| Name | Category | Theorems |
|---|
induced π | CompOp | β |
toNonUnitalCommRing π | CompOp | 2453 mathmath: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, ValueDistribution.logCounting_zero, LinearMap.IsSymmetric.clm_adjoint_eq, Real.hasDerivAt_arccos, InnerProductSpace.Core.inner_smul_right, HasStrictFDerivAt.log, continuousSMul_sphere_ball, WithLp.prod_inner_apply, fderiv_iteratedFDeriv, RCLike.sqrt_eq_ite, FormalMultilinearSeries.comp_rightInv_aux1, tendsto_zero_iff_meromorphicOrderAt_pos, Unitization.isometry_inr, LinearMap.mkContinuousβ_norm_le', ContinuousMultilinearMap.norm_mkPiRing, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, ContinuousLinearMap.derivWithin_of_bilinear, Bundle.ContMDiffRiemannianMetric.isVonNBounded, InnerProductSpace.Core.inner_add_left, meromorphicNFOn_mul_iff_right_of_analyticOnNhd, ProbabilityTheory.cdf_measure_stieltjesFunction, continuous_cfcβHomSuperset_left, hasDerivWithinAt_Iio_iff_Iic, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, LinearMap.mkContinuousβ_apply, Matrix.frobenius_nnnorm_mul, RCLike.pos_iff_exists_ofReal, TensorProduct.inner_tmul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, HasMFDerivAt.mul, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, Orthonormal.inner_left_finsupp, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcβHom, logDeriv_const, RCLike.map_apply, MDifferentiableOn.clm_postcomp, hasDerivWithinAt_ofNat, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, ContinuousLinearMap.analyticWithinAt_bilinear, HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, Meromorphic.mul, ContinuousLinearMap.continuousβ, LinearMap.IsSymmetric.inner_map_polarization, hasDerivWithinAt_add_const_iff, FormalMultilinearSeries.comp_partialSum, HasFDerivWithinAt.ccos, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, hasStrictDerivAt_intCast, cfcβ_norm_nonneg, Complex.linearEquiv_det_conjLIE, LeftInvariantDerivation.leibniz, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.convolution_eq_right', Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, cfcβHom_apply_mem_elemental, curveIntegral_smul, CFC.abs_eq_cfc_norm, inner_vsub_right_eq_zero_symm, CFC.sqrt_eq_one_iff', Filter.Tendsto.cfc, CFC.posPart_one, InnerProductSpace.rankOne_one_left_eq_innerSL, ContinuousMap.abs_mem_subalgebra_closure, Function.FactorizedRational.divisor, AlgHomClass.instStarHomClass, NonUnitalCStarAlgebra.toStarModule, hasDerivAt_sqrt_mul_log, HasFiniteFPowerSeriesAt.neg, HasStrictFDerivAt.csin, Polynomial.isEquivalent_atBot_div, nnnorm_cfcβ_nnreal_le_iff, ContinuousLinearMap.map_add_add, HasFDerivWithinAt.pow, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, WeakDual.isCompact_polar, MeromorphicOn.divisor_fun_smul, nnnorm_cfc_lt, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, Real.hasDerivAt_sigmoid, meromorphicOrderAt_const_ofNat, Asymptotics.IsTheta.const_mul_left, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, LinearMap.IsPositive.ne_zero_iff, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, hasFDerivAt_multiset_prod, MDifferentiableAt.cle_arrowCongr, ProbabilityTheory.covarianceBilinDual_apply', spectrum.subset_closedBall_norm_mul, continuousSMul_sphere_sphere, RCLike.re_add_im, CFC.posPart_natCast, hasFTaylorSeriesUpToOn_top_iff_right, MeasureTheory.convolution_mul, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, FormalMultilinearSeries.radius_pi_eq_iInf, CFC.tendsto_cfc_rpow_sub_one_log, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, Padic.withValUniformEquiv_norm_le_one_iff, tendsto_cobounded_iff_meromorphicOrderAt_neg, Real.hasStrictDerivAt_rpow_const_of_ne, logDeriv_comp, StrongDual.polarSubmodule_eq_setOf, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, CFC.sq_sqrt, RCLike.star_def, OrthonormalBasis.sum_inner_mul_inner, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, meromorphicOrderAt_const, ContinuousLinearMap.hasDerivAtFilter, fderivWithin_csinh, span_fourier_closure_eq_top, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, HasFPowerSeriesOnBall.add, WeakDual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.integral_apply, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', hensels_lemma, Padic.AddValuation.map_one, Real.fderiv_fourierChar_neg_bilinear_right_apply, BoundedContinuousFunction.char_neg, Unitization.real_cfcβ_eq_cfc_inr, norm_cfc_lt_iff, hasFPowerSeriesOnBall_pi_iff, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContDiffMapSupportedIn.structureMapCLM_apply, RCLike.sub_conj, iteratedFDerivWithin_succ_eq_comp_right, NumberField.mem_maximalRealSubfield_iff, HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', SchwartzMap.lineDerivOp_fourier_eq, ValueDistribution.logCounting_zero_mul_le, RCLike.pos_iff, PadicInt.valuation_zero, innerSL_apply_apply, fderiv_multiset_prod, HasFPowerSeriesWithinOnBall.restrictScalars, CFC.abs_eq_cfcβ_coe_norm, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, EuclideanSpace.inner_single_left, HasFTaylorSeriesUpTo.hasFDerivAt, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Submodule.orthogonalProjectionFn_inner_eq_zero, hasDerivAt_neg', Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContMDiffOn.clm_postcomp, inner_eq_norm_mul_iff, ContinuousLinearMap.toBilinForm_apply, ProbabilityTheory.covarianceBilin_apply_eq_cov, iteratedDerivWithin_comp_two, ProbabilityTheory.covarianceBilin_self, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, MeromorphicAt.mul, ContinuousLinearMap.IsPositive.inner_nonneg_right, selfAdjoint.expUnitaryPathToOne_apply, hasDerivAt_bernoulliFun, derivWithin_fderivWithin, CFC.nnnorm_sqrt, MultilinearMap.mkContinuousMultilinear_apply, ProbabilityTheory.uncenteredCovarianceBilin_apply, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, PadicInt.nthHom_zero, Polynomial.isCoveringMapOn_eval, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, BoxIntegral.unitPartition.mem_smul_span_iff, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, ContinuousMap.setOfIdeal_ofSet_eq_interior, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, HasGradientAt.hasDerivAt', iteratedDeriv_pow, Int.padicValuation_lt_one_iff, AffineMap.hasDerivWithinAt, MeromorphicOn.divisor_const, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, instSMulCommClass_sphere_sphere_sphere, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, meromorphicOrderAt_mul, PadicInt.nonarchimedean, NormedSpace.toIsBoundedSMul, ContinuousAt.cfc, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, Submodule.isOrtho_iff_inner_eq, Complex.hasStrictDerivAt_tan, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, curveIntegralFun_smul, hasDerivAt_exp_zero_of_radius_pos, ClosedSubmodule.mem_orthogonal', CFC.sqrt_rpow, hasDerivWithinAt_iff_isLittleO, logDeriv_mul, ContinuousAlternatingMap.piLIE_apply_apply, PreInnerProductSpace.Core.smul_left, Matrix.PosSemidef.sqrt_eq_zero_iff, Differentiable.fderiv_norm_rpow, UnitAddTorus.mFourierSubalgebra_coe, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, hasDerivWithinAt_zero, ContDiffAt.hasStrictDerivAt, RCLike.toStarOrderedRing, MeasureTheory.integral_const_mul, FormalMultilinearSeries.hasSum_of_finite, hasDerivAtFilter_ofNat, iteratedDeriv_comp_const_mul, RCLike.is_real_TFAE, FormalMultilinearSeries.changeOriginSeries_summable_auxβ, curveIntegrable_smul_iff, ContinuousMap.toNNReal_neg_algebraMap, HasFPowerSeriesOnBall.restrictScalars, ContinuousLinearMap.isometry_mul_flip, UpperHalfPlane.num_neg, PadicInt.zmodRepr_mul, fderiv_fun_pow, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, contDiffOn_iff_continuousOn_differentiableOn, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, monomial_has_deriv_aux, LinearIsometryEquiv.conjStarAlgEquiv_apply, LinearMap.toMatrixOrthonormal_reindex, PiTensorProduct.projectiveSeminormAux_smul, MeasureTheory.ConvolutionExistsAt.integrable, CompactlySupportedContinuousMap.nnrealPart_smul_neg, HasStrictFDerivAt.pow, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, norm_cfc_le_iff, fderivWithin_sinh, RCLike.mul_conj, iter_deriv_zpow', Matrix.exp_conj', hasLineDerivAt_iff_isLittleO_nhds_zero, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, HasFiniteFPowerSeriesOnBall.sum, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, CFC.negPart_algebraMap, InnerProductSpace.inner_left_rankOne_apply, Matrix.PosSemidef.commute_iff, cfcβHom_nnreal_eq_restrict, TestFunction.toBoundedContinuousFunctionCLM_apply, HasFDerivAt.finset_prod, ENNReal.orderIsoRpow_symm_apply, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, Matrix.exp_neg, HasSum.hasSum_at_zero, HasFPowerSeriesAt.add, HasFDerivAt.norm_sq, ContinuousAlternatingMap.curryLeft_smul, polynomialFunctions.starClosure_topologicalClosure, antideriv_bernoulliFun, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, hasDerivWithinAt_pi, Real.integrable_prod_sub, HasFDerivWithinAt.csin, PadicAlgCl.isNonarchimedean, ContinuousLinearMap.eq_adjoint_iff, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RCLike.nonpos_iff, RCLike.nonpos_iff_exists_ofReal, Polynomial.div_tendsto_zero_iff_degree_lt, RCLike.wInner_of_isEmpty, Real.volume_val, Continuous.cfc', OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Int.padicValuation_eq_one_iff, HasFPowerSeriesAt.comp, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, FormalMultilinearSeries.sum_of_finite, MeromorphicOn.divisor_pow, gelfandStarTransform_apply_apply, HasFTaylorSeriesUpToOn.zero_eq', NormedSpace.Dual.toWeakDual_continuous, PadicInt.le_valuation_add, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMultilinearMap.norm_smulRightL_le, ContinuousLinearMap.precompL_apply, differentiableAt_comp_add_const, IsSelfAdjoint.adjoint_eq, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ContinuousMultilinearMap.norm_mkPiAlgebra_le, DifferentiableAt.hasDerivAt, Real.hasDerivAt_arcosh, FormalMultilinearSeries.radius_le_smul, MDifferentiable.clm_postcomp, ContinuousLinearMap.isPositive_self_comp_adjoint, LinearMap.adjoint_toContinuousLinearMap, hasDerivAt_iff_isLittleO, Polynomial.toAddCircle_X_pow_eq_fourier, Continuous.cfc_nnreal', hasFPowerSeriesAt_const, fderiv_eq_deriv_mul, Submodule.starProjection_inner_eq_zero, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, FormalMultilinearSeries.radius_compNeg, LinearIsometryEquiv.adjoint_eq_symm, extDeriv_fun_smul, fderivWithin_ccosh, ContinuousAlternatingMap.toAlternatingMap_curryLeft, MeasureTheory.setIntegral_prod_mul, Matrix.toEuclideanLin_apply, HasFDerivWithinAt.mul, LinearMap.IsPositive.isPositive_smul_iff, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, RCLike.im_eq_zero_iff_isSelfAdjoint, HasFDerivWithinAt.multiset_prod, ContinuousLinearMap.opNorm_mul, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, InnerProductSpