_tsum_powerSeries_nhdsWithin_lt, hasDerivWithinAt_arcsin_Iic, hasDerivAt_abs_pos, PiLp.edist_eq_of_L2, quarter_mem_cantorSet, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, MeasureTheory.eLpNorm_indicator_const, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', HurwitzZeta.hurwitzZetaEven_eq, summable_geometric_two_encode, log_doublingGamma_eq, MeasureTheory.condExpL2_indicator_nonneg, PadicInt.coe_pow, Complex.abs_re_div_norm_le_one, Bundle.ContinuousRiemannianMetric.isVonNBounded, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, PartitionOfUnity.sum_finsupport, integrableAtFilter_rpow_atTop_iff, Complex.UnitDisc.sq_norm_lt_one, Complex.continuousOn_one_add_mul_inv, tendsto_one_add_div_pow_exp, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atTop_one, arcsin_one, binEntropy_eq_negMulLog_add_negMulLog_one_sub, HolderConjugate.div_conj_eq_sub_one, Urysohns.CU.lim_mem_Icc, MeasureTheory.Measure.addHaar_closedBall', Height.mulHeight_one, ContinuousMultilinearMap.norm_ofSubsingleton_id, sum_trapezoidal_integral_adjacent_intervals, AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, NNReal.summable_rpow, EisensteinSeries.div_max_sq_ge_one, coe_sinOrderIso_apply, NormedAddGroupHom.norm_id, one_lt_rpow_iff, Stirling.tendsto_self_div_two_mul_self_add_one, Wallis.le_W, SchwartzMap.tsum_eq_tsum_fourier, ZLattice.exists_finsetSum_norm_rpow_le_tsum, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, MeasureTheory.Measure.integrable_pow_neg_integrablePower, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, Complex.normSq_one, binEntropy_eq_zero, MeasureTheory.Measure.toSphere_eq_zero_iff, zero_rpow_le_one, ENNReal.toReal_eq_one_iff, tendsto_Icc_vitaliFamily_right, HurwitzZeta.hasSum_int_evenKernelβ, Affine.Simplex.sum_centroidWeightsWithCircumcenter, sin_sq_pi_over_two_pow_succ, MeasureTheory.Measure.addHaar_real_closedBall, Metric.sphere.instIsTopologicalGroup, cos_arctan, Metric.Sigma.dist_ne, goldenRatio_sq, le_iff_norm_sqrt_mul_sqrt_inv, Angle.cos_coe_pi, Homeomorph.unitBall_symm_apply, log_neg_iff, GromovHausdorff.HD_candidatesBDist_le, exists_cos_eq_zero, Matrix.permMatrix_l2_opNorm_eq, norm_inner_div_norm_mul_norm_eq_one_iff, ofDigits_le_one, Quaternion.norm_star, rpow_lt_one_iff', hasDerivAt_negMulLog, arccos_injOn, eulerMascheroniSeq'_one, ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_ne_top, one_add_norm_le_sqrt_two_mul_sqrt, tendsto_logb_nat_add_one_sub_logb, PadicInt.norm_natCast_lt_one_iff, AkraBazziRecurrence.strictAntiOn_smoothingFn, Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, unitInterval.volume_Ioi, ModularGroup.coe_truncatedFundamentalDomain
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instPreorder π | CompOp | 1295 mathmath: comap_dist_left_atTop_eq_cocompact, HurwitzZeta.hasSum_int_hurwitzZetaOdd, differentiableOn_arcosh, HurwitzZeta.isBigO_atTop_evenKernel_sub, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, range_sin, isFiniteMeasure_restrict_Ioc, hasSum_mellin_pi_mul_sq', NNReal.orderIsoIccZeroCoe_apply_coe_coe, uniqueDiffOn_Icc, isBigO_log_mul_const_log_atTop, exists_continuous_sum_one_of_isOpen_isCompact, ProbabilityTheory.paretoCDFReal_eq_lintegral, seminormFromConst_seq_antitone, exists_contMDiffMap_zero_one_of_isClosed, arcosh_bijOn, EReal.image_coe_Icc, ProbabilityTheory.lintegral_condCDF, isLittleO_logb_id_atTop, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le, tendsto_norm_sub_self_nhdsNE, volume_real_Ioc, NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, gauge_def', IsPicardLindelof.of_contDiffAt_one, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, ODE.FunSpace.next_apply, ConvexOn.rightDeriv_le_slope_of_mem_interior, unitInterval.volume_Ioo, unitInterval.volume_Iic, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, RightDerivMeasurableAux.D_subset_differentiable_set, MeasureTheory.upperCrossingTime_succ_eq, UnitAddCircle.lintegral_preimage, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite, Complex.comap_exp_cobounded, HasCompactSupport.integral_Ioi_deriv_eq, strictMonoOn_sqrt, deriv_abs, Asymptotics.isLittleO_const_left, strictMono_of_hasDerivAt_pos, AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, Complex.exists_mem_frontier_isMaxOn_norm, Complex.norm_sub_mem_Icc_angle, uniqueDiffWithinAt_Iic, CuspFormClass.zero_at_infty_comp_ofComplex, Metric.hasAntitoneBasis_cobounded_compl_ball, CFC.tendsto_cfc_rpow_sub_one_log, integrableOn_exp_mul_Iic, PadicInt.val_mkUnits, mapsTo_cos, unitInterval.strictAnti_symm, ContinuousMap.attachBound_apply_coe, mapsTo_cos_Ioo, Cardinal.mk_Iio_real, strictAntiOn_logb, ProbabilityTheory.unitInterval.cdf_eq_real, monotone_rpow_of_base_ge_one, ProbabilityTheory.gammaCDFReal_eq_lintegral, Affine.Simplex.sign_excenterWeights_singleton_pos, circleIntegral_def_Icc, integral_exp_mul_Iic, ODE.FunSpace.isUniformInducing_toContinuousMap, strictConcaveOn_rpow, not_integrableOn_Ioi_cpow, ContDiffBumpBase.smooth, EReal.image_coe_Ioc, WeakFEPair.hf_modif_int, AkraBazziRecurrence.exists_eventually_const_mul_le_r, ProbabilityTheory.tendsto_condCDF_atBot, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero, Ioo_eq_ball, exists_smooth_one_nhds_of_subset_interior, MeasureTheory.Measure.toSphere_apply_aux, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, LSeries_eventually_eq_zero_iff', intervalIntegrable_iff_integrableOn_Icc_of_le, tendsto_toNNReal_atTop_iff, AkraBazziRecurrence.tendsto_atTop_sumCoeffsExp, ProbabilityTheory.sum_prob_mem_Ioc_le, Metric.exists_forall_closedEBall_subset_auxβ, Path.range_subpath_of_ge, uniqueDiffOn_Iic, Metric.comap_dist_left_atTop, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, antitoneOn_of_hasDerivWithinAt_nonpos, ODE.FunSpace.range_toContinuousMap, tendsto_cos_pi_div_two, Complex.norm_eq_one_iff', BoxIntegral.Box.le_TFAE, IsOpen.exists_smooth_support_eq, ProbabilityTheory.setIntegral_condCDF, tendsto_norm_nhdsNE_one, one_mem_posTangentConeAt_iff_frequently, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, not_IntegrableOn_Ioi_inv, tendsto_tsum_powerSeries_nhdsWithin_lt, strictAntiOn_arccos, isLittleO_log_rpow_rpow_atTop, lintegral_fderiv_lineMap_eq_edist, Set.OrdConnected.image_deriv, monotone_of_deriv_nonneg, ProbabilityTheory.lintegral_gammaPDF_of_nonpos, unitInterval.volume_Ico, EReal.image_coe_Ico, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, intervalIntegrable_iff_integrableOn_Ico_of_le, comap_norm_atTop', uniqueDiffOn_Ioc, Angle.toReal_coe_eq_self_iff_mem_Ioc, Cardinal.Real.Ioc_countable_iff, StrictConvexOn.strictMonoOn_deriv, range_arctan, ProbabilityTheory.cdf_paretoMeasure_eq_integral, Asymptotics.isLittleO_const_id_atTop, tendsto_sigmoid_atTop, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, tendsto_exp_atTop, Gamma_strictAntiOn_Ioc, integrableOn_exp_Iic, log_mul_self_monotoneOn, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, stronglyMeasurable_derivWithin_Ioi, variationOnFromTo.antitoneOn, IsClopen.upperClosure_pi, artanh_bijOn, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, CircleDeg1Lift.tendsto_atBot, EReal.preimage_coe_Ioi, exists_dist_slope_lt_pairwiseDisjoint_hasSum, GroupSeminorm.lt_def, ProbabilityTheory.IsCondKernelCDF.integral, ENNReal.tendsto_rpow_atTop_of_one_lt_base, unitInterval.sigmoid_strictMono, SimpleGraph.antitoneOn_extremalNumber_div_choose_two, WeakFEPair.hf_zero', Icc_isBoundaryPoint_bot, borel_eq_generateFrom_Iio_rat, Tactic.ComputeAsymptotics.Majorized.tendsto_zero_of_neg, integral_exp_neg_mul_rpow, HurwitzKernelBounds.isBigO_atTop_F_int_one, BoxIntegral.unitPartition.prepartition_isSubordinate, differentiableWithinAt_arccos_Ici, ball_eq_Ioo, Tactic.ComputeAsymptotics.WellFormedBasis.head_eventually_pos, iUnion_Iic_rat, integrableOn_Ioi_rpow_of_lt, monotone_arcsin, EReal.image_coe_Iio, tendsto_exp_div_pow_atTop, Affine.Simplex.sign_touchpointWeights_empty, InformationTheory.tendsto_klFun_atTop, comap_norm_nhdsGT_zero, StieltjesFunction.mono', integrableOn_Ioi_norm_cpow_of_lt, IsClosed.lowerClosure_pi, InformationTheory.leftDeriv_klFun_one, integral_Ioi_rpow_of_lt, Complex.arg_mul_eq_add_arg_iff, exists_smooth_tsupport_subset, strictConvexOn_pow, ProbabilityTheory.gammaCDFReal_eq_integral, ConvexOn.monotoneOn_rightDeriv, Polynomial.Chebyshev.isLocalMin_T_real, tendsto_norm_inv_nhdsNE_zero_atTop, Archimedean.embedReal_apply, MeasureTheory.Submartingale.stoppedValue_leastGE, Icc_mem_vitaliFamily_at_left, IsClopen.lowerClosure_pi, arctan_mem_Ioo, nullMeasurableSet_region_between_co, setIntegral_Ioi_zero_rpow, integral_rpow_mul_exp_neg_rpow, GammaIntegral_convergent, borel_eq_generateFrom_Ioo_rat, NNReal.map_coe_atTop, ProbabilityTheory.monotone_cdf, monotoneOn_posLog, volume_real_Ioo, Complex.tendsto_exp_nhds_zero_iff, isLittleO_log_id_atTop, intervalIntegral.integral_pos_iff_support_of_nonneg_ae', indicator_thickening_eventually_eq_indicator_closure, surjOn_log', image_circleMap_Ioc, strictMonoOn_artanh, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', comap_exp_nhds_zero, cosPartialEquiv_target, isLocalMin_of_deriv_deriv_pos, ProbabilityTheory.integral_stieltjesOfMeasurableRat, HasStrictFDerivAt.abs, nullMeasurableSet_regionBetween, NumberField.mixedEmbedding.fundamentalCone.expMap_target, CircleDeg1Lift.strictMono_iff_injective, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, Complex.hasDerivAt_GammaIntegral, exists_continuous_zero_one_of_isClosed, RCLike.toIsStrictOrderedModule, norm_sub_le_mul_volume_of_norm_lineDeriv_le, ValueDistribution.logCounting_mul_zero_eventuallyLE, SmoothBumpFunction.exists_r_pos_lt_subset_ball, cosh_surjOn, EReal.preimage_coe_Ioo, integrableOn_add_rpow_Ioi_of_lt, Angle.toReal_mem_Ioc, antitoneOn_cos, NNReal.image_coe_Ico, closedBall_eq_Icc, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atTop, singleton_eq_inter_Icc, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, mfderivWithin_comp_projIcc_one, EReal.tendsto_coe_atTop, ValueDistribution.logCounting_mul_top_eventuallyLE, Metric.comap_dist_right_atTop, sqrt_monotone, ModularGroup.tendsto_abs_re_smul, strictConcaveOn_log_Iio, Manifold.pathELength_def, ODE.FunSpace.continuousOn_comp_compProj, AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const_real, integrableOn_Ioi_cpow_iff, integral_exp_mul_complex_Ioi, setIntegral_Ioi_zero_cpow, Function.locallyFinsuppWithin.logCounting_eventually_le, volume_pi_Ico, InformationTheory.tendsto_rightDeriv_klFun_atTop, nullMeasurableSet_region_between_cc, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'', NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, volume_real_Ioo_of_le, ContinuousMap.HomotopyRel.trans_apply, range_cos, tendsto_rpow_atTop, ProbabilityTheory.cdf_eq_real, tendsto_exp_neg_atTop_nhds_zero, hasDerivWithinAt_abs, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Complex.tendsto_exp_comap_re_atTop, exists_iUnion_ball_eq_radius_pos_lt, Metric.isBounded_iff_eventually, ContMDiff.piecewise_Iic, volume_Icc_pi, integrableOn_Ioi_norm_cpow_iff, IsOpen.exists_contMDiff_support_eq_aux, sinhHomeomorph_symm_apply, arccos_image_Icc, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, ediam_Ioc, ProbabilityTheory.tendsto_integral_truncation, Metric.exists_forall_closedEBall_subset_auxβ, RCLike.re_monotone, injOn_circleMap_of_abs_sub_le', finite_integral_rpow_sub_one_pow_aux, EReal.preimage_coe_Ioo_top, Complex.comap_exp_nhds_zero, ProbabilityTheory.monotone_defaultRatCDF, Complex.GammaIntegral_ofReal, strictConcaveOn_sqrt_mul_log_Ioi, Chebyshev.integral_one_div_log_sq_isBigO, Complex.norm_ofReal_cpow_eventually_eq_atTop, continuousMap_mem_polynomialFunctions_closure, polarCoord_target, BoxIntegral.TaggedPrepartition.isSubordinate_single, EReal.tendsto_toReal_atTop, hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, MeasureTheory.posConvolution_eq_convolution_indicator, AddCircle.add_projection_respects_measure, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, EReal.tendsto_toReal_atBot, InformationTheory.leftDeriv_klFun, exp_monotone, MeasureTheory.integral_comp_rpow_Ioi_of_pos, tendsto_norm_div_self_nhdsNE, exists_isMinOn_Gamma_Ioi, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, tendsto_exp_comp_nhds_zero, surjOn_logb', volume_pi_Ioc, AkraBazziRecurrence.strictMonoOn_one_sub_smoothingFn, ValueDistribution.isBigO_characteristic_sub_characteristic_shift, Complex.map_exp_comap_re_atTop, isPiSystem_Iic_rat, tendsto_norm_div_self_nhdsGE, analyticOn_log, MeasureTheory.Measure.haar.mem_prehaar_empty, NormedAlgebra.exists_isMinOn_norm_sub_smul, Besicovitch.ae_tendsto_rnDeriv, arcosh_injOn, NormedSpace.normalize_smul, analyticOnNhd_log, toNNReal_monotone, coe_expOrderIso_apply, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, isAddFundamentalDomain_Ioc, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul, MeasureTheory.lowerCrossingTime_zero, MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul, intervalIntegral.integrableOn_Ioo_rpow_iff, Path.Homotopy.hcomp_half, HasFPowerSeriesOnBall.uniform_geometric_approx, volume_Icc_pi_toReal, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, Path.Homotopy.hcomp_apply, NNReal.comap_coe_atTop, sinh_sub_id_strictMono, concaveOn_rpow, Urysohns.CU.approx_mono, IsPicardLindelof.continuousOn, Stirling.stirlingSeq'_antitone, Complex.tendsto_normSq_cocompact_atTop, Ioo_smul_sphere_zero, tendsto_integral_gaussian_smul', unitInterval.volume_Ici, Polynomial.Chebyshev.isLocalMax_T_real, tendsto_cos_neg_pi_div_two, strictMono_of_deriv_pos, HurwitzZeta.continuousOn_cosKernel, EReal.image_coe_Iic, artanh_surjOn, LSeries_eq_mul_integral_of_nonneg, ContDiffBumpBase.mem_Icc, LinearGrowth.Real.eventually_atTop_exists_int_between, StrongFEPair.hf_zero', ProbabilityTheory.IsCondKernelCDF.setIntegral, IntervalIntegrable.aestronglyMeasurable', borel_eq_generateFrom_Ioi_rat, one_mem_posTangentConeAt_iff_mem_closure, strictMonoOn_logb_of_base_lt_one, Function.locallyFinsuppWithin.logCounting_eventuallyLE, ProbabilityTheory.tsum_prob_mem_Ioi_lt_top, intervalIntegrable_iff_integrableOn_Ioc_of_le, not_IntegrableOn_Ici_inv, volume_pi_Ioc_toReal, AkraBazziRecurrence.tendsto_atTop_r_real, Set.OrdConnected.image_derivWithin, Irrational.instOrderTopologySubtypeReal, HasFDerivAt.abs, ArchimedeanClass.stdPart_eq_sInf, volume_real_Ioc_of_le, exists_contMDiffMap_zero_one_nhds_of_isClosed, HasFDerivWithinAt.abs, strictMono_eulerMascheroniSeq, tendsto_sin_neg_pi_div_two, NNReal.range_coe, tendsto_measure_Icc, Polynomial.Chebyshev.strictAntiOn_node, Gamma_strictMonoOn_Ici, EMetric.exists_forall_closedBall_subset_auxβ, volume_Iio, integral_exp_Iic, integral_mul_cexp_neg_mul_sq, aestronglyMeasurable_derivWithin_Ioi, exists_bounded_zero_one_of_closed, NNReal.map_coe_nhdsGT, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, ProbabilityTheory.IsRatCondKernelCDFAux.mono, diam_Ioo, MeasureTheory.tendsto_sum_indicator_atTop_iff, tendsto_rpow_atTop_of_base_gt_one, tendsto_sigmoid_atBot, NNReal.image_coe_Iio, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul', isLittleO_exp_mul_rpow_of_lt, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable, Complex.comap_exp_nhdsNE, Metric.tendsto_dist_left_atTop_iff, ArchimedeanClass.stdPart_map_real, Nat.realSqrt_mem_Ico, ProbabilityTheory.lintegral_exponentialPDF_of_nonpos, isBigO_log_const_mul_log_atTop, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, AddGroupSeminorm.coe_lt_coe, exists_continuous_one_zero_of_isCompact, MeasureTheory.lintegral_rpow_eq_lintegral_meas_lt_mul, ProbabilityTheory.IsCondKernelCDF.setLIntegral, isLittleO_pow_exp_atTop, MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable_of_equiv, log_of_pos, HurwitzKernelBounds.isBigO_atTop_F_nat_one, tendsto_comp_exp_atTop, strictAntiOn_rpow_Ioi_of_exponent_neg, arcsin_mem_Icc, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, MeasureTheory.integrableOn_Ioi_comp_mul_left_iff, exists_pos_lt_subset_ball, integral_rpow_mul_exp_neg_mul_rpow, Convex.taylor_approx_two_segment, Metric.tendsto_dist_left_cobounded_atTop, EReal.preimage_coe_Icc, contMDiff_subtype_coe_Icc, Complex.arg_one_add_mem_Ioo, volume_Ico, Angle.toReal_mem_Ioo_iff_sign_pos, intervalIntegral.FTCFilter.nhdsIcc, Icc_chartedSpaceChartAt, NonarchAddGroupSeminorm.lt_def, instIsOrderBornology, leftDeriv_mul_log, ArchimedeanClass.mk_sub_stdPart_pos, comap_norm_nhdsGT_zero', Set.Icc.coe_convexCombo, Complex.tendsto_norm_tan_atTop, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Complex.IsExpCmpFilter.tendsto_re, strictConvexOn_mul_log, closure_upperClosure_comm_pi, EReal.sign_coe, Affine.Simplex.sign_excenterWeights_singleton_neg, ofDigits_SurjOn, isTopologicalBasis_Ioo_rat, strictAnti_eulerMascheroniSeq', ZetaAsymptotics.continuousOn_term, map_sqrt_atTop, Chebyshev.integrableOn_theta_div_id_mul_log_sq, unitInterval.volume_Icc, tendsto_rpow_div_mul_add, tendsto_rpow_atTop_of_base_lt_one, intervalIntegral.integrableOn_Ioo_cpow_iff, differentiableOn_Gamma_Ioi, unitInterval.range_sigmoid, Complex.arg_mem_Ioc, MeasureTheory.exists_null_frontier_thickening, integrableOn_Ioi_deriv_ofReal_cpow, ExistsContDiffBumpBase.u_exists, Complex.map_exp_comap_re_atBot, CircleDeg1Lift.iterate_monotone, NonarchAddGroupSeminorm.coe_lt_coe, strictMono_rpow_of_base_gt_one, isLittleO_rpow_exp_pos_mul_atTop, preCantorSet_subset_unitInterval, HurwitzZeta.continuousOn_evenKernel, ProbabilityTheory.lintegral_paretoPDF_of_le, injOn_tan, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, strictMonoOn_of_hasDerivWithinAt_pos, monotoneOn_deriv_descPochhammer_eval, eventually_nhdsWithin_sign_eq_of_deriv_neg, Metric.tendsto_dist_right_cobounded_atTop, arctan_strictMono, SmoothBumpFunction.mem_Icc, HasCompactSupport.integral_Iic_deriv_eq, monotoneOn_rpow_Ici_of_exponent_nonneg, measurableSet_region_between_co, intervalIntegral.FTCFilter.nhdsRight, not_integrableOn_Ioi_rpow, tendsto_measure_thickening, integral_comp_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, ContinuousMap.HomotopyWith.trans_apply, isBigO_logb_mul_const_log_atTop, tendsto_rpow_sub_one_log, logb_injOn_pos, convexOn_log_Gamma, ProbabilityTheory.cdf_gammaMeasure_eq_lintegral, Convex.isLittleO_alternate_sum_square, measurableSet_region_between_oc, Matrix.IsHermitian.eigenvaluesβ_antitone, IsPicardLindelof.continuousOn_uncurry, monotoneOn_of_hasDerivWithinAt_nonneg, isPiSystem_Iio_rat, Angle.two_zsmul_toReal_eq_two_mul, MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet, antitone_arccos, monotoneOn_of_deriv_nonneg, ODE.FunSpace.toContinuousMap_apply_eq_apply, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, tendsto_real_toNNReal_atTop, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', comap_toNNReal_atTop, exp_strictMono, Circle.invOn_arg_exp, Chebyshev.primeCounting_sub_theta_div_log_isBigO, isLittleO_log_rpow_nhdsGT_zero, ArchimedeanClass.lt_of_lt_stdPart, MeasureTheory.lintegral_eq_lintegral_meas_le, isPiSystem_Ioi_rat, tendsto_comp_exp_atBot, Cardinal.mk_Icc_real, Complex.IsExpCmpFilter.tendsto_norm, BoxIntegral.Box.mem_mk, Urysohns.CU.approx_mem_Icc_right_left, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding, exists_continuous_zero_one_of_isCompact', IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul, AkraBazziRecurrence.strictAnti_sumCoeffsExp, AkraBazziRecurrence.strictAntiOn_one_add_smoothingFn, Metric.hasAntitoneBasis_cobounded_compl_closedBall, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, isLittleO_log_rpow_atTop, isLittleO_exp_neg_mul_rpow_atTop, Complex.tendsto_exp_comap_re_atBot, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, qaryEntropy_strictAntiOn, HurwitzZeta.continuousOn_oddKernel, borel_eq_generateFrom_Ici_rat, sinOrderIso_apply, Tactic.ComputeAsymptotics.WellFormedBasis.tendsto_atTop, ValueDistribution.characteristic_eventually_nonneg, ConvexOn.monotoneOn_deriv, isPiSystem_Ici_rat, ValueDistribution.characteristic_add_top_eventuallyLE, HasCompactSupport.enorm_le_lintegral_Ici_deriv, doublingGamma_log_convex_Ioi, hasStrictDerivAt_abs, EReal.preimage_coe_Ici, Asymptotics.isLittleO_const_id_atBot, EReal.image_coe_Ioo, HurwitzZeta.continuousOn_sinKernel, StrictConvexOn.strictMonoOn_derivWithin, comap_sqrt_atTop, Function.Periodic.tendsto_atBot_intervalIntegral_of_pos', isBigO_at_im_infty_jacobiTheta_sub_one, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, tendsto_measure_Icc_nhdsWithin_right, ENNReal.monotone_truncateToReal, differentiableWithinAt_arcsin_Ici, BoxIntegral.Box.coe_mk', intervalIntegral.FTCFilter.toTendstoIxxClass, hasDerivWithinAt_arcsin_Ici, NumberField.Ideal.tendsto_norm_le_div_atTopβ, Complex.range_arg, Archimedean.embedReal_injective, convexOn_descPochhammer_eval, MeasureTheory.tendsto_sum_indicator_atTop_iff', Complex.log_mul_eq_add_log_iff, Asymptotics.isLittleO_one_left_iff, injOn_arcsin, antitone_rpow_of_base_le_one, concaveOn_negMulLog, range_exp, tendsto_integral_mulExpNegMulSq_comp, aestronglyMeasurable_derivWithin_Ici, NNReal.image_coe_Ioc, Orientation.oangle_sign_smul_left, exists_polynomial_near_continuousMap, ValueDistribution.logCounting_add_top_eventuallyLE, tendsto_mul_log_one_add_div_atTop, homeomorphUnitSphereProd_symm_apply_coe, exists_monotone_Icc_subset_open_cover_unitInterval_prod_self, MeasureTheory.Measure.haar.mem_addPrehaar_empty, ZLattice.covolume.tendsto_card_le_div', exists_msmooth_support_eq_eq_one_iff, instOrderTopologyReal, volume_Iic, closedBall_zero_eq_Icc, Orientation.oangle_sign_smul_add_smul_smul_add_smul, tendsto_logb_atTop, eventually_nhdsWithin_sign_eq_of_deriv_pos, Path.Homotopy.trans_apply, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, WeakFEPair.hg_top, tendsto_log_nhdsGT_zero, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, isFiniteMeasure_restrict_Ioo, StieltjesFunction.mono, hasMellin_one_Ioc, MeasureTheory.Measure.toSphere_apply', ball_zero_eq_Ioo, volume_Icc, HurwitzZeta.isBigO_atTop_oddKernel, dist_mono_left_pi, range_arcsin, EReal.preimage_coe_Ioc, BoxIntegral.Box.Icc_def, mem_parallelepiped_iff, ValueDistribution.characteristic_mul_zero_eventuallyLE, exists_bounded_mem_Icc_of_closed_of_le, tendsto_log_nhdsLT_zero, NNReal.image_coe_Ici, EReal.image_coe_Ici, convexOn_Gamma, intervalIntegral.integral_of_ge, EMetric.exists_forall_closedBall_subset_auxβ, ContinuousMap.Homotopy.trans_apply, exists_msmooth_zero_iff_one_iff_of_isClosed, Set.OrdConnected.image_coe_nnreal_real, Chebyshev.theta_mono, isTheta_deriv_rpow_const_atTop, IccLeftChart_extend_bot, ValueDistribution.logCounting_top_mul_eventually_le, log_div_self_antitoneOn, MeasureTheory.Integrable.integral_eq_integral_meas_le, Cardinal.Real.Icc_countable_iff, IsPicardLindelof.exists_eq_forall_mem_Icc_eq_picard, IntervalIntegrable.aestronglyMeasurable, uniqueDiffWithinAt_Ioi, gauge_def, ModularGroup.tendsto_normSq_coprime_pair, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, MeasureTheory.Measure.IicSnd_apply, tendsto_rightDeriv_mul_log_atTop, MeasureTheory.integral_comp_rpow_Ioi, strictMonoOn_logb, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, ProbabilityTheory.IsRatStieltjesPoint.mono, integral_exp_neg_rpow, WeakFEPair.hf_zero, ArchimedeanClass.stdPart_monotoneOn, volume_pi_Ioo, MeasureTheory.Integrable.integral_eq_integral_meas_lt, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atBot, Cardinal.mk_Iic_real, LinearGrowth.Real.eventually_atTop_exists_nat_between, MeasureTheory.integral_fun_norm_addHaar, ArchimedeanClass.lt_of_stdPart_lt, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, MeasureTheory.Martingale.ae_not_tendsto_atTop_atTop, exists_subset_iUnion_ball_radius_pos_lt, uniqueDiffOn_Icc_zero_one, ValueDistribution.isBigO_characteristic_sub_characteristic_inv, intervalIntegral.continuousWithinAt_primitive, tendsto_log_div_rpow_nhdsGT_zero, tendsto_logb_nhdsNE_zero_of_base_lt_one, tendsto_exp_comp_atTop, comap_norm_atTop, uniqueDiffWithinAt_Iio, ProbabilityTheory.exponentialCDFReal_eq_integral, InformationTheory.convexOn_klFun, ProbabilityTheory.cdf_expMeasure_eq_integral, BoxIntegral.Box.monotone_upper, Besicovitch.ae_tendsto_measure_inter_div, isFiniteMeasure_restrict_Icc, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, rightDeriv_mul_log, intervalIntegral.integral_of_le, volume_real_Ico_of_le, volume_pi_Ioo_toReal, homeomorphSphereProd_symm_apply_coe, isLittleO_const_log_atTop, Polynomial.Chebyshev.isMinOn_T_real, log_div_sqrt_antitoneOn, unitInterval.mul_pos_mem_iff, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, isLittleO_exp_comp_exp_comp, integrableOn_exp_mul_complex_Iic, LSeries_eq_mul_integral, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, MeasureTheory.Measure.instSigmaFiniteElemRealIoiOfNatVolumeIoiPow, ProbabilityTheory.paretoCDFReal_eq_integral, Polynomial.Chebyshev.isLocalExtr_T_real_iff, antitone_of_deriv_nonpos, ProbabilityTheory.exp_neg_integrableOn_Ioc, isLittleO_rpow_exp_atTop, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, Circle.argEquiv_symm_apply, tendsto_exp_atBot, homeomorphUnitSphereProd_apply_fst_coe, tendsto_rpow_neg_nhdsGT_zero, ProbabilityTheory.Kernel.isRatCondKernelCDF_density_Iic, differentiableWithinAt_arcsin_Iic, isLittleO_zpow_exp_pos_mul_atTop, StrictConcaveOn.strictAntiOn_deriv, contMDiffWithinAt_comp_projIcc_iff, Asymptotics.isLittleO_const_left_of_ne, bijOn_sin, cosh_bijOn, EReal.toReal_image_Ioo_bot_zero, ConvexOn.monotoneOn_leftDeriv, bijOn_cos, tendsto_gauge_nhds_zero_nhdsGE, qaryEntropy_strictMonoOn, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, volume_Ioc, strictMonoOn_arcsin, HasFPowerSeriesOnBall.uniform_geometric_approx', tendsto_dist_left_cocompact_atTop, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, integrableOn_Ioi_rpow_iff, sigmoid_monotone, Affine.Simplex.ExcenterExists.sign_touchpointWeights, IsOpen.exists_msmooth_support_eq_aux, integrableOn_rpow_mul_exp_neg_rpow, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, tendsto_abs_tan_of_cos_eq_zero, Affine.Simplex.sign_touchpointWeights_singleton_pos, EReal.preimage_coe_Ioo_bot, summable_iff_not_tendsto_nat_atTop_of_nonneg, ENNReal.tendsto_ofReal_atTop, exists_contMDiff_zero_iff_one_iff_of_isClosed, integrableOn_exp_mul_Ioi, Orientation.oangle_sign_smul_right, Complex.tendsto_one_add_div_cpow_exp, ENNReal.orderIsoUnitIntervalBirational_apply_coe, isFiniteMeasure_restrict_Ico, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, variationOnFromTo.sub_self_monotoneOn, ValueDistribution.logCounting_zero_mul_eventually_le, isLocalMax_of_deriv_deriv_neg, HasFDerivAt.lim_real, strictConvexOn_rpow, tendsto_tan_pi_div_two, EReal.coe_strictMono, tendsto_log_comp_add_sub_log, BoxIntegral.IntegrationParams.RCond.min, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, integral_exp_neg_Ioi, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, Tactic.ComputeAsymptotics.WellFormedBasis.eventually_pos, surjOn_log, UnitAddCircle.measurePreserving_mk, oneTangentSpaceIcc_def, intervalIntegral.integral_const_of_cdf, NumberField.mixedEmbedding.polarSpaceCoord_target', intervalIntegral.integral_const', AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg, Stirling.log_stirlingSeq'_antitone, intervalIntegrable_iff_integrableOn_Ioo_of_le, IccRightChart_extend_top_mem_frontier, integral_comp_neg_Iic, Asymptotics.IsTheta.tendsto_norm_atTop_iff, cantorSet_subset_unitInterval, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, EReal.preimage_coe_Ico_top, exists_continuous_zero_one_of_isCompact, Polynomial.Chebyshev.isMaxOn_T_real, NNReal.mk_zero, tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding', strictAntiOn_logb_of_base_lt_one, volume_real_Icc, unitInterval.tendsto_sigmoid_atTop, strictMonoOn_arcosh, Gamma_eq_integral, EReal.tendsto_coe_nhds_bot_iff, MeasureTheory.lintegral_eq_lintegral_meas_lt, UpperHalfPlane.IsZeroAtImInfty.zero_at_infty_comp_ofComplex, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, signedDist_smul, EReal.tendsto_coe_atBot, surjOn_sin, tendsto_logb_atTop_of_base_lt_one, StrictConcaveOn.strictAntiOn_derivWithin, RightDerivMeasurableAux.A_mem_nhdsGT, MeasureTheory.norm_stoppedValue_leastGE_le, uniqueDiffOn_Iio, Complex.tendsto_partialGamma, Complex.tendsto_norm_tan_of_cos_eq_zero, strictAnti_of_deriv_neg, tendstoLocallyUniformlyOn_rpow_sub_one_log, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, Function.Periodic.invQParam_tendsto, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, image_tan_Ioo, tendsto_deriv_mul_log_atTop, Affine.Simplex.sign_touchpointWeights_singleton_neg, map_exp_atBot, unitInterval.subtype_Ici_eq_Icc, tendsto_rpow_atBot_of_base_lt_one, ENNReal.tendsto_rpow_atTop_of_base_lt_one, NNReal.image_coe_Iic, UpperHalfPlane.atImInfty_basis, InformationTheory.isMinOn_klFun, expNegInvGlue.monotone, differentiableWithinAt_arccos_Iic, ValueDistribution.logCounting_sum_top_eventuallyLE, tendsto_integral_cexp_sq_smul, mdifferentiableWithinAt_comp_projIcc_iff, FormalMultilinearSeries.isLittleO_of_lt_radius, unitInterval.subtype_Iio_eq_Ico, ZLattice.covolume.tendsto_card_le_div, injOn_sin, NNReal.orderIsoIccZeroCoe_symm_apply_coe, integrableOn_exp_neg_Ioi, logb_injOn_pos_of_base_lt_one, coe_comp_expOrderIso, ProbabilityTheory.IsMeasurableRatCDF.continuousWithinAt_stieltjesFunctionAux_Ici, ODE.FunSpace.dist_iterate_next_le, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, GaussianFourier.tendsto_verticalIntegral, MeasureTheory.Measure.iInf_rat_gt_prod_Iic, AkraBazziRecurrence.exists_eventually_r_le_const_mul, NNReal.coe_mono, Affine.Simplex.sign_signedInfDist_touchpoint_empty, EReal.preimage_coe_Iio, ProbabilityTheory.integral_condCDF, GroupNorm.lt_def, MeasureTheory.Submartingale.stoppedAbove, tendsto_sum_range_one_div_nat_succ_atTop, iccLeftChart_extend_zero, tendsto_tan_neg_pi_div_two, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, preCantorSet_zero, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, Affine.Simplex.sign_excenterWeights_empty, InformationTheory.rightDeriv_klFun, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul', BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, ExistsContDiffBumpBase.y_smooth, ValueDistribution.abs_characteristic_sub_characteristic_shift_eqO, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, unitInterval.volume_Ioc, tendsto_logb_comp_add_sub_logb, ValueDistribution.characteristic_zero_mul_eventually_le, EReal.tendsto_coe_nhds_top_iff, NNReal.image_coe_Ioi, mapsTo_sin, Function.Periodic.qParam_tendsto, CircleDeg1Lift.tendsto_atTop, integrableOn_Ioi_cpow_of_lt, antitone_of_hasDerivAt_nonpos, volume_Ici, Path.trans_apply, RightDerivMeasurableAux.differentiable_set_eq_D, ZetaAsymptotics.continuousOn_term_tsum, arsinh_strictMono, exp_neg_mul_rpow_isLittleO_exp_neg, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, ProbabilityTheory.truncation_eq_of_nonneg, tendsto_arctan_atTop, exp_neg_mul_sq_isLittleO_exp_neg, AkraBazziRecurrence.isLittleO_smoothingFn_one, ediam_Ioo, IsPicardLindelof.mul_max_le, integral_exp_mul_Ioi, tendsto_rpow_div, measurableSet_of_differentiableWithinAt_Ioi, iInter_Iic_rat, Archimedean.exists_orderAddMonoidHom_real_injective, surjOn_cos, BoxIntegral.Box.mem_def, Set.OrdConnected.preimage_ennreal_ofReal, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, tendsto_norm_atTop_iff_cobounded', LSeries.tendsto_cpow_mul_atTop, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, tendsto_norm_atTop_atTop, cosh_strictMonoOn, tendsto_norm_cocompact_atTop', exists_smooth_zero_one_of_isClosed, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, volume_pi_Ico_toReal, ProbabilityTheory.Kernel.isRatCondKernelCDFAux_density_Iic, strictConcaveOn_sqrt, isLittleO_pow_exp_pos_mul_atTop, MeasureTheory.ae_mem_limsup_atTop_iff, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_imp, comap_exp_nhdsGT_zero, monotone_of_hasDerivAt_nonneg, strictMonoOn_one_add_div_one_sub, measurable_derivWithin_Ioi, ProbabilityTheory.Fernique.normThreshold_strictMono, tendsto_mul_add_inv_atTop_nhds_zero, InformationTheory.strictConvexOn_klFun, exists_contMDiff_support_eq_eq_one_iff, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, ContinuousMap.comp_attachBound_mem_closure, isBigO_deriv_ofReal_cpow_const_atTop, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, stronglyMeasurable_derivWithin_Ici, strictMonoOn_log, surjOn_logb, tendsto_rpow_neg_div, ODE.FunSpace.intervalIntegrable_comp_compProj, Circle.surjOn_exp_neg_pi_pi, tendsto_rpow_neg_atTop, BoxIntegral.Box.Icc_eq_pi, rexp_neg_quadratic_isLittleO_rpow_atTop, LSeries.tendsto_atTop, ENNReal.tendsto_rpow_atBot_of_one_lt_base, tendsto_arctan_atBot, variationOnFromTo.monotoneOn, volume_real_Icc_of_le, integrableOn_Ioi_exp_neg_mul_sq_iff, NNReal.image_coe_Ioo, mapsTo_sin_Ioo, tendsto_mulIndicator_thickening_mulIndicator_closure, Hyperreal.tendsto_atBot_iff, Function.locallyFinsuppWithin.logCounting_mono, ZSpan.fundamentalDomain_pi_basisFun, cexp_neg_quadratic_isLittleO_rpow_atTop, sin_arctan_strictMono, IsOpen.exists_contDiff_support_eq, tendsto_sub_mul_tsum_nat_rpow, exists_continuousMap_one_of_isCompact_subset_isOpen, MeasureTheory.integral_comp_mul_right_Ioi, contDiffOn_arcosh, CircleDeg1Lift.monotone, AddCircle.lintegral_preimage, tendsto_sqrt_atTop, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, Manifold.pathELength_eq_lintegral_mfderiv_Icc, ProbabilityTheory.tendsto_cdf_atTop, ProbabilityTheory.lintegral_betaPDF, uniqueDiffOn_Ioi, EReal.toReal_image_Ioo_zero_top, NonarchAddGroupNorm.lt_def, strictAnti_rpow_of_base_lt_one, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, tendsto_norm_cobounded_atTop', InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, ODE.FunSpace.continuous, tendsto_mul_exp_add_div_pow_atTop, tendsto_dist_right_cocompact_atTop, tendsto_integral_comp_smul_smul_of_integrable, tendsto_div_pow_mul_exp_add_atTop, ArchimedeanClass.mk_sub_pos_iff, AddCircle.measurePreserving_mk, InformationTheory.convexOn_Ioi_klFun, integral_comp_neg_Ioi, uniqueDiffOn_Ico, dist_anti_right_pi, isBigO_deriv_rpow_const_atTop, Complex.range_norm, tendsto_norm_cobounded_atTop, cobounded_eq, Chebyshev.integral_theta_div_log_sq_isBigO, CircleDeg1Lift.coe_toOrderHom, strictConcaveOn_sin_Icc, WeakFEPair.hg_int, ProbabilityTheory.cdf_expMeasure_eq_lintegral, tendsto_Icc_vitaliFamily_left, tendsto_measure_Icc_nhdsWithin_right', Complex.HadamardThreeLines.eventuallyle, strictAntiOn_of_deriv_neg, BoxIntegral.Box.coe_eq_pi, contMDiffOn_comp_projIcc_iff, EReal.preimage_coe_Iic, comap_exp_atTop, exists_continuous_one_zero_of_isCompact_of_isGΞ΄, Circle.argPartialEquiv_target, NNReal.summable_mk, ModularFormClass.bounded_at_infty_comp_ofComplex, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Cardinal.mk_Ioo_real, sinh_strictMono, WeakFEPair.hf_int, unitInterval.sigmoid_monotone, Set.OrdConnected.preimage_real_toNNReal, tendsto_abs_logb_atTop, Chebyshev.integral_theta_div_log_sq_isLittleO, tendsto_norm_atTop_iff_cobounded, Angle.sign_toReal, Tactic.ComputeAsymptotics.WellFormedBasis.tail_isLittleO_head, strictAntiOn_log, tendsto_pow_logb_div_mul_add_atTop, strictMonoOn_of_deriv_pos, ODE.FunSpace.compProj_val, homeomorphSphereProd_apply_snd_coe, HurwitzKernelBounds.isBigO_exp_neg_mul_of_le, not_summable_iff_tendsto_nat_atTop_of_nonneg, algNormFromConst_def, ProbabilityTheory.measure_condCDF_Iic, diam_Ico, Complex.isOpen_setOf_mem_nhds_and_isMaxOn_norm, norm_sub_le_mul_volume_of_norm_fderiv_le, Besicovitch.tendsto_filterAt, monotoneOn_sin, Path.extend_extends', tendsto_logb_nhdsGT_zero_of_base_lt_one, strictConvexOn_zpow, volume_real_Ico, ConvexOn.monotoneOn_derivWithin, arctan_mono, tendsto_integral_gaussian_smul, GroupNorm.coe_lt_coe, Cardinal.mk_Ici_real, ConcaveOn.antitoneOn_derivWithin, StrongFEPair.hf_top', arcsin_image_Icc, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, integral_rpow_mul_exp_neg_mul_Ioi, tendsto_log_atTop, strictConcave_binEntropy, EReal.preimage_coe_Ioc_bot, Asymptotics.isBigO_iff_eventually_isBigOWith, tendsto_abs_tan_atTop, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, tendsto_norm_nhdsNE_zero, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, ContinuousMap.polynomial_comp_attachBound, MeasureTheory.upperCrossingTime_succ, integral_Ioi_cpow_of_lt, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, uniqueDiffWithinAt_Ici, tendsto_exp_div_rpow_atTop, DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal, Gamma_integrand_isLittleO, ZLattice.covolume.tendsto_card_le_div'', exists_isMIntegralCurve_iff_exists_isMIntegralCurveOn_Ioo, not_integrableOn_Ici_inv, CircleDeg1Lift.map_add_one', exists_monotone_Icc_subset_open_cover_unitInterval, strictConcaveOn_log_Ioi, homeomorphUnitSphereProd_apply_snd_coe, strictAntiOn_of_hasDerivWithinAt_neg, Orientation.oangle_sign_smul_add_smul_right, strictAntiOn_cos, Angle.nsmul_toReal_eq_mul, uniqueDiffOn_Ioo, EReal.preimage_coe_Ico, ProbabilityTheory.setLIntegral_condCDF, exp_neg_integrableOn_Ioi, nullMeasurableSet_region_between_oc, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, derivWithin_Ioi_eq_Ici, not_integrableOn_Ioi_inv, antitoneOn_rpow_Ioi_of_exponent_nonpos, Cardinal.Real.Ico_countable_iff, WeakFEPair.f_modif_aux1, Complex.IsExpCmpFilter.tendsto_abs_re, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le_of_hasFiniteIntegral, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, ValueDistribution.logCounting_eventually_nonneg, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, Asymptotics.IsBigO.id_rpow_of_le_one, MeasureTheory.Measure.IicSnd_univ, tendsto_atTop_of_geom_le, integral_exp_mul_complex_Iic, homeomorphSphereProd_apply_fst_coe, MeasureTheory.Measure.volumeIoiPow_apply_Iio, Polynomial.Chebyshev.node_mem_Icc, tendsto_card_div_pow_atTop_volume', integrableOn_rpow_mul_exp_neg_mul_sq, ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAux, NNReal.tendsto_coe_atTop, cosPartialEquiv_source, dist_mono_right_pi, binEntropy_strictAntiOn, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, cosh_injOn, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, integral_Ioi_inv_one_add_sq, intervalIntegral.FTCFilter.nhdsLeft, Nat.ratSqrt_mem_Ioc, polynomialFunctions_closure_eq_top', MeasureTheory.integral_comp_mul_left_Ioi, unitInterval.univ_eq_Icc, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul, measurableSet_region_between_cc, strictAnti_of_hasDerivAt_neg, ContinuousMap.polynomial_comp_attachBound_mem, integral_exp_neg_Ioi_zero, Polynomial.Chebyshev.isLocalExtr_T_real, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, UpperHalfPlane.tendsto_coe_atImInfty, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTop, unitInterval.subtype_Iic_eq_Icc, ProbabilityTheory.IsCondKernelCDF.lintegral, exists_contDiff_tsupport_subset, AddGroupNorm.lt_def, tendsto_sin_pi_div_two, hasMellin_cpow_Ioc, Polynomial.Chebyshev.isExtrOn_T_real, aemeasurable_derivWithin_Ici, MeasureTheory.stoppedAbove_le, ArchimedeanClass.stdPart_of_mk_nonneg, isBigO_logb_const_mul_log_atTop, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, integral_gaussian_Ioi, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, strictMonoOn_sin, tendsto_toNNReal_atTop, isTheta_deriv_ofReal_cpow_const_atTop, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, Set.OrdConnected.image_hasDerivWithinAt, Cardinal.mk_Ico_real, Icc_mem_vitaliFamily_at_right, antitoneOn_of_deriv_nonpos, Asymptotics.isBigO_iff_eventually, Complex.image_exp_Ioc_eq_sphere, TFAE_exists_lt_isLittleO_pow, Cardinal.Real.Ioo_countable_iff, exists_tsupport_one_of_isOpen_isClosed, Archimedean.embedReal_one, Angle.toReal_coe_eq_self_add_two_pi_iff, map_toNNReal_atTop, MeasureTheory.integrableOn_Ioi_comp_mul_right_iff, Complex.monotone_ofReal, expPartialHomeomorph_target, smoothTransition.monotone, ProbabilityTheory.cdf_paretoMeasure_eq_lintegral, Path.range_subpath_of_le, artanh_injOn, strictMonoOn_tan, volume_Ioi, Polynomial.tendsto_div_exp_atTop, integral_Iic_inv_one_add_sq, HurwitzZeta.isBigO_atTop_cosKernel_sub, IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul, tendsto_pow_log_div_mul_add_atTop, borel_eq_generateFrom_Iic_rat, RightDerivMeasurableAux.B_mem_nhdsGT, ValueDistribution.characteristic_top_mul_eventually_le, volume_Ioo, gauge_lt_eq, TorusIntegrable.function_integrable, RCLike.tendsto_ofReal_atBot_cobounded, DirichletCharacter.LFunction_isBigO_horizontal, mfderiv_subtype_coe_Icc_one, tendsto_log_nhdsNE_zero, unitInterval.tendsto_sigmoid_atBot, Seminorm.coe_lt_coe, continuousOn_arcosh, Complex.GammaIntegral_convergent, Icc_eq_closedBall, mulIndicator_thickening_eventually_eq_mulIndicator_closure, ProbabilityTheory.IsRatCondKernelCDF.mono, strictMonoOn_rpow_Ici_of_exponent_pos, ENNReal.tendsto_ofReal_nhds_top, IsClosed.upperClosure_pi, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, isLittleO_pow_log_id_atTop, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, unitInterval.subtype_Ioi_eq_Ioc, AddGroupNorm.coe_lt_coe, map_exp_atTop, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', MeasureTheory.integrable_fun_norm_addHaar, NumberField.mixedEmbedding.polarCoordReal_target, unitInterval.two_mul_sub_one_mem_iff, arcosh_surjOn, Cardinal.mk_Ioc_real, exists_smooth_zero_one_nhds_of_isClosed, ValueDistribution.characteristic_sum_top_eventuallyLE, Complex.polarCoord_target, isLittleO_const_logb_atTop, Angle.toReal_coe_eq_self_sub_two_pi_iff, NonarchAddGroupNorm.coe_lt_coe, integral_exp_Iic_zero, Orientation.oangle_sign_smul_add_smul_left, surjOn_tan, tendsto_integral_comp_smul_smul_of_integrable', diam_Ioc, measurable_derivWithin_Ici, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, tendsto_log_mul_rpow_nhdsGT_zero, UpperHalfPlane.tendsto_comap_im_ofComplex, EReal.nhdsWithin_top, parallelepiped_orthonormalBasis_one_dim, Chebyshev.psi_mono, tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding, ENNReal.tendsto_rpow_atBot_of_base_lt_one, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, Manifold.exists_lt_of_riemannianEDist_lt, polynomialFunctions_closure_eq_top, strictConcaveOn_cos_Icc, EReal.image_coe_Ioi, range_norm, NNReal.image_coe_Icc, ValueDistribution.logCounting_monotoneOn, hasConstantSpeedOnWith_iff_ordered, injOn_cos, log_div_self_rpow_antitoneOn, tendsto_measure_thickening_of_isClosed, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, tendsto_logb_nhdsGT_zero, Complex.integral_cpow_mul_exp_neg_mul_Ioi, log_of_ne_zero, sin_mem_Icc, Function.Periodic.tendsto_atTop_intervalIntegral_of_pos, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, exists_contMDiffMap_one_nhds_of_subset_interior, ProbabilityTheory.Fernique.tendsto_normThreshold_atTop, AddGroupSeminorm.lt_def, Archimedean.embedRealFun_strictMono, IccRightChart_extend_top, UnitAddCircle.integral_preimage, tanh_surjOn, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos, hasDerivWithinAt_arccos_Iic, measurableSet_of_differentiableWithinAt_Ici, convexOn_mul_log, Chebyshev.eventually_primeCounting_le, MeasureTheory.Integrable.integral_eq_integral_Ioc_meas_le, boundary_Icc, tendsto_norm_sub_self_nhdsGE, isAddFundamentalDomain_Ioc', strictConcaveOn_negMulLog, range_sigmoid, MeasureTheory.tendsto_integral_meas_thickening_le, sigmoid_strictMono, ConcaveOn.antitoneOn_deriv, tendsto_one_add_div_rpow_exp, tendsto_log_mul_self_nhdsLT_zero, tendsto_indicator_thickening_indicator_closure, Complex.range_normSq, isLittleO_pow_logb_id_atTop, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAtβ, EReal.nhdsWithin_bot, closure_lowerClosure_comm_pi, integral_sin_pow_antitone, tendsto_exp_mul_div_rpow_atTop, cos_mem_Icc, tendsto_exp_atBot_nhdsGT, AddCircle.integral_preimage, gronwallBound_mono, boundary_product, ProbabilityTheory.tendsto_cdf_atBot, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, ODE.FunSpace.dist_iterate_next_apply_le, ENNReal.ofReal_mono, ProbabilityTheory.tendsto_condCDF_atTop, rpowIntegrandββ_eqOn_mul_rpowIntegrandββ_one, tendsto_logb_nhdsNE_zero, Circle.argEquiv_apply_coe, Cardinal.mk_Ioi_real, LSeries_eq_mul_integral', integrableOn_Ioi_deriv_norm_ofReal_cpow, ProbabilityTheory.exponentialCDFReal_eq_lintegral, CircleDeg1Lift.translationNumber_mono, Metric.tendsto_dist_right_atTop_iff, ProbabilityTheory.cdf_gammaMeasure_eq_integral, Function.Periodic.tendsto_atTop_intervalIntegral_of_pos', BoxIntegral.Box.mem_univ_Ioc, strictConcaveOn_qaryEntropy, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, tanh_bijOn, RCLike.tendsto_ofReal_atTop_cobounded, NNReal.map_coe_nhdsGE, IccLeftChart_extend_bot_mem_frontier, ODE.FunSpace.lipschitzWith, GroupSeminorm.coe_lt_coe, convexOn_rpow, Icc_isBoundaryPoint_top, ConvexOn.slope_le_leftDeriv_of_mem_interior, ProbabilityTheory.ofReal_cdf, uniqueDiffOn_Ici, Angle.two_nsmul_toReal_eq_two_mul, isLittleO_one_exp_comp, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.isBigO_atTop_sinKernel, real_inner_mem_Icc_of_norm_eq_one, WeakFEPair.hf_top, ValueDistribution.characteristic_mul_top_eventuallyLE, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atBot, LinearMap.IsSymmetric.eigenvalues_antitone, Complex.tendsto_tsum_powerSeries_nhdsWithin_lt, hasDerivWithinAt_arcsin_Iic, NumberField.mixedEmbedding.fundamentalCone.expMap_single_target, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', MeasureTheory.integrableOn_Ioi_comp_rpow_iff', integral_gaussian_complex_Ioi, log_doublingGamma_eq, tendsto_norm_cocompact_atTop, instIsManifoldIcc, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, integrableAtFilter_rpow_atTop_iff, Euclidean.exists_pos_lt_subset_ball, Complex.continuousOn_one_add_mul_inv, tendsto_pow_mul_exp_neg_atTop_nhds_zero, ediam_Icc, dist_anti_left_pi, Urysohns.CU.lim_mem_Icc, lintegral_Iic_eq_lintegral_Iio_add_Icc, unitInterval.volume_Iio, contMDiffOn_projIcc, diam_Icc, ProbabilityTheory.setLIntegral_toKernel_Iic, log_injOn_pos, coe_sinOrderIso_apply, ArchimedeanClass.stdPart_eq_sSup, ediam_Ico, isPiSystem_Ioo_rat, tendsto_Icc_vitaliFamily_right, integrableOn_rpow_mul_exp_neg_mul_rpow, BoxIntegral.Box.antitone_lower, Hyperreal.tendsto_atTop_iff, Complex.tendsto_exp_comap_re_atBot_nhdsNE, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, integrableOn_exp_mul_complex_Ioi, binEntropy_strictMonoOn, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, tendsto_rpow_atBot_of_base_gt_one, continuousOn_tan_Ioo, Function.Periodic.tendsto_atBot_intervalIntegral_of_pos, exists_cos_eq_zero, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, arccos_injOn, MeasureTheory.Martingale.ae_not_tendsto_atTop_atBot, Hyperreal.coeRingHom_toFun, ODE.FunSpace.compProj_apply, aemeasurable_derivWithin_Ioi, AkraBazziRecurrence.strictAntiOn_smoothingFn, unitInterval.volume_Ioi
|
instRatCast π | CompOp | 168 mathmath: Padic.eq_ratNorm, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, ProbabilityTheory.condCDF_ae_eq, iInf_Ioi_eq_iInf_rat_gt, Irrational.ratCast_sub, SzemerediRegularity.energy_increment, Mathlib.Tactic.Rify.ratCast_le, Padic.eq_padicNorm, LiouvilleWith.sub_rat, LiouvilleWith.rat_sub_iff, ProbabilityTheory.setLIntegral_preCDF_fst, Rat.continuous_coe_real, LiouvilleWith.rat_add_iff, Irrational.ratCast_mul, NumberField.mixedEmbedding.norm_eq_norm, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, isIntegral_two_mul_sin_rat_mul_pi, NumberField.FinitePlace.prod_eq_inv_abs_norm, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_eq, log_add_one_le_harmonic, Mathlib.Tactic.Rify.ratCast_lt, Complex.nnnorm_ratCast, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, Complex.normSq_ratCast, Rat.dist_eq, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, Irrational.ratCast_div, borel_eq_generateFrom_Iio_rat, irrational_sqrt_ratCast_iff, iUnion_Iic_rat, MeasureTheory.Measure.iInf_IicSnd_gt, borel_eq_generateFrom_Ioo_rat, Rat.dist_cast, isIntegral_two_mul_cos_rat_mul_pi, Rat.isDenseEmbedding_coe_real, LiouvilleWith.rat_sub, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, Mathlib.Tactic.Rify.ofNat_rat_real, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, irrational_sqrt_ratCast_iff_of_nonneg, LiouvilleWith.add_rat, NNReal.lt_iff_exists_rat_btwn, isPiSystem_Iic_rat, exists_rat_abs_sub_lt_and_lt_of_irrational, StieltjesFunction.iInf_rat_gt_eq, ProbabilityTheory.ofReal_condCDF_ae_eq, Complex.div_ratCast_re, LiouvilleWith.add_rat_iff, deriv_Gamma_nat, irrational_ratCast_mul_iff, borel_eq_generateFrom_Ioi_rat, Metric.uniformity_basis_dist_rat, exists_seq_rat_strictAnti_tendsto, irrational_mul_ratCast_iff, Complex.ratCast_re, tendsto_harmonic_sub_log, Nat.realSqrt_mem_Ico, isAlgebraic_tan_rat_mul_pi, isAlgebraic_cos_rat_mul_pi, MeasureTheory.SimpleFunc.ennrealRatEmbed_encode, LiouvilleWith.mul_rat, isTopologicalBasis_Ioo_rat, NumberField.mixedEmbedding.covolume_idealLattice, closure_of_rat_image_lt, Irrational.sub_ratCast, harmonic_le_one_add_log, Padic.padicNormE.is_rat, LiouvilleWith.rat_mul_iff, isPiSystem_Iio_rat, Padic.padicNormE.is_norm, isPiSystem_Ioi_rat, Rat.AbsoluteValue.padic_eq_padicNorm, borel_eq_generateFrom_Ici_rat, isPiSystem_Ici_rat, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, SzemerediRegularity.edgeDensity_chunk_uniform, Mathlib.Tactic.Rify.ratCast_eq, Complex.norm_ratCast, ProbabilityTheory.withDensity_preCDF, harmonic_floor_le_one_add_log, isCusp_SL2Z_iff, Rat.norm_cast_real, Nat.realSqrt_lt_ratSqrt_add_inv_prec, ratCast_lt, ProbabilityTheory.stieltjesOfMeasurableRat_eq, ofCauchy_ratCast, irrational_ratCast_div_iff, bernoulliFun_eval_zero, ProbabilityTheory.Kernel.isRatCondKernelCDF_density_Iic, irrational_ratCast_add_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, Irrational.ratCast_add, irrational_sub_ratCast_iff, ProbabilityTheory.setIntegral_preCDF_fst, irrational_div_ratCast_iff, exists_rat_abs_sub_le_and_den_le, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eq, LiouvilleWith.mul_rat_iff, irrational_ratCast_sub_iff, Rat.not_irrational, log_le_harmonic_floor, RCLike.ratCast_re, MeasureTheory.Measure.iInf_rat_gt_prod_Iic, mk_const, convs_eq_convergent, Irrational.add_ratCast, closure_ordConnected_inter_rat, Complex.div_ratCast_im, isAlgebraic_sin_rat_mul_pi, iInter_Iic_rat, ProbabilityTheory.Kernel.isRatCondKernelCDFAux_density_Iic, cosetToCuspOrbit_apply_mk, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, not_bddBelow_coe, ENNReal.exists_upcrossings_of_not_bounded_under, Rat.infinitePlace_apply, not_bddAbove_coe, MeasureTheory.Measure.tendsto_IicSnd_atTop, NumberField.mixedEmbedding.latticeBasis_repr_apply, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, LiouvilleWith.sub_rat_iff, Rat.AbsoluteValue.real_eq_abs, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def, ENNReal.lt_iff_exists_rat_btwn, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def', ProbabilityTheory.lintegral_preCDF_fst, EReal.lt_iff_exists_rat_btwn, Irrational.div_ratCast, SzemerediRegularity.edgeDensity_chunk_not_uniform, Irrational.mul_ratCast, irrational_cos_rat_mul_pi, LiouvilleWith.rat_add, ZetaAsymptotics.term_sum_one, Complex.ofReal_ratCast, MeasureTheory.Measure.tendsto_IicSnd_atBot, Nat.ratSqrt_mem_Ioc, EReal.denseRange_ratCast, cauchy_ratCast, Rat.isUniformEmbedding_coe_real, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, irrational_add_ratCast_iff, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, LiouvilleWith.rat_mul, Nat.ratSqrt_le_realSqrt, NumberField.InfinitePlace.prod_eq_abs_norm, isIntegral_two_mul_cos_rat_mul_pi, borel_eq_generateFrom_Iic_rat, Rat.isEmbedding_coe_real, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, hasDerivAt_Gamma_nat, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, hasSum_zeta_nat, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, exists_rat_of_not_irrational, Padic.padicNormE.image, EReal.exists_rat_btwn_of_lt, ArchimedeanClass.stdPart_ratCast, isCauSeq_iff_lift, tendsto_harmonic_sub_log_add_one, exists_seq_rat_strictMono_tendsto, Complex.div_ratCast, bernoulliFun_eval_half, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, ProbabilityTheory.integral_preCDF_fst, Rat.uniformContinuous_coe_real, RCLike.ofReal_ratCast, isPiSystem_Ioo_rat
|
instRepr π | CompOp | β |
instRing π | CompOp | 833 mathmath: Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint, HasStrictFDerivAt.log, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, Bundle.ContMDiffRiemannianMetric.isVonNBounded, Subgroup.isRegularAtInfty_iff, Bundle.ContMDiffRiemannianMetric.contMDiff, ProbabilityTheory.isGaussian_iff_gaussian_charFun, Collinear.wbtw_of_dist_eq_of_dist_le, taylorWithin_succ, hasFDerivAt_fourierChar_neg_bilinear_left, Isometry.preimage_perpBisector, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, fourierCoeff_tsum_comp_add, Affine.Simplex.sSameSide_excenter_singleton_point, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, SimpleGraph.det_lapMatrix_eq_zero, Chebyshev.theta_eq_theta_coe_floor, UnitAddCircle.lintegral_preimage, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, curveIntegrable_segment, Affine.Simplex.finiteDimensional_direction_altitude, ProbabilityTheory.covarianceBilinDual_apply', AffineSubspace.mem_perpBisector_iff_inner_eq_zero', Affine.Simplex.circumcenter_map, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, UnitAddCircle.intervalIntegral_preimage, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, EuclideanGeometry.Sphere.wbtw_secondInter, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite, EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne, Affine.Simplex.circumcenter_mem_affineSpan, Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude, dist_sq_lineMap_lineMap_of_inner_eq_zero, QuadraticForm.posDef_toMatrix', Affine.Simplex.excenter_singleton_mem_affineSpan_range, ProbabilityTheory.covarianceBilinDual_apply, IsOpen.exists_subset_affineIndependent_span_eq_top, fderiv_fourierChar_neg_bilinear_right_apply, stdSimplexHomeomorphUnitInterval_symm_apply_coe, intervalIntegral.fderiv_integral_of_tendsto_ae, Affine.Simplex.dist_point_faceOppositeCentroid, natFloor_logb_natCast, nat_floor_real_sqrt_eq_nat_sqrt, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, Affine.Simplex.incenter_map, CongruenceSubgroup.exists_Gamma_le_conj', ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, AffineSubspace.left_mem_perpBisector, EuclideanGeometry.preimage_inversion_perpBisector_inversion, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, ProbabilityTheory.uncenteredCovarianceBilin_apply, ContDiffPointwiseHolderAt.isBigO, BoxIntegral.unitPartition.mem_smul_span_iff, Affine.Triangle.sbtw_touchpoint_singleton, Affine.Triangle.dist_point_faceOppositeCentroid, isIntegral_two_mul_sin_rat_mul_pi, Bundle.RiemannianMetric.isVonNBounded, Affine.Simplex.mem_circumsphere, Polynomial.sub_one_pow_totient_le_cyclotomic_eval, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, round_exp_one_eq_three, Differentiable.fderiv_norm_rpow, lintegral_fderiv_lineMap_eq_edist, signedDist_right_congr, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff, CompactlySupportedContinuousMap.nnrealPart_smul_neg, UnitAddTorus.mFourierSubalgebra_closure_eq_top, ModularGroup.one_lt_normSq_T_zpow_smul, EuclideanGeometry.Sphere.mem_tangentsFrom_iff, fderivWithin_sinh, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, CongruenceSubgroup.strictPeriods_Gamma0, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, EuclideanGeometry.Sphere.mem_commonTangents_iff, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, hasStrictFDerivAt_rpow_of_pos, Affine.Simplex.excenterWeightsUnnorm_reindex, IsometryEquiv.midpoint_fixed, AffineIsometryEquiv.pointReflection_midpoint_left, interior_convexHull_nonempty_iff_affineSpan_eq_top, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, AmpleSet.preimage_iff, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', signedDist_left_congr, Chebyshev.psi_eq_psi_coe_floor, jacobiTheta_T_sq_smul, Affine.Simplex.ExcenterExists.touchpoint_map, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, curveIntegralFun_segment, signedDist_triangle, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, ModularForm.levelOne_neg_weight_rank_zero, Subgroup.IsArithmetic.is_commensurable, ModularGroup.sl_moeb, signedDist_linear_apply_apply, Affine.Simplex.sSameSide_incenter_point, EuclideanGeometry.oangle_midpoint_right, Affine.Simplex.ExcenterExists.excenter_map, GaussianInt.toComplex_div_re, one_add_rpow_hasFPowerSeriesOnBall_zero, VectorFourier.fourierPowSMulRight_eq_comp, Polynomial.cyclotomic.eval_apply_ofReal, Polynomial.isRoot_cos_pi_div_five, HasFDerivAt.arctan, cauSeq_converges, Chebyshev.psi_eq_sum_theta, Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne, EuclideanGeometry.Sphere.isTangentAt_of_dist_sq_eq_power, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, Polynomial.cyclotomic_eval_lt_add_one_pow_totient, HasStrictFDerivAt.abs, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, ModularGroup.coe_T_zpow_smul_eq, Euclidean.closedBall_eq_image, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, Affine.Simplex.excenterExists_reindex, Chebyshev.psi_sub_theta_eq_sum_not_prime, isIntegral_two_mul_cos_rat_mul_pi, ApproximatesLinearOn.norm_fderiv_sub_le, MeasureTheory.SignedMeasure.singularPart_smul, ProbabilityTheory.covarianceBilin_apply_basisFun_self, fourierCoeff_bernoulli_eq, signedDist_le_dist, HasStrictFDerivAt.arsinh, EuclideanGeometry.Sphere.IsTangentAt.mem_space, Subgroup.instIsArithmeticRangeSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGL, Affine.Simplex.circumcenter_reindex, HasFDerivWithinAt.exp, EuclideanGeometry.affineSpan_of_orthocentricSystem, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, CircleDeg1Lift.floor_sub_le_translationNumber, AffineBasis.interior_convexHull, fderivWithin_sin, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, Affine.Simplex.excenter_eq_affineCombination, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, fourier_iteratedFDeriv, EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents, ModularGroup.tendsto_abs_re_smul, AffineSubspace.perpBisector_nonempty, signedDist_apply_apply, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, UnitAddTorus.mFourierCoeff_toLp, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, Bundle.ContinuousRiemannianMetric.symm, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, Subgroup.instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex, fderiv.log, descPochhammer_eval_div_factorial_le_sum_choose, CircleDeg1Lift.map_le_of_map_zero, Affine.Simplex.finrank_direction_altitude, CircleDeg1Lift.le_map_of_map_zero, EuclideanGeometry.Sphere.IsDiameter.wbtw, Affine.Simplex.mongePoint_mem_mongePlane, Affine.Simplex.isTangentAt_insphere_touchpoint, ContinuousMap.HomotopyRel.trans_apply, ModularGroup.exists_max_im, Affine.Simplex.excenterWeightsUnnorm_map, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, Nat.closedBall_eq_Icc, Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z, Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, VectorFourier.hasFDerivAt_fourierIntegral, SimpleGraph.triangleRemovalBound_mul_cube_lt, isCusp_SL2Z_iff', VectorFourier.fourierIntegral_iteratedFDeriv, Polynomial.card_eq_of_natDegree_le_of_coeff_le, EuclideanGeometry.oangle_eq_pi_iff_sbtw, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, ModularGroup.im_T_smul, EuclideanGeometry.Sphere.orthRadius_center, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, Complex.arg_cos_add_sin_mul_I_sub, CompactlySupportedContinuousMap.coe_toRealLinearMap, EuclideanGeometry.Sphere.coe_secondInter, Seminorm.gaugeSeminorm_ball, EuclideanGeometry.oangle_midpoint_rev_left, Affine.Triangle.touchpoint_singleton_sbtw, curveIntegral_segment, HasFDerivWithinAt.abs_of_neg, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Affine.Simplex.exradius_map, Affine.Triangle.dist_circumcenter_reflection_orthocenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, sum_mul_eq_sub_integral_mul', one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, hasFDerivAt_norm_rpow, Set.Nonempty.intrinsicInterior, Affine.Simplex.excenterWeights_reindex, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Path.Homotopy.hcomp_apply, dist_affineCombination_lt_of_strictConvexSpace, instIsCompleteAbs, MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real, Affine.Simplex.ExcenterExists.isTangentAt_touchpoint, Subgroup.instIsArithmeticAdjoinNegOne, Subgroup.strictWidthInfty_eq_one_of_T_mem, Affine.Simplex.inradius_reindex, signedDist_eq_zero_of_orthogonal, EuclideanGeometry.preimage_inversion_perpBisector, ProbabilityTheory.covarianceBilin_zero, contDiffOn_stereoToFun, VectorFourier.differentiable_fourierIntegral, Affine.Simplex.incenter_mem_interior, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.altitudeFoot_map, dist_midpoint_midpoint_le, Convex.interior_nonempty_iff_affineSpan_eq_top, stereoInvFun_apply, Isometry.mapsTo_perpBisector, EuclideanGeometry.Cospherical.affineIndependent_of_ne, Affine.Simplex.circumcenter_eq_point, fourierIntegral_convergent_iff', Bundle.ContMDiffRiemannianMetric.symm, LSeries_eq_mul_integral_of_nonneg, EisensteinSeries.G2_S_transform, Chebyshev.sum_PrimePow_eq_sum_sum, EuclideanGeometry.oangle_eq_zero_iff_wbtw, CircleDeg1Lift.le_floor_map_map_zero, RealRMK.rieszMeasure_le_of_eq_one, ModularGroup.SL_to_GL_tower, ModularFormClass.one_mem_strictPeriods_SL2Z, Int.ball_eq_Ioo, HasFDerivAt.abs, Affine.Simplex.signedInfDist_apply_self, VectorFourier.iteratedFDeriv_fourierIntegral, HasStrictFDerivAt.abs_of_neg, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, one_div_one_sub_hasFPowerSeriesOnBall_zero, HasFDerivWithinAt.abs, Subgroup.two_mul_withInfty_mem_strictPeriods, exists_mem_interior_convexHull_affineBasis, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, signedDist_zero, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, Chebyshev.primeCounting_eq_theta_div_log_add_integral, UnitAddCircle.measure_univ, CompactlySupportedContinuousMap.toRealLinearMap_apply, jacobiTheta_S_smul, ProbabilityTheory.covarianceBilinDual_zero, EuclideanGeometry.wbtw_of_collinear_of_dist_center_le_radius, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, Affine.Simplex.incenter_notMem_affineSpan_face, RealRMK.integral_rieszMeasure, ModularForm.levelOne_weight_zero_rank_one, ModularGroup.re_T_smul, Affine.Triangle.affineSpan_pair_eq_orthRadius, CongruenceSubgroup.strictWidthInfty_Gamma0, sum_div_nat_floor_pow_sq_le_div_sq, fderivWithin_cos, isAlgebraic_tan_rat_mul_pi, EuclideanGeometry.image_inversion_perpBisector, Affine.Simplex.mongePlane_def, Affine.Triangle.acuteAngled_iff_angle_lt, one_div_sub_hasFPowerSeriesOnBall_zero, Bundle.ContMDiffRiemannianMetric.pos, HasStrictFDerivAt.sqrt, signedDist_triangle_left, IsContMDiffRiemannianBundle.exists_contMDiff, Affine.Simplex.excenterExists_map, IsClosed.exists_wbtw_isVisible, natCeil_logb_natCast, isAlgebraic_cos_rat_mul_pi, convergent_succ, HasStrictFDerivAt.rpow, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, Affine.Simplex.exsphere_reindex, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, GaussianInt.toComplex_im_div, Subgroup.IsArithmetic.isFiniteRelIndexSL, Affine.Simplex.altitudeFoot_mem_affineSpan, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, Complex.isCauSeq_norm_exp, exists_nat_abs_mul_sub_round_le, UpperHalfPlane.modular_S_smul, IsometryEquiv.map_midpoint, ProbabilityTheory.covarianceBilin_comm, descPochhammer_eval_le_sum_descFactorial, AmpleSet.preimage, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, ModularGroup.re_T_inv_smul, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, SchwartzMap.smulRightCLM_apply_apply, CongruenceSubgroup.isArithmetic_conj_SL2Z, EuclideanGeometry.image_inversion_sphere_dist_center, fderiv_norm_smul_neg, EisensteinSeries.q_expansion_riemannZeta, EuclideanGeometry.Sphere.sbtw_secondInter, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, MeasureTheory.SignedMeasure.re_toComplexMeasure, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, contDiffPointwiseHolderAt_iff, monotoneOn_deriv_descPochhammer_eval, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, EuclideanGeometry.oangle_midpoint_left, Affine.Simplex.circumsphere_unique_dist_eq, Quaternion.re_exp, NormedSpace.ofReal_exp_β_β, ContinuousMap.HomotopyWith.trans_apply, EuclideanGeometry.preimage_inversion_sphere_dist_center, UnitAddTorus.mFourier_norm, HasFDerivWithinAt.log, Orientation.areaForm'_apply, MeasureTheory.hausdorffMeasure_lineMap_image, Affine.Triangle.dist_orthocenter_reflection_circumcenter, signedDist_smul_of_pos, unitInterval.fract_mem, IsContinuousRiemannianBundle.exists_continuous, ModularGroup.normSq_S_smul_lt_one, Affine.Simplex.exradius_reindex, Affine.Simplex.ninePointCircle_reindex, Chebyshev.primeCounting_sub_theta_div_log_isBigO, intervalIntegral.integral_hasStrictFDerivAt, instSeparatingDualRealOfIsTopologicalAddGroupOfContinuousSMulOfLocallyConvexSpaceOfT1Space, signedDist_lineMap_lineMap, ModularGroup.exists_row_one_eq_and_min_re, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, Behrend.exp_neg_two_mul_le, fourier_fderiv, signedDist_vadd_left_swap, floor_real_sqrt_eq_nat_sqrt, VectorFourier.fderiv_fourierIntegral, convergent_zero, EuclideanGeometry.OrthocentricSystem.affineIndependent, Affine.Simplex.touchpointWeights_reindex, Bundle.RiemannianMetric.symm, Affine.Simplex.height_map, sum_mul_eq_sub_integral_mulβ', ModularGroup.re_T_zpow_smul, Affine.Simplex.orthogonalProjection_circumcenter, CircleDeg1Lift.le_map_map_zero, fderiv_cos, HasFDerivAt.abs_of_neg, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Chebyshev.theta_eq_log_primorial, signedDist_vadd_right, HasStrictFDerivAt.arctan, ProbabilityTheory.strong_law_aux6, convexOn_descPochhammer_eval, ModularGroup.im_lt_im_S_smul, ProbabilityTheory.hasFPowerSeriesAt_mgf, Affine.Simplex.touchpoint_mem_affineSpan, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, ProbabilityTheory.covarianceBilin_self_nonneg, Polynomial.hermite_eq_deriv_gaussian', fderiv_exp, Affine.Simplex.direction_mongePlane, fderiv_arctan, ProbabilityTheory.covarianceBilinDual_self_eq_variance, Affine.Simplex.dist_point_centroid, Path.Homotopy.trans_apply, Affine.Simplex.altitudeFoot_reindex, Affine.Simplex.affineCombination_eq_touchpoint_iff, Subgroup.isArithmetic_iff_finiteIndex, Affine.Simplex.altitudeFoot_mem_altitude, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, CircleDeg1Lift.translationNumber_le_ceil_sub, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent, ModularGroup.im_T_zpow_smul, Affine.Triangle.affineSpan_orthocenter_point_le_altitude, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, fderivWithin.log, HasFDerivWithinAt.sinh, EuclideanGeometry.Cospherical.affineIndependent, ContinuousMap.Homotopy.trans_apply, harmonic_floor_le_one_add_log, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, Behrend.ceil_lt_mul, Polynomial.Chebyshev.rootMultiplicity_T_real, ProbabilityTheory.covarianceBilinDual_self_nonneg, HasFDerivAt.log, isCusp_SL2Z_iff, EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, signedDist_lineMap_left, ProbabilityTheory.covarianceBilin_real_self, ModularForm.slash_action_eq'_iff, surjective_cosetToCuspOrbit, GaussianInt.toComplex_re_div, VectorFourier.fourierSMulRight_apply, Affine.Simplex.sOppSide_excenter_singleton_point, CongruenceSubgroup.strictWidthInfty_Gamma1, HasFDerivAt.exp, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, signedDist_anticomm, EisensteinSeries.eisensteinSeries_SIF_apply, Affine.Simplex.dist_circumcenter_eq_circumradius, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, Quaternion.normSq_exp, eq_lineMap_of_dist_eq_mul_of_dist_eq_mul, sum_mul_eq_sub_integral_mulβ, Chebyshev.psi_eq_theta_add_sum_theta, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, stdSimplexHomeomorphUnitInterval_apply_coe, ceil_exp_one_eq_three, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, dist_add_dist_eq_iff, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, EuclideanGeometry.Sphere.IsDiameter.sbtw, RCLike.isCauSeq_norm, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, LSeries_eq_mul_integral, ModularGroup.exists_one_half_le_im_smul, Quaternion.im_exp, fderivWithin_exp, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, ProbabilityTheory.covarianceBilin_apply_pi, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', RCLike.isCauSeq_im, Affine.Simplex.dist_circumcenter_eq_circumradius', EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius, HasFDerivWithinAt.rpow_const, abs_signedDist_eq_dist_iff_vsub_mem_span, AmpleSet.image_iff, Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint, UpperHalfPlane.petersson_slash_SL, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, MeasureTheory.Measure.addHaar_affineSubspace, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair, Affine.Simplex.pointsWithCircumcenter_point, HasFDerivAt.sinh, Affine.Simplex.mongePoint_reindex, Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere, ArithmeticFunction.log_mul_moebius_eq_vonMangoldt, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, ModularForm.SL_slash_def, Affine.Simplex.altitude_reindex, signedDist_neg, ProbabilityTheory.covarianceBilin_apply_basisFun, EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius, VectorFourier.contDiff_fourierIntegral, Convex.dimH_eq_finrank_vectorSpan, CircleDeg1Lift.le_ceil_map_map_zero, signedDist_vsub_self_rev, HasFDerivAt.rpow_const, ceil_pi_eq_four, signedDist_linear_apply, UnitAddCircle.measurePreserving_mk, HasStrictFDerivAt.const_rpow, CongruenceSubgroup.strictPeriods_Gamma1, BoxIntegral.unitPartition.index_apply, HasStrictFDerivAt.cos, Affine.Simplex.incenter_eq_affineCombination, signedDist_self, Matrix.PosDef.of_toQuadraticForm', signedDist_vsub_self, MeasureTheory.SignedMeasure.rnDeriv_smul, Polynomial.Chebyshev.rootMultiplicity_U_real, signedDist_smul, HasFDerivWithinAt.arsinh, Affine.Simplex.sOppSide_point_excenter_singleton, Euclidean.closedBall_eq_preimage, AffineSubspace.mem_perpBisector_iff_dist_eq', Chebyshev.theta_eq_sum_Icc, Affine.Simplex.ninePointCircle_center_mem_affineSpan, log_le_harmonic_floor, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, fourierIntegral_fderiv, MeasureTheory.ComplexMeasure.im_apply, AffineSubspace.perpBisector_eq_top, HasFDerivAt.sin, UnitAddCircle.norm_eq, SlashInvariantForm.slash_action_eqn_SL'', CongruenceSubgroup.strictWidthInfty_Gamma, AffineSubspace.midpoint_mem_perpBisector, CompactlySupportedContinuousMap.toNNRealLinear_apply, Affine.Simplex.touchpoint_reindex, EuclideanGeometry.inner_weightedVSub, nndist_midpoint_midpoint_le, transcendental_liouvilleNumber, EuclideanGeometry.Sphere.center_mem_orthRadius_iff, Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range, ArithmeticFunction.moebius_mul_log_eq_vonMangoldt, Subgroup.strictWidthInfty_mem_strictPeriods, UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStrip, signedDist_smul_of_neg, hasFPowerSeriesOnBall_linear_zero, EisensteinSeries.q_expansion_bernoulli, Affine.Triangle.orthocenter_mem_altitude, ProbabilityTheory.isPosSemidef_covarianceBilinDual, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, Affine.Triangle.eulerPoint_eq_midpoint, HasFDerivWithinAt.sqrt, Affine.Simplex.sign_signedInfDist_touchpoint_empty, one_add_rpow_hasFPowerSeriesAt_zero, signedDist_vadd_right_swap, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, fderivWithin_sqrt, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, ceil_logb_natCast, ProbabilityTheory.covarianceBilin_real, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, ModularGroup.im_smul_eq_div_normSq, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, Euclidean.ball_eq_preimage, fderiv_sinh, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, AffineSubspace.perpBisector_self, Path.trans_apply, ContinuousMap.Homotopy.affine_apply, HasFDerivWithinAt.arctan, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, locallyIntegrableOn_mul_sum_Icc, EuclideanGeometry.oangle_midpoint_rev_right, ProbabilityTheory.covarianceBilinDual_comm, affineSpan_eq_top_of_nonempty_interior, isAlgebraic_sin_rat_mul_pi, HasFDerivWithinAt.rpow, Affine.Simplex.incenter_mem_affineSpan_range, EisensteinSeries.tendsto_double_sum_S_act, intervalIntegral.fderivWithin_integral_of_tendsto_ae, Affine.Simplex.eulerPoint_reindex, one_add_rpow_hasFPowerSeriesAt_zero, Affine.Simplex.excenterWeights_map, CongruenceSubgroup.strictPeriods_Gamma, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, Complex.lim_im, signedDist_vadd_left, cosetToCuspOrbit_apply_mk, Affine.Simplex.incenter_notMem_affineSpan_pair, intervalIntegral.integral_hasFDerivWithinAt, Int.closedBall_eq_Icc, ProbabilityTheory.covarianceBilin_apply, HasFDerivAt.cos, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, Quaternion.norm_exp, Affine.Simplex.touchpoint_eq_point_rev, Affine.Simplex.signedInfDist_reindex, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, Affine.Simplex.ExcenterExists.touchpointWeights_map, ProbabilityTheory.covarianceBilin_map, Affine.Simplex.mongePoint_map, Affine.Simplex.eulerPoint_map, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, AffineSubspace.signedInfDist_singleton, EuclideanGeometry.angle_midpoint_eq_pi, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, HasFDerivAt.const_rpow, intrinsicInterior_nonempty, Bundle.ContinuousRiemannianMetric.pos, ProbabilityTheory.strong_law_aux4, IsCoercive.continuousLinearEquivOfBilin_apply, Affine.Simplex.affineCombination_touchpointWeights, Affine.Triangle.orthocenter_mem_affineSpan, SimpleGraph.triangleRemovalBound_le, floor_logb_natCast, Affine.Simplex.mongePoint_mem_affineSpan, floor_pi_eq_three, CircleDeg1Lift.ceil_map_map_zero_le, EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff, NormedSpace.of_real_exp_β_β, Bundle.RiemannianMetric.pos, HasFDerivAt.arsinh, IsClosed.convexHull_subset_affineSpan_isVisible, Affine.Simplex.incenter_reindex, AffineSubspace.mem_perpBisector_iff_dist_eq, Chebyshev.psi_eq_sum_Icc, Subgroup.strictPeriods_SL2Z, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, surjOn_extremePoints_image, fourierIntegral_continuousLinearMap_apply', Complex.isCauSeq_im, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, EuclideanGeometry.Sphere.mem_tangentSet_iff, VectorFourier.fourierPowSMulRight_apply, Affine.Simplex.altitude_map, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, integrableOn_mul_sum_Icc, EuclideanGeometry.Sphere.isTangentAt_center_iff, iter_deriv_rpow_const, HasFDerivAt.hasFDerivAt_norm_smul_neg, fderiv_sqrt, Affine.Simplex.ExcenterExists.signedInfDist_excenter, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, SlashInvariantForm.vAdd_width_periodic, MeasureTheory.hausdorffMeasure_affineSegment, ModularGroup.exists_smul_mem_fd, Affine.Triangle.sbtw_touchpoint_empty, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, dist_lt_dist_add_dist_iff, ProbabilityTheory.strong_law_aux1, Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne, norm_sub_le_mul_volume_of_norm_fderiv_le, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Complex.lim_norm, differentiable_fourierChar_neg_bilinear_right, Affine.Simplex.sSameSide_point_excenter_singleton, AffineSubspace.signedInfDist_def, Affine.Simplex.acuteAngled_reindex_iff, Submodule.angle_coe, Affine.Simplex.mem_altitude, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, Polynomial.cyclotomic_eval_le_add_one_pow_totient, EisensteinSeries.eisensteinSeriesSIF_apply, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, Affine.Simplex.mongePlane_reindex, ModularGroup.im_T_inv_smul, CompactlySupportedContinuousMap.nnrealPart_smul_pos, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, VectorFourier.norm_fourierSMulRight_le, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, Affine.Simplex.signedInfDist_affineCombination, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, ProbabilityTheory.strong_law_aux2, one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, UpperHalfPlane.modular_T_zpow_smul, AddCircle.norm_eq, Behrend.div_lt_floor, EuclideanGeometry.dist_affineCombination, HasStrictFDerivAt.sin, signedDist_eq_dist_iff_vsub_mem_span, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, AffineSubspace.direction_perpBisector, AffineSubspace.angle_coe, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, HasFDerivWithinAt.const_rpow, fderivWithin_cosh, Affine.Simplex.ninePointCircle_map, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, VectorFourier.norm_fourierPowSMulRight_le, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Complex.isCauSeq_norm, hasFDerivAt_fourierChar_neg_bilinear_right, AffineSubspace.mem_perpBisector_iff_inner_eq, VectorFourier.norm_fourierSMulRight, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, Polynomial.sub_one_pow_totient_lt_cyclotomic_eval, sum_mul_eq_sub_sub_integral_mul', NumberField.mixedEmbedding.euclidean.finrank, differentiable_fourierChar_neg_bilinear_left, AffineBasis.centroid_mem_interior_convexHull, Subgroup.IsArithmetic.finiteIndex_comap, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, CircleDeg1Lift.map_fract_sub_fract_eq, ModularForm.SL_slash_apply, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, floor_exp_one_eq_two, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange, HasFDerivAt.sqrt, EisensteinSeries.eisSummand_SL2_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, sum_mul_eq_sub_integral_mul, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, Affine.Simplex.touchpoint_mem_affineSpan_simplex, exp_eq_exp_β, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, fderiv_norm_rpow, HasStrictFDerivAt.cosh, Affine.Simplex.circumsphere_reindex, EuclideanGeometry.Sphere.direction_orthRadius, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, Affine.Simplex.circumradius_reindex, ArithmeticFunction.vonMangoldt_mul_zeta, AffineSubspace.signedInfDist_apply_self, ProbabilityTheory.covarianceBilinDual_of_not_memLp, fderivWithin_arctan, CircleDeg1Lift.floor_map_map_zero_le, MeasureTheory.charFun_map_eq_charFunDual_smul, zero_at_infty_vector_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, AddCircle.norm_eq', EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, isIntegral_two_mul_cos_rat_mul_pi, fderiv_cosh, IsOpen.affineSpan_eq_top, Path.segment_apply, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, Complex.Gamma_def, HasStrictFDerivAt.sinh, abs_signedDist_le_dist, hasStrictFDerivAt_rpow_of_neg, Complex.arg_mul_cos_add_sin_mul_I_sub, intervalIntegral.integral_hasFDerivAt, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, intervalIntegral.fderiv_integral, EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq, ProbabilityTheory.IsGaussian.charFunDual_eq', RealRMK.le_rieszMeasure_tsupport_subset, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.height_reindex, HasFDerivAt.cosh, Affine.Simplex.inradius_map, Liouville.transcendental, EuclideanGeometry.Sphere.secondInter_eq_lineMap, sum_mul_eq_sub_integral_mulβ, CircleDeg1Lift.map_map_zero_le, signedDist_apply_linear, CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zero, Bundle.RiemannianMetric.continuousAt, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, Subgroup.widthInfty_mem_periods, VectorFourier.hasFDerivAt_fourierChar_smul, HasFDerivWithinAt.cos, exists_extension_norm_eq, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, ProbabilityTheory.covarianceBilinDual_of_not_memLp', Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite, AmpleSet.image, RCLike.isCauSeq_re, EuclideanGeometry.inversion_eq_lineMap, Collinear.sbtw_of_dist_eq_of_dist_lt, Subgroup.strictPeriods_eq_zmultiples_strictWidthInfty, Subgroup.strictWidthInfty_SL2Z, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, Affine.Simplex.signedInfDist_apply_of_ne, sum_mul_eq_sub_sub_integral_mul, dist_sq_lineMap_of_inner_eq_zero, signedDist_left_lineMap, Affine.Simplex.direction_altitude, VectorFourier.fourierIntegral_fderiv, UnitAddCircle.integral_preimage, ModularGroup.SL_neg_smul, Affine.Simplex.circumcenter_eq_centroid, Affine.Simplex.excenter_reindex, Chebyshev.eventually_primeCounting_le, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, eq_midpoint_of_dist_eq_half, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, fderiv_fourierChar_neg_bilinear_left_apply, fourierIntegral_continuousMultilinearMap_apply', Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, fourierIntegral_iteratedFDeriv, Complex.isCauSeq_re, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, Subgroup.periods_eq_zmultiples_widthInfty, one_add_rpow_hasFPowerSeriesOnBall_zero, ArithmeticFunction.zeta_mul_vonMangoldt, isCauSeq_iff_lift, Affine.Simplex.incenter_notMem_affineSpan_faceOpposite, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, RCLike.re_extendToπ'β, one_div_sub_sq_hasFPowerSeriesOnBall_zero, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, HasFDerivAt.rpow, round_pi_eq_three, LSeries_eq_mul_integral', AffineSubspace.right_mem_perpBisector, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, ModularGroup.exists_eq_T_zpow_of_c_eq_zero, HasFDerivWithinAt.sin, Quaternion.exp_coe, HasStrictFDerivAt.exp, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, fderiv_sin, mul_pow_le_nat_floor_pow, EuclideanGeometry.Sphere.finrank_orthRadius, Affine.Simplex.points_vsub_eulerPoint, UpperHalfPlane.modular_T_smul, Quaternion.exp_eq, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, EuclideanGeometry.angle_eq_pi_iff_sbtw, ModularGroup.smul_eq_lcRow0_add, hasFDerivAt_stereoInvFunAux_comp_coe, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj, Affine.Triangle.dist_point_centroid, Affine.Triangle.orthocenter_reindex, Path.eqOn_extend_segment, Affine.Simplex.circumradius_map, Bundle.ContinuousRiemannianMetric.isVonNBounded, AffineIsometryEquiv.pointReflection_midpoint_right, ofDigits_digits_sum_eq, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, Affine.Simplex.altitude_def, GaussianInt.toComplex_div_im, MeasureTheory.SignedMeasure.im_toComplexMeasure, Complex.lim_re, signedDist_vadd_vadd, parallelepiped_single, Urysohns.CU.lim_eq_midpoint, EuclideanGeometry.Sphere.self_mem_orthRadius, HasFDerivWithinAt.cosh, SlashInvariantForm.T_zpow_width_invariant, Affine.Simplex.insphere_reindex, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, HasStrictFDerivAt.rpow_const, Affine.Simplex.sSameSide_point_incenter, Complex.lim_eq_lim_im_add_lim_re, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, Affine.Simplex.signedInfDist_incenter, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq
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instSemigroup π | CompOp | β |
instSemilatticeInf π | CompOp | 8 mathmath: Set.Finite.infsep_of_nontrivial, Finset.coe_infsep_of_offDiag_nonempty, Set.Nontrivial.infsep_of_fintype, Set.Finite.infsep, Set.infsep_of_fintype, ContinuousMap.inf_mem_subalgebra_closure, ContinuousMap.inf_mem_closed_subalgebra, Finset.coe_infsep
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instSemilatticeSup π | CompOp | 11 mathmath: Finset.Nonempty.norm_sum_le_sup'_norm, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, MeasureTheory.smul_le_stoppedValue_hittingBtwn, ContinuousMap.sup_mem_closed_subalgebra, ContinuousMap.sup_mem_subalgebra_closure, MeasureTheory.smul_le_stoppedValue_hitting, IsUltrametricDist.norm_sum_eq_sup'_of_pairwise_ne, Polynomial.supNorm_def', Finset.Nonempty.norm_prod_le_sup'_norm, IsUltrametricDist.norm_prod_eq_sup'_of_pairwise_ne, MeasureTheory.maximal_ineq
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instSub π | CompOp | 1161 mathmath: hasDerivAt_arccos, HurwitzZeta.isBigO_atTop_evenKernel_sub, norm_sub_sq_real, ProbabilityTheory.variance_eq_integral, aux_hasSum_of_le_geometric, abs_exp_sub_one_le, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound, sin_add_sin, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, lt_norm_sub_of_not_sameRay, LiouvilleWith.nat_sub_iff, MonotoneOn.intervalIntegral_slope_le, NNReal.rpow_sub_intCast, MeasureTheory.SimpleFunc.posPart_sub_negPart, InformationTheory.integral_llr_add_mul_log_nonneg, sinh_eq, sinh_log, HasDerivWithinAt.liminf_right_slope_norm_le, Stirling.log_stirlingSeq_bounded_aux, integral_cos, ProbabilityTheory.gammaPDF_of_nonneg, volume_real_Ioc, tan_pi_sub, arcsin_eq_pi_div_two_sub_arccos, HasStrictDerivAt.rpow, bernoulliFun_eval_one_sub, Irrational.ratCast_sub, CircleDeg1Lift.map_sub_int, IsPicardLindelof.of_contDiffAt_one, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, unitInterval.volume_Ioo, Seminorm.norm_sub_map_le_sub, MeasureTheory.MeasuredSets.real_sub_real_le_dist, Complex.norm_sub_one_sq_eq_of_norm_eq_one, ContractingWith.dist_fixedPoint_le, Complex.norm_sub_eq, exp_sub_sinh, ProbabilityTheory.betaPDF_eq, deriv_negMulLog, hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, integral_sin_mul_cosβ, LiouvilleWith.sub_rat, MeasureTheory.Submartingale.sum_mul_sub', norm_jacobiThetaβ_term_le, deriv_binEntropy, LiouvilleWith.rat_sub_iff, cos_sub_pi, Angle.cos_add, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, CFC.tendsto_cfc_rpow_sub_one_log, intervalIntegral.mul_integral_comp_mul_sub, log_div_le_sum_range_add, BumpCovering.toPartitionOfUnity_apply, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, MeasureTheory.probReal_compl_eq_one_subβ, countingFunction_finsum_eq_finsum_add, hasStrictDerivAt_rpow_const_of_ne, MeasureTheory.SignedMeasure.rnDeriv_def, hasDerivWithinAt_taylorWithinEval, InformationTheory.mul_log_le_klDiv, ProbabilityTheory.covarianceBilinDual_apply, LiouvilleWith.sub_nat, LiouvilleWith.int_sub, HolderWith.of_le, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, ProbabilityTheory.Fernique.lt_normThreshold_zero, Ioo_eq_ball, InnerProductGeometry.sin_angle, isMIntegralCurve_comp_sub, bernoulliFun_two, intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le, add_sqrt_self_sq_sub_one_inv, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, selfAdjoint.norm_sq_expUnitary_sub_one, Complex.mul_re, intervalIntegral.integral_comp_sub_div, intervalIntegral.integral_comp_mul_sub, TopologicalSpace.Opens.CompleteCopy.dist_eq, Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub, AkraBazziRecurrence.isBigO_apply_r_sub_b, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, HasDerivWithinAt.liminf_right_norm_slope_le, interval_average_eq_div, ediam_eq, Polynomial.sub_one_pow_totient_le_cyclotomic_eval, integral_pow, norm_exp_sub_one_sub_id_le, intervalIntegral.integral_comp_sub_left, Differentiable.fderiv_norm_rpow, unitInterval.volume_Ico, MeasureTheory.Submartingale.mul_integral_upcrossingsBefore_le_integral_pos_part, HasConstantSpeedOnWith.ratio, ProbabilityTheory.sub_half_inf_sub_mem_Ioo, BohrMollerup.le_logGammaSeq, tan_sub', PNat.dist_eq, ProbabilityTheory.variance_const_sub, MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul, integral_exp, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, norm_sub_mul_self, MeasureTheory.lintegral_prod_lintegral_pow_le, LiouvilleWith.sub_int, monomial_has_deriv_aux, StieltjesFunction.measure_Ioo, setOf_liouvilleWith_subset_aux, deriv_arccos, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, Complex.norm_one_add_mul_inv_le, integral_sin_pow_three, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, ProbabilityTheory.cdf_expMeasure_eq, ProbabilityTheory.tilted_mul_apply_cgf, Rat.dist_eq, sin_pi_sub, one_sub_sq_div_two_le_cos, MeasureTheory.Submartingale.sum_upcrossingStrat_mul, Convex.image_sub_le_mul_sub_of_deriv_le, hasStrictFDerivAt_rpow_of_pos, HurwitzKernelBounds.f_int_negSucc, exists_dist_slope_lt_pairwiseDisjoint_hasSum, rpow_sum_le_const_mul_sum_rpow_of_nonneg, one_sub_le_exp_neg, mellin_convergent_zero_of_isBigO, sigmoid_neg, MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, IntervalIntegrable.comp_sub_left_iff, Stirling.log_stirlingSeq_formula, ball_eq_Ioo, EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero, exp_bound, Polynomial.Chebyshev.integral_measureT, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, BoxIntegral.Box.upper_sub_lower_splitCenterBox, ENNReal.lintegral_mul_rpow_le_lintegral_rpow_mul_lintegral_rpow, InformationTheory.klFun_apply, Besicovitch.SatelliteConfig.exists_normalized_aux2, hasDerivAt_arcosh, inv_logb_div_base, Complex.norm_log_one_add_le, enorm_fderiv_norm_rpow_le, RCLike.ofReal_sub, Path.extend_symm_apply, one_sub_gold, cos_arcsin, ProbabilityTheory.covariance_sub_const_right, ProbabilityTheory.Kernel.measurable_singularPart_fun_right, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonneg, MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_part, GammaIntegral_convergent, Affine.Simplex.dist_circumcenter_sq_eq_sq_sub_circumradius, tan_arccos, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonpos', sinh_arcosh, LiouvilleWith.int_sub_iff, volume_real_Ioo, LiouvilleNumber.aux_calc, StieltjesFunction.measure_singleton, abs_lt_norm_sub_of_not_sameRay, integral_cos_pow, cos_nat_mul_two_pi_sub_pi, AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const, hasStrictDerivAt_arccos, Complex.sub_im, Stirling.log_stirlingSeq_diff_hasSum, norm_sub_pow_two_real, intervalIntegral.integral_comp_sub_right, artanh_eq_half_log, sin_sub_pi_div_two, Chebyshev.psi_sub_theta_eq_sum_not_prime, norm_sub_sq, rpowIntegrandββ_le_rpow_sub_two_mul_self, stereoInvFunAux_apply, ENNReal.rpow_sub, Gamma_mul_Gamma_add_half, sin_gt_sub_cube, LiouvilleWith.rat_sub, two_mul_arctan_inv_2_sub_arctan_inv_7, CircleDeg1Lift.floor_sub_le_translationNumber, closedBall_eq_Icc, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, singleton_eq_inter_Icc, log_two_near_10, ProbabilityTheory.centralMoment_one', MeasureTheory.Measure.integral_toReal_rnDeriv', re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, Stirling.le_log_factorial_stirling, ProbabilityTheory.variance_le_sub_mul_sub, IntervalIntegrable.comp_sub_right, curveIntegralFun_trans_aeeq_right, tsum_geometric_le_of_norm_lt_one, BoundedContinuousFunction.integral_const_sub, ZLattice.tsum_norm_rpow_le, integral_sin_sq, StieltjesFunction.measure_univ, exp_sub_sum_range_succ_isLittleO_pow, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, cauchy_sub, AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const_real, taylor_tendsto, SameRay.norm_sub, volume_pi_Ico, deriv_norm_ofReal_cpow, gronwallBound_of_K_ne_0, MeasureTheory.integral_mul_upcrossingsBefore_le_integral, volume_real_Ioo_of_le, ContinuousMap.HomotopyRel.trans_apply, Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, curveIntegralFun_symm_apply, tan_nat_mul_pi_sub, arccos_eq_pi_div_two_sub_arcsin, cos_add_cos, deriv_rpow_const, Nat.closedBall_eq_Icc, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', Gamma_mul_Gamma_one_sub, Complex.arg_neg_eq_arg_sub_pi_of_im_pos, sin_sub, exists_ratio_deriv_eq_ratio_slope, MeasureTheory.Integrable.tendsto_eLpNorm_condExp, cos_three_mul, irrational_intCast_sub_iff, InnerProductGeometry.angle_neg_right, volume_Icc_pi, ProbabilityTheory.Kernel.rnDeriv_def', abs_exp_sub_one_sub_id_le, norm_image_sub_le_of_norm_deriv_le_segment, integral_cos_pow_aux, tan_two_mul, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, Convex.image_sub_lt_mul_sub_of_deriv_lt, InformationTheory.toReal_klDiv, ENNReal.le_toReal_sub, ediam_Ioc, HolderConjugate.one_sub_inv, UniformConvexSpace.uniform_convex, rpow_sub', dist_le_of_approx_trajectories_ODE, finite_integral_rpow_sub_one_pow_aux, cos_two_pi_sub, Complex.ofReal_comp_sub, MeasureTheory.Submartingale.sum_mul_sub, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, Complex.arg_cos_add_sin_mul_I_sub, Complex.sub_re, Complex.sq_norm_sub_sq_re, Asymptotics.IsBigOWith.right_le_sub_of_lt_one, BohrMollerup.f_add_nat_ge, sin_sq, Complex.GammaIntegral_ofReal, tanh_arcosh, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, exp_arcosh, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, Complex.norm_log_sub_logTaylor_le, NNReal.rpow_sub_natCast, le_ofDigits_cantorToTernary_sum, taylor_mean_remainder_lagrange_iteratedDeriv, two_mul_arctan, one_sub_goldConj, hasDerivWithinAt_arccos_Ici, MeasureTheory.posConvolution_eq_convolution_indicator, unitInterval.symm_projIcc, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, MeasureTheory.integral_comp_rpow_Ioi_of_pos, NNReal.rpow_sub, NNReal.rpow_sub', summable_schlomilch_iff_of_nonneg, InnerProductSpace.Core.cauchy_schwarz_aux, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, volume_pi_Ioc, AkraBazziRecurrence.strictMonoOn_one_sub_smoothingFn, ValueDistribution.isBigO_characteristic_sub_characteristic_shift, ZLattice.tsumNormRPowBound_spec, exists_rat_abs_sub_lt_and_lt_of_irrational, cos_le_one_sub_mul_cos_sq, RCLike.div_im, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, abs_dist_sub_le, hasFDerivAt_norm_rpow, ofDigitsTerm_le, trapezoidal_error_le_of_c2, MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul, logb_div, volume_Icc_pi_toReal, ValueDistribution.characteristic_sub_characteristic_eq_proximity_sub_proximity, Path.Homotopy.hcomp_apply, HurwitzZeta.hasSum_nat_hurwitzZetaEven, NNReal.rpow_sum_le_const_mul_sum_rpow, expNear_sub, sinh_sub_id_strictMono, norm_sub_le_of_geometric_bound_of_hasSum, hasDerivAt_abs_rpow, isMIntegralCurveOn_comp_sub, StrictMonoOn.exists_slope_lt_deriv_aux, ZetaAsymptotics.term_tsum_of_lt, unitInterval.volume_Ici, abs_dist_sub_le_dist_mul_mul, Complex.norm_log_one_add_sub_self_le, norm_jacobiThetaβ_term, MeasureTheory.crossing_pos_eq, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, stereoInvFun_apply, dist_le_of_le_geometric_of_tendstoβ, ContractingWith.apriori_dist_iterate_fixedPoint_le, hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, ValueDistribution.characteristic_sub_characteristic_inv_of_ne_zero, hasDerivAt_qaryEntropy, goldenRatio_pow_sub_goldenRatio_pow, Complex.div_im, Int.ball_eq_Ioo, Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, volume_pi_Ioc_toReal, ofCauchy_sub, BoxIntegral.BoxAdditiveMap.volume_apply, volume_real_Ioc_of_le, Circle.exp_sub, intervalIntegral.integral_deriv_comp_mul_deriv', one_div_one_sub_hasFPowerSeriesOnBall_zero, BoundedVariationOn.sub_le, UpperHalfPlane.dist_coe_center, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, tendsto_measure_Icc, coe_fib_eq, intervalIntegral.smul_integral_comp_mul_sub, Complex.sq_norm_sub_sq_im, EReal.coe_sub, mellin_convergent_of_isBigO_scalar, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, norm_sub_norm_le', AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, posLog_sub_posLog_inv, ValueDistribution.characteristic_sub_characteristic_inv_at_zero, bernstein.variance, tsum_geometric_of_lt_one, diam_Ioo, bernstein_apply, ProbabilityTheory.covariance_sub_right, sum_div_nat_floor_pow_sq_le_div_sq, tendsto_harmonic_sub_log, sin_nat_mul_two_pi_sub, Complex.isBigO_re_sub_re, mul_sub_le_image_sub_of_le_deriv, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos, hasStrictDerivAt_arcosh, HurwitzKernelBounds.F_nat_one_le, ProbabilityTheory.variance_sub, dist_integral_mulExpNegMulSq_comp_le, CircleDeg1Lift.tendsto_translation_number', StieltjesFunction.length_subadditive_Icc_Ioo, ProbabilityTheory.betaPDF_of_pos_lt_one, ball_eq_openSegment, Complex.HadamardThreeLines.norm_invInterpStrip, MeasureTheory.lintegral_rpow_eq_lintegral_meas_lt_mul, sin_pi_div_two_sub, BumpCovering.toPartitionOfUnity_eq_mul_prod, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, intervalIntegrable_sub_inv_iff, one_div_sub_hasFPowerSeriesOnBall_zero, Convex.mul_sub_le_image_sub_of_le_deriv, exp_one_near_20, StrictMonoOn.exists_deriv_lt_slope_aux, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf', signedDist_triangle_left, integral_sin_pow_mul_cos_pow_odd, arccos_neg, deriv2_binEntropy, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, HasStrictFDerivAt.rpow, le_rpow_one_add_norm_iff_norm_le, hasDerivAt_arcsin, gold_sub_goldConj, exp_bound_div_one_sub_of_interval, Complex.normSq_sub, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, volume_Ico, MeasureTheory.integral_llr_tilted_left, InformationTheory.integral_klFun_rnDeriv, MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ, integral_id, tan_add, Complex.arg_of_re_neg_of_im_neg, deriv_tan_sub_id, inner_le_weight_mul_Lp_of_nonneg, Finset.norm_prod_one_add_sub_one_le, tan_sub_pi, stereoToFun_apply, arcsin_eq_arccos, rpow_sum_le_const_mul_sum_rpow, unitInterval.one_minus_le_one, exists_nat_abs_mul_sub_round_le, Set.Icc.coe_convexCombo, ProbabilityTheory.evariance_eq_lintegral_ofReal, arctan_inv_of_neg, UniformConcaveOn.sub, InformationTheory.klDiv_of_ac_of_integrable, ModularGroup.re_T_inv_smul, unitInterval.volume_Icc, BoxIntegral.Box.dist_le_distortion_mul, cos_int_mul_pi_sub, NumberField.house.exists_ne_zero_int_vec_house_le, abs_log_sub_add_sum_range_le, MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_aux, volume_regionBetween_eq_lintegral', InformationTheory.klDiv_def, Nat.dist_eq, taylor_mean_remainder, sin_sq_eq_half_sub, Unitary.norm_sub_one_sq_eq, LiouvilleWith.sub_int_iff, norm_inv_mul_rpow_sub_one_sub_log_le, norm_jacobiTheta_sub_one_le, exists_polynomial_near_of_continuousOn, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, MonotoneOn.intervalIntegral_deriv_mem_uIcc, deriv_qaryEntropy, Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, CircleDeg1Lift.commute_sub_int, monotoneOn_deriv_descPochhammer_eval, eventually_nhdsWithin_sign_eq_of_deriv_neg, mellin_convergent_top_of_isBigO, HasDerivWithinAt.rpow, Irrational.sub_ratCast, UpperHalfPlane.dist_self_center, integral_sin_mul_cosβ, intervalIntegral.smul_integral_comp_sub_mul, arccos_eq_arcsin, ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, integral_sin_pow_aux, hasDerivWithinAt_taylorWithinEval_at_Icc, ContinuousMap.HomotopyWith.trans_apply, RCLike.sqrt_eq_real_add_ite, integral_div_sq_add_sq, tendsto_rpow_sub_one_log, Set.Icc.eq_convexCombo, norm_sub_le_norm_mul, abs_sin_sub_sin_le, BoxIntegral.Box.volume_face_mul, hasStrictDerivAt_const_rpow_of_neg, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, log_lt_sub_one_of_pos, HasDerivWithinAt.limsup_norm_slope_le, Irrational.natCast_sub, sum_range_le_log_div, StieltjesFunction.measure_Ici, Chebyshev.primeCounting_sub_theta_div_log_isBigO, NNReal.sub_def, ProbabilityTheory.gaussianPDFReal_def, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, ENNReal.rpow_add_le_mul_rpow_add_rpow, cos_eq_cos_iff, sinh_sq, signedDist_lineMap_lineMap, ProbabilityTheory.variance_eq_sub, intervalIntegral.inv_smul_integral_comp_sub_div, hasDerivWithinAt_taylor_coeff_within, Behrend.exp_neg_two_mul_le, sinh_sub, dist_le_of_mem_Icc, ValueDistribution.characteristic_sub_characteristic_inv_le, integral_sin_pow_even_mul_cos_pow_even, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, sin_two_pi_sub, qaryEntropy_strictAntiOn, exp_sub_cosh, ProbabilityTheory.meas_ge_le_variance_div_sq, norm_fderiv_norm_rpow_le, Angle.angle_eq_iff_two_pi_dvd_sub, exists_taylor_mean_remainder_bound, ProbabilityTheory.gaussianPDFReal_sub, MeasureTheory.integral_posConvolution, curveIntegralFun_trans_of_half_lt, Finset.doubling_lt_golden_ratio, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, ProbabilityTheory.Fernique.normThreshold_eq, deriv_rpow_const, MeasureTheory.measureReal_diff, le_sum_ofDigitsTerm_digits, sin_eq_sin_iff, BoxIntegral.Box.volume_apply', intervalIntegral.inv_mul_integral_comp_sub_div, CircleDeg1Lift.map_sub_nat, MeasureTheory.Submartingale.sum_mul_upcrossingStrat_le, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, tsum_geometric_of_abs_lt_one, HasDerivWithinAt.limsup_slope_norm_le, SzemerediRegularity.edgeDensity_chunk_uniform, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, tendsto_measure_Icc_nhdsWithin_right, abs_norm_sub_norm_le, ProbabilityTheory.covariance_eq_sub, hasDerivWithinAt_arcsin_Ici, unitInterval.coe_symm_eq, hasSum_sq_fourierCoeffOn, CFC.monotoneOn_one_sub_one_add_inv_real, convexOn_descPochhammer_eval, unitary.norm_argSelfAdjoint, ProbabilityTheory.variance_le_sq_of_bounded, ProbabilityTheory.Kernel.measurable_singularPart_fun, norm_div_sub_norm_div_le_norm_div, Angle.coe_sub, derivWithin_rpow_const, exists_polynomial_near_continuousMap, ProbabilityTheory.covariance_sub_left, abs_sin_half, two_mul_cos_mul_cos, taylorWithinEval_succ, abs_sin_eq_sqrt_one_sub_cos_sq, ZetaAsymptotics.term_one, log_div, Orientation.oangle_sign_smul_add_smul_smul_add_smul, eventually_nhdsWithin_sign_eq_of_deriv_pos, MeasureTheory.log_rnDeriv_tilted_left_self, Path.Homotopy.trans_apply, IntervalIntegrable.comp_add_right, ProbabilityTheory.Kernel.withDensity_one_sub_rnDerivAux, diam_eq, tan_pi_div_two_sub, cos_add, Liouville.frequently_exists_num, cos_pi_sub, sin_int_mul_two_pi_sub, ContinuousMap.exists_mem_subalgebra_near_continuous_of_isCompact_of_separatesPoints, volume_Icc, tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, unitary.two_mul_one_sub_le_norm_sub_one_sq, InformationTheory.mul_log_le_toReal_klDiv, sin_half_eq_neg_sqrt, CircleDeg1Lift.translationNumber_le_ceil_sub, hasDerivAt_rpow_const, coe_intFib_eq, intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le_real, intervalIntegral.inv_smul_integral_comp_div_sub, rpowIntegrandββ_apply_mul, ContinuousMap.Homotopy.trans_apply, MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part, StieltjesFunction.measure_Ioi, ZetaAsymptotics.term_tsum_one, isTheta_deriv_rpow_const_atTop, Irrational.sub_intCast, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', HurwitzKernelBounds.F_int_eq_of_mem_Icc, lp.norm_compl_sum_single, MeasureTheory.integral_comp_rpow_Ioi, sin_int_mul_pi_sub, ProbabilityTheory.add_half_inf_sub_mem_Ioo, InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm, ValueDistribution.characteristic_sub_characteristic_inv, inv_sqrt_two_sub_one, mul_sub_lt_image_sub_of_lt_deriv, volume_pi_Ioo, cos_sub_nat_mul_two_pi, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, closedBall_eq_segment, HolderConjugate.conjugate_eq, unique_unit_speed, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.L1.integral_eq_norm_posPart_sub, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, taylor_tendsto, Complex.cpow_inv_two_im_eq_sqrt, ValueDistribution.isBigO_characteristic_sub_characteristic_inv, ZetaAsymptotics.zeta_limit_aux1, pi_gt_sqrtTwoAddSeries, image_sub_le_mul_sub_of_deriv_le, Hyperreal.IsSt.sub, rpow_sub_one, LiouvilleWith.frequently_lt_rpow_neg, volume_real_Ico_of_le, UpperHalfPlane.le_dist_coe, volume_pi_Ioo_toReal, one_sub_mul_le_cos, irrational_natCast_sub_iff, integral_cos_pow_three, isLittleO_exp_comp_exp_comp, abs_cos_sub_cos_le, HasDerivAt.rpow, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, arccos_eq_arctan, IntervalIntegrable.comp_sub_left, intervalIntegral.integral_comp_sub_mul, binEntropy_eq_negMulLog_add_negMulLog_one_sub', NNReal.rpow_sub_one, signedDist_triangle_right, sin_pi_over_two_pow_succ, trapezoidal_integral_one, HasFDerivWithinAt.rpow_const, deriv_arcsin, Complex.isBigO_im_sub_im, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, NNReal.rpow_one_sub', cos_sq', qaryEntropy_strictMonoOn, volume_Ioc, irrational_sub_intCast_iff, ProbabilityTheory.variance_fun_sub, one_sub_lt_exp_neg, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, ZetaAsymptotics.term_sum_of_lt, not_sameRay_iff_abs_lt_norm_sub, irrational_sub_ratCast_iff, rpowIntegrandββ_eq_pow_div, cos_sub_int_mul_pi, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', rpow_sub_one', AkraBazziRecurrence.eventually_one_sub_smoothingFn_nonneg, unitInterval.image_coe_preimage_symm, integral_inv_sq_add_sq, Complex.stolzCone_subset_stolzSet_aux, locallyFinsuppWithin.logCounting_divisor, MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part, ProbabilityTheory.HasSubgaussianMGF.sub_of_indepFun, NNReal.rpow_add_le_mul_rpow_add_rpow, ContractingWith.dist_inequality, sin_sub_int_mul_pi, norm_sub_sub_norm_sub_le_norm_sub, one_sub_goldenConj, integral_rpow, variationOnFromTo.sub_self_monotoneOn, HasFDerivAt.rpow_const, exists_rat_abs_sub_le_and_den_le, tendsto_log_comp_add_sub_log, SimpleGraph.triangle_counting', NNReal.coe_sub_def, EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, binEntropy_one_sub, intervalIntegral.integral_const_of_cdf, cosh_sub, bernoulliFun_one, intervalIntegral.integral_const', nndist_eq, Liouville.exists_pos_real_of_irrational_root, sinh_sub_cosh, volume_real_interval, MeasureTheory.tendsto_eLpNorm_condExp, integral_log, circleMap_zero_div, volume_real_Icc, integral_sqrt_one_sub_sq, ProbabilityTheory.gaussianReal_map_sub_const, ProbabilityTheory.exponentialCDFReal_eq, Gamma_eq_integral, irrational_ratCast_sub_iff, cos_nat_mul_pi_sub, StieltjesFunction.measure_Icc, IntervalIntegrable.comp_add_left, sin_bound, MeasureTheory.le_sub_of_le_upcrossingsBefore, taylor_isLittleO, sin_pi_div_thirty_two, Int.dist_eq, intervalIntegral.inv_mul_integral_comp_div_sub, BoxIntegral.Box.diam_Icc_le_of_distortion_le, trapezoidal_error_le, rpow_sub_intCast', cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, integral_log_from_zero_of_pos, tendstoLocallyUniformlyOn_rpow_sub_one_log, norm_le_gronwallBound_of_norm_deriv_right_le, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, sin_sub_pi, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, ENNReal.inner_le_weight_mul_Lp_of_nonneg, NNReal.inner_le_weight_mul_Lp, Probability.cauchyPDFReal_def', dist_eq, UnitAddCircle.norm_eq, integral_sin, ProbabilityTheory.gaussianReal_const_sub, tan_add', le_integral_rpowIntegrandββ_one, StieltjesFunction.length_eq, LiouvilleWith.exists_pos, pi_lt_sqrtTwoAddSeries, coe_fib_eq', ProbabilityTheory.gaussianReal_sub_const, ContractingWith.dist_le_of_fixedPoint, intervalIntegral.norm_integral_le_of_norm_le_const_ae, nnnorm_fderiv_norm_rpow_le, hasFPowerSeriesOnBall_linear_zero, sin_sub_sin, isTheta_exp_comp_exp_comp, ODE.FunSpace.dist_iterate_next_le, Gamma_mul_Gamma_add_half_of_pos, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, MeasureTheory.eLpNorm'_add_le_of_le_one, Complex.norm_sub_one_sq_eqOn_sphere, exists_ratio_hasDerivAt_eq_ratio_slope, ENNReal.toReal_sub_of_le, integral_sin_pow_odd_mul_cos_pow, Complex.sqrt_eq_real_add_ite, ContractingWith.one_sub_K_pos, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, image_sub_lt_mul_sub_of_deriv_lt, cos_sub_cos, iccLeftChart_extend_zero, cos_nat_mul_two_pi_sub, norm_jacobiThetaβ'_term_le, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, fourierCoeffOn_of_hasDerivAt_Ioo, binEntropy_two_inv_add, one_sub_div_pow_le_exp_neg, sin_arccos, ODE.FunSpace.dist_iterate_next_iterate_next_le, tan_int_mul_pi_sub, BumpCovering.sum_toPartitionOfUnity_eq, Unitary.two_mul_one_sub_le_norm_sub_one_sq, ValueDistribution.abs_characteristic_sub_characteristic_shift_eqO, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, ProbabilityTheory.condVar_bot', unitInterval.volume_Ioc, Irrational.sub_natCast, tendsto_logb_comp_add_sub_logb, abs_cos_eq_sqrt_one_sub_sin_sq, ProbabilityTheory.condVar_of_sigmaFinite, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, Path.trans_apply, norm_sub_le_norm_add, mellin_convergent_iff_norm, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, tsum_sq_fourierCoeffOn, sameRay_iff_norm_sub, ProbabilityTheory.iteratedDeriv_two_cgf, ediam_Ioo, IsPicardLindelof.mul_max_le, integral_sin_mul_cos_sq, HasFDerivWithinAt.rpow, volume_uIoo, MeasureTheory.measureReal_complβ, dist_le_of_approx_trajectories_ODE_of_mem, intervalIntegral.integral_le_sub_of_hasDeriv_right_of_le, real_inner_sub_sub_self, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, HurwitzKernelBounds.F_nat_zero_zero_sub_le, deriv_sigmoid, exists_ratio_deriv_eq_ratio_slope', NNReal.rpow_sub_one', quadratic_root_cos_pi_div_five, rpow_sub_natCast', norm_sub_norm_le, AkraBazziRecurrence.dist_r_b, lp.norm_sub_norm_compl_sub_single, cosh_three_mul, volume_pi_Ico_toReal, InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, ApproximatesLinearOn.closedBall_subset_target, CircleDeg1Lift.lt_map_map_zero, strictMonoOn_one_add_div_one_sub, NNReal.rpow_sub_natCast', HolderConjugate.one_sub_inv_inv, Int.closedBall_eq_Icc, one_sub_sq_div_two_lt_cos, HasDerivWithinAt.rpow_const, ProbabilityTheory.gammaPDF_eq, isBigO_exp_comp_exp_comp, NumberField.mixedEmbedding.logMap_apply, isBigO_deriv_ofReal_cpow_const_atTop, volume_regionBetween_eq_integral', cos_sub_nat_mul_pi, hasDerivAt_norm_rpow, two_mul_arctan_sub_pi, Irrational.intCast_sub, LiouvilleWith.sub_nat_iff, sin_three_mul, Path.extend_symm, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, HolderConjugate.inv_one_sub_inv, fib_golden_conj_exp, two_mul_arctan_add_pi, ProbabilityTheory.strong_law_aux4, Complex.norm_sub_eq_iff, volume_real_Icc_of_le, ProbabilityTheory.covariance_const_sub_left, BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter, abs_dist_sub_le_dist_add_add, Complex.GammaSeq_eq_approx_Gamma_integral, SimpleGraph.triangleRemovalBound_le, ProbabilityTheory.condVar_bot_ae_eq, deriv2_qaryEntropy, hasStrictDerivAt_arcsin, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, intervalIntegral.integral_deriv_comp_mul_deriv, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonpos, integral_zpow, tendsto_sub_mul_tsum_nat_rpow, exists_hasDerivAt_eq_slope, isMIntegralCurveAt_comp_sub, ENNReal.ofReal_sub, sin_pi_div_sixteen, integral_one_div_one_add_sq, integral_one, ArchimedeanClass.stdPart_sub, ProbabilityTheory.lintegral_betaPDF, BohrMollerup.tendsto_logGammaSeq, MeasureTheory.measureReal_compl, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, arctan_inv_of_pos, BoundedContinuousFunction.norm_sub_nonneg, Complex.dist_mk, MeasureTheory.measureReal_diff', cos_sub_two_pi, cos_two_mul, signedDist_right_lineMap, StieltjesFunction.measure_Ioc, cos_int_mul_two_pi_sub_pi, MeasureTheory.llr_tilted_left, intervalIntegral.norm_integral_le_of_norm_le_const, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf, isBigO_deriv_rpow_const_atTop, deriv_rpow_const', Convex.mul_sub_lt_image_sub_of_lt_deriv, sin_sub_nat_mul_pi, HasDerivAt.rpow_const, exists_forall_sphere_dist_add_le_two_sub, exp_artanh, tendsto_measure_Icc_nhdsWithin_right', BumpCovering.exists_finset_toPOUFun_eventuallyEq, intervalIntegral.mul_integral_comp_sub_mul, tan_sub_nat_mul_pi, ProbabilityTheory.meas_ge_le_evariance_div_sq, iter_deriv_rpow_const, HolderConjugate.sub_one_mul_conj, logb_div_base, integral_sin_sq_mul_cos, rpow_one_sub', LiouvilleWith.sub_rat_iff, BoxIntegral.Box.volume_apply, Complex.ofReal_sub, rpow_sub_natCast, hasSum_geometric_of_abs_lt_one, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero, abs_norm_sub_norm_le', sub_le_dist, sin_sq_pi_over_two_pow, ProbabilityTheory.gaussianReal_map_const_sub, stereographic_apply, ProbabilityTheory.variance_sub_const, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, StieltjesFunction.measure_Iio, Stirling.log_stirlingSeq_diff_le_geo_sum, ProbabilityTheory.strong_law_aux1, Behrend.le_sqrt_log, diam_Ico, MonotoneOn.eVariationOn_le, HolderOnWith.of_le, Behrend.two_div_one_sub_two_div_e_le_eight, MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ, isMIntegralCurveAt_comp_add, SimpleGraph.regularityReduced_edges_card_aux, cosh_sub_sinh, volume_real_Ico, StieltjesFunction.outer_Ioc, closedBall_rpow_sub_one_eq_empty_aux, Complex.norm_log_one_sub_inv_sub_self_le, tanh_eq, ValueDistribution.logCounting_zero_sub_logCounting_top_eq_circleAverage_sub_const, exists_ratio_hasDerivAt_eq_ratio_slope', sum_div_pow_sq_le_div_sq, RCLike.mul_re, Besicovitch.SatelliteConfig.exists_normalized_aux1, sin_nat_mul_pi_sub, signedDist_lineMap_right, schnirelmannDensity_le_of_notMem, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, integral_rpow_mul_exp_neg_mul_Ioi, MeasureTheory.Measure.toSignedMeasure_sub_apply, Complex.cpow_inv_two_im_eq_neg_sqrt, ENNReal.lintegral_Lp_add_le_of_le_one, UniformConvexOn.sub, cos_sub_int_mul_two_pi, SzemerediRegularity.edgeDensity_chunk_not_uniform, integral_inv_one_add_sq, EuclideanGeometry.law_cos, ProbabilityTheory.strong_law_aux2, SimpleGraph.triangle_removal, one_div_sub_pow_hasFPowerSeriesOnBall_zero, goldenRatio_sub_goldenConj, AddCircle.norm_eq, Unitary.norm_argSelfAdjoint, fourierCoeffOn_eq_integral, HurwitzKernelBounds.F_nat_zero_le, UpperHalfPlane.dist_coe_le, EuclideanGeometry.dist_affineCombination, ContractingWith.fixedPoint_lipschitz_in_map, curveIntegralFun_symm, volume_regionBetween_eq_integral, BohrMollerup.logGammaSeq_add_one, ZetaAsymptotics.term_welldef, irrational_sub_natCast_iff, unitInterval.one_minus_nonneg, ProbabilityTheory.measure_le_mul_measure_gt_le_of_map_rotation_eq_self, exp_one_near_10, summable_pow_mul_jacobiThetaβ_term_bound, intervalIntegral.integral_comp_div_sub, ProbabilityTheory.Kernel.singularPart_def, ZetaAsymptotics.term_sum_one, ProbabilityTheory.strong_law_aux3, cos_int_mul_two_pi_sub, cantorSequence_eq_self_sub_sum_cantorToTernary, LiouvilleWith.nat_sub, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, dist_le_of_trajectories_ODE, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, taylor_mean_remainder_cauchy, abs_ofDigits_sub_ofDigits_le, strongConvexOn_iff_convex, norm_add_sub_norm_sub_le_two_mul_min, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip', ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, sum_range_sub_log_div_le, exists_deriv_eq_slope, exp_approx_end, CircleDeg1Lift.tendsto_translationNumber, MeasureTheory.le_measureReal_diff, NNReal.dist_eq, ProbabilityTheory.strong_law_aux5, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, Polynomial.sub_one_pow_totient_lt_cyclotomic_eval, StieltjesFunction.measure_Ico, tendsto_euler_sin_prod, sin_pi_div_eight, arctan_add, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, integral_Ioi_inv_one_add_sq, taylor_mean_remainder_bound, Nat.ratSqrt_mem_Ioc, CircleDeg1Lift.map_fract_sub_fract_eq, exp_sub, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, EReal.toReal_sub, rpow_sub_intCast, UpperHalfPlane.dist_coe_center_sq, Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, MeasureTheory.exists_upperSemicontinuous_le_integral_le, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle, MeasureTheory.sub_eq_zero_of_upcrossingsBefore_lt, ProbabilityTheory.gaussianPDFReal_add, ruzsaSzemerediNumberNat_lower_bound, MeasureTheory.llr_smul_right, rpow_sub, unitary.norm_sub_one_sq_eq, deriv_arcsin_aux, StieltjesFunction.length_Ioc, integral_sin_pow, norm_image_sub_le_of_norm_deriv_right_le_segment, arctan_add_eq_sub_pi, StieltjesFunction.measure_Iic, AkraBazziRecurrence.growsPolynomially_one_sub_smoothingFn, fderiv_norm_rpow, UpperHalfPlane.cosh_dist', MeasureTheory.GridLines.T_univ, isTheta_deriv_ofReal_cpow_const_atTop, hasSum_pow_div_log_of_abs_lt_one, rpowIntegrandββ_le_rpow_sub_one, GaussianFourier.verticalIntegral_norm_le, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, Complex.borelCaratheodory, BumpCovering.toPOUFun_eq_mul_prod, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, StrictMonoOn.exists_slope_lt_deriv, fourierCoeffOn_of_hasDerivAt, cosh_sq_sub_sinh_sq, volume_uIoc, EuclideanGeometry.Sphere.IsIntTangent.dist_center, KuratowskiEmbedding.embeddingOfSubset_coe, integral_sin_sq_mul_cos_sq, integral_mul_rpow_one_add_sq, StrictMonoOn.exists_deriv_lt_slope, tendsto_log_nat_add_one_sub_log, ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, exp_bound_div_one_sub_of_interval', norm_sub_pow_two, intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Ico, dist_le_of_le_geometric_of_tendsto, AddCircle.norm_eq', Complex.arg_eq_nhds_of_re_neg_of_im_neg, HurwitzZeta.isBigO_atTop_cosKernel_sub, rothNumberNat_le_ruzsaSzemerediNumberNat', Asymptotics.IsBigOWith.right_le_add_of_lt_one, compact_inner_le_weight_mul_Lp_of_nonneg, interval_average_eq, ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le', volume_Ioo, HolderConjugate.inv_sub_one, BoxIntegral.unitPartition.box.upper_sub_lower, sin_sub_two_pi, cos_sub, Complex.Gamma_def, integral_cos_sq, ContinuousMap.exists_mem_subalgebra_near_continuous_of_separatesPoints, arcsin_eq_arctan, cos_eq_sqrt_one_sub_sin_sq, hasStrictFDerivAt_rpow_of_neg, hasStrictDerivAt_rpow_const, Complex.arg_mul_cos_add_sin_mul_I_sub, Besicovitch.SatelliteConfig.exists_normalized, Icc_eq_closedBall, tan_sub, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, spectralValueTerms_of_lt_natDegree, Complex.abs_cpow_inv_two_im, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', MeasureTheory.integral_norm_eq_pos_sub_neg, unitInterval.two_mul_sub_one_mem_iff, ZLattice.sum_piFinset_Icc_rpow_le, Angle.toReal_coe_eq_self_sub_two_pi_iff, fib_succ_sub_goldenConj_mul_fib, tan_arcsin, norm_mul_sub_norm_div_le_two_mul_min, diam_Ioc, RCLike.mul_re_ax, MeasureTheory.mul_upcrossingsBefore_le, sin_sub_int_mul_two_pi, MeasureTheory.integral_llr_tilted_right, ValueDistribution.log_counting_zero_sub_logCounting_top, norm_sub_mul_self_real, integral_log_from_zero, dist_smul_add_one_sub_smul_le, InnerProductGeometry.sin_angle_add, cos_sub_pi_div_two, integral_cos_sq_sub_sin_sq, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, ZetaAsymptotics.term_of_lt, hasConstantSpeedOnWith_iff_ordered, OpenPartialHomeomorph.univUnitBall_symm_apply, norm_mul_sub_norm_div_le_two_mul, nndist_eq', taylor_mean_remainder_lagrange, Complex.borelCaratheodory_zero, HolderConjugate.sub_one_pos, IsMIntegralCurveAt.comp_add, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, HurwitzZeta.hasSum_nat_cosKernelβ, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, mem_closure_iff, fib_succ_sub_goldenRatio_mul_fib, holderConjugate_iff_eq_conjExponent, Circle.exp_sub_two_pi, Complex.norm_sub_one_sq_eq_of_norm_one, norm_fderiv_norm_id_rpow, MeasureTheory.upcrossingsBefore_pos_eq, rpowIntegrandββ_one_ge_rpow_sub_two, exp_sub_sum_range_isBigO_pow, norm_image_sub_le_of_norm_deriv_le_segment', ProbabilityTheory.covariance_sub_const_left, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonneg', taylor_within_apply, hasDerivWithinAt_arccos_Iic, Complex.approx_Gamma_integral_tendsto_Gamma_integral, IsMIntegralCurve.periodic_of_eq, BohrMollerup.tendsto_logGammaSeq_of_le_one, tan_sub_int_mul_pi, sinh_artanh, ProbabilityTheory.Kernel.rnDeriv_def, gold_pow_sub_gold_pow, cos_pi_div_two_sub, one_sub_goldenRatio, volume_regionBetween_eq_lintegral, exists_forall_closed_ball_dist_add_le_two_mul_sub, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, InnerProductGeometry.sin_angle_mul_norm_mul_norm, smoothTransition.pos_denom, HolderTriple.inv_sub_inv_eq_inv, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStripββ', Complex.arg_neg_eq_arg_sub_pi_iff, integral_pow_abs_sub_uIoc, BumpCovering.sum_toPOUFun_eq, exists_forall_closed_ball_dist_add_le_two_sub, sin_half_eq_sqrt, sin_eq_sqrt_one_sub_cos_sq, fourierCoeffOn_of_hasDeriv_right, two_mul_sin_mul_sin, ProbabilityTheory.covariance_const_sub_right, CircleDeg1Lift.commute_sub_nat, tendsto_harmonic_sub_log_add_one, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, ODE.FunSpace.dist_iterate_next_apply_le, dist_le_of_trajectories_ODE_of_mem, one_div_sub_sq_hasFPowerSeriesOnBall_zero, rpowIntegrandββ_eqOn_mul_rpowIntegrandββ_one, HasFDerivAt.rpow, cos_two_mul', Path.extend_trans_of_half_le, RCLike.normSq_sub, SimpleGraph.triangle_counting, log_le_sub_one_of_pos, exists_int_int_abs_mul_sub_le, four_mul_arctan_inv_5_sub_arctan_inv_239, one_sub_inv_le_log_of_pos, cantorSequence_get_succ, unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, Hyperreal.coe_sub, ValueDistribution.proximity_sub_proximity_inv_eq_circleAverage, cosh_artanh, ProbabilityTheory.tilted_mul_apply_cgf', hasSum_log_sub_log_of_abs_lt_one, RightDerivMeasurableAux.le_of_mem_A, mul_pow_le_nat_floor_pow, MeasureTheory.probReal_compl_eq_one_sub, Affine.Simplex.points_vsub_eulerPoint, bernoulliFun_eval_half, domain_mvt, cos_bound, intervalIntegral.integral_const, hasConstantSpeedOnWith_iff_variationOnFromTo_eq, Int.Matrix.exists_ne_zero_int_vec_norm_le, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, NNReal.rpow_sub_intCast', LiouvilleNumber.remainder_lt', hasDerivWithinAt_arcsin_Iic, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, NNReal.coe_sub, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', hasSum_geometric_of_lt_one, log_doublingGamma_eq, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, two_mul_sin_mul_cos, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, Orientation.inner_mul_areaForm_sub, InnerProductGeometry.angle_neg_left, ediam_Icc, binEntropy_eq_negMulLog_add_negMulLog_one_sub, HolderConjugate.div_conj_eq_sub_one, ConvexOn.lipschitzOnWith_of_abs_le, rpowIntegrandββ_eqOn_pow_div, volume_interval, diam_Icc, ZLattice.exists_finsetSum_norm_rpow_le_tsum, ENNReal.rpow_sum_le_const_mul_sum_rpow, ediam_Ico, HurwitzZeta.hasSum_int_evenKernelβ, sin_sq_pi_over_two_pow_succ, Int.Matrix.exists_ne_zero_int_vec_norm_le', HasStrictFDerivAt.rpow_const, Complex.dist_eq_re_im, Complex.angle_exp_exp, norm_add_sub_norm_sub_le_two_mul, MeasureTheory.BorelCantelli.process_difference_le, Besicovitch.SatelliteConfig.exists_normalized_aux3, Probability.cauchyPDFReal_def, ProbabilityTheory.integral_tilted_mul_eq_cgf, ConcaveOn.lipschitzOnWith_of_abs_le, MeasureTheory.SignedMeasure.rnDeriv_sub, arctan_add_eq_add_pi, hasDerivAt_negMulLog, sin_sub_nat_mul_two_pi, tendsto_logb_nat_add_one_sub_logb, Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, unitInterval.volume_Ioi
|
instZero π | CompOp | 2516 mathmath: ArithmeticFunction.vonMangoldt.residueClass_eq, SchwartzMap.norm_toLp_le_seminorm, IsLocalMaxOn.fderivWithin_nonpos, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, Polynomial.logMahlerMeasure_one, norm_eq_zero, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Angle.abs_toReal_neg_coe_eq_self_iff, Metric.hausdorffDist_empty', BoundingSieve.nu_lt_one_of_dvd_prodPrimes, hasDerivAt_fourier, HurwitzZeta.isBigO_atTop_evenKernel_sub, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, LinearMap.mkContinuousβ_norm_le', NNReal.orderIsoIccZeroCoe_apply_coe_coe, ProbabilityTheory.tendsto_defaultRatCDF_atBot, real_inner_div_norm_mul_norm_eq_neg_one_iff, MeasureTheory.SignedMeasure.toMeasureOfZeroLE_apply, Polynomial.mahlerMeasure_def_of_ne_zero, exists_continuous_sum_one_of_isOpen_isCompact, EulerSine.integral_cos_mul_cos_pow, RCLike.pos_iff_exists_ofReal, MeasureTheory.llr_self, logb_zero_left, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, GroupSeminorm.apply_one, MeasureTheory.SimpleFunc.posPart_sub_negPart, ProbabilityTheory.gaussianReal_map_const_mul, NormedCommGroup.tendsto_nhds_nhds, exists_contMDiffMap_zero_one_of_isClosed, arcosh_bijOn, InformationTheory.integral_llr_add_mul_log_nonneg, Complex.restrictScalars_one_smulRight', MeasureTheory.setIntegral_nonpos_ae, HasCompactSupport.convolution_integrand_bound_left, iInf_of_isEmpty, Mathlib.Meta.Positivity.log_pos_of_isNat, ContDiffBump.nonneg_normed, comap_gauge_nhds_zero_le, NumberField.mixedEmbedding.logMap_one, Quaternion.coeComplex_re, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le, sin_eq_zero_iff_cos_eq, tendsto_norm_sub_self_nhdsNE, ProbabilityTheory.condDistrib_ae_eq_condExp, volume_real_Ioc, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, norm_of_subsingleton', NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, Complex.normSq_pos, ProbabilityTheory.condCDF_nonneg, gauge_def', sqrt_eq_cases, fourierCoeff_tsum_comp_add, Orientation.inner_rotation_pi_div_two_right_smul, contDiffOn_log, ContinuousLinearMap.exists_preimage_norm_le, ExistsContDiffBumpBase.u_support, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, norm_eq_iInf_iff_real_inner_le_zero, SmoothBumpFunction.support_eq_symm_image, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, SimpleGraph.det_lapMatrix_eq_zero, ProbabilityTheory.betaPDF_eq, Metric.exists_continuous_real_forall_closedEBall_subset, EuclideanGeometry.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero, Metric.uniformContinuous_iff_le, taylorWithinEval_hasDerivAt_Ioo, UnitAddCircle.lintegral_preimage, IsLocalMin.hasDerivAt_eq_zero, exists_hasDerivAt_eq_zero, ProbabilityTheory.gaussianReal_const_mul, strictMonoOn_sqrt, ProbabilityTheory.condIndep_iff, deriv_abs, curveIntegrable_segment, MeasureTheory.SimpleFunc.posPart_map_norm, Sbtw.angleβββ_eq_zero, AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, covBySMul_zero, logb_one, MeasureTheory.upcrossingStrat_nonneg, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', lebesgue_number_lemma_of_metric_sUnion, cos_eq_zero_iff, SmoothBumpCovering.mem_support_ind, MeasureTheory.Measure.hausdorffMeasure_zero_singleton, conformalAt_iff, NNReal.coe_indicator, intervalIntegral.integral_hasDerivWithinAt_right, unitInterval.zero_mem, UpperHalfPlane.normSq_pos, ENNReal.toReal_pos_iff, CFC.tendsto_cfc_rpow_sub_one_log, IsLocalMaxOn.hasFDerivWithinAt_nonpos, AkraBazziRecurrence.T_gt_zero', UnitAddCircle.intervalIntegral_preimage, SchwartzMap.pairing_apply_apply, tan_int_mul_pi, sSup_empty, SmoothBumpFunction.rOut_pos, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, inseparable_one_iff_norm, SmoothBumpCovering.IsSubordinate.support_subset, ENNReal.rpow_eq_zero_iff, hasDerivWithinAt_taylorWithinEval, sinh_nonneg_iff, SeminormedGroup.disjoint_nhds, mapsTo_cos_Ioo, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, strictAntiOn_logb, Seminorm.finset_sup_apply, norm_pos_iff, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, Affine.Simplex.sign_excenterWeights_singleton_pos, HasDerivWithinAt.complexToReal_fderiv', circleIntegral_def_Icc, Urysohns.CU.approx_of_mem_C, arctan_nonneg, ContinuousLinearMap.integral_apply, ProbabilityTheory.mgf_nonneg, QuotientGroup.norm_mk_eq_zero, ContDiffBump.support_normed_eq, circleIntegrable_iff, CFC.exists_pos_algebraMap_le_iff, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, iInf_of_not_bddBelow, not_integrableOn_Ioi_cpow, NormedCommGroup.nhds_one_basis_norm_lt, WithSeminorms.mem_nhds_iff, LinearMap.IsPositive.re_inner_nonneg_right, PMF.bernoulli_expectation, toNNReal_le_toNNReal_iff', intervalIntegral.fderiv_integral_of_tendsto_ae, WeakFEPair.hf_modif_int, Quaternion.continuous_imI, LinearMap.IsSymmetric.im_inner_self_apply, Disjoint.exists_cthickenings, ConvexOn.uniformConvexOn_zero, PseudoMetricSpace.dist_self, Quaternion.coeComplex_mul, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, lp.norm_eq_zero_iff, bernoulliFun_eval_half_eq_zero, AkraBazziRecurrence.exists_eventually_const_mul_le_r, ProbabilityTheory.tendsto_condCDF_atBot, NumberField.mixedEmbedding.norm_eq_zero_iff', SchwartzMap.lineDerivOp_fourier_eq, RCLike.pos_iff, log_neg_natCast_nonneg, Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_one, MeasureTheory.Integrable.neg_part, ProbabilityTheory.condVar_const, MeasureTheory.norm_setToFun_le_mul_norm', SmoothPartitionOfUnity.locallyFinite, MeasureTheory.lpNorm_nonneg, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Angle.sin_eq_zero_iff, SeminormFamily.filter_eq_iInf, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, exists_smooth_one_nhds_of_subset_interior, indicator_indepFun_pi_of_prod_bcf, MeasureTheory.Measure.toSphere_apply_aux, Metric.eventually_prod_nhds_iff, mul_log_nonneg, Topology.CWComplex.continuousOn, Complex.arg_div_self, closure_one_eq, expNegInvGlue.not_analyticAt_zero, gauge_smul_of_nonneg, SmoothPartitionOfUnity.nonneg, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, UpperHalfPlane.subset_verticalStrip_of_isCompact, QuasispectrumRestricts.nnreal_iff, UpperHalfPlane.im_pos, sin_arctan_nonneg, covByVAdd_zero, NNReal.canLift, Metric.exists_forall_closedEBall_subset_auxβ, arctan_pos, Metric.sphere_zero, limsup_of_not_isBoundedUnder, HasDerivAt.comp_ofReal, BumpCovering.point_finite, Continuous.integral_hasStrictDerivAt, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, circleAverage_log_norm_sub_constβ, LinearMap.IsPositive.nonneg_eigenvalues, cauchySeq_iff_tendsto_dist_atTop_0, SchwartzMap.bilinLeftCLM_apply, tendsto_cos_pi_div_two, Affine.Simplex.circumradius_nonneg, IsOpen.exists_msmooth_support_eq, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, UpperHalfPlane.specialLinearGroup_apply, ArchimedeanClass.stdPart_zero, EuclideanHalfSpace.ext_iff, IsOpen.exists_smooth_support_eq, SmoothPartitionOfUnity.locallyFinite', BoundedContinuousFunction.indicator_apply, tendsto_norm_nhdsNE_one, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, ProbabilityTheory.mgf_zero_fun, Module.Basis.exists_opNorm_le, Quaternion.imI_coeComplex, UpperHalfPlane.canLift, QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure, NNReal.tendsto_dist_agmSequences_atTop_zero, differentiableOn_log, integral_log_sin_zero_pi_div_two, lintegral_fderiv_lineMap_eq_edist, Subgroup.widthInfty_pos, Path.range_subpathAux, sin_two_pi, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, RCLike.is_real_TFAE, norm_nonneg', ENNReal.ofReal_eq_zero, UniformSpace.Completion.mem_uniformity_dist, Set.infsep_zero_iff_subsingleton_of_finite, ContinuousMultilinearMap.opNorm_zero_iff, one_le_exp_iff, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Topology.RelCWComplex.pairwiseDisjoint', SchwartzMap.laplacianCLM_eq, DirichletCharacter.LSeries_twist_vonMangoldt_eq, HolderTriple.inv_nonneg', MeasureTheory.lpNorm_fun_zero, UnitAddTorus.mFourierSubalgebra_closure_eq_top, pi_nonneg, rpowIntegrandββ_zero_right, UpperHalfPlane.center_zero, Gamma_strictAntiOn_Ioc, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, Matrix.PosDef.eigenvalues_pos, CircleDeg1Lift.dist_map_zero_translationNumber_le, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, IsCompact.exists_thickening_image_subset, ProbabilityTheory.IsCondKernelCDF.nonneg, ContinuousAlternatingMap.norm_def, ValueDistribution.logCounting_eval_zero, sInf_of_not_bddBelow, AkraBazziRecurrence.T_pos, ContDiffBump.pos_of_mem_ball, Metric.tendsto_nhds_nhds, tendsto_norm_div_self, sin_pi, Complex.arg_one, arcsin_nonpos, NumberField.Units.pos_at_place, BumpCovering.support_toPOUFun_subset, arcosh_nonneg, ProbabilityTheory.Kernel.densityProcess_empty, SpectrumRestricts.nnreal_iff, smul_map_diagonal_volume_pi, Polynomial.supNorm_zero, RCLike.nonpos_iff, WeakFEPair.hf_zero', RCLike.nonpos_iff_exists_ofReal, HurwitzKernelBounds.isBigO_atTop_F_int_one, PartitionOfUnity.nonneg', MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAtβ, sinc_eq_dslope, arcosh_zero, Matrix.IsHermitian.rank_eq_rank_diagonal, Tactic.ComputeAsymptotics.WellFormedBasis.head_eventually_pos, Complex.neg_pi_div_two_lt_arg_iff, Chebyshev.theta_eq_zero_of_lt_two, MeasureTheory.tilted_zero, EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two, IsCompact.uniform_oscillation, integral_sin_pow_pos, Affine.Simplex.sign_touchpointWeights_empty, ProbabilityTheory.centralMoment_one, ProbabilityTheory.HasSubgaussianMGF.const_mul, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, artanh_zero, exists_deriv_eq_zero, cos_neg_of_pi_div_two_lt_of_lt, Function.locallyFinsuppWithin.logCounting_nonneg, comap_norm_nhdsGT_zero, QuadraticForm.equivalent_signType_weighted_sum_squared, InformationTheory.leftDeriv_klFun_one, IsClosed.mem_iff_infDist_zero, curveIntegralFun_segment, exists_smooth_tsupport_subset, strictConvexOn_pow, ProbabilityTheory.stieltjesOfMeasurableRat_nonneg, Seminorm.bound_of_continuous_normedSpace, Similar.exists_pos_dist_eq, arctan_eq_zero_iff, sinh_zero, PartitionOfUnity.locallyFinite, integral_bernoulliFun, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, Height.logHeightβ_one, Metric.equicontinuousAt_iff, Complex.integral_circleTransform, sigmoid_nonneg, schnirelmannDensity_setOf_prime, arsinh_zero, Complex.arg_le_pi_div_two_iff, instZeroLEOneClass, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, SemilinearMapClass.bound_of_continuous, BoxIntegral.hasIntegral_GP_pderiv, setIntegral_Ioi_zero_rpow, IsLocalExtr.lineDeriv_eq_zero, EReal.coe_nonpos, ofCauchy_zero, Topology.RelCWComplex.source_eq, CircleDeg1Lift.translationNumber_one, logb_eq_zero, one_add_rpow_hasFPowerSeriesOnBall_zero, arccos_pos, Polynomial.Chebyshev.integral_measureT_eq_integral_cos_of_continuous, monotoneOn_posLog, volume_real_Ioo, Quaternion.instCStarRingReal, RCLike.im_eq_zero_iff_isSelfAdjoint, EuclideanGeometry.angle_self_of_ne, Sbtw.angleβββ_eq_zero, VitaliFamily.eventually_filterAt_iff, indicator_thickening_eventually_eq_indicator_closure, surjOn_log', comap_norm_nhds_zero, image_circleMap_Ioc, MulRingSeminorm.apply_one, sInf_smul_of_nonneg, Complex.cosh_ofReal_im, Metric.inseparable_iff, comap_exp_nhds_zero, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, CStarModule.norm_nonneg, CovBySMul.nonneg, log_list_prod, HasStrictFDerivAt.abs, UpperHalfPlane.coe_pos_real_smul, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, Function.locallyFinsuppWithin.logCounting_eval_zero, QuotientGroup.norm_mk_eq_zero_iff_mem_closure, Topology.RelCWComplex.continuousOn, NumberField.mixedEmbedding.fundamentalCone.expMap_target, continuousOn_log, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, Absorbent.gauge_set_nonempty, exists_continuous_zero_one_of_isClosed, tan_int_mul_pi_div_two, Chebyshev.psi_sub_theta_eq_sum_not_prime, MeasureTheory.L1.setToL1_smul_left, RCLike.toIsStrictOrderedModule, stdSimplex_subset_closedBall, ValueDistribution.logCounting_const_zero, NNReal.rpow_zero_pos, BoxIntegral.unitPartition.integralSum_eq_tsum_div, norm_sub_le_mul_volume_of_norm_lineDeriv_le, Quaternion.linearIsometryEquivTuple_symm_apply, trapezoidal_error_eq, PiLp.dist_eq_card, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, PowerSeries.gaussNorm_zero, RCLike.I_re_ax, Topology.RelCWComplex.union', MeasureTheory.measureReal_empty, norm_curveIntegral_segment_le, fourierCoeff_bernoulli_eq, ArchimedeanClass.stdPart_of_mk_ne_zero, cosh_surjOn, EuclideanGeometry.angle_pos_of_not_collinear, not_continuousAt_deriv_mul_log_zero, RCLike.re_nonneg_of_nonneg, torusMap_zero_radius, EulerSine.integral_cos_mul_cos_pow_aux, SchwartzMap.fourier_lineDerivOp_eq, antitoneOn_cos, sSup_smul_of_nonneg, arccos_one, ENNReal.top_rpow_def, TemperedDistribution.instLineDerivLeftSMulReal, Cardinal.cantorFunctionAux_false, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atBot_zero, cos_two_neg, RCLike.ofReal_nonneg, schnirelmannDensity_finite, singleton_eq_inter_Icc, EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, ValueDistribution.proximity_nonneg, AddSubgroup.norm_trivial_quotient_mk, Metric.mem_closure_iff_infDist_zero, ProbabilityTheory.iCondIndep_iff, Polynomial.mahlerMeasure_nonneg, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, IsMIntegralCurveOn.hasDerivWithinAt, Metric.hausdorffDist_self_closure, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, EuclideanGeometry.Sphere.nonempty_iff, ProbabilityTheory.covariance_fst_snd_prod, SchwartzMap.smulLeftCLM_real_smul, EReal.toReal_nonpos, Finset.infsep_pos_iff_nontrivial, IsMIntegralCurve.periodic_xor_injective, norm_indicator_eq_indicator_norm, not_summable_indicator_one_div_natCast, Metric.uniformEquicontinuous_iff, continuous_tan, norm_add_eq_sqrt_iff_real_inner_eq_zero, strictConcaveOn_log_Iio, UnitAddTorus.mFourierCoeff_toLp, exp_sub_sum_range_succ_isLittleO_pow, IccLeftChart_extend_interior_pos, Complex.ratCast_im, NormedField.exists_norm_lt_one, ProperCone.hyperplane_separation', ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, HasFDerivAt.curveIntegral_segment_source, hasDerivWithinAt_Iic_of_tendsto_deriv, Chebyshev.psi_eq_zero_of_lt_two, ProbabilityTheory.cgf_zero_fun, setIntegral_Ioi_zero_cpow, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, Complex.ofNat_arg, CircleDeg1Lift.map_le_of_map_zero, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, Complex.natCast_im, arccos_eq_zero, CircleDeg1Lift.le_map_of_map_zero, exp_list_sum, MeasureTheory.Lp.norm_zero, Metric.measure_closedBall_pos_iff, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'', strongConcaveOn_zero, norm_one', gauge_zero', norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero, ContinuousMap.HomotopyRel.trans_apply, inner_re_zero_right, ProbabilityTheory.cgf_zero, Metric.hausdorffDist_zero_iff_closure_eq_closure, tendsto_norm_sub_self, Metric.continuous_iff, tendsto_exp_neg_atTop_nhds_zero, liminf_of_not_isBoundedUnder, hasDerivWithinAt_abs, ContDiffBump.nonneg, riemannZeta_im_eq_zero_of_one_lt, MeasureTheory.MemLp.pos_part, SzemerediRegularity.eps_pos, PartitionOfUnity.exists_finset_nhds, eventually_norm_mfderivWithin_symm_extChartAt_lt, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, CircleDeg1Lift.dist_map_map_zero_lt, MeasureTheory.Measure.haar.prehaar_pos, norm_pos_iff', NNReal.coe_eq_zero, Valued.integer.exists_norm_lt_one, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, MeasureTheory.convolution_precompR_apply, ProbabilityTheory.condIndepSets_singleton_iff, Metric.diam_eq_zero_of_unbounded, niven_sin, antilipschitzWith_iff_exists_mul_le_norm', Seminorm.closedBall_zero_eq_preimage_closedBall, EisensteinSeries.r_pos, gauge_eq_zero, EisensteinSeries.r1_pos, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, InnerProductGeometry.sin_angle_nonneg, IsOpen.exists_contMDiff_support_eq_aux, ArithmeticFunction.vonMangoldt.residueClass_apply, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, arccos_image_Icc, torusMap_eq_center_iff, Urysohns.CU.approx_nonneg, continuous_log, mem_closure_one_iff_norm, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, MeasureTheory.measureReal_union_null_iff, Metric.exists_forall_closedEBall_subset_auxβ, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, indiscreteTopology_iff_forall_norm_eq_zero, coe_toNNReal', Multipliable.eventually_bounded_finset_prod, limsSup_of_not_isCobounded, Quaternion.nnnorm_star, VitaliFamily.filterAt_basis_closedBall, norm_zero, finite_integral_rpow_sub_one_pow_aux, RCLike.im_ofReal_pow, holderTriple_iff, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, ProbabilityTheory.covariance_zero_right, arsinh_nonpos_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, EReal.toReal_zero, Complex.abs_re_eq_norm, Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, Complex.GammaIntegral_ofReal, gronwallBound_Ξ΅0_Ξ΄0, CircleDeg1Lift.map_int_of_map_zero, zero_eq_dist, HolderTriple.inv_nonneg, Set.Finite.infsep, NumberField.InfinitePlace.pos_iff, smoothTransition.zero, CompactlySupportedContinuousMap.coe_toRealLinearMap, dist_nonneg, intervalIntegral.integral_hasDerivWithinAt_left, ContinuousLinearMap.bounds_nonempty, MeasureTheory.measureReal_nonneg, SmoothBumpFunction.support_mem_nhds, Asymptotics.bound_of_isBigO_cofinite, differentiableOn_rpow_const, inner_self_im, HolderTriple.left_pos, spectrum_star_mul_self_nonneg, bernoulliFun_eval_one, polarCoord_target, NonarchAddGroupSeminorm.coe_zero, BoxIntegral.TaggedPrepartition.isSubordinate_single, Polynomial.gaussNorm_zero, arsinh_nonneg_iff, SchwartzMap.smulLeftCLM_sum, MeasureTheory.Measure.haar.prehaar_empty, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_pos_eq_zero_of_hasSubGaussianMGF_zero, has_fderiv_at_filter_real_equiv, Metric.mem_nhdsWithin_iff, MeasureTheory.posConvolution_eq_convolution_indicator, unitInterval.symm_projIcc, ContinuousLinearMap.isPositive_def, indicator_norm_le_norm_self, MeasureTheory.Measure.haar.addCHaar_nonneg, Seminorm.gaugeSeminorm_ball, Metric.eventually_nhds_iff, integral_bernoulliFun_eq_zero, logb_zero_left_eq_zero, pi_div_two_pos, Complex.HadamardThreeLines.mem_verticalClosedStrip_of_scale_id_mem_verticalClosedStrip, curveIntegral_segment, InnerProductSpace.Core.normSq_eq_zero_of_eq_zero, tendsto_norm_div_self_nhdsNE, sqrt_le_iff, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atBot_zero, inner_re_zero_left, exists_isMinOn_Gamma_Ioi, tendsto_exp_comp_nhds_zero, ValueDistribution.logCounting_nonneg, ProbabilityTheory.moment_zero, Polynomial.mahlerMeasure_eq_zero_iff, tendsto_norm_div_self_nhdsGE, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Quaternion.coeComplex_add, analyticOn_log, MeasureTheory.Measure.haar.mem_prehaar_empty, Seminorm.ball_zero_eq_preimage_ball, MeasureTheory.lpNorm_measure_zero, Besicovitch.ae_tendsto_rnDeriv, ContDiffBump.hasCompactSupport, ContinuousLinearMap.exists_approx_preimage_norm_le, ValueDistribution.logCounting_const, NormedSpace.normalize_smul, analyticOnNhd_log, coe_expOrderIso_apply, MeasureTheory.MemLp.neg_part, PartitionOfUnity.coe_finsupport, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, InnerProductGeometry.angle_eq_zero_iff, norm_cauchyPowerSeries_le, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, lebesgue_number_lemma_of_metric, ProbabilityTheory.cdf_nonneg, curveIntegral_def, Euclidean.nhds_basis_closedBall, Path.Homotopy.hcomp_half, HasFPowerSeriesOnBall.uniform_geometric_approx, BoundedContinuousFunction.dist_eq, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, summable_jacobiThetaβ_term_fderiv_iff, ProbabilityTheory.covariance_const_left, Metric.tendsto_nhdsWithin_nhds, Metric.exists_smooth_forall_closedBall_subset, QuotientGroup.nhds_one_hasBasis, SmoothBumpFunction.support_eq_inter_preimage, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, Path.Homotopy.hcomp_apply, dist_le_zero, Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter, PartitionOfUnity.exists_finset_nhds_support_subset, RCLike.im_to_real, eq_zero_or_norm_pos, unitInterval.volume_uIcc, cos_nonpos_of_pi_div_two_le_of_le, EReal.toReal_neg, ContinuousAlternatingMap.bounds_bddBelow, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, SchwartzMap.smulLeftCLM_fun_neg, tendsto_cos_neg_pi_div_two, MeasureTheory.crossing_pos_eq, ProbabilityTheory.condExpKernel_ae_eq_condExp', Rat.AbsoluteValue.equiv_on_nat_iff_equiv, Path.Homotopy.transAssocReparamAux_zero, eq_one_or_norm_pos, ENNReal.rpow_zero_pos, iInf_const_zero, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, CircleDeg1Lift.map_map_zero_lt, tan_pi_div_two, HurwitzZeta.continuousOn_cosKernel, ENNReal.toReal_mul_top, MeasureTheory.measureReal_zero, cos_nonneg_of_mem_Icc, Inseparable.dist_eq_zero, SeminormedAddGroup.disjoint_nhds_zero, Height.mulHeight_pos, rpow_zero, arccos_le_pi_div_two, SchwartzMap.pairing_apply, variationOnFromTo.eq_zero_iff_of_le, ContinuousMultilinearMap.isLeast_opNorm, Affine.Simplex.touchpointWeights_empty_pos, zero_mem_cantorSet, Set.Finite.infsep_pos_iff_nontrivial, TorusIntegrable.torusIntegrable_zero_radius, AkraBazziRecurrence.T_nonneg, Metric.uniformity_basis_dist, ContDiffBumpBase.mem_Icc, MultilinearMap.exists_bound_of_continuous, real_inner_div_norm_mul_norm_eq_one_iff, SmoothBumpFunction.tsupport_subset_symm_image_closedBall, WeakFEPair.hk, HolderTriple.pos, CircleDeg1Lift.le_floor_map_map_zero, StrongFEPair.hf_zero', exists_pos_bound_of_bound, Complex.im_nnratCast, NormedCommGroup.uniformity_basis_dist, sign_zero, NNReal.coe_zero, curveIntegral_segment_const, Complex.tan_ofReal_im, HasFDerivAt.abs, Metric.hausdorffDist_empty, self_lt_sinh_iff, Quaternion.continuous_imJ, HolderTriple.nonneg', exists_contMDiffMap_zero_one_nhds_of_isClosed, one_div_one_sub_hasFPowerSeriesOnBall_zero, HasFDerivWithinAt.abs, EuclideanGeometry.Sphere.IsTangentAt.inner_right_eq_zero_of_mem, LinearMap.norm_mkContinuousβ_aux, projIcc_eq_one, norm_sub_eq_sqrt_iff_real_inner_eq_zero, bernoulliFun_endpoints_eq_of_ne_one, NNReal.range_coe, tendsto_measure_Icc, sqrtTwoAddSeries_two, AkraBazziRecurrence.eventually_asympBound_pos, EisensteinSeries.div_linear_zpow_differentiableOn, tendsto_exp_nhds_zero_nhds_one, Subgroup.widthInfty_nonneg, MeasureTheory.hasFDerivAt_convolution_right_with_param, ContDiffBumpBase.support, sin_zero, signedDist_zero, EMetric.exists_forall_closedBall_subset_auxβ, sinh_lt_self_iff, Orientation.oangle_eq_zero_iff_angle_eq_zero, EulerSine.sin_pi_mul_eq, Complex.arg_neg_eq_arg_add_pi_iff, UnitAddCircle.measure_univ, CompactlySupportedContinuousMap.toRealLinearMap_apply, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, zero_eq_arcsin_iff, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, not_irrational_zero, exists_bounded_zero_one_of_closed, exp_eq_one_iff, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, BoundedContinuousFunction.norm_eq, ProbabilityTheory.exponentialPDF_eq, sigmoid_pos, ValueDistribution.characteristic_sub_characteristic_inv_at_zero, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, circleAverage_zero, Quaternion.coeComplex_zero, Irrational.eventually_forall_le_dist_cast_div_of_denom_le, ContinuousLinearMap.bounds_bddBelow, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, RealRMK.integral_rieszMeasure, Hyperreal.coe_nonneg, Complex.abs_im_eq_norm, Metric.isUniformInducing_iff, lp.norm_nonneg', SmoothBumpCovering.locallyFinite', isEquivalent_sin, tendsto_rpow_atTop_of_base_gt_one, tendsto_sigmoid_atBot, Quaternion.instCompleteSpaceReal, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left, NNReal.image_coe_Iio, RCLike.normSq_nonneg, Height.logHeight_one, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul', Height.logHeight_zero, ENNReal.mul_rpow_eq_ite, circleAverage_log_norm_sub_constβ, Metric.infDist_zero_of_mem, ProbabilityTheory.condIndepSet_iff, norm_eq_zero', AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos, ContinuousMultilinearMap.opNorm_nonneg, InnerProductGeometry.angle_self, CircleDeg1Lift.transnumAuxSeq_zero, IsLocalExtr.hasLineDerivAt_eq_zero, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, Set.infsep_eq_iInf, Besicovitch.SatelliteConfig.rpos, SmoothBumpFunction.hasCompactSupport, Polynomial.intervalIntegrable_mahlerMeasure, exists_continuous_one_zero_of_isCompact, Submodule.norm_eq_iInf_iff_real_inner_eq_zero, one_div_sub_hasFPowerSeriesOnBall_zero, AlternatingMap.exists_bound_of_continuous, Metric.infDist_empty, ContDiff.euclidean_dist, norm_sub_eq_zero_iff, MeasureTheory.norm_setToFun_le', Metric.cthickening_zero, Height.zero_le_logHeightβ, Path.truncate_zero_zero, Bundle.ContMDiffRiemannianMetric.pos, arccos_eq_pi_div_two, Gamma_eq_zero_iff, ProbabilityTheory.centralMoment_zero, InnerProductGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi, Mathlib.Meta.Positivity.log_pos_of_isNNRat, AnalyticAt.exists_ball_analyticOnNhd, Affine.Simplex.exradius_nonneg, Height.fun_logHeight_zero, cos_pi_div_two, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_pos, gronwallBound_K0, gauge_closure_zero, ProbabilityTheory.HasSubgaussianMGF.fun_zero, Matrix.PosSemidef.eigenvalues_nonneg, exists_continuous_nonneg_pos, Hyperreal.coe_pos, MeasureTheory.Lp.coeFn_negPart_eq_max, Orientation.inner_rotation_pi_div_two_right, EuclideanGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Metric.nonempty_ball, eulerMascheroniSeq_zero, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, MeasureTheory.Measure.haar.prehaar_nonneg, ProbabilityTheory.Kernel.rnDeriv_toReal_pos, VitaliFamily.ae_tendsto_average_norm_sub, hasFDerivAt_integral_of_dominated_loc_of_lip', Angle.toReal_mem_Ioo_iff_sign_pos, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, IsLocalMinOn.hasFDerivWithinAt_nonneg, ExistsContDiffBumpBase.u_int_pos, Mathlib.Meta.Positivity.log_pos_of_isRat_neg, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, Angle.toReal_nonneg_iff_sign_nonneg, NumberField.mixedEmbedding.realSpace.volume_eq_zero, Bornology.IsBounded.exists_pos_norm_lt', comap_norm_nhdsGT_zero', Metric.thickening_eq_empty_iff, pi_pos, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', log_one, strictConvexOn_mul_log, diam_stdSimplex_of_subsingleton, EReal.sign_coe, Orientation.inner_rotation_pi_div_two_left, ProbabilityTheory.centralMoment_zero_measure, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, gauge_empty, Affine.Simplex.sign_excenterWeights_singleton_neg, Probability.cauchyPDF_pos, ofDigits_SurjOn, MeasureTheory.integral_indicator_one, Metric.ball_zero, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, Metric.nonneg_of_mem_sphere, EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius, SmoothBumpFunction.tsupport_subset_chartAt_source, real_inner_self_nonneg, sin_arctan_pos, ArithmeticFunction.convolution_vonMangoldt_const_one, indiscreteTopology_iff_forall_norm_eq_zero', tendsto_rpow_atTop_of_base_lt_one, schnirelmannDensity_setOf_even, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, ProbabilityTheory.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, ProbabilityTheory.variance_zero_measure, SchwartzMap.smulRightCLM_apply_apply, log_pos, differentiableOn_Gamma_Ioi, differentiableOn_mul_log, arsinh_pos_iff, Complex.arg_lt_pi_div_two_iff, MeasureTheory.setToFun_smul_left, HasDerivAt.complexToReal_fderiv', PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ExistsContDiffBumpBase.u_exists, ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem, Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos, CompactlySupportedContinuousMap.toReal_apply, EuclideanHalfSpace.convex, Polynomial.supNorm_nonneg, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, Metric.uniformContinuousOn_iff, NormedAddGroupHom.mkNormedAddGroupHom_norm_le', IndiscreteTopology.norm_eq_zero, ContinuousMultilinearMap.opNorm_zero, ArithmeticFunction.convolution_vonMangoldt_zeta, MeasureTheory.SignedMeasure.re_toComplexMeasure, NNReal.val_eq_coe, IsCoercive.bounded_below, ContDiffBump.support_eq, preCantorSet_subset_unitInterval, Hyperreal.Infinite.st_eq, HurwitzZeta.continuousOn_evenKernel, Complex.zero_im, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_mem, MonotoneOn.intervalIntegral_deriv_mem_uIcc, mem_closure_zero_iff_norm, Urysohns.CU.lim_of_mem_C, RingNorm.apply_one, SchwartzMap.smulLeftCLM_const, Metric.closure_eq_iInter_cthickening, IsLocalMinOn.hasFDerivWithinAt_eq_zero, sign_eq_zero_iff, BumpCovering.locallyFinite, Complex.arg_eq_zero_iff_zero_le, Set.infsep_pos_iff_nontrivial_of_finite, Metric.exists_ball_inter_eq_singleton_of_mem_discrete, NumberField.mixedEmbedding.neg_of_mem_negA_plusPart, SmoothBumpFunction.mem_Icc, Set.infsep_zero, ProperCone.hyperplane_separation_point, ProbabilityTheory.iCondIndepSets_singleton_iff, continuousOn_logb, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, Orientation.inner_rotation_pi_div_two_left_smul, ProbabilityTheory.mgf_zero, ProbabilityTheory.mgf_zero_measure, ENNReal.toReal_nonneg, sqrtTwoAddSeries_zero_nonneg, Complex.arg_zero, InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, artanh_eq_zero_iff, Topology.CWComplex.union', Quaternion.re_exp, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, not_integrableOn_Ioi_rpow, BoundingSieve.nu_lt_one_of_prime, RCLike.neg_iff, MeasureTheory.Measure.haar.chaar_nonneg, hasDerivWithinAt_taylorWithinEval_at_Icc, integral_comp_abs, Complex.sq_nonneg_iff, ContinuousMap.HomotopyWith.trans_apply, RCLike.sqrt_eq_real_add_ite, sinh_eq_zero, ENNReal.rpow_eq_top_iff, SmoothPartitionOfUnity.mem_finsupport, binEntropy_zero, Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, convergent_of_zero, Set.Icc.eq_convexCombo, logb_injOn_pos, has_antideriv_at_fourier_neg, SmoothBumpFunction.tsupport_mem_nhds, EReal.coe_zero, IsOpen.exists_contMDiff_support_eq, convexOn_log_Gamma, UnitAddTorus.mFourier_norm, posLog_eq_zero_iff, hasFDerivAt_iff_tendsto, Orientation.areaForm'_apply, inner_eq_norm_sq_left_iff, log_eq_zero, Set.infsep_of_fintype, UpperHalfPlane.normSq_denom_pos, MeasureTheory.BorelCantelli.process_zero, ENNReal.ofReal_le_ofReal_iff', RCLike.ofReal_mul_pos_iff, sin_nat_mul_pi, Complex.neg_iff, ArithmeticFunction.log_apply, Wbtw.angleβββ_eq_zero_of_ne, Quaternion.normSq_eq_norm_mul_self, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, tendsto_pow_const_mul_const_pow_of_abs_lt_one, spectralValueTerms_nonneg, mem_nullAddSubgroup_iff, Metric.diam_nonneg, ArithmeticFunction.vonMangoldt_pos_iff, MeasureTheory.Submartingale.ae_tendsto_limitProcess_of_uniformIntegrable, ENNReal.lt_iff_exists_real_btwn, EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left, gauge_of_subset_zero, Polynomial.mahlerMeasure_pos_of_ne_zero, Metric.tendsto_nhdsWithin_nhdsWithin, norm_of_subsingleton, ProbabilityTheory.condExp_set_generateFrom_singleton, two_pi_pos, RCLike.one_im, intervalIntegral.integral_hasStrictFDerivAt, ProbabilityTheory.HasCondSubgaussianMGF.zero, tendsto_comp_exp_atBot, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, InnerProductSpace.Core.inner_self_nonneg, exists_continuous_zero_one_of_isCompact', cfcHom_real_eq_restrict, SeparationQuotient.normedMk_eq_zero_iff, hasDerivWithinAt_taylor_coeff_within, MeasureTheory.SimpleFunc.negPart_map_norm, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, circleIntegral.integral_radius_zero, ArithmeticFunction.vonMangoldt_sum, IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul, SmoothBumpFunction.nhds_basis_support, toNNReal_pos, Metric.hausdorffDist_self_zero, expNegInvGlue.tendsto_polynomial_inv_mul_zero, WithSeminorms.isOpen_iff_mem_balls, arctan_zero, ProbabilityTheory.variance_zero, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, gronwallBound_x0, SeparationQuotient.mk_eq_zero_iff, HurwitzZeta.continuousOn_oddKernel, StieltjesFunction.zero_apply, Seminorm.preimage_metric_closedBall, ValueDistribution.characteristic_eventually_nonneg, PartitionOfUnity.nonneg, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, hasDerivAt_fourier_neg, NNReal.mk_one, Angle.cos_eq_zero_iff, IsPrimitiveRoot.arg_eq_zero_iff, schnirelmannDensity_eq_zero_of_one_notMem, Complex.nonpos_iff, deriv_abs_zero, RCLike.ofReal_im, NumberField.FinitePlace.instNonnegHomClassReal, expNegInvGlue.nonneg, Metric.exists_continuous_real_forall_closedBall_subset, doublingGamma_log_convex_Ioi, hasStrictDerivAt_abs, BoundingSieve.siftedSum_eq_sum_support_mul_ite, ContinuousAlternatingMap.isLeast_opNorm, Complex.arg_lt_pi_iff, SchwartzMap.fourierInv_lineDerivOp_eq, real_inner_add_sub_eq_zero_iff, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, MeasureTheory.Lp.lipschitzWith_pos_part, RCLike.nonneg_iff, Topology.CWComplex.source_eq, RCLike.ofReal_zero, Topology.CWComplex.pairwiseDisjoint', AffineSubspace.signedInfDist_eq_const_of_mem, ProbabilityTheory.IsMeasurableRatCDF.nonneg, HurwitzZeta.continuousOn_sinKernel, GroupSeminorm.zero_apply, BoundedContinuousFunction.norm_eq_zero_of_empty, CStarModule.norm_pos, Complex.arg_eq_pi_div_two_iff, PiNat.isOpen_iff_dist, ProbabilityTheory.gaussianReal_mul_const, iSup_const_zero, CircleDeg1Lift.le_map_map_zero, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, indicator_indepFun_pi_of_bcf, Asymptotics.IsBigO.exists_mem_basis, Bornology.IsBounded.exists_pos_norm_lt, log_div_self, limsup_of_not_isCoboundedUnder, nhds_comap_dist, zero_rpow_eq_iff, AkraBazziRecurrence.bi_min_div_two_pos, CStarModule.norm_zero, sign_mul_nonneg, ContDiffMapSupportedIn.locallyConvexSpace, Probability.cauchyPDFReal_scale_zero, ContinuousMultilinearMap.bounds_bddBelow, CircleDeg1Lift.transnumAuxSeq_def, continuous_logb, gauge_smul_left_of_nonneg, RingSeminorm.eq_zero_iff, eq_zero_rpow_iff, ContinuousLinearMap.norm_def, tendsto_measure_Icc_nhdsWithin_right, Angle.sin_coe_pi, circleAverage_def, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, Set.infsep_nonneg, RCLike.zero_re, ConcaveOn.uniformConcaveOn_zero, EuclideanGeometry.Sphere.isExtTangentAt_center_iff, liminf_of_not_isCoboundedUnder, CStarModule.norm_zero_iff, NormedSpace.equicontinuous_TFAE, hasDerivAt_taylorWithinEval_succ, MeasureTheory.tendsto_sum_indicator_atTop_iff', Besicovitch.exists_goodΞ΄, gauge_pos, ProbabilityTheory.condVar_zero, Affine.Simplex.exradius_singleton_pos, LSeries.norm_term_eq, IsLocalMin.hasLineDerivAt_eq_zero, cosh_zero, concaveOn_negMulLog, range_exp, tendsto_integral_mulExpNegMulSq_comp, Polynomial.logMahlerMeasure_X, continuous_logb', Orientation.oangle_sign_smul_left, HurwitzZeta.sinKernel_zero, Complex.exp_ofReal_im, Height.mulHeightβ_pos, indicator_indepFun_process_of_bcf, SmoothBumpCovering.point_finite, Quaternion.coeComplex_imK, PartitionOfUnity.locallyFinite', Metric.closedBall_zero, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, Complex.slitPlane_eq_union, HurwitzZeta.oddKernel_zero, Path.range_subpath, MeasureTheory.Measure.toSignedMeasure_apply, homeomorphUnitSphereProd_symm_apply_coe, ProbabilityTheory.covarianceBilin_self_nonneg, QuotientAddGroup.nhds_zero_hasBasis, Complex.I_re, MeasureTheory.Measure.haar.mem_addPrehaar_empty, exists_msmooth_support_eq_eq_one_iff, closedBall_zero_eq_Icc, NormedAddGroupHom.SurjectiveOnWith.exists_pos, ProbabilityTheory.condIndepSets_iff, EReal.coe_coe_sign, inner_vsub_vsub_right_eq_dist_sq_left_iff, ProbabilityTheory.condVar_of_not_le, Orientation.oangle_sign_smul_add_smul_smul_add_smul, Complex.normSq_zero, smoothingFun_nonneg, NormedAddGroupHom.bounds_nonempty, CompactlySupportedContinuousMap.integralLinearMap_apply, ProbabilityTheory.iCondIndepSet_iff, Path.Homotopy.trans_apply, Height.fun_logHeight_one, SmoothPartitionOfUnity.coe_finsupport, Finset.coe_infsep, tendsto_log_nhdsGT_zero, Emetric.exists_contMDiffMap_forall_closedBall_subset, GroupSeminorm.coe_zero, cos_arcsin_nonneg, NumberField.mixedEmbedding.convexBodySumFun_nonneg, BumpCovering.nonneg', norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, NormedAddGroupHom.opNorm_zero_iff, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, cos_one_pos, MeasureTheory.Measure.toSphere_apply', TemperedDistribution.instLineDerivSMulReal, ball_zero_eq_Ioo, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, HurwitzZeta.isBigO_atTop_oddKernel, Topology.CWComplex.mapsTo', AbsoluteValue.IsEquiv.log_div_log_pos, UpperHalfPlane.ofComplex_apply_eq_ite, PUnit.norm_eq_zero, LinearMap.re_inner_adjoint_mul_self_nonneg, range_euclideanHalfSpace, mem_parallelepiped_iff, DirichletCharacter.convolution_twist_vonMangoldt, tendsto_log_nhdsLT_zero, zero_rpow, circleAverage_eq_integral_add, EReal.toReal_top, Metric.exists_contMDiffMap_forall_closedBall_subset, convexOn_Gamma, NumberField.mixedEmbedding.norm_nonneg, EMetric.exists_forall_closedBall_subset_auxβ, ProbabilityTheory.gaussianPDFReal_pos, EReal.coe_neg', cos_eq_one_iff_of_lt_of_lt, ContinuousMap.Homotopy.trans_apply, exists_msmooth_zero_iff_one_iff_of_isClosed, Asymptotics.isBigO_atTop_iff_eventually_exists_pos, ProbabilityTheory.covarianceBilinDual_self_nonneg, iSup_of_isEmpty, ProbabilityTheory.mgf_pos', binEntropy_neg_of_one_lt, logb_one_left, Orientation.inner_eq_zero_of_oangle_eq_neg_pi_div_two, ProbabilityTheory.evariance_zero, NormedAddCommGroup.tendsto_nhds_nhds, ProbabilityTheory.Kernel.densityProcess_nonneg, gauge_def, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, MeasureTheory.integral_comp_rpow_Ioi, strictMonoOn_logb, posLog_def, tendsto_self_mul_const_pow_of_abs_lt_one, PseudoMetricSpace.uniformity_dist, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, logb_one_left_eq_zero, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, WeakFEPair.hf_zero, ProbabilityTheory.Kernel.rnDerivAux_nonneg, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, UpperHalfPlane.pos_real_smul_injective, toNNReal_eq_zero, ProbabilityTheory.IsKolmogorovProcess.q_pos, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, ValueDistribution.characteristic_nonneg, LinearMap.isPositive_iff_complex, bernstein_nonneg, cosh_pos, Metric.hasBasis_nhdsSet_cthickening, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atBot, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, binEntropy_one, PartitionOfUnity.locallyFinite_tsupport, exists_hasDerivAt_eq_zero', MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, NormedAddGroupHom.bound, continuous_log', variationOnFromTo.eq_zero_iff_of_ge, SmoothPartitionOfUnity.sum_nonneg, Manifold.riemannianEDist_def, Seminorm.coe_bot, hasDerivAt_circleMap, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.integral_fun_norm_addHaar, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, BumpCovering.locallyFinite_tsupport, Affine.Simplex.height_pos, IsOpen.measure_eq_biSup_integral_continuous, PartitionOfUnity.continuous_finsum_smul, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, SchwartzMap.smulLeftCLM_add, ContinuousLinearEquiv.norm_symm_pos, Metric.closedBall_zero', goldenConj_neg, MultilinearMap.mkContinuousLinear_norm_le', taylor_tendsto, zero_lt_one, tendsto_uniformity_iff_dist_tendsto_zero, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, uniqueDiffOn_Icc_zero_one, ofDigits_nonneg, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, dist_self, pi_gt_sqrtTwoAddSeries, Quaternion.normSq_exp, ContinuousMultilinearMap.integral_apply, ENNReal.toReal_pos, IsSelfAdjoint.im_eq_zero_of_mem_spectrum, differentiableOn_negMulLog, Complex.abs_arg_le_pi_div_two_iff, hasGradientAt_iff_tendsto, InformationTheory.convexOn_klFun, hasDerivAt_fourier, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, arcsin_eq_zero_iff, closure_zero_eq, Besicovitch.ae_tendsto_measure_inter_div, SmoothBumpFunction.c_mem_support, ProbabilityTheory.gaussianReal_map_mul_const, Metric.continuousWithinAt_iff, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, ofDigitsTerm_nonneg, Metric.uniformity_basis_dist_le, IndiscreteTopology.norm_eq_zero', MeasureTheory.Measure.one_le_hausdorffMeasure_zero_of_nonempty, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero, real_inner_self_nonpos, Complex.HadamardThreeLines.diffContOnCl_interpStrip, tan_nat_mul_pi, ContinuousLinearMap.opNorm_subsingleton, Asymptotics.IsBigO.exists_nonneg, Height.mulHeightβ_nonneg, HolderTriple.inv_pos, Topology.RelCWComplex.map_zero_mem_openCell, VitaliFamily.mem_filterAt_iff, Complex.zero_lt_real, Complex.tanh_ofReal_im, bernoulliFun_eval_zero, zero_mem_preCantorSet, AddGroupSeminorm.apply_one, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, MeasureTheory.Measure.instSigmaFiniteElemRealIoiOfNatVolumeIoiPow, self_le_sinh_iff, InnerProductGeometry.angle_nonneg, Quaternion.im_exp, HasCompactSupport.exists_pos_le_norm, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, SchwartzMap.integral_bilinear_laplacian_right_eq_left, Path.Homotopy.transReflReparamAux_zero, NonarchAddGroupSeminorm.apply_one, ExistsContDiffBumpBase.y_nonneg, Quaternion.re_coeComplex, BoundingSieve.weights_nonneg, ENNReal.zero_rpow_def, tendsto_exp_atBot, ProbabilityTheory.condExpKernel_ae_eq_condExp, BoundedContinuousFunction.dist_zero_of_empty, spectralNorm_nonneg, homeomorphUnitSphereProd_apply_fst_coe, Metric.nonempty_closedBall, LiouvilleNumber.remainder_pos, Asymptotics.isBigOWith_zero', negMulLog_one, Orientation.inner_smul_rotation_pi_div_two_right, NonarchAddGroupSeminorm.zero_apply, Orientation.inner_eq_zero_of_oangle_eq_pi_div_two, HasStrictDerivAt.complexToReal_fderiv', sin_pi_over_two_pow_succ, ProbabilityTheory.variance_nonneg, Polynomial.supNorm_def', EReal.coe_nonneg, cosh_bijOn, RCLike.I_to_real, EReal.toReal_image_Ioo_bot_zero, Metric.exists_isCompact_closedBall, ArithmeticFunction.LSeries_vonMangoldt_eq, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, MultilinearMap.mkContinuousMultilinear_norm_le', bijOn_cos, tendsto_pow_atTop_nhds_zero_of_abs_lt_one, tendsto_gauge_nhds_zero_nhdsGE, qaryEntropy_strictMonoOn, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, cos_pos_of_mem_Ioo, Stirling.stirlingSeq'_bounded_by_pos_constant, WithLp.prod_dist_eq_card, HasFPowerSeriesOnBall.uniform_geometric_approx', IsBoundedLinearMap.bound, Hyperreal.coe_eq_zero, Complex.ofReal_eq_zero, arsinh_neg_iff, MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply, not_differentiableAt_inv_log_zero, uniformConcaveOn_zero, goldenRatio_pos, Complex.ofReal_zero, Affine.Simplex.ExcenterExists.sign_touchpointWeights, ZLattice.exists_forall_abs_repr_le_norm, ArithmeticFunction.log_mul_moebius_eq_vonMangoldt, IsOpen.exists_msmooth_support_eq_aux, Sbtw.angleβββ_eq_zero, EuclideanGeometry.Sphere.IsDiameter.left_eq_right_iff, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, integral_log_sin_zero_pi, integrableOn_rpow_mul_exp_neg_rpow, Asymptotics.bound_of_isBigO_nat_atTop, cauchySeq_iff_le_tendsto_0, Affine.Simplex.sign_touchpointWeights_singleton_pos, exists_contMDiff_zero_iff_one_iff_of_isClosed, arsinh_eq_zero_iff, Orientation.oangle_sign_smul_right, Angle.toReal_neg_iff_sign_neg, tendsto_norm_one, log_natCast_nonneg, AkraBazziRecurrence.eventually_one_sub_smoothingFn_nonneg, arcsin_lt_zero, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, tendsto_iff_norm_div_tendsto_zero, ENNReal.orderIsoUnitIntervalBirational_apply_coe, Height.logHeight_nonneg, ProbabilityTheory.paretoPDF_eq, eventually_ball_subset, sqrt_pos, Wbtw.angleβββ_eq_zero_of_ne, AddGroupNorm.apply_one, Set.Finite.infsep_zero_iff_subsingleton, ENNReal.ofReal_pos, Finset.coe_infsep_of_offDiag_empty, ENNReal.toReal_top_mul, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, Module.Basis.norm_nonneg, Metric.isOpen_iff, Euclidean.nhds_basis_ball, ENNReal.toReal_pos_iff_ne_top, arcosh_pos, CircleDeg1Lift.le_ceil_map_map_zero, EMetric.exists_continuous_real_forall_closedBall_subset, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, NormedAddGroupHom.bounds_bddBelow, ProbabilityTheory.iCondIndepSets_iff, tsum_geometric_inv_two_ge, strictConvexOn_rpow, Tactic.ComputeAsymptotics.Majorized.zero, ProperCone.relative_hyperplane_separation, tendsto_log_comp_add_sub_log, BoxIntegral.IntegrationParams.RCond.min, ZLattice.normBound_pos, Hyperreal.coe_zero, sSup_univ, HasDerivAt.ofReal_comp, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, ProbabilityTheory.IsKolmogorovProcess.p_pos, surjOn_log, NNReal.coe_sub_def, PreInnerProductSpace.Core.re_inner_nonneg, UnitAddCircle.measurePreserving_mk, isBoundedSMul, Affine.Simplex.circumradius_pos, Metric.closedBall_eq_empty, continuous_inv, MeasureTheory.tendstoInMeasure_iff_measureReal_enorm, ProbabilityTheory.cgf_zero', AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg, RCLike.ofReal_eq_zero, CompactlySupportedContinuousMap.toReal_add, cantorSet_subset_unitInterval, ProbabilityTheory.moment_zero_measure, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, Module.Basis.parallelepiped_eq_map, ProbabilityTheory.Kernel.HasSubgaussianMGF.zero, Complex.UnitDisc.im_zero, SchwartzMap.hasDerivAt, exists_continuous_zero_one_of_isCompact, limsInf_of_not_isBounded, NNReal.mk_zero, signedDist_self, comap_norm_nhds_one, QuotientAddGroup.norm_mk_eq_zero, volume_real_Icc, hasDerivAtFilter_iff_tendsto, strictMonoOn_arcosh, Set.infsep_singleton, Complex.norm_natCast_cpow_pos_of_pos, Gamma_zero, isBoundedLinearMap_iff, lp.norm_zero, UpperHalfPlane.pos_real_re, Subgroup.strictWidthInfty_nonneg, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, signedDist_smul, ENNReal.tendsto_toReal_zero_iff, Metric.diam_singleton, ContinuousLinearMap.opNorm_zero, ProbabilityTheory.gaussianPDFReal_inv_mul, Orientation.inner_smul_rotation_pi_div_two_left, InformationTheory.klFun_zero, ProbabilityTheory.IndepFun.covariance_eq_zero, UpperHalfPlane.im_pos_of_dist_center_le, rpow_left_injOn, Circle.exp_zero, Complex.arg_neg_iff, LinearMap.mkContinuous_norm_le', sqrtTwoAddSeries_one, ProbabilityTheory.poissonPMFReal_pos, GroupNorm.apply_one, isConformalMap_complex_linear_conj, re_inner_self_pos, Quaternion.continuous_im, EReal.toReal_bot, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, ArithmeticFunction.vonMangoldt.residueClass_nonneg, IsLocalMax.lineDeriv_eq_zero, Mathlib.Meta.Positivity.nnreal_coe_pos, ProbabilityTheory.Fernique.logRatio_pos, MeasureTheory.setIntegral_nonpos_le, Tactic.ComputeAsymptotics.Majorized.const, WithLp.prod_norm_eq_card, EulerSine.integral_cos_pow_eq, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, tendstoLocallyUniformlyOn_rpow_sub_one_log, sqrt_zero, SchwartzMap.tsupport_smulLeftCLM_subset, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, MeasureTheory.integral_condExp_indicator, eventually_norm_symmL_trivializationAt_lt, AkraBazziRecurrence.eventually_atTop_sumTransform_le, cfcβHom_real_eq_restrict, posLog_zero, Angle.toReal_eq_zero_iff, MeasureTheory.lpNorm_zero, MeasureTheory.ComplexMeasure.im_apply, RCLike.nonneg_iff_exists_ofReal, IsLocalMax.hasLineDerivAt_eq_zero, Metric.mem_nhds_iff, tendsto_zero_iff_norm_tendsto_zero, IsLocalMin.deriv_eq_zero, one_lt_exp_iff, indicator_cthickening_eventually_eq_indicator_closure, Affine.Simplex.sign_touchpointWeights_singleton_neg, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, tendsto_gauge_nhds_zero, gauge_nonneg, map_exp_atBot, RCLike.ofReal_nonpos, Metric.mem_uniformity_dist, tendsto_mod_div_atTop_nhds_zero_nat, EuclideanGeometry.Sphere.radius_nonneg_of_mem, dist_pos, Polynomial.sum_derivRootWeight_pos, NumberField.house_nonneg, CompactlySupportedContinuousMap.toNNRealLinear_apply, arctan_lt_zero, ContinuousLinearMap.opNorm_zero_iff, hasDerivAt_fourierChar, ContinuousLinearMap.intervalIntegral_apply, Mathlib.Meta.Positivity.log_nonneg_of_isNegNat, LindemannWeierstrass.integral_exp_mul_eval, circleIntegrable_zero_radius, NNReal.image_coe_Iic, SchwartzMap.smulLeftCLM_neg, InformationTheory.isMinOn_klFun, ArithmeticFunction.vonMangoldt.residueClass_le, Complex.HadamardThreeLines.sSupNormIm_scale_left, Wbtw.angleβββ_eq_zero_of_ne, Quaternion.imK_coeComplex, ArithmeticFunction.moebius_mul_log_eq_vonMangoldt, sin_arctan_eq_zero, Set.infsep_empty, pi_lt_sqrtTwoAddSeries, FormalMultilinearSeries.isLittleO_of_lt_radius, ODE.hasDerivWithinAt_picard_Icc, hasFPowerSeriesOnBall_linear_zero, ProbabilityTheory.gaussianPDFReal_zero_var, NNReal.orderIsoIccZeroCoe_symm_apply_coe, MeasureTheory.Lp.coe_posPart, NormedAddCommGroup.uniformity_basis_dist, RCLike.natCast_im, coe_comp_expOrderIso, EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ENNReal.coe_rpow_def, Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zero, Complex.ofReal_mem_slitPlane, fderiv_norm_smul, MeasureTheory.measureReal_univ_pos, ContinuousAlternatingMap.bounds_nonempty, HasFDerivAt.hasFDerivAt_norm_smul, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos, NumberField.Units.regulator_pos, exists_lt_of_gauge_lt, MeasureTheory.SimpleFunc.map_coe_nnreal_restrict, sigmoid_zero, Complex.normSq_nonneg, AkraBazziRecurrence.eventually_atTop_sumTransform_ge, variationOnFromTo.nonneg_of_le, goldConj_neg, Complex.arg_eq_zero_iff, AkraBazziRecurrence.exists_eventually_r_le_const_mul, HasFDerivWithinAt.curveIntegral_segment_source, Quaternion.inner_def, Complex.abs_arg_lt_pi_div_two_iff, Metric.cthickening_eq_iInter_thickening'', hahnEmbedding_isOrderedModule_rat, MeasureTheory.setIntegral_nonneg_ae, Affine.Simplex.sign_signedInfDist_touchpoint_empty, ProbabilityTheory.covariance_zero_measure, iSup_of_not_bddAbove, Irrational.eventually_forall_le_dist_cast_div, SchwartzMap.pairing_continuous_left, one_add_rpow_hasFPowerSeriesAt_zero, Angle.abs_toReal_coe_eq_self_iff, sInf_empty, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, Complex.sqrt_eq_real_add_ite, SchwartzMap.integralCLM_apply, NonarchAddGroupSeminorm.toZeroHom_eq_coe, AddCircle.coe_real_preimage_closedBall_period_zero, circleIntegrable_sub_zpow_iff, HolderTriple.right_pos, mem_nullSubmodule_iff, ContDiffBump.tsupport_eq, UniformSpace.Completion.uniformity_dist, ContractingWith.one_sub_K_pos, RCLike.im_eq_zero_of_le, Polynomial.mahlerMeasure_zero, Complex.not_le_zero_iff, dist_0_eq_abs, not_DifferentiableAt_log_mul_zero, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, exp_lt_one_iff, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, CircleDeg1Lift.tendsto_translation_numberβ, NumberField.mixedEmbedding.volume_eq_zero, RCLike.normSq_pos, Complex.pos_iff, Wbtw.angleβββ_eq_zero_of_ne, sInf_univ, cos_pi_over_two_pow, Asymptotics.isBigO_const_left_iff_pos_le_norm, preCantorSet_zero, SmoothBumpFunction.coe_def, Seminorm.zero_or_exists_apply_eq_finset_sup, SchwartzMap.lineDerivOp_fourierInv_eq, Hyperreal.infinitesimal_real_iff, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, EuclideanGeometry.Sphere.mul_dist_eq_zero_of_mem_sphere, cos_eq_zero_iff_sin_eq, Path.truncate_zero_one, Affine.Simplex.sign_excenterWeights_empty, sign_mul_pos_of_ne_zero, MeasureTheory.Lp.norm_exponent_zero, EuclideanGeometry.inner_nonneg_of_dist_le_radius, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MeasureTheory.Measure.haar.addPrehaar_nonneg, interior_range_modelWithCornersEuclideanHalfSpace, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, ExistsContDiffBumpBase.y_smooth, Metric.hasBasis_nhdsSet_thickening, unitInterval.coe_pos, tendsto_logb_comp_add_sub_logb, sq_sqrt', MeasureTheory.L1.norm_setToL1_le_mul_norm', SmoothBumpCovering.locallyFinite, mk_zero, GroupSeminorm.map_one', ProbabilityTheory.variance_of_not_memLp, ContinuousLinearMap.isPositive_def', SmoothBumpFunction.isOpen_support, Valued.norm_nonneg, ProbabilityTheory.Fernique.logRatio_nonneg, exists_deriv_eq_zero', not_differentiableAt_rpow_const_zero, inner_vsub_vsub_left_eq_dist_sq_right_iff, variationOnFromTo.nonpos_of_ge, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, EulerSine.antideriv_cos_comp_const_mul, ProbabilityTheory.condVar_of_sigmaFinite, torusIntegral_radius_zero, InformationTheory.klFun_one, curveIntegral_eq_intervalIntegral_deriv, Complex.sinh_ofReal_im, Path.trans_apply, NormedAddGroupHom.opNorm_nonneg, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, IsClosed.hausdorffDist_zero_iff_eq, norm_le_zero_iff, MeasureTheory.HasFiniteIntegral.max_zero, ArithmeticFunction.vonMangoldt_nonneg, NumberField.FinitePlace.pos_iff, tendsto_closedBall_smallSets, ArithmeticFunction.sum_moebius_mul_log_eq, MeasureTheory.Integrable.pos_part, CPolynomialAt.exists_ball_cpolynomialOn, NNReal.forall, EReal.coe_pos, ENNReal.rpow_zero, surjOn_cos, SmoothPartitionOfUnity.exists_pos_of_mem, Archimedean.embedRealFun_zero, MeasureTheory.Measure.haar.addPrehaar_pos, conformalFactorAt_pos, ENNReal.toReal_zero, Topology.RelCWComplex.mapsTo, quadratic_root_cos_pi_div_five, Asymptotics.IsBigOWith.exists_nonneg, intervalIntegral.fderivWithin_integral_of_tendsto_ae, one_add_rpow_hasFPowerSeriesAt_zero, cosh_strictMonoOn, ProbabilityTheory.iCondIndepFun_iff, Matrix.PosSemidef.re_dotProduct_nonneg, Complex.integrable_pow_mul_norm_one_add_mul_inv, ArithmeticFunction.vonMangoldt_apply, exists_smooth_zero_one_of_isClosed, sqrtTwoAddSeries_lt_two, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atBot_zero, Quaternion.inner_self, sign_apply_eq, EulerSine.antideriv_sin_comp_const_mul, strictConcaveOn_sqrt, InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, arcsin_nonneg, Complex.zero_le_real, EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_right, MeasureTheory.ae_mem_limsup_atTop_iff, ProbabilityTheory.HasCondSubgaussianMGF.fun_zero, comap_exp_nhdsGT_zero, CircleDeg1Lift.lt_map_map_zero, ZetaAsymptotics.term_nonneg, cauchy_zero, RCLike.ofReal_pos, tendsto_mul_add_inv_atTop_nhds_zero, intervalIntegral.integral_hasFDerivWithinAt, Chebyshev.theta_nonneg, ContinuousLinearMap.isPositive_iff_complex, smoothTransition.nonneg, InformationTheory.strictConvexOn_klFun, exists_contMDiff_support_eq_eq_one_iff, NNReal.coe_nonneg, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, ProbabilityTheory.gammaPDF_eq, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, Quaternion.norm_exp, MeasureTheory.L1.norm_setToL1_le', EuclideanGeometry.hasFDerivAt_inversion, Absorbs.exists_pos, RCLike.ofNat_im, Metric.eventually_nhds_prod_iff, strictMonoOn_log, Finset.infsep_zero_iff_subsingleton, AkraBazziRecurrence.a_pos, hasDerivAt_ofReal_cpow_const, ArithmeticFunction.vonMangoldt_apply_one, Mathlib.Meta.Positivity.log_nonneg_of_isNat, EReal.coe_eq_zero, Metric.cthickening_max_zero, Asymptotics.IsBigOWith.exists_pos, not_continuousAt_deriv_qaryEntropy_zero, NumberField.mixedEmbedding.unit_smul_eq_zero, sinc_zero, arccos_lt_pi_div_two, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, ProbabilityTheory.variance_dirac, inseparable_zero_iff_norm, Complex.UnitDisc.re_zero, Complex.mem_slitPlane_iff, log_intCast_nonneg, tan_eq_zero_iff, IsUnifLocDoublingMeasure.scalingScaleOf_pos, HasFDerivAt.curveIntegral_segment_source', zero_mem_lowerBounds_smoothingSeminormSeq_range, SeminormedGroup.disjoint_nhds_one, IsCompact.exists_cthickening_subset_open, NumberField.mixedEmbedding.norm_eq_zero_iff, ArchimedeanClass.stdPart_nonneg, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, SchwartzMap.derivCLM_apply, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', RCLike.ratCast_im, integrableOn_Ioi_exp_neg_mul_sq_iff, NumberField.mixedEmbedding.normAtPlace_nonneg, Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, tendsto_mulIndicator_thickening_mulIndicator_closure, log_nonneg, HasCompactMulSupport.exists_pos_le_norm, gauge_lt_eq', circleMap_eq_center_iff, RCLike.conj_eq_iff_im, BoundedContinuousFunction.dist_set_exists, intervalIntegral.integral_hasDerivAt_right, indicator_indepFun_of_bcf, isConformalMap_iff, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, NormedCommGroup.nhds_basis_norm_lt, Topology.RelCWComplex.disjointBase', Function.locallyFinsuppWithin.logCounting_mono, MeasureTheory.lpNorm_of_isEmpty, riemannZeta_re_pos_of_one_lt, Height.logHeightβ_zero, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, CircleDeg1Lift.ceil_map_map_zero_le, MeasureTheory.tilted_zero', NumberField.mixedEmbedding.logMap_real, ZSpan.fundamentalDomain_pi_basisFun, comap_gauge_nhds_zero, Affine.Simplex.touchpointWeights_singleton_neg, ProperCone.mem_innerDual, MeasureTheory.Submartingale.ae_tendsto_limitProcess, Metric.exists_ball_subset_ball, Metric.eventually_notMem_cthickening_of_infEdist_pos, Bundle.RiemannianMetric.pos, IsOpen.exists_contDiff_support_eq, Angle.sin_zero, exists_continuousMap_one_of_isCompact_subset_isOpen, Polynomial.logMahlerMeasure_zero, Complex.HadamardThreeLines.scale_bddAbove, PiNat.dist_nonneg, EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi, mem_nullSubgroup_iff, Complex.log_eq_integral, BoundedContinuousFunction.add_norm_nonneg, tendsto_indicator_cthickening_indicator_closure, ProbabilityTheory.lintegral_betaPDF, toNNReal_zero, Chebyshev.psi_eq_sum_Icc, MeasureTheory.exists_null_frontiers_thickening, ProbabilityTheory.mgf_zero', EReal.toReal_image_Ioo_zero_top, Complex.sq_nonpos_iff, circleAverage_eq_intervalAverage, ContinuousMultilinearMap.bound, MeasureTheory.Lp.coeFn_negPart, dist_eq_zero, Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, CompactlySupportedContinuousMap.toReal_smul, Submodule.re_inner_starProjection_nonneg, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, BoundedContinuousFunction.norm_sub_nonneg, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, EuclideanGeometry.Sphere.isIntTangentAt_center_iff, Angle.tan_coe_pi, Affine.Simplex.touchpointWeights_eq_zero, spectralValueTerms_of_natDegree_le, ArchimedeanClass.stdPart_eq_zero, ZLattice.covolume_pos, integral_sin_pow_succ_le, limsInf_of_not_isCobounded, smoothTransition.zero_iff_nonpos, Delone.DeloneSet.subset_ball_singleton, tendsto_div_pow_mul_exp_add_atTop, MeasureTheory.Measure.haar.chaar_empty, circleIntegrable_def, sinh_neg_iff, InformationTheory.convexOn_Ioi_klFun, Path.extend_zero, hasFDerivAt_integral_of_dominated_of_fderiv_le, PiTensorProduct.projectiveSeminormAux_nonneg, Metric.eventually_notMem_thickening_of_infEdist_pos, ContinuousMap.Homotopy.extend_zero, BumpCovering.nonneg, Metric.eventually_nhds_iff_ball, NormedAddGroupHom.lipschitz, SeparationQuotient.mk_eq_one_iff, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, Complex.range_norm, SchwartzMap.decay, Complex.zero_re, exp_nonneg, max_norm_root_eq_spectralValue, Stirling.stirlingSeq'_pos, Module.Basis.parallelepiped_map, IsLocalMaxOn.fderivWithin_eq_zero, strictConcaveOn_sin_Icc, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg', MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative, tendsto_one_iff_norm_tendsto_zero, Metric.uniformity_eq_comap_nhds_zero, ENNReal.trichotomy, WeakFEPair.hg_int, tendsto_measure_Icc_nhdsWithin_right', EuclideanGeometry.Sphere.isTangentAt_center_iff, NumberField.mixedEmbedding.normAtAllPlaces_nonneg, Metric.eventually_notMem_cthickening_of_infEDist_pos, continuousOn_tan, sSup_def, eventually_closedBall_subset, variationOnFromTo.eq_zero_iff, NormedSpace.sphere_nonempty, Complex.not_lt_zero_iff, Metric.diam_pos, NNReal.coe_image, AkraBazziRecurrence.b_pos, Sbtw.angleβββ_eq_zero, exists_continuous_one_zero_of_isCompact_of_isGΞ΄, Stirling.stirlingSeq_zero, CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos, MeasureTheory.lpNorm_of_not_aestronglyMeasurable, Metric.infDist_pos_iff_notMem_closure, circleIntegrable_sub_inv_iff, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, RCLike.ofReal_mul_neg_iff, CuspFormClass.exp_decay_atImInfty', Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, re_inner_self_nonpos, LinearMap.IsSymmetric.im_inner_apply_self, Metric.uniformContinuousOn_iff_le, absolutelyContinuousOnInterval_iff, arcsin_pos, curveIntegralFun_trans_aeeq_left, SmoothPartitionOfUnity.finite_tsupport, WeakFEPair.hf_int, ContDiffAt.exists_eventually_eq_hasDerivAt, hasFDerivAtFilter_iff_tendsto, NNReal.coe_pos, InnerProductSpace.Core.cauchy_schwarz_aux', EulerSine.integral_cos_pow_pos, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, arctan_le_zero, ENNReal.ofReal_zero, cos_nonneg_of_neg_pi_div_two_le_of_le, CovByVAdd.nonneg, MeasureTheory.SignedMeasure.zero_mem_measureOfNegatives, Angle.sign_toReal, ContinuousLinearMap.opNorm_nonneg, ContDiffBump.hasCompactSupport_normed, sin_sq_pi_over_two_pow, Metric.ball_eq_empty, IsCompact.measure_eq_biInf_integral_hasCompactSupport, UpperHalfPlane.I_re, circleMap_zero_radius, CompactlySupportedContinuousMap.nnrealPart_apply, Complex.toMatrix_conjAe, Cardinal.cantorFunctionAux_zero, ArithmeticFunction.vonMangoldt_eq_zero_iff, MeasureTheory.levyProkhorovDist_self, strictAntiOn_log, tendsto_pow_logb_div_mul_add_atTop, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, TestFunction.instLocallyConvexSpaceReal, HolderTriple.pos', UpperHalfPlane.im_inv_neg_coe_pos, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty', algNormFromConst_def, Subgroup.strictWidthInfty_pos_iff, Complex.neg_pi_div_two_le_arg_iff, PartitionOfUnity.sum_nonneg, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBot, Complex.canLift, norm_sub_le_mul_volume_of_norm_fderiv_le, Metric.eventually_notMem_thickening_of_infEDist_pos, UpperHalfPlane.val_J, Metric.diam_subsingleton, Besicovitch.tendsto_filterAt, Module.Basis.norm_zero, SmoothBumpFunction.tsupport_subset_extChartAt_source, CompactlySupportedContinuousMap.toReal_nonneg, logb_zero, ProbabilityTheory.Kernel.densityProcess_fst_univ, SzemerediRegularity.coe_m_add_one_pos, Path.extend_extends', strictConvexOn_zpow, Besicovitch.BallPackage.rpos, Seminorm.coe_zero, hasDerivAt_ofReal_cpow_const', SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable, Orientation.areaForm_apply_self, MeasureTheory.Lp.norm_measure_zero, Affine.Simplex.excenterWeights_empty_pos, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, smul_iSup_of_nonneg, InnerProductGeometry.cos_eq_one_iff_angle_eq_zero, AlternatingMap.mkContinuousAlternating_norm_le_max, volume_real_Ico, BoundingSieve.nu_pos_of_dvd_prodPrimes, SchwartzMap.seminorm_apply, variationOnFromTo.eq_left_iff, Complex.conj_eq_iff_im, NNReal.coeNNRealReal_zero, AddGroupSeminorm.zero_apply, EReal.toReal_eq_zero_iff, AddGroupSeminorm.coe_zero, NNReal.mk_natCast, unitInterval.nonneg, Metric.controlled_of_isUniformEmbedding, ProbabilityTheory.Kernel.density_nonneg, Metric.thickening_nonempty_iff, tendsto_measure_cthickening_of_isCompact, posLog_one, BoundingSieve.nu_pos_of_prime, cauchySeq_bdd, ProbabilityTheory.condVar_of_not_sigmaFinite, nnreal_trichotomy, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, UnitAddTorus.span_mFourier_closure_eq_top, Metric.isUniformEmbedding_iff, SchwartzMap.tsupport_derivCLM_subset, RCLike.normSq_zero, Chebyshev.psi_nonneg, MeasureTheory.Lp.norm_eq_zero_iff, sin_eq_zero_iff, strictConcave_binEntropy, tendsto_norm_nhdsNE_zero, sin_arctan_le_zero, Complex.sin_ofReal_im, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, RCLike.neg_iff_exists_ofReal, Seminorm.preimage_metric_ball, Affine.Simplex.touchpointWeights_singleton_pos, EisensteinSeries.eisSummand_extension_differentiableOn, DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal, isMIntegralCurveAt_iff', exp_zero, BoundingSieve.multSum_eq_main_err, HolderTriple.one_div_pos, norm_div_eq_zero_iff, Complex.HadamardThreeLines.scale_diffContOnCl, Metric.nhds_basis_ball, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, Set.infsep_pos, Subgroup.strictWidthInfty_pos, one_div_sub_pow_hasFPowerSeriesOnBall_zero, Quaternion.coeComplex_imJ, exists_isMIntegralCurve_iff_exists_isMIntegralCurveOn_Ioo, qaryEntropy_zero, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, ENNReal.ofReal_lt_ofReal_iff', strictConcaveOn_log_Ioi, homeomorphUnitSphereProd_apply_snd_coe, sinc_apply, tendsto_pow_const_div_const_pow_of_one_lt, integral_sin_pow_odd, similar_iff_exists_pos_pairwise_dist_eq, NNReal.rpow_zero, Orientation.oangle_sign_smul_add_smul_right, RCLike.normSq_eq_zero, strictAntiOn_cos, HolderTriple.one_div_nonneg', IsLocalExtr.hasDerivAt_eq_zero, Complex.HadamardThreeLines.sSupNormIm_nonneg, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, Metric.diam_empty, Quaternion.imJ_coeComplex, Complex.ofReal_im, Metric.infDist_zero_of_mem_closure, unitInterval.one_minus_nonneg, RCLike.I_re, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, spectralValue_nonneg, EuclideanGeometry.dist_smul_vadd_eq_dist, exp_le_one_iff, integrable_exp_neg_mul_sq_iff, SmoothPartitionOfUnity.mem_fintsupport_iff, EuclideanGeometry.Sphere.center_mem_iff, Emetric.exists_smooth_forall_closedBall_subset, MeasureTheory.measureReal_zero_apply, Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos, logb_pos, not_summable_one_div_on_primes, WeakFEPair.f_modif_aux1, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, ValueDistribution.logCounting_eventually_nonneg, RCLike.ofReal_im_ax, Asymptotics.isBigO_iff'', Asymptotics.IsBigO.id_rpow_of_le_one, NormedAddCommGroup.nhds_zero_basis_norm_lt, smoothTransition.projIcc, Angle.coe_zero, indicator_indepFun_process_of_prod_bcf, NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamily, MeasureTheory.Measure.volumeIoiPow_apply_Iio, Quaternion.coeComplex_imI, Metric.continuousAt_iff, UpperHalfPlane.pos_real_im, Metric.nhds_basis_closedBall, SchwartzMap.smulLeftCLM_sub, MeasureTheory.Martingale.ae_eq_condExp_limitProcess, SchwartzMap.smulLeftCLM_apply_apply, arcsin_zero, InnerProductSpace.Core.inner_self_im, Matrix.IsHermitian.eigenvalues_eq_zero_iff, intervalIntegral.integral_hasStrictDerivAt_right, strongConvexOn_zero, SchwartzMap.fourier_fderivCLM_eq, MeasureTheory.eLpNorm'_measure_zero_of_exponent_zero, PartitionOfUnity.finite_tsupport, Units.norm_pos, exp_approx_end, ENNReal.toReal_ofReal_eq_iff, AbsoluteValue.isEquiv_iff_exists_rpow_eq, HolderTriple.one_div_pos', NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSet, ArithmeticFunction.vonMangoldt_le_log, intervalIntegral.integral_hasStrictDerivAt_left, cosPartialEquiv_source, IsLocalMaxOn.hasFDerivWithinAt_eq_zero, IsCompact.exists_thickening_subset_open, zero_lt_one_add_norm_sq, MeasureTheory.Lp.coeFn_posPart, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, NNReal.tendsto_coe', cosh_injOn, Quaternion.coe_ofComplex, NNReal.zero_le_coe, NonarchAddGroupNorm.apply_one, fourierCoeff_liftIoc_eq, SeminormedSpace.Core.norm_nonneg, EuclideanGeometry.angle_nonneg, Metric.pos_of_mem_ball, polynomialFunctions_closure_eq_top', sinh_pos_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero', Complex.nonneg_iff, MeasureTheory.HasFiniteIntegral.min_zero, TestFunction.instContinuousSMulReal, IsLocalMinOn.fderivWithin_nonneg, Complex.im_eq_zero_iff_isSelfAdjoint, Subgroup.widthInfty_pos_iff, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul, range_modelWithCornersEuclideanHalfSpace, ContinuousMapZero.toNNReal_neg_smul, ProbabilityTheory.condVar_of_not_integrable, Complex.arg_nonneg_iff, MeasureTheory.sub_eq_zero_of_upcrossingsBefore_lt, AddMonoidHom.mkNormedAddGroupHom_norm_le', integral_exp_neg_Ioi_zero, ContinuousMultilinearMap.bounds_nonempty, gauge_smul_left, Affine.Simplex.sum_excenterWeights, sqrt_nonneg, HasCompactSupport.norm, ENNReal.toReal_top, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, hasGradientWithinAt_iff_tendsto, AddGroupSeminorm.map_zero', Matrix.IsHermitian.rank_eq_card_non_zero_eigs, Hyperreal.stdPart_omega, inner_self_nonneg, HasFDerivWithinAt.curveIntegral_segment_source', ArithmeticFunction.LSeriesSummable_vonMangoldt, ProbabilityTheory.HasSubgaussianMGF.zero, ProperCone.hyperplane_separation, IsLocalMin.lineDeriv_eq_zero, MeasureTheory.tilted_eq_withDensity_nnreal, spectralNorm_zero_lt, exists_contDiff_tsupport_subset, EReal.toReal_pos, Similar.exists_pos_pairwise_dist_eq, ContDiffBump.nonneg', MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, arccos_zero, Orientation.inner_smul_rotation_pi_div_two_smul_left, NumberField.mixedEmbedding.fundamentalCone.zero_mem_compactSet, hasDerivAt_iff_tendsto, Polynomial.instTwoPiPos, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, integral_gaussian_Ioi, SchwartzMap.smulLeftCLM_ofReal, spectralValue_eq_zero_iff, projIcc_eq_zero, gold_pos, intervalIntegral.integral_hasDerivAt_left, PartitionOfUnity.mem_fintsupport_iff, ExistsContDiffBumpBase.w_nonneg, Complex.neg_ofReal_mem_slitPlane, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, ContDiffBump.tsupport_normed_eq, Orientation.inner_smul_rotation_pi_div_two_smul_right, spectralNorm_zero, cos_arctan_pos, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, CircleIntegrable.out, Irrational.eventually_forall_le_dist_cast_rat_of_den_le, Quaternion.instNormOneClassReal, ZLattice.tsumNormRPowBound_pos, curveIntegral_def', MeasureTheory.SignedMeasure.null_of_totalVariation_zero, hasDerivAt_fourierIntegral, mulIndicator_cthickening_eventually_eq_mulIndicator_closure, Complex.natCast_arg, ContinuousAlternatingMap.bound, EuclideanGeometry.inner_pos_of_dist_lt_radius, ProbabilityTheory.mgf_pos, MeasureTheory.Submartingale.memLp_limitProcess, ArithmeticFunction.vonMangoldt_mul_zeta, IsBoundedBilinearMap.bound, RingSeminorm.apply_one, ContinuousMapZero.toNNReal_smul, SmoothBumpFunction.support_subset_source, Bornology.IsBounded.exists_pos_norm_le, expNegInvGlue.zero, posLog_nonneg, arcosh_eq_zero_iff, ProbabilityTheory.covarianceBilinDual_of_not_memLp, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, TFAE_exists_lt_isLittleO_pow, isSquare_iff, Metric.diam_zero, InnerProductGeometry.angle_eq_pi_iff, deriv_circleMap_eq_zero_iff, CircleDeg1Lift.floor_map_map_zero_le, Complex.exists_cthickening_tendstoUniformlyOn, inner_vsub_vsub_left_eq_dist_sq_left_iff, tendsto_log_nat_add_one_sub_log, ProbabilityTheory.gaussianPDFReal_mul, exists_tsupport_one_of_isOpen_isClosed, EuclideanGeometry.inversion_eq_center', ContinuousMultilinearMap.norm_def, Affine.Simplex.inradius_pos, NNReal.coe_list_sum, MulRingNorm.apply_one, isConformalMap_complex_linear, sSup_of_not_bddAbove, SchwartzMap.smulLeftCLM_apply, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, expPartialHomeomorph_target, ExistsContDiffBumpBase.u_compact_support, Quaternion.linearIsometryEquivTuple_apply, Polynomial.tendsto_div_exp_atTop, CFC.rpow_zero, ExistsContDiffBumpBase.u_nonneg, HurwitzZeta.isBigO_atTop_cosKernel_sub, log_pos_of_lt_neg_one, EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere, arccos_nonneg, IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul, tendsto_pow_log_div_mul_add_atTop, Metric.uniformity_edist_aux, ProbabilityTheory.condIndepFun_iff, Topology.CWComplex.mapsTo, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, NonarchAddGroupSeminorm.add_le_max', IsLocalMax.hasDerivAt_eq_zero, TemperedDistribution.derivCLM_apply_apply, gauge_lt_eq, NormedAddGroupHom.norm_def, TorusIntegrable.function_integrable, EReal.coe_ennreal_ofReal, NNReal.exists, negMulLog_zero, DirichletCharacter.LFunction_isBigO_horizontal, BumpCovering.locallyFinite', Metric.continuousOn_iff, hasDerivWithinAt_Ici_of_tendsto_deriv, NumberField.Units.sum_mult_mul_log, tendsto_log_nhdsNE_zero, norm_div_pos_iff, MeasureTheory.weightedSMul_smul_measure, norm_le_zero_iff', intervalIntegral.integral_hasFDerivAt, PartitionOfUnity.exists_finset_nhds', tendsto_norm_zero, Metric.diam_one, Orientation.inner_rightAngleRotation_self, Complex.intCast_im, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, MeasureTheory.setIntegral_le_nonneg, tanh_zero, zero_lt_one_add_norm_sq', WithSeminorms.isVonNBounded_iff_seminorm_bounded, InnerProductSpace.Core.normSq_eq_zero, intervalIntegral.fderiv_integral, EuclideanGeometry.Sphere.isIntTangent_self_iff, cos_zero, eventually_norm_trivializationAt_lt, hasCompactSupport_norm_iff, NormedAddGroupHom.opNorm_zero, mulIndicator_thickening_eventually_eq_mulIndicator_closure, SmoothBumpFunction.nonneg, PartitionOfUnity.exists_pos, NumberField.mixedEmbedding.pos_of_notMem_negAt_plusPart, HolderTriple.inv_pos', ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self, IsCompact.exists_isCompact_cthickening, ProbabilityTheory.covariance_zero_left, limsSup_of_not_isBounded, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, AffineSubspace.signedInfDist_apply_of_mem, ContinuousLinearMap.bound, EuclideanGeometry.cos_eq_one_iff_angle_eq_zero, Disjoint.exists_thickenings, UpperHalfPlane.im_pnat_div_pos, EuclideanGeometry.sin_pos_of_not_collinear, Metric.nhdsWithin_basis_ball, tendsto_const_div_pow, MeasureTheory.integrable_fun_norm_addHaar, NumberField.mixedEmbedding.polarCoordReal_target, MeasureTheory.integral_norm_eq_pos_sub_neg, MeasureTheory.Measure.haar.addCHaar_empty, arcosh_surjOn, Orientation.inner_rev_eq_zero_of_oangle_eq_pi_div_two, exists_smooth_zero_one_nhds_of_isClosed, Complex.polarCoord_target, integral_exp_Iic_zero, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right, Orientation.oangle_sign_smul_add_smul_left, log_zero, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, hasFDerivWithinAt_iff_tendsto, Quaternion.coeComplex_one, ArithmeticFunction.vonMangoldt_apply_prime, LinearMap.im_inner_adjoint_mul_self_eq_zero, EuclideanGeometry.inversion_zero_radius, ContDiffBump.rIn_pos, CircleDeg1Lift.map_map_zero_le, CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zero, Complex.cos_ofReal_im, parallelepiped_orthonormalBasis_one_dim, MeasureTheory.measureReal_eq_zero_iff, pi_rpow_zero, arccos_of_one_le, NumberField.dedekindZeta_residue_pos, MeasureTheory.tendsto_integral_norm_approxOn_sub, integral_log_from_zero, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int, Orientation.inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two, Manifold.exists_lt_of_riemannianEDist_lt, Valued.norm_pos_iff_valuation_pos, SeminormFamily.basisSets_iff, SeminormedAddGroup.disjoint_nhds, NumberField.mixedEmbedding.logMap_zero, MeasureTheory.lpNorm_eq_zero, ContinuousLinearMap.isLeast_opNorm, InformationTheory.not_differentiableAt_klFun_zero, tendsto_mulIndicator_cthickening_mulIndicator_closure, ArithmeticFunction.vonMangoldt.residueClass_apply_zero, Quaternion.continuous_imK, range_norm, Metric.uniformContinuous_iff, ValueDistribution.logCounting_monotoneOn, NumberField.Units.dirichletUnitTheorem.exists_unit, NonarchAddGroupSeminormClass.map_zero, Metric.exists_closedBall_inter_eq_singleton_of_discrete, Asymptotics.IsBigO.exists_pos, ProbabilityTheory.cgf_zero_measure, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, Gamma_neg_nat_eq_zero, injOn_cos, Urysohns.CU.disjoint_C_support_lim, SmoothPartitionOfUnity.nonneg', UpperHalfPlane.isometry_pos_mul, Set.Subsingleton.infsep_zero, tendsto_nhds_unique_dist, ProbabilityTheory.covarianceBilinDual_of_not_memLp', HolderConjugate.sub_one_pos, SchwartzMap.fourier_convolution, Complex.log_inv_eq_integral, NumberField.mixedEmbedding.fundamentalCone.expMap_pos, tan_pi, tendsto_iff_dist_tendsto_zero, tendsto_logb_nhdsGT_zero, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousMapZero.continuous_toNNReal, InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, tendsto_factorial_div_pow_self_atTop, gauge_zero, spectralValue_X_pow, Bornology.IsBounded.exists_pos_norm_le', Complex.upperHalfPlane_inter_integerComplement, PiNat.dist_self, AlternatingMap.mkContinuousLinear_norm_le_max, ProbabilityTheory.poissonPMFReal_nonneg, IsCompact.uniform_oscillationWithin, inner_eq_norm_sq_right_iff, log_of_ne_zero, Metric.hausdorffDist_nonneg, norm_nonneg, MeasureTheory.lpNorm_of_not_memLp, MeasureTheory.lpNorm_exponent_zero, Affine.Simplex.signedInfDist_apply_of_ne, Metric.eventually_isCompact_closedBall, BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space, exists_contMDiffMap_one_nhds_of_subset_interior, MeasureTheory.upcrossingsBefore_pos_eq, ENNReal.trichotomyβ, deriv_mul_log_zero, Rat.AbsoluteValue.apply_le_sum_digits, ContDiffBump.zero_of_le_dist, Wallis.W_pos, ENNReal.zero_eq_ofReal, Quaternion.coe_real_complex_mul, exp_sub_sum_range_isBigO_pow, schnirelmannDensity_empty, Hyperreal.stdPart_epsilon, PartitionOfUnity.continuous_smul, UnitAddCircle.integral_preimage, sinh_nonpos_iff, Hyperreal.Infinitesimal.eq_zero, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos, Orientation.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero, CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_neg, convexOn_mul_log, eventually_norm_mfderiv_extChartAt_lt, Complex.ofReal_def, MeasureTheory.JordanDecomposition.real_smul_def, cos_pos_of_le_one, tendsto_norm_sub_self_nhdsGE, ProbabilityTheory.covariance_const_right, MultilinearMap.mkContinuous_norm_le', ProbabilityTheory.mgf_undef, strictConcaveOn_negMulLog, EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq, range_sigmoid, MeasureTheory.tendsto_integral_meas_thickening_le, UpperHalfPlane.coe_im_pos, ENNReal.toReal_eq_zero_iff, ArithmeticFunction.vonMangoldt_apply_pow, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, tendsto_log_mul_self_nhdsLT_zero, tendsto_indicator_thickening_indicator_closure, summable_jacobiThetaβ'_term_iff, Metric.uniformSpace_eq_bot, AddCircle.norm_eq_of_zero, Complex.range_normSq, SmoothBumpFunction.nhds_basis_tsupport, Metric.infDist_nonneg, smoothTransition.pos_denom, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAtβ, binEntropy_nonpos_of_one_le, ProbabilityTheory.IsAEKolmogorovProcess.q_pos, UpperHalfPlane.mdifferentiable_iff, ModularFormClass.exp_decay_sub_atImInfty', integral_sin_pow_antitone, Complex.arg_neg_eq_arg_sub_pi_iff, Seminorm.zero_apply, WithSeminorms.hasBasis_ball, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_nonneg, intervalIntegrable_inv_iff, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union, RCLike.intCast_im, tendsto_exp_atBot_nhdsGT, tan_zero, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, sqrt_eq_zero', Quaternion.continuous_re, one_add_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.integral_exp_pos, ArithmeticFunction.zeta_mul_vonMangoldt, HasCompactSupport.convolution_integrand_bound_right, Complex.re_nonneg_iff_nonneg, ProbabilityTheory.tendsto_cdf_atBot, BumpCovering.coe_single, mk_pos, polarCoord_source, HolderTriple.nonneg, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ProbabilityTheory.cgf_undef, Polynomial.supNorm_eq_zero_iff, Complex.arg_eq_pi_iff, RCLike.re_extendToπ'β, toNNReal_lt_toNNReal_iff', NumberField.Units.regOfFamily_eq_zero, ENNReal.toReal_ofReal', one_div_sub_sq_hasFPowerSeriesOnBall_zero, summable_exp_nat_mul_iff, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, real_inner_self_pos, tendsto_logb_nhdsNE_zero, ContinuousMapZero.toNNReal_apply, SzemerediRegularity.eps_pow_five_pos, Metric.isOpen_singleton_iff, ProbabilityTheory.truncation_zero, ArchimedeanClass.stdPart_nonpos, Complex.normSq_eq_zero, UniformSpace.Completion.uniformity_dist', zero_rpow_nonneg, HasCompactSupport.convolution_integrand_bound_right_of_subset, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_nonneg, Angle.tan_zero, sqrt_ne_zero', ContinuousLinearMap.IsPositive.re_inner_nonneg_right, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, not_differentiableAt_abs_zero, hasDerivWithinAt_iff_tendsto, norm_sub_pos_iff, antilipschitzWith_iff_exists_mul_le_norm, HolderTriple.one_div_nonneg, CircleDeg1Lift.tendsto_translation_numberβ', Valued.integer.exists_norm_coe_lt_one, strictConcaveOn_qaryEntropy, Metric.Sigma.isOpen_iff, EuclideanGeometry.Sphere.secondInter_eq_self_iff, Polynomial.derivRootWeight_nonneg, UniformSpace.Completion.dist_self, ProbabilityTheory.mgf_pos_iff, Metric.exists_real_pos_lt_infEDist_of_notMem_closure, MeasureTheory.Measure.haar.addPrehaar_empty, SchwartzMap.smulLeftCLM_smul, similar_iff_exists_pos_dist_eq, fourierCoeff_liftIco_eq, Urysohns.CU.lim_nonneg, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, SmoothBumpFunction.nonempty_support, tan_eq_zero_iff', NNReal.coe_single, ProbabilityTheory.defaultRatCDF_nonneg, Complex.arg_eq_neg_pi_div_two_iff, NormedAddCommGroup.nhds_basis_norm_lt, convexOn_rpow, EulerSine.integral_cos_mul_cos_pow_even, AlternatingMap.mkContinuous_norm_le', InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero, Quaternion.norm_toLp_equivTuple, integral_sin_pow_even, rpow_zero_pos, Quaternion.exp_eq, Metric.diam_univ_of_noncompact, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, EMetric.exists_real_pos_lt_infEdist_of_notMem_closure, trapezoidal_integral_eq, variationOnFromTo.self, inner_vsub_vsub_right_eq_dist_sq_right_iff, seminormFromConst_seq_nonneg, HurwitzZeta.isBigO_atTop_sinKernel, Asymptotics.isBigO_iff', SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, logb_nonneg, niven, smul_iInf_of_nonneg, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atBot, conformalAt_iff', sin_int_mul_pi, NumberField.mixedEmbedding.fundamentalCone.expMap_single_target, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, NonarchAddGroupSeminorm.neg', Chebyshev.theta_pos, tendsto_mulExpNegMulSq, IsMIntegralCurveAt.eventually_hasDerivAt, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', Affine.Simplex.ExcenterExists.exradius_pos, ExistsContDiffBumpBase.w_mul_Ο_nonneg, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg, log_doublingGamma_eq, MeasureTheory.condExpL2_indicator_nonneg, HasCompactSupport.hasFDerivAt_convolution_left, hahnEmbedding_isOrderedAddMonoid, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, Topology.RelCWComplex.map_zero_mem_closedCell, TemperedDistribution.smulLeftCLM_apply_apply, schnirelmannDensity_finset, MeasureTheory.eLpNorm'_exponent_zero, summable_jacobiThetaβ_term_iff, Complex.continuousOn_one_add_mul_inv, WithSeminorms.hasBasis_zero_ball, tendsto_pow_mul_exp_neg_atTop_nhds_zero, EReal.toReal_nonneg, exp_pos, Metric.closure_eq_iInter_thickening, PowerSeries.gaussNorm_nonneg, Urysohns.CU.lim_mem_Icc, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, uniformConvexOn_zero, ENNReal.ofReal_ne_zero_iff, MeasureTheory.SignedMeasure.im_toComplexMeasure, Complex.im_ofNat, ContDiffBump.integral_pos, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, log_injOn_pos, Metric.exists_contMDiffMap_forall_closedEBall_subset, parallelepiped_single, gronwallBound_Ξ΅0, Complex.one_im, sin_eq_zero_iff_of_lt_of_lt, PiLp.norm_eq_card, Mathlib.Meta.Positivity.log_pos_of_isNegNat, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Stirling.stirlingSeq_has_pos_limit_a, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, hasFDerivAt_integral_of_dominated_loc_of_lip, Angle.toReal_zero, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, ContinuousLinearEquiv.norm_pos, real_inner_I_smul_self, Matrix.PosDef.re_dotProduct_pos, binEntropy_eq_zero, ProbabilityTheory.IsAEKolmogorovProcess.p_pos, zero_rpow_le_one, NumberField.Units.regOfFamily_pos, sin_arctan_lt_zero, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero_of_measurable, tendsto_iff_norm_sub_tendsto_zero, isEquivalent_sinh, BoundingSieve.prod_primeFactors_nu, sin_sq_pi_over_two_pow_succ, Valued.integer.norm_irreducible_pos, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, ProbabilityTheory.gaussianPDFReal_nonneg, NumberField.InfinitePlace.instNonnegHomClassReal, ENNReal.truncateToReal_nonneg, BumpCovering.support_toPartitionOfUnity_subset, NormedSpace.Core.norm_eq_zero_iff, binEntropy_strictMonoOn, summable_indicator_mod_iff, Metric.isUniformEmbedding_iff', tendsto_rpow_atBot_of_base_gt_one, LinearMap.IsPositive.re_inner_nonneg_left, ProbabilityTheory.Kernel.HasSubgaussianMGF.fun_zero, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, Complex.restrictScalars_toSpanSingleton', IsClosed.notMem_iff_infDist_pos, RCLike.zero_im, EuclideanGeometry.center_eq_inversion', exists_cos_eq_zero, NumberField.mixedEmbedding.convexBodySumFun_eq_zero_iff, RCLike.im_eq_zero, ENNReal.log_ofReal, IsLocalMinOn.fderivWithin_eq_zero, Quaternion.norm_star, PartitionOfUnity.mem_finsupport, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, sinh_le_self_iff, expNegInvGlue.zero_iff_nonpos, tendsto_logb_nat_add_one_sub_logb, schnirelmannDensity_nonneg, RCLike.ofReal_lt_zero, ContDiffBump.rOut_pos, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_of_antitone, ModularGroup.coe_truncatedFundamentalDomain, AkraBazziRecurrence.asympBound_pos
|
lattice π | CompOp | 542 mathmath: EuclideanGeometry.Sphere.mul_dist_eq_abs_power, MeasureTheory.Measure.integral_comp_inv_smul, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Angle.abs_toReal_neg_coe_eq_self_iff, Complex.verticalSegment_eq, Complex.norm_circleTransformBoundingFunction_le, Angle.sign_two_zsmul_eq_sign_iff, Angle.neg_coe_abs_toReal_of_sign_nonpos, norm_torusIntegral_le_of_norm_le_const, HasStrictFDerivAt.abs_of_pos, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, MeasureTheory.Measure.addHaar_image_continuousLinearMap, abs_sinc_le_one, smul_map_volume_mul_right, ContinuousMap.abs_mem_subalgebra_closure, 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, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, Asymptotics.IsBigOWith.abs_right, Asymptotics.isBigO_abs_abs, ModularForm.mul_slash, intervalIntegrable_iff', deriv_abs, Complex.norm_le_abs_re_add_abs_im, abs_cos_le_one, isLittleO_exp_neg_mul_sq_cocompact, young_inequality, range_circleMap, Asymptotics.IsBigO.abs_left, ZLattice.covolume_eq_det_inv, Angle.eq_iff_sign_eq_and_abs_toReal_eq, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, differentiableWithinAt_abs_pos, NumberField.dedekindZeta_residue_def, Asymptotics.isLittleO_abs_abs, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Complex.angle_exp_one, log_abs, cosh_abs, UpperHalfPlane.im_smul_eq_div_normSq, TopologicalSpace.Opens.CompleteCopy.dist_eq, NumberField.Units.regOfFamily_eq_det, summable_one_div_nat_add_rpow, abs_tanh_lt_one, Path.range_subpathAux, PNat.dist_eq, RCLike.abs_im_div_norm_le_one, ModularForm.prod_slash, setOf_liouvilleWith_subset_aux, differentiableWithinAt_abs, ProbabilityTheory.integrable_pow_abs_of_integrable_exp_mul, CFC.negPart_algebraMap, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, Rat.dist_eq, Asymptotics.IsLittleO.abs_left, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, smul_map_diagonal_volume_pi, deriv_abs_neg, 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, Angle.abs_toReal_le_pi, MeasureTheory.Measure.addHaar_preimage_smul, abs_sinh, RCLike.abs_re_le_norm, Asymptotics.isBigO_abs_left, 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, Orientation.abs_volumeForm_apply_of_orthonormal, RCLike.norm_ofReal, abs_lt_norm_sub_of_not_sameRay, image_circleMap_Ioc, instHasSolidNormReal, cauSeq_converges, 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, Angle.sign_two_nsmul_eq_neg_sign_iff, AbsolutelyContinuousOnInterval.boundedVariationOn, RCLike.abs_re_div_norm_le_one, NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, log_two_near_10, coe_toNNReal_le, Differentiable.abs, abs_real_inner_le_norm, MeasureTheory.Measure.integral_comp_inv_mul_left, ModularGroup.tendsto_abs_re_smul, isTheta_exp_comp_one, SameRay.norm_sub, volume_preimage_mul_left, summable_abs_int_rpow, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, hasDerivAt_abs_neg, ProbabilityTheory.integrable_exp_mul_abs, norm_circleMap_zero, sqrt_sq_eq_abs, map_matrix_volume_pi_eq_smul_volume_pi, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', hasDerivWithinAt_abs, Asymptotics.IsLittleO.abs_abs, NNReal.image_coe_uIcc, intervalIntegral.abs_intervalIntegral_eq, smul_map_volume_mul_left, Complex.abs_re_eq_norm, Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, Angle.abs_toReal_neg, ZSpan.measureReal_fundamentalDomain, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, ProbabilityTheory.abs_truncation_le_bound, NumberField.Units.regulator_eq_det, ConvexOn.isBoundedUnder_abs, 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, eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo, exists_rat_abs_sub_lt_and_lt_of_irrational, abs_le_sqrt, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, norm_cauchyPowerSeries_le, abs_dist_sub_le, Angle.coe_abs_toReal_of_sign_nonneg, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, Complex.abs_arg_le_pi, AddCircle.norm_coe_mul, HurwitzZeta.hasSum_nat_hurwitzZetaEven, NumberField.Units.finrank_mul_regOfFamily_eq_det, instIsCompleteAbs, MeasureTheory.volume_sum_rpow_lt, Asymptotics.isBigOWith_abs_left, hasDerivAt_abs_rpow, unitInterval.volume_uIcc, ZSpan.volume_fundamentalDomain, abs_dist_sub_le_dist_mul_mul, AddCircle.norm_half_period_eq, ZSpan.measure_fundamentalDomain, logb_abs_base, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, MeasureTheory.crossing_pos_eq, Complex.abs_im_le_norm, MeasureTheory.Measure.integral_comp_smul, intervalIntegral.FTCFilter.nhdsUIcc, HasFDerivAt.abs_of_pos, abs_cos_int_mul_pi, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, HasFDerivAt.abs, abs_iteratedDeriv_cos_le_one, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, HasStrictFDerivAt.abs_of_neg, HasFDerivWithinAt.abs, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_integrable_exp_mul, MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin, Complex.abs_im_eq_norm, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, DifferentiableWithinAt.abs, NumberField.mixedEmbedding.convexBodySumFun_smul, abs_mulExpNegMulSq_comp_le_norm, contDiffOn_abs, coe_nnabs, dist_integral_mulExpNegMulSq_comp_le, intervalIntegrable_sub_inv_iff, ProbabilityTheory.integrable_exp_abs_mul_abs_add, exp_one_near_20, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, MeasureTheory.volume_sum_rpow_le, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul', MeasureTheory.integral_image_eq_integral_abs_deriv_smul, ContinuousMap.sup_mem_closed_subalgebra, ProperCone.innerDual_singleton, intervalIntegral.abs_integral_mono_interval, Complex.isCauSeq_norm_exp, ContDiffOn.abs, rpow_sum_le_const_mul_sum_rpow, exists_nat_abs_mul_sub_round_le, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, exp_abs_le, Nat.dist_eq, RCLike.abs_wInner_le, exists_polynomial_near_of_continuousOn, NumberField.mixedEmbedding.covolume_idealLattice, Complex.angle_eq_abs_arg, Function.locallyFinsuppWithin.toClosedBall_divisor, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, 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, AbsolutelyContinuousOnInterval.uniformContinuousOn, integral_comp_abs, MeasureTheory.Measure.addHaar_parallelepiped, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, posLog_eq_zero_iff, UpperHalfPlane.im_smul, abs_sin_sub_sin_le, rpow_logb_eq_abs, Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_pi, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, abs_rpow_of_nonneg, ModularGroup.exists_row_one_eq_and_min_re, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, ValueDistribution.characteristic_sub_characteristic_inv_le, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, 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, deriv_abs_zero, hasStrictDerivAt_abs, RCLike.abs_im_le_norm, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', ContinuousMap.sup_mem_subalgebra_closure, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, HasFDerivAt.abs_of_neg, ContinuousLinearMap.rayleighQuotient_le_norm, abs_norm_sub_norm_le, NumberField.Ideal.tendsto_norm_le_div_atTopβ, MeasureTheory.lpNorm_abs, deriv_abs_pos, abs_sin_half, ContinuousMap.inf_mem_subalgebra_closure, Path.range_subpath, DifferentiableOn.abs, abs_sin_eq_sqrt_one_sub_cos_sq, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, AkraBazziRecurrence.GrowsPolynomially.abs, ContinuousMap.inf_mem_closed_subalgebra, abs_rpow_le_abs_rpow, MeasureTheory.Measure.integral_comp_mul_left, Asymptotics.isBigOWith_abs_abs, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, Liouville.frequently_exists_num, Complex.norm_ratCast, Complex.abs_im_lt_norm, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul, Affine.Simplex.inradius_eq_abs_inv_sum, MeasureTheory.setIntegral_abs_condExp_le, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, MeasurableEmbedding.gaussianReal_comap_apply, Angle.sign_two_nsmul_eq_sign_iff, enorm_eq_ofReal_abs, NumberField.mixedEmbedding.norm_smul, circleMap_preimage_codiscrete, Complex.abs_arg_inv, MeasureTheory.integral_comp_rpow_Ioi, posLog_abs, InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm, abs_real_inner_div_norm_mul_norm_le_one, MeasureTheory.Measure.addHaar_image_linearMap, intervalIntegral.abs_integral_le_integral_abs, differentiableWithinAt_abs_neg, Complex.abs_arg_le_pi_div_two_iff, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, LiouvilleWith.frequently_lt_rpow_neg, Asymptotics.IsBigOWith.abs_abs, hasStrictDerivAt_abs_neg, RCLike.isCauSeq_norm, DifferentiableWithinAt.abs_of_neg, abs_cos_sub_cos_le, AddCircle.norm_coe_eq_abs_iff, ZLattice.covolume_eq_det_mul_measureReal, RCLike.isCauSeq_im, NumberField.mixedEmbedding.covolume_integerLattice, nnnorm_abs, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul, abs_signedDist_eq_dist_iff_vsub_mem_span, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, ProbabilityTheory.integrable_exp_mul_abs_add, Angle.sign_two_zsmul_eq_neg_sign_iff, not_sameRay_iff_abs_lt_norm_sub, Orientation.abs_areaForm_le, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, tendsto_abs_tan_of_cos_eq_zero, Angle.abs_cos_eq_of_two_zsmul_eq, sin_div_le_inv_abs, MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part, ProbabilityTheory.integrable_exp_abs_mul_abs, Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_zsmul_add_eq_zero_of_sign_eq, Lp_add_le, exists_rat_abs_sub_le_and_den_le, abs_sin_lt_abs, MeasureTheory.measureReal_abs_gt_le_integral_charFun, EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, cosh_lt_cosh, NumberField.Units.abs_det_eq_abs_det, abs_circleAverage_le_circleAverage_abs, HasFDerivWithinAt.abs_of_pos, Liouville.exists_pos_real_of_irrational_root, volume_real_interval, Complex.abs_im_div_norm_le_one, ProbabilityTheory.integrable_rpow_abs_of_integrable_exp_mul, ConcaveOn.isBoundedUnder_abs, ProbabilityTheory.gaussianPDFReal_inv_mul, abs_log_mul_self_rpow_lt, Complex.abs_re_le_norm, map_linearMap_volume_pi_eq_smul_volume_pi, Int.dist_eq, mellin_comp_rpow, 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, ContDiffWithinAt.abs, dist_eq, Orientation.abs_areaForm_of_orthogonal, UnitAddCircle.norm_eq, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, sqrt_mul_self_eq_abs, MeasureTheory.Measure.map_addHaar_smul, LiouvilleWith.exists_pos, intervalIntegral.norm_integral_le_of_norm_le_const_ae, differentiableAt_abs_pos, NNReal.abs_eq, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, isTheta_exp_comp_exp_comp, Complex.abs_arg_lt_pi_div_two_iff, Angle.abs_toReal_coe_eq_self_iff, NumberField.exists_ideal_in_class_of_norm_le, circleIntegrable_sub_zpow_iff, dist_0_eq_abs, cosh_le_cosh, abs_dist, Affine.Simplex.exradius_eq_abs_inv_sum, NumberField.Ideal.tendsto_norm_le_div_atTop, hasDerivAt_abs, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, abs_cos_eq_sqrt_one_sub_sin_sq, Asymptotics.isLittleO_abs_right, MeasureTheory.Measure.addHaar_preimage_linearMap, sameRay_iff_norm_sub, uniformContinuous_abs, volume_uIoo, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Orientation.volumeForm_robust', InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, EuclideanGeometry.angle_eq_abs_oangle_toReal, Complex.lim_im, ExistsContDiffBumpBase.w_def, MeasureTheory.Measure.setIntegral_comp_smul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, circleAverage_log_norm_factorizedRational, toNNReal_abs, EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, ProbabilityTheory.rpow_abs_le_mul_max_exp, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Complex.norm_sub_eq_iff, abs_sin_eq_one_iff, Orientation.angle_eq_abs_oangle_toReal, Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, circleIntegral.norm_integral_le_of_norm_le_const', abs_dist_sub_le_dist_add_add, abs_iteratedDeriv_sin_le_one, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, MeasureTheory.abs_integral_le_integral_abs, isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo, DifferentiableAt.abs, BoundedContinuousFunction.add_norm_nonneg, IntervalIntegrable.abs, AbsolutelyContinuousOnInterval.uniformlyContinuousOn, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, ProbabilityTheory.rpow_abs_le_mul_exp_abs, BoundedContinuousFunction.norm_sub_nonneg, EReal.abs_def, Complex.isCauSeq_im, ProbabilityTheory.integrable_pow_abs_mul_exp_of_integrable_exp_mul, logb_abs, MeasureTheory.lintegral_image_eq_lintegral_abs_deriv_mul, ContDiff.abs, intervalIntegral.norm_integral_le_of_norm_le_const, ProbabilityTheory.abs_truncation_le_abs_self, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, AddCircle.norm_le_half_period, NumberField.mixedEmbedding.normAtPlace_smul, Complex.abs_re_lt_norm, intervalIntegral.abs_integral_eq_abs_integral_uIoc, inner_le_Lp_mul_Lq, ProbabilityTheory.meas_ge_le_evariance_div_sq, map_volume_mul_right, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul', Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, ModularForm.prod_fintype_slash, circleIntegrable_sub_inv_iff, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, tendsto_abs_logb_atTop, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Complex.angle_one_left, InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero, CFC.posPart_algebraMap, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, abs_norm_sub_norm_le', hasDerivWithinAt_abs_neg, contDiffWithinAt_abs, abs_sin_le_abs, ProbabilityTheory.strong_law_aux1, Hyperreal.coe_abs, ContinuousLinearMap.bddAbove_rayleighQuotient, Asymptotics.IsBigO.abs_abs, Complex.angle_one_right, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_imageβ, ModularForm.slash_def, Complex.lim_norm, abs_sin_le_one, CFC.negPart_def, tendsto_abs_tan_atTop, enorm_abs, SchwartzMap.le_seminorm', NumberField.mixedEmbedding.norm_real, AlternatingMap.measure_parallelepiped, abs_mulExpNegMulSq_le, intervalIntegral.norm_integral_le_abs_integral_norm, AddCircle.norm_eq, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, exp_one_near_10, Angle.abs_cos_eq_of_two_nsmul_eq, Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_nsmul_add_eq_zero_of_sign_eq, Complex.isCauSeq_norm, ENNReal.abs_toReal, Complex.IsExpCmpFilter.tendsto_abs_re, Asymptotics.IsBigO.abs_right, differentiableOn_abs, abs_ofDigits_sub_ofDigits_le, circleAverage_abs_radius, CFC.posPart_def, ContDiffAt.abs, EReal.coe_abs, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, NNReal.dist_eq, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Angle.abs_sin_eq_of_two_zsmul_eq, abs_norm, 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, abs_rpow_le_exp_log_mul, UpperHalfPlane.mem_verticalStrip_iff, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, half_mul_log_add_log_abs, MeasurableEquiv.gaussianReal_map_symm_apply, abs_real_inner_div_norm_mul_norm_eq_one_iff, Angle.abs_sin_eq_of_two_nsmul_eq, GaussianFourier.verticalIntegral_norm_le, volume_uIoc, CircleIntegrable.abs, TFAE_exists_lt_isLittleO_pow, ProbabilityTheory.gaussianPDFReal_mul, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, AddCircle.norm_eq', NumberField.Units.finrank_mul_regulator_eq_det, abs_cos_eq_one_iff, abs_signedDist_le_dist, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, 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, MeasureTheory.integral_abs_condExp_le, Complex.norm_intCast, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, mem_closure_iff, Asymptotics.IsLittleO.abs_right, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, OrthonormalBasis.abs_det_adjustToOrientation, RCLike.isCauSeq_re, log_of_ne_zero, MeasureTheory.upcrossingsBefore_pos_eq, AbsolutelyContinuousOnInterval.continuousOn, exp_log_eq_abs, NumberField.Units.regOfFamily_eq_det', Asymptotics.IsBigOWith.abs_left, sinc_le_inv_abs, AddCircle.norm_eq_of_zero, abs_log_mul_self_lt, volume_preimage_mul_right, UpperHalfPlane.smulAux'_im, integral_pow_abs_sub_uIoc, intervalIntegrable_inv_iff, MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar, Complex.isCauSeq_re, isCauSeq_iff_lift, ODE.FunSpace.dist_iterate_next_apply_le, DifferentiableAt.abs_of_pos, circleMap_mem_sphere', norm_eq_abs, DifferentiableAt.abs_of_neg, exists_int_int_abs_mul_sub_le, Complex.horizontalSegment_eq, not_differentiableAt_abs_zero, MeasureTheory.volume_sum_rpow_lt_one, Complex.dist_conj_self, summable_one_div_int_add_rpow, cos_abs, MeasureTheory.Measure.integral_comp_div, 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, infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, Complex.abs_re_div_norm_le_one, contDiffAt_abs, volume_interval, Angle.eq_iff_abs_toReal_eq_of_sign_eq, Complex.lim_re, parallelepiped_single, Asymptotics.isBigO_abs_right, Asymptotics.isLittleO_abs_left, ZLattice.covolume_eq_det, NumberField.mixedEmbedding.normAtPlace_real, PowerSeries.IsRestricted.isRestricted_iff_abs, ModularForm.slash_apply, Complex.angle_exp_exp, abs_exp, Complex.lim_eq_lim_im_add_lim_re, MeasureTheory.Measure.integral_comp_inv_mul_right, MeasureTheory.BorelCantelli.process_difference_le, MeasureTheory.Measure.addHaar_smul, Orientation.abs_volumeForm_apply_le, UpperHalfPlane.petersson_slash, map_volume_mul_left, MeasureTheory.Measure.addHaar_image_homothety, ModularGroup.coe_truncatedFundamentalDomain
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linearOrder π | CompOp | 378 mathmath: NumberField.mixedEmbedding.fundamentalDomain_integerLattice, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, IsUltrametricDist.isNonarchimedean_norm, ProbabilityTheory.paretoCDFReal_eq_lintegral, ModularGroup.SLOnGLPos_smul_apply, ProbabilityTheory.condCDF_ae_eq, MeasureTheory.SimpleFunc.posPart_sub_negPart, ProbabilityTheory.gaussianReal_map_const_mul, IsUltrametricDist.isNonarchimedean_invariantExtension, ProbabilityTheory.lintegral_condCDF, ProbabilityTheory.condCDF_nonneg, Complex.lim_conj, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, ZSpan.volume_real_fundamentalDomain, ProbabilityTheory.IsCondKernelCDF.le_one, ZSpan.fundamentalDomain_measurableSet, rank_le_card_isVisible, Complex.instIsComplete, Chebyshev.theta_eq_theta_coe_floor, ProbabilityTheory.gaussianReal_const_mul, MeasureTheory.SimpleFunc.posPart_map_norm, intervalIntegrable_iff, Seminorm.finset_sup_apply, ProbabilityTheory.unitInterval.cdf_eq_real, NonarchAddGroupSeminormClass.toNonarchimedeanHomClass, ProbabilityTheory.gammaCDFReal_eq_lintegral, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, intervalIntegral.intervalIntegral_eq_integral_uIoc, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, ZLattice.covolume_eq_det_inv, natFloor_logb_natCast, ProbabilityTheory.tendsto_condCDF_atBot, nat_floor_real_sqrt_eq_nat_sqrt, Complex.angle_exp_one, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, interval_average_eq_div, ProbabilityTheory.setIntegral_condCDF, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, round_exp_one_eq_three, exists_eq_interval_average_of_noAtoms, ProbabilityTheory.cdf_paretoMeasure_eq_integral, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, ProbabilityTheory.IsCondKernelCDF.nonneg, ENNReal.orderIsoRpow_symm_apply, ProbabilityTheory.cdf_expMeasure_eq, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, ProbabilityTheory.IsCondKernelCDF.integral, PadicAlgCl.isNonarchimedean, volume_val, OrthonormalBasis.toBasis_adjustToOrientation, Complex.isCauSeq_conj, ProbabilityTheory.HasSubgaussianMGF.const_mul, ModularGroup.coe_apply_complex, Chebyshev.psi_eq_psi_coe_floor, Complex.exp_def, ProbabilityTheory.stieltjesOfMeasurableRat_nonneg, ProbabilityTheory.gammaCDFReal_eq_integral, Angle.toReal_coe, GaussianInt.toComplex_div_re, ProbabilityTheory.monotone_cdf, mfderivWithin_projIcc_one, cauSeq_converges, Chebyshev.psi_eq_sum_theta, ProbabilityTheory.integral_stieltjesOfMeasurableRat, Chebyshev.psi_sub_theta_eq_sum_not_prime, AbsolutelyContinuousOnInterval.boundedVariationOn, Complex.log_exp_eq_re_add_toIocMod, ProbabilityTheory.integrable_condCDF, NNReal.image_coe_uIoc, CircleDeg1Lift.floor_sub_le_translationNumber, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atTop, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, mfderivWithin_comp_projIcc_one, curveIntegralFun_trans_aeeq_right, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_norm, CircleDeg1Lift.map_le_of_map_zero, CircleDeg1Lift.le_map_of_map_zero, ProbabilityTheory.stieltjesOfMeasurableRat_le_one, StieltjesFunction.id_leftLim, ContinuousMap.HomotopyRel.trans_apply, LipschitzWith.locallyBoundedVariationOn, ProbabilityTheory.cdf_eq_real, Nat.closedBall_eq_Icc, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, SimpleGraph.triangleRemovalBound_mul_cube_lt, intervalIntegral.abs_intervalIntegral_eq, Polynomial.card_eq_of_natDegree_le_of_coeff_le, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, volume_eq_stieltjes_id, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, Complex.arg_cos_add_sin_mul_I_sub, ZSpan.measureReal_fundamentalDomain, Height.AdmissibleAbsValues.isNonarchimedean, unitInterval.symm_projIcc, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MeasureTheory.MemLp.memLp_liftIoc, sum_mul_eq_sub_integral_mul', ProbabilityTheory.cdf_nonneg, StieltjesFunction.iInf_rat_gt_eq, ProbabilityTheory.IsMeasurableRatCDF.stronglyMeasurable_stieltjesFunction, Path.Homotopy.hcomp_apply, instIsCompleteAbs, ProbabilityTheory.ofReal_condCDF_ae_eq, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, LipschitzWith.projIcc, ZSpan.volume_fundamentalDomain, ZSpan.measure_fundamentalDomain, unitInterval.volume_uIoo, LSeries_eq_mul_integral_of_nonneg, Chebyshev.sum_PrimePow_eq_sum_sum, Monotone.ae_hasDerivAt, CircleDeg1Lift.le_floor_map_map_zero, Quaternion.expSeries_odd_of_imaginary, ProbabilityTheory.IsCondKernelCDF.setIntegral, ModularGroup.SL_to_GL_tower, Int.ball_eq_Ioo, projIcc_eq_one, Chebyshev.primeCounting_eq_theta_div_log_add_integral, sum_div_nat_floor_pow_sq_le_div_sq, intervalIntegral.integral_cases, Complex.log_exp_eq_sub_toIocDiv, ProbabilityTheory.IsCondKernelCDF.setLIntegral, IsClosed.exists_wbtw_isVisible, natCeil_logb_natCast, isBounded_iff_asymptoticCone_subset_singleton, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, convergent_succ, GaussianInt.toComplex_im_div, Complex.arg_exp_mul_I, Complex.isCauSeq_norm_exp, exists_nat_abs_mul_sub_round_le, interval_average_symm, ProbabilityTheory.cdf_le_one, Quaternion.exp_of_re_eq_zero, Quaternion.re_exp, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, ContinuousMap.HomotopyWith.trans_apply, ProbabilityTheory.cdf_gammaMeasure_eq_lintegral, SzemerediRegularity.biUnion_star_subset_nonuniformWitness, unitInterval.fract_mem, Chebyshev.primeCounting_sub_theta_div_log_isBigO, MeasureTheory.SimpleFunc.negPart_map_norm, Behrend.exp_neg_two_mul_le, PadicComplex.isNonarchimedean, floor_real_sqrt_eq_nat_sqrt, convergent_zero, sum_mul_eq_sub_integral_mulβ', Quaternion.expSeries_even_of_imaginary, intervalIntegral.norm_intervalIntegral_eq, ProbabilityTheory.gaussianReal_mul_const, CircleDeg1Lift.le_map_map_zero, Chebyshev.theta_eq_log_primorial, ProbabilityTheory.strong_law_aux6, isNonarchimedean_spectralNorm, NNReal.coe_tsum_of_nonneg, ZSpan.isAddFundamentalDomain', Path.Homotopy.trans_apply, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, ProbabilityTheory.stronglyMeasurable_stieltjesOfMeasurableRat, CircleDeg1Lift.translationNumber_le_ceil_sub, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, szemeredi_regularity, ContinuousMap.Homotopy.trans_apply, harmonic_floor_le_one_add_log, Behrend.ceil_lt_mul, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, ProbabilityTheory.IsCondKernelCDF.measurable, GaussianInt.toComplex_re_div, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atBot, ZSpan.fundamentalDomain_subset_parallelepiped, ProbabilityTheory.measurable_stieltjesOfMeasurableRat, Quaternion.normSq_exp, ProbabilityTheory.exponentialCDFReal_eq_integral, sum_mul_eq_sub_integral_mulβ, ProbabilityTheory.stieltjesOfMeasurableRat_eq, Chebyshev.psi_eq_theta_add_sum_theta, ProbabilityTheory.cdf_expMeasure_eq_integral, ProbabilityTheory.instIsProbabilityMeasureCondCDF, ceil_exp_one_eq_three, ProbabilityTheory.gaussianReal_map_mul_const, IsUltrametricDist.algNormOfAlgEquiv_apply, LSeries_eq_mul_integral, ProbabilityTheory.paretoCDFReal_eq_integral, Quaternion.im_exp, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, CauSeq.tendsto_limit, ZLattice.covolume_eq_det_mul_measureReal, AddCircle.measurePreserving_equivIoc, RCLike.isCauSeq_im, contMDiffWithinAt_comp_projIcc_iff, ZSpan.isAddFundamentalDomain, AbsolutelyContinuousOnInterval.biUnion_uIoc_subset_of_mem_disjWithin, intervalIntegrable_const_iff, CauSeq.cauchySeq, Valued.isNonarchimedean_norm, ProbabilityTheory.measure_cdf, ProbabilityTheory.IsCondKernelCDF.integrable, exists_convs_eq_rat, CircleDeg1Lift.le_ceil_map_map_zero, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, BoxIntegral.IntegrationParams.RCond.min, ceil_pi_eq_four, oneTangentSpaceIcc_def, BoxIntegral.unitPartition.index_apply, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eq, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, isCauSeq_iff_cauchySeq, ProperCone.dual_flip_dual, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, ProbabilityTheory.exponentialCDFReal_eq, ProbabilityTheory.gaussianPDFReal_inv_mul, ZLattice.volume_image_eq_volume_div_covolume, ProbabilityTheory.IsMeasurableRatCDF.measurable_stieltjesFunction, Chebyshev.theta_eq_sum_Icc, log_le_harmonic_floor, UnitAddCircle.norm_eq, OrthonormalBasis.orthonormal_adjustToOrientation, mdifferentiableWithinAt_comp_projIcc_iff, Complex.toIocMod_arg, MeasureTheory.Lp.coe_posPart, Angle.coe_toIocMod, convs_eq_convergent, ProbabilityTheory.integral_condCDF, ProbabilityTheory.condCDF_le_one, ceil_logb_natCast, Angle.toIocMod_toReal, HasConstantSpeedOnWith.hasLocallyBoundedVariationOn, isNonarchimedean_spectralNorm_of_finiteDimensional_normal, Path.trans_apply, locallyIntegrableOn_mul_sum_Icc, volume_uIoo, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnorm, LinearMap.IsSymmetric.eigenvalues_def, ZLattice.volume_image_eq_volume_div_covolume', ProperCone.dual_dual_flip, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, NNReal.orderIsoRpow_symm_eq, ArchimedeanClass.ofArchimedean_stdPart, injOn_circleMap_of_abs_sub_le, Complex.lim_im, AffineSpace.asymptoticNhds_le_cobounded, Int.closedBall_eq_Icc, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, Quaternion.norm_exp, ProbabilityTheory.strong_law_aux4, SimpleGraph.triangleRemovalBound_le, floor_logb_natCast, floor_pi_eq_three, CircleDeg1Lift.ceil_map_map_zero_le, ZSpan.fundamentalDomain_pi_basisFun, ZLattice.isAddFundamentalDomain, Angle.coe_toIcoMod, exists_eq_interval_average_of_measure, ModularGroup.coe_one, IsClosed.convexHull_subset_affineSpan_isVisible, ProbabilityTheory.tendsto_cdf_atTop, Chebyshev.psi_eq_sum_Icc, circleAverage_eq_intervalAverage, Complex.isCauSeq_im, IntervalIntegrable.def', integrableOn_mul_sum_Icc, ProbabilityTheory.cdf_expMeasure_eq_lintegral, contMDiffOn_comp_projIcc_iff, intervalIntegral.abs_integral_eq_abs_integral_uIoc, AbsolutelyContinuousOnInterval.uIoc_subset_of_mem_disjWithin, asymptoticCone_subset_singleton_of_bounded, curveIntegralFun_trans_aeeq_left, ProbabilityTheory.stronglyMeasurable_condCDF, StieltjesFunction.ae_hasDerivAt, ProbabilityTheory.strong_law_aux1, ProbabilityTheory.measure_condCDF_Iic, StieltjesFunction.id_apply, ProbabilityTheory.measurable_measure_condCDF, Complex.lim_norm, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, intervalIntegral.norm_integral_eq_norm_integral_uIoc, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, ProbabilityTheory.strong_law_aux2, AddCircle.norm_eq, Behrend.div_lt_floor, ProbabilityTheory.setLIntegral_condCDF, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, ProbabilityTheory.measure_condCDF_univ, Complex.equiv_limAux, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, smoothTransition.projIcc, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, sum_mul_eq_sub_sub_integral_mul', AddCircle.integral_liftIoc_eq_intervalIntegral, Quaternion.coe_ofComplex, fourierCoeff_liftIoc_eq, LipschitzOnWith.locallyBoundedVariationOn, ProbabilityTheory.measurable_condCDF, CircleDeg1Lift.map_fract_sub_fract_eq, floor_exp_one_eq_two, IntervalIntegrable.aestronglyMeasurable_restrict_uIoc, sum_mul_eq_sub_integral_mul, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTop, Complex.arg_exp, ProbabilityTheory.IsCondKernelCDF.lintegral, Quaternion.hasSum_expSeries_of_imaginary, projIcc_eq_zero, PadicInt.complete, ModularGroup.det_coe, NumberField.FinitePlace.instNonarchimedeanHomClassReal, volume_uIoc, CircleDeg1Lift.floor_map_map_zero_le, ProbabilityTheory.gaussianPDFReal_mul, unitInterval.volume_uIoc, AddCircle.norm_eq', ProbabilityTheory.cdf_paretoMeasure_eq_lintegral, interval_average_eq, instNonemptySeedRatReal, Complex.Gamma_def, Complex.arg_mul_cos_add_sin_mul_I_sub, Padic.complete, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, exists_eq_interval_average, IsUltrametricDist.isNonarchimedean_nnnorm, sum_mul_eq_sub_integral_mulβ, CircleDeg1Lift.map_map_zero_le, CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zero, CauchySeq.isCauSeq, Complex.isCauSeq_exp, hasConstantSpeedOnWith_iff_ordered, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, ModularGroup.coeHom_apply, RCLike.isCauSeq_re, log_of_ne_zero, NumberField.Units.basisOfIsMaxRank_fundSystem, intervalIntegral.norm_integral_le_integral_norm_uIoc, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, sum_mul_eq_sub_sub_integral_mul, NNReal.image_coe_uIoo, Chebyshev.eventually_primeCounting_le, ArchimedeanClass.stdPart_real, integral_pow_abs_sub_uIoc, Complex.isCauSeq_re, ProbabilityTheory.tendsto_cdf_atBot, isCauSeq_iff_lift, ProbabilityTheory.tendsto_condCDF_atTop, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, round_pi_eq_three, LSeries_eq_mul_integral', ProbabilityTheory.exponentialCDFReal_eq_lintegral, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_nonneg, ProbabilityTheory.cdf_gammaMeasure_eq_integral, fourierCoeff_liftIco_eq, Quaternion.exp_coe, mul_pow_le_nat_floor_pow, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, arcsin_projIcc, ProbabilityTheory.ofReal_cdf, Quaternion.exp_eq, hasConstantSpeedOnWith_iff_variationOnFromTo_eq, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atBot, ofDigits_digits_sum_eq, ZSpan.fundamentalDomain_ae_parallelepiped, GaussianInt.toComplex_div_im, contMDiffOn_projIcc, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, Complex.lim_re, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, ProbabilityTheory.instIsProbabilityMeasurecdf, Complex.angle_exp_exp, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Complex.lim_eq_lim_im_add_lim_re, LinearMap.IsSymmetric.eigenvectorBasis_def, ODE.FunSpace.compProj_apply
|
mk π | CompOp | β |
partialOrder π | CompOp | 608 mathmath: NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, NumberField.InfinitePlace.isNontrivial, NumberField.InfinitePlace.eq_iff_isEquiv, isCompact_stdSimplex, ProbabilityTheory.cdf_measure_stieltjesFunction, completelyRegularSpace_iff_isOpen, ProbabilityTheory.gaussianReal_map_const_mul, ProperCone.innerDual_le_innerDual, Collinear.wbtw_of_dist_eq_of_dist_le, bernsteinApproximation.apply_zero, segment_subset_closedBall_right, instIsOrderedRing, MeasureTheory.hausdorffMeasure_segment, fourierCoeff_tsum_comp_add, Affine.Simplex.sSameSide_excenter_singleton_point, NumberField.prod_nonarchAbsVal_eq, Chebyshev.theta_eq_theta_coe_floor, UnitAddCircle.lintegral_preimage, Height.mulHeightβ_eq, ProbabilityTheory.gaussianReal_const_mul, UnitAddCircle.intervalIntegral_preimage, EuclideanGeometry.Sphere.wbtw_secondInter, ProbabilityTheory.unitInterval.cdf_eq_real, ProperCone.innerDual_univ, StrictConvexSpace.of_norm_add_ne_two, WithSeminorms.toLocallyConvexSpace, NumberField.isInfinitePlace_iff, strictConcaveOn_rpow, instStarOrderedRing, NumberField.InfinitePlace.isometry_embedding, stdSimplexHomeomorphUnitInterval_symm_apply_coe, natFloor_logb_natCast, nat_floor_real_sqrt_eq_nat_sqrt, RCLike.norm_expect_le, CongruenceSubgroup.exists_Gamma_le_conj', ContinuousMap.Homotopy.curveIntegral_add_curveIntegral_eq_of_hasFDerivWithinAt, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, ContinuousMap.Homotopy.apply_zero_path, Orientation.volumeForm_neg_orientation, Metric.exists_forall_closedEBall_subset_auxβ, instArchimedean, Complex.re_balance, Affine.Triangle.sbtw_touchpoint_singleton, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, RingSeminorm.ringSeminormClass, Complex.convexHull_reProdIm, unitInterval.pos_iff_ne_zero, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, NumberField.InfiniteAdeleRing.algebraMap_apply, MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iff, Complex.im_expect, ContinuousMap.HomotopyLike.map_zero_left, ContinuousMap.Homotopy.evalAt_eq, MeasureTheory.SignedMeasure.exists_compl_positive_negative, UnitAddTorus.mFourierSubalgebra_closure_eq_top, MeasureTheory.average_mem_openSegment_compl_self, ENNReal.orderIsoRpow_symm_apply, NumberField.InfinitePlace.Completion.norm_coe, RCLike.ofReal_balance, IsometryEquiv.midpoint_fixed, Orientation.volumeForm_map, convexHull_union_neg_eq_absConvexHull, volume_val, PartitionOfUnity.nonneg', AffineIsometryEquiv.pointReflection_midpoint_left, interior_convexHull_nonempty_iff_affineSpan_eq_top, ProbabilityTheory.HasSubgaussianMGF.const_mul, Chebyshev.psi_eq_psi_coe_floor, stdSimplexHomeomorphUnitInterval_zero, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, RCLike.ofReal_comp_balance, strictConvexOn_pow, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, convexOn_univ_dist, Path.Homotopy.target, Affine.Simplex.sSameSide_incenter_point, sameRay_iff_inv_norm_smul_eq_of_ne, NumberField.InfinitePlace.coe_apply, UniformConvexOn.strictConvexOn, Chebyshev.psi_eq_sum_theta, Path.delayReflRight_zero, UpperHalfPlane.coe_pos_real_smul, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, Complex.starConvex_ofReal_slitPlane, Chebyshev.psi_sub_theta_eq_sum_not_prime, ContinuousMap.HomotopyWith.apply_one, stdSimplex_subset_closedBall, balancedHull_subset_convexHull_union_neg, Path.Homotopy.eval_zero, fourierCoeff_bernoulli_eq, strictConvexOn_exp, AffineSubspace.isConnected_setOf_wOppSide, Complex.starConvex_one_slitPlane, Orientation.areaForm_neg_orientation, AffineBasis.interior_convexHull, unitInterval.qRight_one_left, ProperCone.innerDual_sUnion, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, strictConcaveOn_log_Iio, UnitAddTorus.mFourierCoeff_toLp, strictConcaveOn_univ_of_deriv2_neg, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, Path.delayReflLeft_one, Complex.sameRay_of_arg_eq, ProbabilityTheory.setBernoulli_one, EuclideanGeometry.Sphere.IsDiameter.wbtw, strongConcaveOn_zero, ContinuousMap.HomotopyRel.trans_apply, convexHull_diam, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, StrictConvexSpace.of_norm_combo_ne_one, Nat.closedBall_eq_Icc, convexOn_rpow_left, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, convex_halfSpace_re_le, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, SimpleGraph.triangleRemovalBound_mul_cube_lt, Set.Finite.isCompact_convexHull, norm_injOn_ray_right, diam_stdSimplex, Even.strictConvexOn_pow, EuclideanGeometry.oangle_eq_pi_iff_sbtw, Orientation.volumeForm_zero_pos, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, volume_eq_stieltjes_id, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, Seminorm.convexOn, strictConcaveOn_sqrt_mul_log_Ioi, ContinuousLinearMapWOT.instLocallyConvexSpace, SimplexCategory.toTop_obj, ContinuousMap.Homotopy.curveIntegral_add_curveIntegral_eq_of_hasFDerivWithinAt_off_countable, unitInterval.toNNReal_zero, Seminorm.gaugeSeminorm_ball, Affine.Triangle.touchpoint_singleton_sbtw, Orientation.oangle_eq_zero_iff_sameRay, convexOn_univ_norm, SimplexCategory.toTop_map, openSegment_subset_ball_of_ne, Orientation.angle_eq_iff_oangle_eq_or_sameRay, Path.subpathAux_one, Orientation.rotation_map, sum_mul_eq_sub_integral_mul', unitInterval.lt_one_iff_ne_one, Complex.re_comp_balance, MulAlgebraNormClass.toMulRingNormClass, StrictConvexSpace.of_pairwise_sphere_norm_ne_two, ProperCone.innerDual_zero, sameRay_iff_of_norm_eq, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Set.Icc.convexCombo_one, Path.Homotopy.hcomp_apply, concaveOn_rpow, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, Affine.Simplex.incenter_mem_interior, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, convex_halfSpace_im_gt, dist_midpoint_midpoint_le, Rat.AbsoluteValue.equiv_on_nat_iff_equiv, Path.Homotopy.transAssocReparamAux_zero, NumberField.InfinitePlace.Completion.locallyCompactSpace, ContinuousMap.Homotopy.apply_one_path, Complex.ofReal_balance, LSeries_eq_mul_integral_of_nonneg, Chebyshev.sum_PrimePow_eq_sum_sum, EuclideanGeometry.oangle_eq_zero_iff_wbtw, Monotone.ae_hasDerivAt, SimplexCategory.toTopβ_map, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, RealRMK.rieszMeasure_le_of_eq_one, projIcc_eq_one, ConvexBody.convex, Polynomial.gaussNorm_intAdicAbv_le_one, exists_mem_interior_convexHull_affineBasis, Polynomial.gaussNorm_lt_one_iff_contentIdeal_le, StieltjesFunction.measurable_measure, EMetric.exists_forall_closedBall_subset_auxβ, Chebyshev.primeCounting_eq_theta_div_log_add_integral, UnitAddCircle.measure_univ, EuclideanGeometry.wbtw_of_collinear_of_dist_center_le_radius, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, RealRMK.integral_rieszMeasure, sum_div_nat_floor_pow_sq_le_div_sq, CongruenceSubgroup.IsArithmetic.conj, totallyBounded_absConvexHull, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, ball_eq_openSegment, NumberField.InfinitePlace.isInfinitePlace, IsClosed.exists_wbtw_isVisible, natCeil_logb_natCast, Path.Homotopy.transAssocReparamAux_one, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, isClosed_stdSimplex, NormMulClass.isAbsoluteValue_norm, SimplexCategory.toTopβ_obj, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, ProperCone.innerDual_singleton, Path.Homotopy.transReflReparamAux_one, NumberField.InfinitePlace.smul_coe_apply, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, IsometryEquiv.map_midpoint, strictConvexOn_mul_log, diam_stdSimplex_of_subsingleton, Orientation.kahler_neg_orientation, convex_eball, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, NonarchAddGroupSeminormClass.toAddGroupSeminormClass, unitInterval.range_sigmoid, StrictMono.strictConvexOn_univ_of_deriv, CongruenceSubgroup.isArithmetic_conj_SL2Z, Path.source', MeasureTheory.JordanDecomposition.exists_compl_positive_negative, EuclideanGeometry.Sphere.sbtw_secondInter, EuclideanHalfSpace.convex, unitInterval.mul_le_left, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, AffineSubspace.isConnected_setOf_wSameSide, CStarAlgebra.instNonnegSpectrumClass, IsPreconnected.convex, NumberField.place_apply, AffineSubspace.isPreconnected_setOf_wOppSide, Path.reparam_id, Orientation.rightAngleRotation_map', MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE, ContinuousMap.HomotopyWith.trans_apply, convex_halfSpace_im_lt, Polynomial.rootSet_derivative_subset_convexHull_rootSet, convexOn_log_Gamma, UnitAddTorus.mFourier_norm, Orientation.rotation_neg_orientation_eq_neg, Matrix.instNonnegSpectrumClass, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, Set.Finite.isClosed_convexHull, Chebyshev.primeCounting_sub_theta_div_log_isBigO, Path.Homotopy.trans_assoc_reparam, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, UniformConvexOn.convexOn, Behrend.exp_neg_two_mul_le, Rat.AbsoluteValue.padic_eq_padicNorm, sameRay_iff_norm_add, diam_stdSimplex_le, bounded_stdSimplex, doublingGamma_log_convex_Ioi, strongConcaveOn_iff_convex, sum_mul_eq_sub_integral_mulβ', unitInterval.symm_one, ProbabilityTheory.gaussianReal_mul_const, Path.delayReflLeft_zero, concaveOn_univ_of_deriv2_nonpos, ContDiffMapSupportedIn.locallyConvexSpace, Chebyshev.theta_eq_log_primorial, NumberField.isFinitePlace_iff, unitInterval.qRight_zero_right, not_sameRay_iff_of_norm_eq, ProbabilityTheory.strong_law_aux6, convexOn_descPochhammer_eval, concaveOn_negMulLog, NNReal.coe_tsum_of_nonneg, MulRingNorm.mulRingNormClass, unitInterval.mul_le_right, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, exists_monotone_Icc_subset_open_cover_unitInterval_prod_self, WeakBilin.locallyConvexSpace, EuclideanQuadrant.convex, unitInterval.nonneg', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, unitInterval.le_one', ProperCone.innerDual_union, Path.Homotopy.trans_apply, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, BumpCovering.nonneg', AlgebraNormClass.toRingNormClass, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, Height.mulHeight_eq, NumberField.FinitePlace.coe_apply, isBounded_convexHull, Complex.ofReal_comp_balance, convexOn_Gamma, Seminorm.convex_ball, ContinuousMap.Homotopy.trans_apply, harmonic_floor_le_one_add_log, IsCompact.extremePoints_nonempty, isConnected_setOf_sameRay_and_ne_zero, Behrend.ceil_lt_mul, Path.range_segment, convexHull_sphere_eq_closedBall, ProbabilityTheory.setBernoulli_zero, unitInterval.qRight_zero_left, bernsteinApproximation.apply_one, convex_closedEBall, Height.AdmissibleAbsValues.mulSupport_finite, convex_ball, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, UpperHalfPlane.pos_real_smul_injective, StrongConcaveOn.strictConcaveOn, Affine.Simplex.sOppSide_excenter_singleton_point, closedBall_eq_segment, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, segment_subset_closedBall_left, totallyBounded_convexHull, Complex.im_balance, Complex.ofReal_expect, sum_mul_eq_sub_integral_mulβ, Chebyshev.psi_eq_theta_add_sum_theta, GroupNorm.groupNormClass, MeasureTheory.average_union_mem_segment, convex_iff_isPreconnected, unitInterval.symm_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, InformationTheory.convexOn_klFun, ProbabilityTheory.instIsProbabilityMeasureCondCDF, stdSimplexHomeomorphUnitInterval_apply_coe, ProbabilityTheory.gaussianReal_map_mul_const, dist_add_dist_eq_iff, CongruenceSubgroup.finiteIndex_conjGL, EuclideanGeometry.Sphere.IsDiameter.sbtw, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, LSeries_eq_mul_integral, WithAbs.norm_eq_abv, isPathConnected_stdSimplex, convex_halfSpace_re_ge, Path.Homotopy.transReflReparamAux_zero, isCompact_closedAbsConvexHull_of_totallyBounded, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, UniformConcaveOn.concaveOn, UniformConvexSpace.toStrictConvexSpace, convex_halfSpace_im_ge, not_sameRay_iff_abs_lt_norm_sub, uniformConcaveOn_zero, bernstein.z_zero, convex_halfSpace_re_lt, NumberField.count_multisetInfinitePlace_eq_mult, ModelWithCorners.convex_range, ProbabilityTheory.measure_cdf, Padic.isAbsoluteValue, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius, NumberField.InfinitePlace.denseRange_algebraMap_pi, sameRay_iff_inv_norm_smul_eq, CompletelyRegularSpace.completely_regular, strictConvexOn_rpow, ProperCone.relative_hyperplane_separation, UniformConcaveOn.strictConcaveOn, UnitAddCircle.measurePreserving_mk, Complex.im_comp_balance, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, ProperCone.innerDual_insert, ContinuousMap.HomotopyLike.map_one_left, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff, NumberField.InfinitePlace.isometry_embedding_of_isReal, ContinuousLinearMap.instNonnegSpectrumClassRealId, ProperCone.dual_flip_dual, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, unitInterval.tendsto_sigmoid_atTop, rank_rat_real, UpperHalfPlane.pos_real_re, NNReal.convex_iff, ProbabilityTheory.gaussianPDFReal_inv_mul, not_sameRay_iff_norm_add_lt, NNReal.coe_expect, unitInterval.symm_zero, Affine.Simplex.sOppSide_point_excenter_singleton, AffineSubspace.isPreconnected_setOf_wSameSide, convex_RCLike_iff_convex_real, Chebyshev.theta_eq_sum_Icc, log_le_harmonic_floor, Monotone.convexOn_univ_of_deriv, RCLike.ofReal_expect, unitInterval.subtype_Ici_eq_Icc, CompactlySupportedContinuousMap.toNNRealLinear_apply, nndist_midpoint_midpoint_le, unitInterval.coe_lt_one, Rat.AbsoluteValue.padic_le_one, convexHull_ediam, unitInterval.subtype_Iio_eq_Ico, Path.target', MulRingSeminorm.mulRingSeminormClass, convex_parallelepiped, hahnEmbedding_isOrderedModule_rat, RingNorm.ringNormClass, unitInterval.coe_pos, ProperCone.innerDual_empty, stdSimplexHomeomorphUnitInterval_one, Orientation.oangle_map, Path.trans_apply, NumberField.mixedEmbedding.convexBodyLT_convex, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, locallyIntegrableOn_mul_sum_Icc, sameRay_iff_norm_sub, SchwartzMap.instLocallyConvexSpace, ProperCone.dual_dual_flip, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, NNReal.orderIsoRpow_symm_eq, Orientation.rightAngleRotation_trans_neg_orientation, ModelWithCorners.convex_range', Path.range_coe, NormedSpace.toLocallyConvexSpace, strictConcaveOn_sqrt, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, parallelepiped_eq_sum_segment, MeasureTheory.SignedMeasure.exists_subset_restrict_nonpos, InformationTheory.strictConvexOn_klFun, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, Orientation.kahler_map, GroupSeminorm.groupSeminormClass, AffineSubspace.isPreconnected_setOf_sOppSide, ContinuousMap.Homotopy.apply_zero, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ProbabilityTheory.strong_law_aux4, StrictAnti.strictConcaveOn_univ_of_deriv, Orientation.volumeForm_zero_neg, Orientation.areaForm_map, SimpleGraph.triangleRemovalBound_le, Rat.AbsoluteValue.not_real_equiv_padic, Balanced.starConvex, ContinuousMap.Homotopy.curveIntegral_add_curveIntegral_eq_of_diffContOnCl, AddGroupSeminorm.addGroupSeminormClass, ProperCone.mem_innerDual, CStarAlgebra.instNonnegSpectrumClass', convexOn_exp, AffineSubspace.isConnected_setOf_sOppSide, strictConvexOn_univ_of_deriv2_pos, Chebyshev.psi_eq_sum_Icc, Path.id_apply, surjOn_extremePoints_image, InformationTheory.convexOn_Ioi_klFun, Path.source, NumberField.AdeleRing.algebraMap_fst_apply, skewAdjointPart_eq_I_smul_imaginaryPart, ContinuousMap.Homotopy.map_one_left, SeminormClass.toAddGroupSeminormClass, integrableOn_mul_sum_Icc, ContinuousMap.Homotopy.apply_one, strictConcaveOn_sin_Icc, convexOn_univ_of_deriv2_nonneg, Complex.sameRay_iff, Rat.AbsoluteValue.eq_on_nat_iff_eq, ConvexBody.convex', dimH_segment, NNReal.summable_mk, Complex.sameRay_iff_arg_div_eq_zero, Complex.starConvex_slitPlane, Rat.AbsoluteValue.real_eq_abs, mem_openSegment_of_gauge_lt_one, MeasureTheory.hausdorffMeasure_affineSegment, Affine.Triangle.sbtw_touchpoint_empty, AddGroupNorm.addGroupNormClass, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, Rat.AbsoluteValue.not_real_isEquiv_padic, dist_lt_dist_add_dist_iff, TestFunction.instLocallyConvexSpaceReal, StieltjesFunction.ae_hasDerivAt, ProbabilityTheory.strong_law_aux1, ProbabilityTheory.measure_condCDF_Iic, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, NumberField.toNNReal_valued_eq_adicAbv, StrongConvexOn.strictConvexOn, Path.Homotopy.trans_refl_reparam, CompactlySupportedContinuousMap.toReal_nonneg, strictConvexOn_zpow, ProbabilityTheory.measurable_measure_condCDF, Affine.Simplex.sSameSide_point_excenter_singleton, NNReal.mk_natCast, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, UnitAddTorus.span_mFourier_closure_eq_top, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, strictConcave_binEntropy, Orientation.rightAngleRotation_map, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, ProbabilityTheory.strong_law_aux2, Complex.re_expect, exists_monotone_Icc_subset_open_cover_unitInterval, Behrend.div_lt_floor, strictConcaveOn_log_Ioi, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, OrthonormalBasis.same_orientation_iff_det_eq_det, NumberField.mem_multisetInfinitePlace, Path.delayReflRight_one, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, ProbabilityTheory.measure_condCDF_univ, Orientation.finOrthonormalBasis_orientation, UpperHalfPlane.pos_real_im, NumberField.FinitePlace.isFinitePlace, Path.subpathAux_zero, strongConvexOn_iff_convex, Orientation.oangle_eq_pi_iff_sameRay_neg, strongConvexOn_zero, AbsoluteValue.isEquiv_iff_exists_rpow_eq, Path.Homotopy.eval_one, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, sum_mul_eq_sub_sub_integral_mul', Path.target, Antitone.concaveOn_univ_of_deriv, AffineBasis.centroid_mem_interior_convexHull, Path.Homotopy.source, fourierCoeff_liftIoc_eq, bernstein.z_last, completelyRegularSpace_iff, unitInterval.univ_eq_Icc, instIsOrderedAddMonoid, NumberField.mixedEmbedding.convexBodySum_convex, convex_halfSpace_im_le, sum_mul_eq_sub_integral_mul, NumberField.prod_archAbsVal_eq, OrthonormalBasis.orientation_adjustToOrientation, unitInterval.subtype_Iic_eq_Icc, ContinuousMap.HomotopyWith.apply_zero, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, projIcc_eq_zero, instLocallyConvexSpaceRealOfPolynormableSpace, unitInterval.sigmoid_pos, Path.subpath_zero_one, ProbabilityTheory.gaussianPDFReal_mul, ProperCone.innerDual_iUnion, norm_injOn_ray_left, Complex.isAbsoluteValueNorm, parallelepiped_eq_convexHull, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, Complex.Gamma_def, ContDiffPointwiseHolderAt.zero_exponent_iff, unitInterval.tendsto_sigmoid_atBot, ProperCone.innerDual_toSubmodule, convex_halfSpace_re_gt, BumpCovering.le_one', NormedSpace.toLocallyConvexSpace', isConnected_setOf_sameRay, ContinuousMap.Homotopy.curry_one, RealRMK.le_rieszMeasure_tsupport_subset, unitInterval.subtype_Ioi_eq_Ioc, Height.AdmissibleAbsValues.product_formula, CongruenceSubgroup.IsCongruenceSubgroup.conjGL, Orientation.oangle_neg_orientation_eq_neg, sum_mul_eq_sub_integral_mulβ, MeasureTheory.average_union_mem_openSegment, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, strictConcaveOn_cos_Icc, Seminorm.convex_closedBall, unitInterval.symm_eq_one, UpperHalfPlane.isometry_pos_mul, Collinear.sbtw_of_dist_eq_of_dist_lt, StrictConvexSpace.of_norm_combo_lt_one, log_of_ne_zero, sum_mul_eq_sub_sub_integral_mul, Rat.AbsoluteValue.apply_le_sum_digits, unitInterval.sigmoid_lt_one, stdSimplex.instCompactSpace_coe, UnitAddCircle.integral_preimage, Polynomial.isPrimitive_iff_forall_gaussNorm_eq_one, convexOn_mul_log, Chebyshev.eventually_primeCounting_le, AbsoluteValue.isEquiv_iff_isHomeomorph, eq_midpoint_of_dist_eq_half, strictConcaveOn_negMulLog, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, Orientation.rightAngleRotation_neg_orientation, unitInterval.qRight_one_right, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, convex_closedBall, sameRay_iff_norm_smul_eq, LSeries_eq_mul_integral', Subgroup.IsArithmetic.conj, ProbabilityTheory.convex_integrableExpSet, NonarchAddGroupNormClass.toAddGroupNormClass, strictConcaveOn_qaryEntropy, ProperCone.innerDual_innerDual, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, fourierCoeff_liftIco_eq, ContinuousMap.Homotopy.map_zero_left, mul_pow_le_nat_floor_pow, AffineSubspace.isConnected_setOf_sSameSide, NNRat.instContinuousSMulRatReal, convexOn_rpow, arcsin_projIcc, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, Complex.nonempty_linearEquiv_real, NumberField.FinitePlace.norm_def, NumberField.mixedEmbedding.convexBodySum_mem, unitInterval.toNNReal_one, EuclideanGeometry.angle_eq_pi_iff_sbtw, NumberField.mixedEmbedding.convexBodyLT'_convex, hahnEmbedding_isOrderedAddMonoid, AffineIsometryEquiv.pointReflection_midpoint_right, ofDigits_digits_sum_eq, uniformConvexOn_zero, CompletelyRegularSpace.completely_regular_isOpen, MeasureTheory.Measure.zero_le_toSignedMeasure, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, ProbabilityTheory.instIsProbabilityMeasurecdf, Urysohns.CU.lim_eq_midpoint, Set.Icc.convexCombo_zero, ContinuousMap.Homotopy.curry_zero, RCLike.norm_nnqsmul, Affine.Simplex.sSameSide_point_incenter, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', AffineSubspace.isPreconnected_setOf_sSameSide, Complex.rectangle_eq_convexHull, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, instIsStrictOrderedRing, instIsOrderedCancelAddMonoid, IsCoveringMap.liftPath_trans
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ringEquivCauchy π | CompOp | 2 mathmath: ringEquivCauchy_apply, ringEquivCauchy_symm_apply_cauchy
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semiring π | CompOp | 2158 math, 1 bridgemath: range_cfcβ_nnreal, Orientation.rightAngleRotationAuxβ_rightAngleRotationAuxβ, MeasureTheory.Measure.integral_comp_inv_smul, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Orientation.oangle_sign_smul_add_right, MeasureTheory.setIntegral_tilted, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, Seminorm.isBounded_const, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, isConformalMap_conj, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, CFC.posPart_smul_of_nonpos, MeasureTheory.mulEquivHaarChar_smul_integral_map, EuclideanGeometry.dist_smul_vadd_sq, Bundle.ContMDiffRiemannianMetric.isVonNBounded, SchwartzMap.lineDerivOpCLM_eq, NumberField.InfinitePlace.isNontrivial, real_inner_div_norm_mul_norm_eq_neg_one_iff, NumberField.InfinitePlace.eq_iff_isEquiv, uniqueDiffOn_Icc, Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent, isCompact_stdSimplex, ProbabilityTheory.cdf_measure_stieltjesFunction, MeasureTheory.condExpInd_of_measurable, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, ModularForm.smul_slash, completelyRegularSpace_iff_isOpen, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ProbabilityTheory.gaussianReal_map_const_mul, ProperCone.innerDual_le_innerDual, RCLike.map_apply, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, Complex.restrictScalars_one_smulRight', MeasureTheory.aestronglyMeasurable_condExpInd, MeasureTheory.Martingale.smul, Complex.coe_realPart, IsSelfAdjoint.quasispectrumRestricts, mellin_eq_fourier, SchwartzMap.instLineDerivLeftSMulReal, bernsteinApproximation.apply_zero, taylorWithin_succ, Complex.UnitDisc.normSq_lt_one, MeasureTheory.Measure.addHaar_image_continuousLinearMap, Matrix.IsHermitian.isClosedEmbedding_cfcAux, RCLike.ofRealCLM_apply, RCLike.normSq_to_real, NumberField.InfinitePlace.norm_embedding_of_isReal, dimH_of_mem_nhds, MeasureTheory.charFun_eq_fourierIntegral', hasFDerivAt_fourierChar_neg_bilinear_left, geometric_hahn_banach_point_point, segment_subset_closedBall_right, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, Complex.linearEquiv_det_conjLIE, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, instIsOrderedRing, Complex.normSq_pos, RCLike.reCLM_apply, gauge_def', NumberField.Units.finrank_eq_rank, MeasureTheory.hausdorffMeasure_segment, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, AddDissociated.randomisation, Orientation.inner_rotation_pi_div_two_right_smul, tendsto_tsum_div_pow_atTop_integral, Orientation.oangle_add_left_smul_rotation_pi_div_two, CFC.monotoneOn_one_sub_one_add_inv, fourierIntegral_comp_linearIsometry, fderiv_fourierIntegral, MeasureTheory.integral_smul_nnreal_measure, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, ContinuousMap.abs_mem_subalgebra_closure, LinearMap.IsSymmetric.restrictScalars, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, nnnorm_cfcβ_nnreal_le_iff, ZSpan.volume_real_fundamentalDomain, realPart_idem, NumberField.mixedEmbedding.convexBodyLT'_mem, Complex.ofRealCLM_coe, Complex.kahler, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, NumberField.prod_nonarchAbsVal_eq, MeasureTheory.Measure.integral_comp_mul_right, Complex.areaForm, intervalIntegral.inv_smul_integral_comp_div_add, finrank_real_complex_fact', Chebyshev.theta_eq_theta_coe_floor, hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, Complex.normSq_natCast, Matrix.IsHermitian.det_abs, RCLike.ofRealLI_apply, ModularForm.mul_slash, Height.mulHeightβ_eq, ProbabilityTheory.gaussianReal_const_mul, curveIntegrable_segment, ProbabilityTheory.covarianceBilinDual_apply', MeasureTheory.charFunDual_apply, uniqueDiffWithinAt_Iic, Complex.ofRealLI_apply, conformalAt_iff, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, UpperHalfPlane.normSq_pos, norm_add_eq_iff_real, Complex.integral_comp_pi_polarCoord_symm, contDiffAt_norm_smul_iff, ProbabilityTheory.IsGaussian.integrable_dual, Complex.norm_mul_self_eq_normSq, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, ContDiffMapSupportedIn.iteratedFDerivLM_apply, MeasureTheory.weightedSMul_apply, ContinuousLinearMap.comp_condExp_comm, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Commute.cfcβ_nnreal, realPart_ofReal, Orientation.linearEquiv_det_rotation, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, UpperHalfPlane.re_smul, ProbabilityTheory.unitInterval.cdf_eq_real, PeriodPair.basis_one, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, RCLike.conjCLE_norm, ProperCone.innerDual_univ, HasDerivWithinAt.complexToReal_fderiv', Orientation.kahler_comp_rightAngleRotation', MeasureTheory.integral_unique, Orientation.rotation_eq_self_iff, setIntegral_withDensity_eq_setIntegral_smulβ, WithSeminorms.toLocallyConvexSpace, NumberField.isInfinitePlace_iff, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, intervalIntegral.intervalIntegral_eq_integral_uIoc, ContinuousLinearMap.integral_apply, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, ProbabilityTheory.covarianceBilinDual_apply, hasFDerivAt_stereoInvFunAux, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, strictConcaveOn_rpow, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, NNReal.coe_toRealHom, fderiv_fourierChar_neg_bilinear_right_apply, NumberField.InfinitePlace.isometry_embedding, stdSimplexHomeomorphUnitInterval_symm_apply_coe, real_inner_smul_self_left, intervalIntegral.fderiv_integral_of_tendsto_ae, NumberField.mixedEmbedding.normAtAllPlaces_apply, SmoothPartitionOfUnity.contMDiffAt_finsum, imaginaryPart_I_smul, ContDiffMapSupportedIn.structureMapCLM_apply, natFloor_logb_natCast, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, det_fderivPolarCoordSymm, setIntegral_withDensity_eq_setIntegral_toReal_smul, nat_floor_real_sqrt_eq_nat_sqrt, RCLike.norm_expect_le, MeasureTheory.Measure.toSphere_apply_aux, Orientation.neg_rotation, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, GaussianFourier.integral_cexp_neg_mul_sq_norm, tendsto_integral_peak_smul_of_integrable_of_tendsto, RCLike.map_same_eq_id, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, ContinuousMap.Homotopy.apply_zero_path, Orientation.eq_rotation_self_iff_angle_eq_zero, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, NumberField.mixedEmbedding.norm_unit_smul, Complex.nndist_self_conj, NumberField.mixedEmbedding.norm_eq_norm, IsometryEquiv.toRealLinearIsometryEquiv_apply, MeasureTheory.condExpIndL1Fin_smul, Metric.exists_forall_closedEBall_subset_auxβ, SlashInvariantForm.quotientFunc_mk, ProbabilityTheory.uncenteredCovarianceBilin_apply, InnerProductGeometry.angle_smul_right_of_pos, ModularForm.SL_slash, intervalIntegral.integral_comp_sub_div, Complex.ofRealCLM_norm, Complex.reLm_coe, intervalIntegral.integral_comp_mul_left, uniqueDiffOn_Iic, LipschitzWith.ae_exists_fderiv_of_countable, rotation_injective, NumberField.mixedEmbedding.mem_idealLattice, Complex.re_balance, UpperHalfPlane.im_smul_eq_div_normSq, BoxIntegral.unitPartition.mem_smul_span_iff, intervalIntegral.integral_comp_mul_sub, SchwartzMap.bilinLeftCLM_apply, IsConformalMap.is_complex_or_conj_linear, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, HasGradientAt.hasDerivAt', UpperHalfPlane.specialLinearGroup_apply, ContinuousLinearMap.comp_condExp_add_const_comm, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, Bundle.RiemannianMetric.isVonNBounded, RingSeminorm.ringSeminormClass, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Complex.convexHull_reProdIm, Complex.conjLIE_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, unitInterval.pos_iff_ne_zero, fourierIntegral_gaussian_innerProductSpace', ProbabilityTheory.integral_gaussianReal_eq_integral_smul, Matrix.PosSemidef.sqrt_eq_zero_iff, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, combo_mem_ball_of_ne, NumberField.InfiniteAdeleRing.algebraMap_apply, RCLike.normSq_neg, MeasureTheory.isAddHaarMeasure_hausdorffMeasure, instStarModuleNNRealOfReal, ContinuousMap.toNNReal_neg_algebraMap, Complex.im_expect, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, ContinuousMap.HomotopyLike.map_zero_left, ContinuousMap.Homotopy.evalAt_eq, UpperHalfPlane.num_neg, conformal_const_smul, Complex.hasStrictFDerivAt_exp_real, UpperHalfPlane.moebius_im, ModularForm.prod_slash, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, uniqueDiffOn_Ioc, Module.Basis.parallelepiped_basisFun, SchwartzMap.laplacianCLM_eq, vector_fourierIntegral_eq_integral_exp_smul, ModularGroup.one_lt_normSq_T_zpow_smul, ProbabilityTheory.covarianceOperator_apply, InnerProductGeometry.angle_smul_left_of_neg, MeasureTheory.integral_tilted, ContDiffAt.laplacian_CLM_comp_left, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, MeasureTheory.average_mem_openSegment_compl_self, CongruenceSubgroup.strictPeriods_Gamma0, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, Complex.normSq_ratCast, MeasureTheory.Measure.toSphere_real_apply_univ, cfcβHom_nnreal_eq_restrict, RCLike.continuous_normSq, Conformal.const_smul, ContinuousLinearEquiv.hasTemperateGrowth, ENNReal.orderIsoRpow_symm_apply, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, ModularForm.norm_eq_zero_iff, HasFDerivAt.norm_sq, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, AddCircle.integral_haarAddCircle, hasStrictFDerivAt_rpow_of_pos, InnerProductSpace.HarmonicAt.const_smul, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, NumberField.InfinitePlace.Completion.norm_coe, RCLike.ofReal_balance, Orientation.oangle_smul_left_of_neg, Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, Complex.normSq_mk, MeasureTheory.Measure.addHaar_ball_of_pos, convexHull_union_neg_eq_absConvexHull, volume_val, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, ModularForm.prod_slash_sum_weights, smul_unitClosedBall_of_nonneg, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, GaussianInt.normSq_le_normSq_of_re_le_of_im_le, interior_convexHull_nonempty_iff_affineSpan_eq_top, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, ProbabilityTheory.HasSubgaussianMGF.const_mul, MeasureTheory.weightedSMul_nonneg, instStarModuleNNRealReal, Chebyshev.psi_eq_psi_coe_floor, stdSimplexHomeomorphUnitInterval_zero, Orientation.inner_rightAngleRotation_swap', MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', QuadraticForm.equivalent_signType_weighted_sum_squared, Module.Basis.parallelepiped_reindex, RCLike.ofReal_comp_balance, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, curveIntegralFun_segment, strictConvexOn_pow, RCLike.reCLM_norm, Besicovitch.SatelliteConfig.exists_normalized_aux2, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, ModularForm.levelOne_neg_weight_rank_zero, Subgroup.IsArithmetic.is_commensurable, Subgroup.IsArithmetic.inter, convexOn_univ_dist, Path.Homotopy.target, Orientation.abs_volumeForm_apply_of_orthonormal, setIntegral_withDensity_eq_setIntegral_toReal_smulβ, fourier_gaussian_innerProductSpace, ProbabilityTheory.HasGaussianLaw.smul, NumberField.mixedEmbedding.negAt_apply_snd, Orientation.neg_rotation_neg_pi_div_two, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, sameRay_iff_inv_norm_smul_eq_of_ne, CuspForm.coe_trace, Polynomial.isRoot_cos_pi_div_five, norm_sum_lt_of_strictConvexSpace, NumberField.mixedEmbedding.convexBodyLT_mem, NumberField.InfinitePlace.coe_apply, UniformConvexOn.strictConvexOn, 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, RCLike.conjCLE_apply, Chebyshev.psi_eq_sum_theta, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, MeasureTheory.Measure.quasiMeasurePreserving_smul, unitInterval.mem_unitIntervalSubmonoid, Path.delayReflRight_zero, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Complex.reCLM_nnnorm, UpperHalfPlane.coe_pos_real_smul, UpperHalfPlane.J_sq, Orientation.rightAngleRotation_def, Euclidean.closedBall_eq_image, NumberField.mixedEmbedding.negAt_preimage, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, Complex.starConvex_ofReal_slitPlane, Chebyshev.psi_sub_theta_eq_sum_not_prime, MeasureTheory.L1.SimpleFunc.setToL1S_add_left, ContinuousMap.HomotopyWith.apply_one, fderiv_fourier, ApproximatesLinearOn.norm_fderiv_sub_le, MeasureTheory.charFunDual_pi', stdSimplex_subset_closedBall, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MeasureTheory.Measure.addHaar_ball_mul, Quaternion.linearIsometryEquivTuple_symm_apply, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, ProbabilityTheory.covarianceBilin_apply_basisFun_self, NumberField.mixedEmbedding.normAtPlace_apply_of_isReal, MeasureTheory.condExpInd_nonneg, balancedHull_subset_convexHull_union_neg, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, Orientation.areaForm_to_volumeForm, Path.Homotopy.eval_zero, stereoInvFunAux_apply, norm_curveIntegral_segment_le, Polynomial.card_roots_le_derivative, UpperHalfPlane.denom_cocycle_Ο, NNReal.algebraMap_eq_coe, Subgroup.instIsArithmeticRangeSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGL, strictConvexOn_exp, SchwartzMap.fourier_lineDerivOp_eq, Complex.starConvex_one_slitPlane, TemperedDistribution.instLineDerivLeftSMulReal, Orientation.areaForm_neg_orientation, tendsto_card_div_pow_atTop_volume, Complex.normSq_mul, AffineBasis.interior_convexHull, EuclideanGeometry.inversion_vsub_center, Orientation.rightAngleRotation_trans_rightAngleRotation, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, MeasureTheory.condExpL2_indicator_ae_eq_smul, conformalAt_const_smul, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, CFC.negPart_smul_of_nonpos, SchwartzMap.smulLeftCLM_real_smul, dimH_univ_eq_finrank, MeasureTheory.Measure.integral_comp_inv_mul_left, ContDiffBump.measure_closedBall_div_le_integral, Orientation.kahler_eq_zero_iff, unitInterval.qRight_one_left, MeasureTheory.measure_smul_average, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', InnerProductSpace.HarmonicOnNhd.comp_CLM, Orientation.oangle_sign_sub_smul_right, ProperCone.innerDual_sUnion, Complex.integral_comp_polarCoord_symm, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, Orientation.oangle_smul_left_self_of_nonneg, strictConcaveOn_log_Iio, ProbabilityTheory.gaussianReal_map_continuousLinearMap, strictConcaveOn_univ_of_deriv2_neg, LinearMap.extendToπ'_apply, Orientation.areaForm_swap, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, ProbabilityTheory.covarianceOperator_zero, HasFDerivAt.curveIntegral_segment_source, Bundle.ContinuousRiemannianMetric.symm, Path.delayReflLeft_one, mellin_hasDerivAt_of_isBigO_rpow, LinearIsometryEquiv.measurePreserving, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, Subgroup.instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex, MulRingSeminorm.map_mul', Affine.Simplex.finrank_direction_altitude, ProbabilityTheory.setBernoulli_one, SlashInvariantForm.coe_translate, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, hasDerivAt_abs_neg, Orientation.kahler_swap, Orientation.det_rotation, strongConcaveOn_zero, Orientation.rotation_pi_apply, integral_withDensity_eq_integral_smul, intervalIntegral.integral_comp_add_div, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, Orientation.rotation_rotation, convexHull_diam, Matrix.PosSemidef.det_sqrt, BoxIntegral.HasIntegral.smul, Nat.closedBall_eq_Icc, CStarModule.inner_smul_right_real, SameRay.inv_norm_smul_eq, convexOn_rpow_left, hasDerivWithinAt_abs, Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, MeasureTheory.Measure.integral_comp_smul_of_nonneg, convex_halfSpace_re_le, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, MeasureTheory.convolution_precompR_apply, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, SimpleGraph.triangleRemovalBound_mul_cube_lt, Set.Finite.isCompact_convexHull, isCusp_SL2Z_iff', VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, InformationTheory.hasDerivAt_klFun, ContinuousMap.toNNReal_algebraMap, diam_stdSimplex, stereographic_apply_neg, StarAlgHom.continuous_realContinuousMapOfNNReal, Orientation.kahler_comp_rightAngleRotation, Seminorm.ball_smul, Even.strictConvexOn_pow, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, affinity_unitClosedBall, ContinuousLinearMap.contDiffPointwiseHolderAt, ContDiffBump.normed_le_div_measure_closedBall_rOut, MeasureTheory.integral_singleton', NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, selfAdjoint.imaginaryPart_coe, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, volume_eq_stieltjes_id, MeasureTheory.charFunDual_prod, NumberField.Units.span_basisOfIsMaxRank, nnnorm_cfcβ_nnreal_lt, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, normHom_apply, range_stereographic_symm, Complex.equivRealProdCLM_symm_apply, Seminorm.convexOn, ProbabilityTheory.strong_law_ae, HasDerivWithinAt.norm_sq, HasGradientAtFilter.hasDerivAtFilter', strictConcaveOn_sqrt_mul_log_Ioi, Module.Basis.prod_addHaar, CompactlySupportedContinuousMap.coe_toRealLinearMap, ZSpan.measureReal_fundamentalDomain, SmoothPartitionOfUnity.contDiffAt_finsum, isOpenEmbedding_stereographic_symm, Polynomial.ofReal_eval, NumberField.Units.basisOfIsMaxRank_apply, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, ContinuousLinearMapWOT.instLocallyConvexSpace, MeasureTheory.lpNorm_smul_measure_of_ne_zero, SimplexCategory.toTop_obj, isBigO_rpow_top_log_smul, Complex.sq_norm, SchwartzMap.smulLeftCLM_sum, UpperHalfPlane.Ο_mul, unitInterval.toNNReal_zero, CFC.sqrt_map_prod, PeriodPair.basis_zero, has_fderiv_at_filter_real_equiv, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, MeasureTheory.setIntegral_condExpInd, Seminorm.gaugeSeminorm_ball, tendsto_integral_exp_smul_cocompact, MeasureTheory.integral_comp_rpow_Ioi_of_pos, StarAlgHom.realContinuousMapOfNNReal_apply, curveIntegral_segment, Orientation.rotation_symm, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, gauge_norm_smul, RCLike.conjLIE_apply, convexOn_univ_norm, SimplexCategory.toTop_map, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Complex.normSq_I, MeasureTheory.Submartingale.smul_nonneg, RCLike.imLm_coe, openSegment_subset_ball_of_ne, NormedSpace.normalize_smul, MeasureTheory.integrable_withDensity_iff_integrable_smul', IsMIntegralCurveOn.comp_mul, fourierIntegralInv_comp_linearIsometry, nnabs_of_nonneg, ConvexBody.coe_smul, Path.subpathAux_one, InnerProductGeometry.angle_eq_zero_iff, Orientation.rotation_map, sum_mul_eq_sub_integral_mul', RCLike.div_im, Orientation.oangle_rotation_left, unitInterval.lt_one_iff_ne_one, Complex.re_comp_balance, MulAlgebraNormClass.toMulRingNormClass, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, ProperCone.innerDual_zero, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Set.Icc.convexCombo_one, fourier_gaussian_innerProductSpace', norm_smul_of_nonneg, concaveOn_rpow, MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real, ContDiffAt.contDiffAt_norm_smul, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, MeasureTheory.L1.integral_def, Subgroup.strictWidthInfty_eq_one_of_T_mem, hasDerivAt_abs_rpow, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, realPart.norm_le, ZSpan.volume_fundamentalDomain, Complex.tendsto_normSq_cocompact_atTop, ProbabilityTheory.covarianceBilin_zero, NumberField.mixedEmbedding.convexBodySumFun_apply, RCLike.conjCLE_coe, Ioo_smul_sphere_zero, tendsto_integral_gaussian_smul', contDiffOn_stereoToFun, hasFDerivAt_fourier, VectorFourier.differentiable_fourierIntegral, finrank_eq_int_finrank_of_discrete, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, SchwartzMap.smulLeftCLM_fun_neg, ZSpan.measure_fundamentalDomain, convex_halfSpace_im_gt, RCLike.normSq_inv, Matrix.PosSemidef.sqrt_eq_one_iff, Rat.AbsoluteValue.equiv_on_nat_iff_equiv, Path.Homotopy.transAssocReparamAux_zero, stereoInvFun_apply, NumberField.InfinitePlace.Completion.locallyCompactSpace, ProbabilityTheory.isGaussian_map_equiv_iff, fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, Complex.normSq_add, ContinuousMap.Homotopy.apply_one_path, Complex.ofReal_balance, MeasureTheory.integral_indicatorConstLp, MeasureTheory.Measure.toSphere_apply_univ, Bundle.ContMDiffRiemannianMetric.symm, MeasureTheory.charFunDual_eq_prod_iff, SchwartzMap.pairing_apply, fourier_comp_linearIsometry, MeasureTheory.Measure.integral_comp_smul, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, setIntegral_withDensity_eq_setIntegral_smulβ', LSeries_eq_mul_integral_of_nonneg, real_inner_div_norm_mul_norm_eq_one_iff, Chebyshev.sum_PrimePow_eq_sum_sum, Complex.re_sq_le_normSq, Monotone.ae_hasDerivAt, SimplexCategory.toTopβ_map, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, MeasureTheory.integrable_withDensity_iff_integrable_smulβ', Complex.div_im, RealRMK.rieszMeasure_le_of_eq_one, ContDiffMapSupportedIn.uniformSpace_eq_iInf, ModularFormClass.one_mem_strictPeriods_SL2Z, LinearIsometryEquiv.coe_toMeasurableEquiv, RCLike.rank_le_two, curveIntegral_segment_const, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, MeasureTheory.L1.integral_eq_setToL1, ArchimedeanClass.stdPart_eq_sInf, BoxIntegral.BoxAdditiveMap.volume_apply, ProbabilityTheory.HasGaussianLaw.fun_smul, VectorFourier.iteratedFDeriv_fourierIntegral, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, RCLike.reCLM_coe, ProbabilityTheory.gaussianReal_map_linearMap, realPart_add_I_smul_imaginaryPart, projIcc_eq_one, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, ConvexBody.convex, Polynomial.gaussNorm_intAdicAbv_le_one, exists_mem_interior_convexHull_affineBasis, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Seminorm.comp_smul, IsGreatest.nnnorm_cfcβ_nnreal, intervalIntegral.smul_integral_comp_mul_sub, fourierInv_comp_linearIsometry, Polynomial.gaussNorm_lt_one_iff_contentIdeal_le, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, StieltjesFunction.measurable_measure, MeasureTheory.condExpL1CLM_indicatorConstLp, EMetric.exists_forall_closedBall_subset_auxβ, LinearIsometryEquiv.reflections_generate, Chebyshev.primeCounting_eq_theta_div_log_add_integral, CompactlySupportedContinuousMap.toRealLinearMap_apply, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, Complex.normSq_eq_norm_sq, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, ProbabilityTheory.covarianceBilinDual_zero, RealRMK.integral_rieszMeasure, ModularForm.levelOne_weight_zero_rank_one, HasFDerivWithinAt.inner, CongruenceSubgroup.strictWidthInfty_Gamma0, MeasureTheory.SimpleFunc.integral_eq_sum, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, sum_div_nat_floor_pow_sq_le_div_sq, CFC.posPart_smul, RCLike.normSq_nonneg, NumberField.InfinitePlace.instMonoidWithZeroHomClassReal, NormedSpace.normalize_smul_of_pos, MeasureTheory.condExpInd_disjoint_union, Orientation.oangle_rotation_oangle_right, CongruenceSubgroup.IsArithmetic.conj, ArchimedeanClass.stdPart_map_real, LinearMap.extendToπ_apply, coe_nnabs, UpperHalfPlane.denom_cocycle, innerβ_apply, MeasureTheory.setIntegral_condExpIndSMul, Orientation.rightAngleRotation_symm, MeasureTheory.weightedSMul_empty, totallyBounded_absConvexHull, MeasureTheory.integrable_withDensity_iff_integrable_smulβ, inv_norm_smul_mem_unitClosedBall, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, Affine.Simplex.mongePlane_def, ModularGroup.lcRow0Extend_apply, ball_eq_openSegment, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, UpperHalfPlane.coe_smul_of_det_pos, Seminorm.bound_of_continuous, ContDiff.euclidean_dist, intervalIntegral.integral_comp_add_mul, NumberField.InfinitePlace.isInfinitePlace, ConvexBody.ext_iff, MeasureTheory.setIntegral_rnDeriv_smul, Bundle.ContMDiffRiemannianMetric.pos, Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, HasDerivWithinAt.complexToReal_fderiv, IsContMDiffRiemannianBundle.exists_contMDiff, natCeil_logb_natCast, Path.Homotopy.transAssocReparamAux_one, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, isClosed_stdSimplex, CFC.nnrpow_def, NormMulClass.isAbsoluteValue_norm, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, SimplexCategory.toTopβ_obj, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, ContinuousMap.sup_mem_closed_subalgebra, RCLike.real_smul_eq_coe_smul, Orientation.inner_rotation_pi_div_two_right, integral_comp_polarCoord_symm, Complex.normSq_sub, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, ProbabilityTheory.IsGaussianProcess.comp_left, ProperCone.innerDual_singleton, Path.Homotopy.transReflReparamAux_one, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, Subgroup.IsArithmetic.isFiniteRelIndexSL, NumberField.InfinitePlace.smul_coe_apply, hasFDerivAt_integral_of_dominated_loc_of_lip', Complex.inv_re, Orientation.oangle_rotation, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, MeasureTheory.weightedSMul_null, stereoToFun_apply, ArchimedeanClass.mk_sub_stdPart_pos, Module.Basis.addHaar_reindex, orthogonalBilin_innerβ, NumberField.mixedEmbedding.mem_span_latticeBasis, strictConvexOn_mul_log, diam_stdSimplex_of_subsingleton, ProbabilityTheory.covarianceBilin_comm, Orientation.inner_rotation_pi_div_two_left, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, Orientation.oangle_rotation_self_left, ContinuousLinearEquiv.contDiffPointwiseHolderAt, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, Orientation.kahler_neg_orientation, affinity_unitBall, convex_eball, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, unitInterval.range_sigmoid, HasDerivAt.complexToReal_fderiv', StrictMono.strictConvexOn_univ_of_deriv, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', Path.source', InnerProductSpace.volume_ball, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, MeasureTheory.aemeasurable_fderivWithin, lipschitzWith_circleMap, fderiv_norm_smul_neg, EisensteinSeries.q_expansion_riemannZeta, HasDerivAt.complexToReal_fderiv, EuclideanHalfSpace.convex, unitInterval.coe_unitIntervalSubmonoid, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, unitInterval.mul_le_left, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, exists_polynomial_near_of_continuousOn, MeasureTheory.SignedMeasure.re_toComplexMeasure, IsPreconnected.convex, NumberField.place_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, NumberField.mixedEmbedding.volume_preserving_negAt, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, NumberField.mixedEmbedding.normAtPlace_add_le, setIntegral_withDensity_eq_setIntegral_toReal_smulβ', SchwartzMap.smulLeftCLM_const, MeasureTheory.integral_fintype, Path.reparam_id, intervalIntegral.smul_integral_comp_sub_mul, Orientation.rightAngleRotation_map', NumberField.mixedEmbedding.negAt_apply_isComplex, Orientation.inner_rotation_pi_div_two_left_smul, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, LinearMap.extendToπ'_apply_re, MeasureTheory.Measure.toSignedMeasure_smul, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, hasDerivWithinAt_taylorWithinEval_at_Icc, convex_halfSpace_im_lt, Polynomial.rootSet_derivative_subset_convexHull_rootSet, RCLike.inv_im, MeasureTheory.norm_condExpInd_apply_le, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, convexOn_log_Gamma, Orientation.eq_rotation_self_iff, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, Complex.selfAdjointEquiv_apply, UpperHalfPlane.im_smul, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, Orientation.areaForm'_apply, UpperHalfPlane.normSq_denom_pos, Continuous.cfcβ_nnreal, intervalIntegral.integral_smul_measure, hasSum_one_div_nat_pow_mul_cos, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, signedDist_smul_of_pos, Distribution.mapCLM_apply, OnePoint.IsZeroAt.smul_iff, UpperHalfPlane.Ο_neg, IsContinuousRiemannianBundle.exists_continuous, Set.Finite.isClosed_convexHull, SMulCommClass.complexToReal, Chebyshev.primeCounting_sub_theta_div_log_isBigO, Path.Homotopy.trans_assoc_reparam, ArchimedeanClass.lt_of_lt_stdPart, UpperHalfPlane.coe_smul, Complex.inv_def, MeasureTheory.Measure.addHaar_real_closedBall', Complex.equivRealProdLm_apply, Orientation.inner_comp_rightAngleRotation, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, intervalIntegral.integral_hasStrictFDerivAt, CStarAlgebra.linear_combination_nonneg, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, Complex.ofRealCLM_apply, cfcHom_real_eq_restrict, intervalIntegral.inv_smul_integral_comp_sub_div, UniformConvexOn.convexOn, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Behrend.exp_neg_two_mul_le, ContinuousAt.cfcβ_nnreal, star_mul_self_add_self_mul_star, inner_map_complex, Rat.AbsoluteValue.padic_eq_padicNorm, BoundedContinuousFunction.probCharDual_zero, expNegInvGlue.tendsto_polynomial_inv_mul_zero, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, Complex.normSq_ofNat, IsSelfAdjoint.spectrumRestricts, diam_stdSimplex_le, imaginaryPart.norm_le, Seminorm.const_isBounded, HasFDerivWithinAt.norm_sq, MeasureTheory.norm_weightedSMul_le, Complex.restrictScalars_one_smulRight, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, Orientation.rotation_zero, ProbabilityTheory.HasGaussianLaw.map, VectorFourier.fderiv_fourierIntegral, bounded_stdSimplex, Algebra.norm_complex_eq, realPart_comp_subtype_selfAdjoint, doublingGamma_log_convex_Ioi, MeasureTheory.integral_posConvolution, hasStrictDerivAt_abs, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, RCLike.finrank_le_two, IsOpen.smul_sphere, EuclideanGeometry.Sphere.secondInter_smul, InnerProductSpace.harmonicAt_comp_CLE_iff, Bundle.RiemannianMetric.symm, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, strongConcaveOn_iff_convex, linear_isometry_complex, sum_mul_eq_sub_integral_mulβ', MeasureTheory.condExpIndL1_smul, unitInterval.symm_one, ProbabilityTheory.isGaussian_map, instIsZLatticeRealSpan, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_increments, ProbabilityTheory.gaussianReal_mul_const, Path.delayReflLeft_zero, concaveOn_univ_of_deriv2_nonpos, ContinuousMap.sup_mem_subalgebra_closure, MeasureTheory.weightedSMul_add_measure, MeasureTheory.Measure.NullMeasurableSet.const_smul, MDifferentiable.slash, MeasureTheory.Measure.map_conv_continuousLinearMap, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, ContDiffMapSupportedIn.locallyConvexSpace, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, Orientation.oangle_rotation_oangle_left, smul_unitBall_of_pos, map_real_smul, ProbabilityTheory.IsGaussian.charFunDual_eq, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, circleAverage_def, CuspForm.coe_translate, RCLike.sqrt_map, Chebyshev.theta_eq_log_primorial, NumberField.isFinitePlace_iff, cfcβ_tsub, unitInterval.qRight_zero_right, rotationOf_rotation, ProbabilityTheory.strong_law_aux6, convexOn_descPochhammer_eval, IsMIntegralCurveAt.hasMFDerivAt, skewAdjoint.negISMul_apply_coe, PMF.integral_eq_tsum, SpectrumRestricts.real_iff, intervalIntegral.integral_comp_div, Complex.rank_real_complex', concaveOn_negMulLog, MulRingNorm.mulRingNormClass, Orientation.oangle_sign_smul_left, ContDiffPointwiseHolderAt.continuousLinearMap_comp, ContinuousWithinAt.cfcβ_nnreal, unitInterval.mul_le_right, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, ConvexBody.isBounded, exists_polynomial_near_continuousMap, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, ZSpan.isAddFundamentalDomain', EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, ContinuousMap.inf_mem_subalgebra_closure, homeomorphUnitSphereProd_symm_apply_coe, ProbabilityTheory.covarianceBilin_self_nonneg, exists_monotone_Icc_subset_open_cover_unitInterval_prod_self, Orientation.rightAngleRotation_rightAngleRotation, taylorWithinEval_succ, HasDerivAt.norm_sq, WeakBilin.locallyConvexSpace, ProbabilityTheory.integral_linearMap_gaussianReal, EuclideanQuadrant.convex, ContinuousMap.inf_mem_closed_subalgebra, unitInterval.nonneg', dimH_of_nonempty_interior, Polynomial.hermite_eq_deriv_gaussian', imaginaryPart_realPart, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ProbabilityTheory.indepFun_iff_charFunDual_prod', Affine.Simplex.direction_mongePlane, Complex.normSq_zero, MeasureTheory.Measure.integral_comp_mul_left, unitInterval.le_one', uniqueDiffWithinAt_Ioo, ProbabilityTheory.covarianceBilinDual_self_eq_variance, ProperCone.innerDual_union, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, SchwartzMap.fourier_evalCLM_eq, ContinuousWithinAt.integral_sub_linear_isLittleO_ae, Subgroup.isArithmetic_iff_finiteIndex, Orientation.oangle_sign_smul_sub_left, AlgebraNormClass.toRingNormClass, QuasispectrumRestricts.real_iff, MeasureTheory.memL1_smul_of_L1_withDensity, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, MeasureTheory.Measure.toSphere_apply', TemperedDistribution.instLineDerivSMulReal, range_cfcβ_nnreal_eq_image_cfcβ_real, SchwartzMap.evalCLM_apply_apply, Orientation.rotation_eq_self_iff_angle_eq_zero, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, Height.mulHeight_eq, NumberField.FinitePlace.coe_apply, isBounded_convexHull, Filter.Tendsto.cfcβ_nnreal, tendsto_integral_exp_smul_cocompact_of_inner_product, mem_parallelepiped_iff, MeasureTheory.integral_biUnion_eq_sum_powerset, Orientation.oangle_rotation_right, Complex.ofReal_comp_balance, RCLike.normSq_mul, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, differentiableAt_norm_smul, circleAverage_eq_integral_add, intervalIntegral.inv_smul_integral_comp_div_sub, Module.Basis.prod_parallelepiped, convexOn_Gamma, NumberField.mixedEmbedding.norm_nonneg, parallelepiped_basis_eq, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, Seminorm.convex_ball, PartitionOfUnity.sum_finsupport_smul_eq_finsum, harmonic_floor_le_one_add_log, ProbabilityTheory.IsGaussian.memLp_dual, Complex.normSq_conj, IsCompact.extremePoints_nonempty, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, Behrend.ceil_lt_mul, Complex.continuous_normSq, ProbabilityTheory.covarianceBilinDual_self_nonneg, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, Path.range_segment, convexHull_sphere_eq_closedBall, isCusp_SL2Z_iff, Complex.equivRealProdLm_symm_apply, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', MeasureTheory.charFunDual_map_const_add, MeasureTheory.charFunDual_map_add_const, Complex.equivRealProdLm_symm_apply_im, ProbabilityTheory.setBernoulli_zero, Complex.coe_basisOneI_repr, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, realPart_I_smul, Orientation.rotation_trans, uniqueDiffWithinAt_Ioi, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, selfAdjoint.realPart_unitarySelfAddISMul, gauge_def, ModularGroup.tendsto_normSq_coprime_pair, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, nnnorm_cfcβ_nnreal_lt_iff, NumberField.mixedEmbedding.norm_smul, Complex.normSq_intCast, unitInterval.qRight_zero_left, MeasureTheory.integral_comp_rpow_Ioi, bernsteinApproximation.apply_one, convex_closedEBall, MeasureTheory.condExp_ae_eq_condExpL1CLM, LinearMap.norm_extendToπ'_apply_sq, NumberField.mixedEmbedding.span_latticeBasis, Height.AdmissibleAbsValues.mulSupport_finite, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, RCLike.realLinearIsometryEquiv_symm_apply, convex_ball, real_inner_smul_right, ContinuousLinearMap.hasTemperateGrowth, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, UpperHalfPlane.pos_real_smul_injective, Orientation.oangle_sub_right_smul_rotation_pi_div_two, VectorFourier.fourierSMulRight_apply, stereographic_neg_apply, StrongConcaveOn.strictConcaveOn, MeasureTheory.Measure.addHaar_image_linearMap, closedBall_eq_segment, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, CongruenceSubgroup.strictWidthInfty_Gamma1, Seminorm.closedBall_smul, MeasureTheory.condExpL1CLM_indicatorConst, isScalarTower, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, NormedSpace.normalize_smul_of_neg, MeasureTheory.L1.nnnorm_Integral_le_one, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.integral_fun_norm_addHaar, MeasureTheory.setIntegral_ge_of_const_le, ArchimedeanClass.lt_of_stdPart_lt, imaginaryPart_apply_coe, SchwartzMap.smulLeftCLM_add, MeasureTheory.weightedSMul_smul, MeasureTheory.integral_continuousLinearMap_prod, EisensteinSeries.eisensteinSeries_SIF_apply, intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, segment_subset_closedBall_left, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Orientation.areaForm_comp_rightAngleRotation, NumberField.mixedEmbedding.continuous_norm, uniqueDiffOn_Icc_zero_one, totallyBounded_convexHull, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, ZSpan.fundamentalDomain_subset_parallelepiped, ContinuousLinearMap.norm_extendToπ'_bound, sum_mem_ball_of_strictConvexSpace, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, uniqueDiffWithinAt_Iio, Complex.im_balance, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, Complex.ofReal_expect, sum_mul_eq_sub_integral_mulβ, MeasureTheory.integral_comp, Chebyshev.psi_eq_theta_add_sum_theta, RCLike.complexLinearIsometryEquiv_symm_apply, MeasureTheory.average_union_mem_segment, UpperHalfPlane.denom_neg, Complex.div_re, convex_iff_isPreconnected, unitInterval.symm_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, InformationTheory.convexOn_klFun, cfcβ_real_eq_nnreal, ProbabilityTheory.instIsProbabilityMeasureCondCDF, imaginaryPart_comp_subtype_selfAdjoint, stdSimplexHomeomorphUnitInterval_apply_coe, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, ProbabilityTheory.gaussianReal_map_mul_const, BoxIntegral.BoxAdditiveMap.toSMul_apply, ProbabilityTheory.IsGaussian.map_rotation_eq_self, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, homeomorphSphereProd_symm_apply_coe, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, MeasureTheory.integrable_tilted_iff, ProbabilityTheory.covarianceOperator_inner, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, mellin_eq_fourierIntegral, hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, MeasureTheory.AEStronglyMeasurable.fourierPowSMulRight, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, LSeries_eq_mul_integral, HasFDerivAt.inner, WithAbs.norm_eq_abv, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, MeasureTheory.integrable_withDensity_iff_integrable_smul, isPathConnected_stdSimplex, MeasureTheory.condExpL1CLM_lpMeas, Module.Basis.coe_parallelepiped, NumberField.InfinitePlace.embedding_of_isReal_apply, ProbabilityTheory.HasGaussianLaw.map_fun, convex_halfSpace_re_ge, EuclideanGeometry.inversion_def, ProbabilityTheory.covarianceBilin_apply_pi, SchwartzMap.integral_bilinear_laplacian_right_eq_left, Path.Homotopy.transReflReparamAux_zero, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', intervalIntegral.integral_comp_sub_mul, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, homeomorphUnitSphereProd_apply_fst_coe, CFC.posPart_smul_of_nonneg, realPart_surjective, Orientation.kahler_apply_self, Polynomial.hermite_eq_deriv_gaussian, isCompact_closedAbsConvexHull_of_totallyBounded, Orientation.inner_smul_rotation_pi_div_two_right, ZSpan.instDiscreteTopologySubtypeMemSubmoduleIntSpanRangeCoeBasisRealOfFinite, UniformConcaveOn.concaveOn, Complex.conjCLE_nnorm, HasStrictDerivAt.complexToReal_fderiv', Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, fourierIntegral_gaussian_innerProductSpace, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ZSpan.isAddFundamentalDomain, MeasureTheory.weightedSMul_union, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, abs_signedDist_eq_dist_iff_vsub_mem_span, MeasureTheory.uniformIntegrable_average, Orientation.kahler_rotation_left', MeasureTheory.setIntegral_rnDeriv_smul', ContDiff.fourierPowSMulRight, convex_halfSpace_im_ge, intervalIntegral.smul_integral_comp_mul_left, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, ContinuousLinearMap.extendToπ_apply, rotation_trans, ProbabilityTheory.IsGaussian.integral_dual, uniformConcaveOn_zero, Orientation.abs_areaForm_le, ArithmeticFunction.log_mul_moebius_eq_vonMangoldt, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, bernstein.z_zero, ContinuousLinearMap.norm_extendToπ', InnerProductGeometry.angle_smul_smul, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, convex_halfSpace_re_lt, NumberField.count_multisetInfinitePlace_eq_mult, ModelWithCorners.convex_range, ProbabilityTheory.covarianceBilin_apply_basisFun, ContDiffBump.integral_normed_smul, Complex.restrictScalars_toSpanSingleton, ProbabilityTheory.measure_cdf, Orientation.oangle_sign_smul_right, Orientation.normSq_kahler, Padic.isAbsoluteValue, Complex.normSq_inv, ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, SmoothBumpFunction.contMDiff_smul, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, VectorFourier.contDiff_fourierIntegral, NumberField.InfinitePlace.denseRange_algebraMap_pi, sameRay_iff_inv_norm_smul_eq, imaginaryPart_surjective, CompletelyRegularSpace.completely_regular, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, cfcHom_nnreal_eq_restrict, BoxIntegral.integral_smul, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, ProbabilityTheory.integral_tilted_mul_eq_mgf, MeasureTheory.integral_simpleFunc_larger_space, ContDiffBump.apply, Orientation.oangle_sign_add_smul_left, HasFDerivAt.lim_real, strictConvexOn_rpow, Matrix.PosSemidef.sq_sqrt, UpperHalfPlane.coe_J_smul, Orientation.neg_rotation_pi_div_two, ProperCone.relative_hyperplane_separation, Complex.normSq_div, UniformConcaveOn.strictConcaveOn, ContinuousOn.cfcβ_nnreal', Complex.normSq_ofReal, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Orientation.rotation_eq_matrix_toLin, MeasureTheory.AEStronglyMeasurable.fourierSMulRight, intervalIntegral.integral_const_of_cdf, Orientation.inner_rightAngleRotation_swap, intervalIntegral.integral_const', Complex.im_comp_balance, RCLike.normSq_eq_def', UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, CongruenceSubgroup.strictPeriods_Gamma1, rotationOf_coe, nndist_eq, Algebra.norm_complex_apply, NumberField.mixedEmbedding.volume_negAt_plusPart, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, Orientation.oangle_sub_left_smul_rotation_pi_div_two, tangentConeAt_real_subset_isRCLikeNormedField, ProperCone.innerDual_insert, Module.Basis.parallelepiped_eq_map, selfAdjoint.realPart_coe, ContinuousMap.HomotopyLike.map_one_left, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff, Complex.norm_def, integral_withDensity_eq_integral_toReal_smul, ZLattice.covolume.tendsto_card_div_pow', NumberField.InfinitePlace.isometry_embedding_of_isReal, OnePoint.IsBoundedAt.smul_iff, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, Unitization.nnreal_cfcβ_eq_cfc_inr, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_prodMk, ProperCone.dual_flip_dual, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, RCLike.ofRealCLM_norm, unitInterval.tendsto_sigmoid_atTop, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, CStarModule.inner_smul_left_real, rank_rat_real, Complex.sqrt_map, InnerProductSpace.HarmonicOnNhd.const_smul, MeasureTheory.setIntegral_indicatorConstLp, UpperHalfPlane.pos_real_re, stereographic_target, MeasureTheory.SignedMeasure.rnDeriv_smul, ProbabilityTheory.iIndepFun.hasGaussianLaw, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, signedDist_smul, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, Orientation.oangle_add_right_smul_rotation_pi_div_two, ProbabilityTheory.gaussianPDFReal_inv_mul, NNReal.coe_expect, Orientation.inner_smul_rotation_pi_div_two_left, unitInterval.symm_zero, BoxIntegral.hasIntegral_const, MeasureTheory.Supermartingale.smul_nonpos, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, map_linearMap_volume_pi_eq_smul_volume_pi, setIntegral_withDensity_eq_setIntegral_smul, SlashInvariantForm.coe_trace, isConformalMap_complex_linear_conj, Euclidean.closedBall_eq_preimage, mellin_comp_rpow, MeasureTheory.Submartingale.sum_smul_sub', NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Matrix.PosSemidef.inv_sqrt, uniqueDiffOn_Iio, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, convex_RCLike_iff_convex_real, Chebyshev.theta_eq_sum_Icc, intervalIntegral.smul_integral_comp_mul_add, log_le_harmonic_floor, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, Orientation.kahler_rightAngleRotation_left, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, SchwartzMap.tsupport_smulLeftCLM_subset, cfcβHom_real_eq_restrict, Complex.equivRealProdLm_symm_apply_re, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, MeasureTheory.ComplexMeasure.im_apply, Monotone.convexOn_univ_of_deriv, MeasureTheory.Measure.addHaar_smul_of_nonneg, NumberField.mixedEmbedding.normAtPlace_neg, RCLike.ofReal_expect, Orientation.oangle_smul_right_of_neg, ProbabilityTheory.HasGaussianLaw.map_equiv, Orientation.abs_areaForm_of_orthogonal, innerβ_apply_apply, ConvexBody.nonempty, CongruenceSubgroup.strictWidthInfty_Gamma, MeasureTheory.integral_rnDeriv_smul, NumberField.mixedEmbedding.unitSMul_smul, fourierCoeff_eq_intervalIntegral, CStarAlgebra.conjugate_le_norm_smul', NumberField.mixedEmbedding.continuous_normAtPlace, SchwartzMap.tsupport_fderivCLM_subset, unitInterval.subtype_Ici_eq_Icc, inner_sum_smul_sum_smul_of_sum_eq_zero, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, MeasureTheory.Measure.map_addHaar_smul, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, PMF.integral_eq_sum, MeasureTheory.average_add_measure, Orientation.kahler_rotation_left, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, unitInterval.coe_lt_one, GaussianInt.intCast_real_norm, Complex.conjCLE_enorm, Rat.AbsoluteValue.padic_le_one, MeasureTheory.charFunDual_eq_pi_iff, MeasureTheory.aestronglyMeasurable_condExpL1CLM, Continuous.cfcβ_nnreal_of_mem_nhdsSet, ArithmeticFunction.moebius_mul_log_eq_vonMangoldt, instIsDomain, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, ContDiffMapSupportedIn.seminorm_apply, convexHull_ediam, aemeasurable_withDensity_iff, unitInterval.subtype_Iio_eq_Ico, Orientation.inner_sq_add_areaForm_sq, signedDist_smul_of_neg, ContinuousLinearMap.rotation_apply, iteratedFDeriv_fourier, RCLike.reLm_coe, EisensteinSeries.q_expansion_bernoulli, Path.target', UpperHalfPlane.coe_specialLinearGroup_apply, hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, fderiv_norm_smul, MulRingSeminorm.mulRingSeminormClass, expNegInvGlue.continuous_polynomial_eval_inv_mul, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, isMIntegralCurveAt_comp_mul_ne_zero, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, StarModule.complexToReal, Complex.normSq_nonneg, range_mfderiv_coe_sphere, IsMIntegralCurve.comp_mul, MeasureTheory.weightedSMul_union', MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, stereographic_source, convex_parallelepiped, SchwartzMap.pairing_continuous_left, hasFDerivAt_fourierIntegral, NumberField.mixedEmbedding.normAtPlace_apply, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, Complex.coe_selfAdjointEquiv, ConvexBody.isClosed, Complex.conjCLE_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, Complex.nndist_conj_self, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, imaginaryPart_ofReal, ProbabilityTheory.strong_law_Lp, RCLike.normSq_pos, ModularGroup.im_smul_eq_div_normSq, MeasureTheory.integral_const, Euclidean.ball_eq_preimage, CStarAlgebra.star_left_conjugate_le_norm_smul, MeasureTheory.L1.SimpleFunc.setToL1S_zero_left, SchwartzMap.lineDerivOp_fourierInv_eq, finrank_real_of_complex, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, 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, RingNorm.ringNormClass, unitInterval.coe_pos, gaugeRescale_def, nnabs_coe, ConvexBody.isCompact, hasDerivAt_Gamma_one, Complex.coe_smul, NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex, CongruenceSubgroup.mem_conjGL, ProperCone.innerDual_empty, stdSimplexHomeomorphUnitInterval_one, OpenPartialHomeomorph.univUnitBall_apply, NumberField.mixedEmbedding_injective, Orientation.oangle_map, MeasureTheory.Measure.addHaar_preimage_linearMap, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, BoxIntegral.integralSum_smul, StarAlgHom.realContinuousMapOfNNReal_injective, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, NumberField.mixedEmbedding.convexBodyLT_convex, MeasureTheory.setIntegral_tilted', Complex.normSq_add_mul_I, locallyIntegrableOn_mul_sum_Icc, Orientation.kahler_mul, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', ProbabilityTheory.covarianceBilinDual_comm, ProbabilityTheory.isGaussian_iff_charFunDual_eq, ContinuousOn.integral_sub_linear_isLittleO_ae, Nonneg.instNonUnitalContinuousFunctionalCalculus, SchwartzMap.instLocallyConvexSpace, NormedAlgebra.Real.nonempty_algEquiv_or, Orientation.oangle_smul_smul_self_of_nonneg, ProperCone.dual_dual_flip, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, flip_innerβ, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, NNReal.orderIsoRpow_symm_eq, MeasureTheory.Measure.addHaar_ball_mul_of_pos, Orientation.rightAngleRotation_trans_neg_orientation, Orientation.volumeForm_robust', ProbabilityTheory.HasGaussianLaw.map_equiv_fun, integrableOn_peak_smul_of_integrableOn_of_tendsto, ModelWithCorners.convex_range', Path.range_coe, NormedSpace.toLocallyConvexSpace, strictConcaveOn_sqrt, CongruenceSubgroup.strictPeriods_Gamma, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, ModularGroup.tendsto_lcRow0, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, parallelepiped_eq_sum_segment, cosetToCuspOrbit_apply_mk, ContDiffBump.convolution_eq_right, ExistsContDiffBumpBase.w_def, MeasureTheory.Measure.setIntegral_comp_smul, Complex.imCLM_coe, isBoundedBilinearMap_inner, expNegInvGlue.contDiff_polynomial_eval_inv_mul, intervalIntegral.integral_hasFDerivWithinAt, Polynomial.aeval_ofReal, MeasureTheory.charFunDual_prod', toNNReal_abs, LinearIsometryEquiv.toMeasurableEquiv_symm, InformationTheory.strictConvexOn_klFun, ProbabilityTheory.covarianceBilin_apply, BoxIntegral.integralSum_sub_partitions, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, MeasureTheory.withDensitySMulLI_apply, MeasureTheory.Measure.addHaar_nnreal_smul, NumberField.mixedEmbedding.logMap_apply, ContinuousMap.comp_attachBound_mem_closure, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, dist_div_norm_sq_smul, hasDerivAt_norm_rpow, ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite, NumberField.mixedEmbedding.latticeBasis_apply, MeasureTheory.Measure.addHaar_submodule, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, ContinuousMap.Homotopy.apply_zero, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, Complex.selfAdjointEquiv_symm_apply, Matrix.IsHermitian.cfcAux_id, ProbabilityTheory.IsGaussianProcess.smul, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Complex.ofRealHom_eq_coe, image_parallelepiped, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, ProbabilityTheory.covarianceBilin_map, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, Orientation.two_zsmul_oangle_smul_right_self, HasFDerivAt.curveIntegral_segment_source', hasSum_one_div_nat_pow_mul_sin, NumberField.mixedEmbedding.fundamentalCone.intNorm_coe, Orientation.coe_basisRightAngleRotation, NumberField.mixedEmbedding.norm_eq_zero_iff, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, SchwartzMap.fderivCLM_fourier_eq, CStarModule.inner_mul_inner_swap_le, Bundle.ContinuousRiemannianMetric.pos, ProbabilityTheory.strong_law_aux4, SchwartzMap.derivCLM_apply, Seminorm.gauge_ball, RCLike.map_nonneg_iff, StrictAnti.strictConcaveOn_univ_of_deriv, Complex.finrank_real_complex, IsCoercive.continuousLinearEquivOfBilin_apply, MeasureTheory.integral_fun_fst, SmoothPartitionOfUnity.contMDiff_finsum_smul, MeasureTheory.pdf.integrable_pdf_smul_iff, NumberField.mixedEmbedding.normAtPlace_nonneg, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, Orientation.areaForm_map, SimpleGraph.triangleRemovalBound_le, det_fderivPiPolarCoordSymm, isConformalMap_iff, Rat.AbsoluteValue.not_real_equiv_padic, Complex.finrank_real_complex_fact, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.commMap_apply_of_isReal, ZSpan.fundamentalDomain_pi_basisFun, ProperCone.mem_innerDual, Seminorm.finset_sup_smul, Bundle.RiemannianMetric.pos, CStarAlgebra.conjugate_le_norm_smul, convexOn_exp, Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, norm_midpoint_lt_iff, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', MeasureTheory.Submartingale.sum_smul_sub, RCLike.mul_self_norm, ContDiffMapSupportedIn.structureMapLM_zero_injective, strictConvexOn_univ_of_deriv2_pos, Complex.equivRealProdCLM_symm_apply_re, MeasureTheory.integrable_withDensity_iff_integrable_coe_smulβ, MeasureTheory.charFunDual_eq_pi_iff', uniqueDiffOn_Ioi, Besicovitch.card_le_of_separated, Chebyshev.psi_eq_sum_Icc, realPart_imaginaryPart, ModularForm.coe_norm, Path.id_apply, MeasureTheory.integral_countable, CongruenceSubgroup.mem_conjGL', CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, norm_cfcβ_one_sub_one_add_inv_lt_one, NumberField.mixedEmbedding.latticeBasis_repr_apply, NumberField.FinitePlace.instMonoidWithZeroHomClassReal, continuousOn_cfcβ_nnreal, surjOn_extremePoints_image, BoxIntegral.Integrable.smul, isMIntegralCurveOn_comp_mul_ne_zero, Complex.mul_conj, ProbabilityTheory.uncenteredCovarianceBilin_zero, ArchimedeanClass.mk_sub_pos_iff, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, rank_real_of_complex, InformationTheory.convexOn_Ioi_klFun, Path.source, NumberField.AdeleRing.algebraMap_fst_apply, hasFDerivAt_integral_of_dominated_of_fderiv_le, IsScalarTower.complexToReal, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, VectorFourier.fourierPowSMulRight_apply, skewAdjointPart_eq_I_smul_imaginaryPart, uniqueDiffOn_Ico, inner_eq_norm_mul_iff_real, Complex.inv_im, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, MeasureTheory.Submartingale.smul_nonpos, ContinuousMap.Homotopy.map_one_left, RCLike.normSq_div, RCLike.im_sq_le_normSq, integrableOn_mul_sum_Icc, NumberField.mixedEmbedding.normAtPlace_negAt, Module.Basis.parallelepiped_map, AlternatingMap.measure_def, ContinuousMap.Homotopy.apply_one, strictConcaveOn_sin_Icc, MeasureTheory.charFunDual_dirac, Filter.Tendsto.integral_sub_linear_isLittleO_ae, LinearIsometryEquiv.reflections_generate_dim, convexOn_univ_of_deriv2_nonneg, Complex.isometryOfOrthonormal_apply, ProbabilityTheory.IndepFun.hasGaussianLaw, intervalIntegral.smul_integral_comp_mul_right, Circle.normSq_coe, intervalIntegral.integral_comp_div_add, conformalFactorAt_inner_eq_mul_inner, Rat.AbsoluteValue.eq_on_nat_iff_eq, BoxIntegral.integral_const, NumberField.mixedEmbedding.normAtPlace_smul, ConvexBody.convex', NumberField.mixedEmbedding.finrank, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, dimH_segment, Complex.imCLM_nnnorm, ContDiffAt.laplacian_CLM_comp_left_nhds, Orientation.inner_rightAngleRotation_right, ModularForm.prod_fintype_slash, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Orientation.volumeForm_apply_le, nonempty_algEquiv_or, Complex.starConvex_slitPlane, MeasureTheory.norm_condExpInd_le, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, Rat.AbsoluteValue.real_eq_abs, NumberField.mixedEmbedding.negAt_apply_norm_isReal, MeasureTheory.integrable_comp_smul_iff, MeasureTheory.Measure.addHaar_preimage_linearEquiv, cfcβ_nnreal_eq_real, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, expMonoidHom_apply, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, SlashInvariantForm.vAdd_width_periodic, UpperHalfPlane.denom_one, IsMIntegralCurveAt.comp_mul_ne_zero, stereographic_apply, Orientation.rotation_apply, SameRay.norm_smul_eq, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Rat.AbsoluteValue.not_real_isEquiv_padic, iteratedFDeriv_fourierIntegral, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, StieltjesFunction.ae_hasDerivAt, ProbabilityTheory.strong_law_aux1, MeasureTheory.withDensityα΅₯_rnDeriv_smul, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero_symm, MeasureTheory.condExpInd_disjoint_union_apply, ProbabilityTheory.measure_condCDF_Iic, Mathlib.Meta.Positivity.nnabs_pos_of_pos, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, UpperHalfPlane.val_J, NumberField.toNNReal_valued_eq_adicAbv, StrongConvexOn.strictConvexOn, Orientation.kahler_apply_apply, RCLike.imCLM_coe, RCLike.re_sq_le_normSq, imaginaryPart_imaginaryPart, Orientation.inner_rightAngleRotationAuxβ_left, MeasureTheory.integral_indicator_const, Path.Homotopy.trans_refl_reparam, strictConvexOn_zpow, Complex.normSq_eq_conj_mul_self, Orientation.areaForm_apply_self, ModularForm.slash_def, ProbabilityTheory.measurable_measure_condCDF, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, MeasureTheory.integrable_rnDeriv_smul_iff, differentiable_fourierChar_neg_bilinear_right, ProbabilityTheory.strong_law_ae_simpleFunc_comp, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, Complex.conjCLE_norm, ProbabilityTheory.variance_linearMap_gaussianReal, UpperHalfPlane.instContinuousGLSMul, MeasureTheory.Measure.addHaar_closedBall, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, Submodule.angle_coe, tendsto_integral_gaussian_smul, NNReal.mk_natCast, MeasureTheory.L1.norm_Integral_le_one, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, ContDiff.dimH_range_le, ModularForm.is_invariant_one', Complex.imCLM_enorm, EisensteinSeries.eisensteinSeriesSIF_apply, SchwartzMap.tsupport_derivCLM_subset, Filter.Tendsto.cesaro_smul, RCLike.normSq_zero, det_rotation, MeasureTheory.integrable_continuousLinearMap_prod, strictConcave_binEntropy, Continuous.fourierPowSMulRight, UpperHalfPlane.mul_smul', imaginaryPart_smul, NumberField.mixedEmbedding.norm_real, VectorFourier.fourierIntegral_probChar, ContinuousMap.polynomial_comp_attachBound, Orientation.rightAngleRotation_map, VectorFourier.norm_fourierSMulRight_le, AlternatingMap.measure_parallelepiped, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, MeasureTheory.charFunDual_map, Orientation.two_zsmul_oangle_smul_left_self, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, AddMonoidHom.coe_toRealLinearMap, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, uniqueDiffWithinAt_Ici, ZSpan.discreteTopology_pi_basisFun, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, ProbabilityTheory.strong_law_aux2, CFC.nnrpow_eq_nnrpow_prod, fourierCoeffOn_eq_integral, Complex.re_expect, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, exists_monotone_Icc_subset_open_cover_unitInterval, MeasureTheory.SimpleFunc.integral_const, Behrend.div_lt_floor, strictConcaveOn_log_Ioi, ProbabilityTheory.variance_dual_prod, ProbabilityTheory.isGaussian_map_equiv, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Orientation.oangle_sign_smul_add_smul_right, RCLike.normSq_eq_zero, uniqueDiffOn_Ioo, AffineSubspace.direction_perpBisector, Besicovitch.multiplicity_le, realPart_apply_coe, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, intervalIntegral.integral_comp_mul_right, rotation_symm, ContinuousLinearMap.extendToπ'_apply, NumberField.mem_multisetInfinitePlace, VectorFourier.norm_fourierPowSMulRight_le, EuclideanGeometry.dist_smul_vadd_eq_dist, Complex.equivRealProdCLM_symm_apply_im, MeasureTheory.integral_singleton, intervalIntegral.integral_comp_div_sub, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, ConvexBody.hausdorffDist_coe, hasFDerivAt_fourierChar_neg_bilinear_right, nnabs_pos, Path.delayReflRight_one, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, ProbabilityTheory.measure_condCDF_univ, ContDiffMapSupportedIn.continuous_iff_comp, VectorFourier.norm_fourierSMulRight, InnerProductSpace.volume_closedBall, ProbabilityTheory.hasDerivAt_mgf, NormedSpace.norm_smul_normalize, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, LinearMap.mem_span_iff_bound, homeomorphSphereProd_apply_fst_coe, ContinuousOn.cfcβ_nnreal, UpperHalfPlane.pos_real_im, SchwartzMap.smulLeftCLM_sub, NumberField.FinitePlace.isFinitePlace, Path.subpathAux_zero, SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, tendsto_card_div_pow_atTop_volume', MeasureTheory.charFunDual_pi, strongConvexOn_zero, SchwartzMap.fourier_fderivCLM_eq, ConvexBody.hausdorffEDist_coe, MeasureTheory.SimpleFunc.integral_eq, integral_withDensity_eq_integral_toReal_smulβ, AbsoluteValue.isEquiv_iff_exists_rpow_eq, Complex.hasStrictFDerivAt_log_real, MeasureTheory.SimpleFunc.setToSimpleFunc_const', Path.Homotopy.eval_one, real_inner_smul_left, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, sum_mul_eq_sub_sub_integral_mul', Orientation.oangle_rotation_self_right, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, NumberField.mixedEmbedding.euclidean.finrank, Path.target, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, differentiable_fourierChar_neg_bilinear_left, MeasureTheory.lpNorm_expect_le, ConvexBody.hausdorffEdist_coe, Antitone.concaveOn_univ_of_deriv, AffineBasis.centroid_mem_interior_convexHull, fderiv_norm_smul_pos, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Path.Homotopy.source, MeasureTheory.Measure.addHaar_closedBall_mul, NNReal.instIsStrictOrderedModule, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, CStarAlgebra.star_right_conjugate_le_norm_smul, NNReal.instContinuousMapZero.UniqueHom, bernstein.z_last, TestFunction.instContinuousSMulReal, MeasureTheory.integral_comp_mul_left_Ioi, Complex.reCLM_norm, completelyRegularSpace_iff, unitInterval.univ_eq_Icc, Zsqrtd.toReal_apply, ContinuousMapZero.toNNReal_neg_smul, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, MeasureTheory.SimpleFunc.map_integral, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NumberField.mixedEmbedding.convexBodySum_convex, ContinuousMap.polynomial_comp_attachBound_mem, Complex.normSq_apply, convex_halfSpace_im_le, MeasureTheory.measure_smul_setAverage, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, MeasureTheory.Integrable.comp_smul, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, ProbabilityTheory.variance_smul', ContDiffMapSupportedIn.structureMapCLM_zero_injective, sum_mul_eq_sub_integral_mul, NumberField.prod_archAbsVal_eq, RCLike.normSq_to_complex, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, MeasureTheory.setIntegral_condExpL1CLM, unitInterval.subtype_Iic_eq_Icc, Module.Basis.map_addHaar, ContinuousMap.HomotopyWith.apply_zero, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, intervalIntegral.integral_comp_mul_add, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, RCLike.normSq_add, RCLike.div_re, Submodule.isPathConnected, Orientation.inner_smul_rotation_pi_div_two_smul_left, IsSelfAdjoint.coe_realPart, MeasureTheory.Measure.addHaar_ball, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, ArchimedeanClass.stdPart_of_mk_nonneg, Complex.im_sq_le_normSq, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, MeasureTheory.condExp_bot', SchwartzMap.smulLeftCLM_ofReal, Orientation.oangle_smul_right_of_pos, realPart_smul, MeasureTheory.lpNorm_smul_measure_of_ne_top, abs_real_inner_div_norm_mul_norm_eq_one_iff, projIcc_eq_zero, ProbabilityTheory.instIsGaussianProdProdOfSecondCountableTopologyEither, instLocallyConvexSpaceRealOfPolynormableSpace, MeasureTheory.integral_finset, Orientation.inner_smul_rotation_pi_div_two_smul_right, ContinuousAt.integral_sub_linear_isLittleO_ae, EuclideanGeometry.Sphere.direction_orthRadius, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, Complex.rightAngleRotation, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, CFC.negPart_smul, ArithmeticFunction.vonMangoldt_mul_zeta, unitInterval.sigmoid_pos, ContinuousMapZero.toNNReal_smul, ProbabilityTheory.covarianceBilinDual_of_not_memLp, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, UpperHalfPlane.denom_cocycle', ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, ModularGroup.lcRow0_apply, Complex.ofRealAm_coe, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, Path.subpath_zero_one, ProbabilityTheory.gaussianPDFReal_mul, ConvexBody.coe_add, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, PeriodPair.indep, isConformalMap_complex_linear, zero_at_infty_vector_fourierIntegral, ModularForm.coe_translate, ProperCone.innerDual_iUnion, SchwartzMap.smulLeftCLM_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, MeasureTheory.condExpIndSMul_ae_eq_smul, UpperHalfPlane.neg_smul, Quaternion.linearIsometryEquivTuple_apply, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, Polynomial.tendsto_div_exp_atTop, Complex.isAbsoluteValueNorm, parallelepiped_eq_convexHull, SmoothPartitionOfUnity.contMDiff_smul, compact_inner_le_weight_mul_Lp_of_nonneg, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, interval_average_eq, RCLike.sqrt_normSq_eq_norm, TemperedDistribution.derivCLM_apply_apply, Complex.Gamma_def, MeasureTheory.Supermartingale.smul_nonneg, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, hasStrictFDerivAt_rpow_of_neg, Complex.isometryOfOrthonormal_symm_apply, ContDiffPointwiseHolderAt.zero_exponent_iff, MeasureTheory.weightedSMul_smul_measure, unitInterval.tendsto_sigmoid_atBot, RCLike.normSq_apply, intervalIntegral.integral_hasFDerivAt, ProperCone.innerDual_toSubmodule, InnerProductSpace.HarmonicAt.comp_CLM, Orientation.inner_rightAngleRotation_self, ModularForm.coe_trace, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, RCLike.ofRealCLM_coe, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, InnerProductSpace.laplacian_CLE_comp_left, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, integral_withDensity_eq_integral_smulβ, ProbabilityTheory.IsGaussian.charFunDual_eq', convex_halfSpace_re_gt, NormedSpace.toLocallyConvexSpace', ContinuousMap.Homotopy.curry_one, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, RealRMK.le_rieszMeasure_tsupport_subset, unitInterval.subtype_Ioi_eq_Ioc, hasDerivAt_Gamma_nat, Orientation.oangle_smul_right_self_of_nonneg, HasStrictFDerivAt.inner, Height.AdmissibleAbsValues.product_formula, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, MeasureTheory.integrable_fun_norm_addHaar, skewAdjoint.I_smul_neg_I, ProbabilityTheory.isPositive_covarianceOperator, MeasureTheory.dominatedFinMeasAdditive_weightedSMul, Complex.coe_basisOneI, CFC.abs_smul, Complex.map_isometryOfOrthonormal, Orientation.oangle_sign_smul_add_smul_left, sum_mul_eq_sub_integral_mulβ, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, UpperHalfPlane.contMDiff_smul, MeasureTheory.average_union_mem_openSegment, signedDist_apply_linear, ConvexBody.coe_nsmul, Bundle.RiemannianMetric.continuousAt, continuous_stereoInvFun, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, CFC.negPart_smul_of_nonneg, Complex.reCLM_enorm, MeasureTheory.integral_fun_snd, MeasureTheory.condExpInd_empty, ZLattice.covolume.tendsto_card_div_pow'', MeasureTheory.condExpL1CLM_smul, real_inner_smul_self_right, dist_smul_add_one_sub_smul_le, Subalgebra.SeparatesPoints.rclike_to_real, VectorFourier.hasFDerivAt_fourierChar_smul, Orientation.rotation_pi, strictConcaveOn_cos_Icc, PeriodPair.lattice_eq_span_range_basis, MeasureTheory.measure_unitBall_eq_integral_div_gamma, exists_extension_norm_eq, Seminorm.convex_closedBall, ContDiffMapSupportedIn.structureMapLM_zero_apply, nnnorm_cfcβ_nnreal_le, RCLike.ofRealAm_coe, RCLike.normSq_one, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, MeasureTheory.average_union, OpenPartialHomeomorph.univUnitBall_symm_apply, unitInterval.symm_eq_one, SmoothBumpCovering.embeddingPiTangent_coe, nndist_eq', EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, apply_le_nnnorm_cfcβ_nnreal, UpperHalfPlane.isometry_pos_mul, ProbabilityTheory.covarianceBilinDual_of_not_memLp', intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Orientation.two_zsmul_oangle_smul_smul_self, SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, Orientation.rotation_symm_apply, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, VectorFourier.integrable_fourierPowSMulRight, expNegInvGlue.differentiable_polynomial_eval_inv_mul, continuousOn_cfcβ_nnreal_setProd, ENNReal.toReal_smul, InnerProductGeometry.IsConformalMap.preserves_angle, Subgroup.strictWidthInfty_SL2Z, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, IsSelfAdjoint.imaginaryPart, Complex.normSq_neg, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Orientation.rotation_oangle_eq_iff_norm_eq, sum_mul_eq_sub_sub_integral_mul, ProbabilityTheory.Kernel.integral_withDensity, Rat.AbsoluteValue.apply_le_sum_digits, NumberField.mixedEmbedding.norm_negAt, Orientation.oangle_sign_smul_sub_right, unitInterval.sigmoid_lt_one, NumberField.mixedEmbedding.norm_unit, MonotoneOn.nnnorm_cfcβ, VectorFourier.fourierIntegral_fderiv, MeasureTheory.L1.integral_eq, stdSimplex.instCompactSpace_coe, gaugeRescale_smul, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, MeasureTheory.weightedSMul_zero_measure, taylor_within_apply, Polynomial.isPrimitive_iff_forall_gaussNorm_eq_one, convexOn_mul_log, fderivInnerCLM_apply, Chebyshev.eventually_primeCounting_le, AbsoluteValue.isEquiv_iff_isHomeomorph, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, Affine.Simplex.ninePointCircle_center, Polynomial.card_roots_toFinset_le_derivative, MeasureTheory.integral_smul_measure, strictConcaveOn_negMulLog, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, fderiv_fourierChar_neg_bilinear_left_apply, Module.Basis.addHaar_self, isConformalMap_iff_is_complex_or_conj_linear, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, RCLike.span_one_I, MulRingSeminorm.map_one', Complex.range_normSq, MeasureTheory.charFunDual_eq_prod_iff', Subgroup.IsArithmetic.discreteTopology, UpperHalfPlane.smulAux'_im, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, Matrix.PosDef.posDef_sqrt, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, Orientation.rightAngleRotation_neg_orientation, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, unitInterval.qRight_one_right, Orientation.rotationAux_apply, ArithmeticFunction.zeta_mul_vonMangoldt, integral_comp_pi_polarCoord_symm, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, Complex.imLm_coe, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, MeasureTheory.condExpL2_comp_continuousLinearMap, RCLike.re_extendToπ'β, MeasureTheory.charFun_map_smul, ZSpan.setFinite_inter, convex_closedBall, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, sameRay_iff_norm_smul_eq, LSeries_eq_mul_integral', ContDiffMapSupportedIn.structureMapLM_apply, Complex.normSq_eq_zero, ContinuousLinearMap.circleAverage_comp_comm, RCLike.normSq_sub, Subgroup.IsArithmetic.conj, SlashInvariantForm.coe_norm, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, Complex.det_conjLIE, ProbabilityTheory.convex_integrableExpSet, MeasureTheory.integral_countable', RCLike.realLinearIsometryEquiv_apply, strictConcaveOn_qaryEntropy, isBigO_rpow_zero_log_smul, ConvexBody.coe_smul', MeasureTheory.SignedMeasure.toJordanDecomposition_smul, ProperCone.innerDual_innerDual, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Orientation.areaForm_rightAngleRotation_left, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, LinearIsometry.angle_map, NumberField.mixedEmbedding.disjoint_negAt_plusPart, ContinuousMap.Homotopy.map_zero_left, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, GaussianInt.normSq_div_sub_div_lt_one, RCLike.imCLM_apply, CFC.nnrpow_map_prod, RightDerivMeasurableAux.le_of_mem_A, mul_pow_le_nat_floor_pow, EuclideanGeometry.Sphere.finrank_orthRadius, convexOn_rpow, aestronglyMeasurable_withDensity_iff, InnerProductGeometry.ConformalAt.preserves_angle, Affine.Simplex.points_vsub_eulerPoint, InnerProductGeometry.angle_smul_left_of_pos, uniqueDiffOn_Ici, GaussianInt.intCast_complex_norm, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, Seminorm.smul_le_smul, Complex.nonempty_linearEquiv_real, MeasureTheory.addEquivAddHaarChar_smul_integral_map, MeasureTheory.Measure.toSphere_apply_univ', Complex.ofReal_choose, IsCusp.smul, MeasureTheory.condExp_bot_ae_eq, Complex.equivRealProdCLM_apply, NumberField.FinitePlace.norm_def, NumberField.mixedEmbedding.convexBodySum_mem, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', unitInterval.toNNReal_one, MeasureTheory.condExpL1_eq, ModularGroup.smul_eq_lcRow0_add, cast_natAbs_eq_nnabs_cast, surjective_stereographic, hasDerivAt_abs_pos, ContDiffMapSupportedIn.structureMapLM_eq, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Complex.rank_real_complex, Orientation.oangle_smul_left_of_pos, hasFDerivAt_stereoInvFunAux_comp_coe, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving, HasCompactSupport.hasFDerivAt_convolution_left, NumberField.mixedEmbedding.convexBodyLT'_convex, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Orientation.inner_mul_areaForm_sub, ProbabilityTheory.covarianceOperator_of_not_memLp, MeasureTheory.Measure.addHaar_closedBall', ofDigits_digits_sum_eq, uniformConvexOn_zero, NumberField.mixedEmbedding.norm_apply, CompletelyRegularSpace.completely_regular_isOpen, RCLike.normSq_conj, ZSpan.fundamentalDomain_ae_parallelepiped, MeasureTheory.SignedMeasure.im_toComplexMeasure, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, Complex.rotation, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, BoxIntegral.unitPartition.tag_mem_smul_span, RCLike.complexLinearIsometryEquiv_apply, parallelepiped_single, Continuous.cfcβ_nnreal', ProbabilityTheory.instIsProbabilityMeasurecdf, BoundedContinuousFunction.probCharDual_apply, intervalIntegral.inv_smul_integral_comp_add_div, ArchimedeanClass.stdPart_eq_sSup, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, RCLike.inv_re, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, Set.Icc.convexCombo_zero, SlashInvariantForm.T_zpow_width_invariant, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, Complex.normSq_one, GaussianFourier.integral_rexp_neg_mul_sq_norm, NumberField.mixedEmbedding.normAtPlace_real, bernsteinApproximation.apply, MeasureTheory.Measure.addHaar_real_closedBall, ContinuousMap.Homotopy.curry_zero, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, UpperHalfPlane.mdifferentiable_smul, ModularForm.slash_apply, MeasureTheory.average_eq, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, ProbabilityTheory.indepFun_iff_charFunDual_prod, intervalIntegral.smul_integral_comp_add_mul, Complex.restrictScalars_toSpanSingleton', IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', MeasureTheory.Measure.integral_comp_inv_mul_right, Besicovitch.SatelliteConfig.exists_normalized_aux3, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, ProbabilityTheory.integral_tilted_mul_eq_cgf, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, MeasureTheory.Measure.addHaar_smul, Complex.reCLM_apply, Orientation.abs_volumeForm_apply_le, instIsStrictOrderedRing, Complex.conjLIE_symm, UpperHalfPlane.petersson_slash, Hyperreal.coeRingHom_toFun, MeasureTheory.Measure.addHaar_image_homothety, MeasureTheory.setIntegral_const, IsCoveringMap.liftPath_trans, norm_combo_lt_of_ne, Zsqrtd.toReal_injective
bridge: BoxIntegral.hasIntegralIndicatorConst
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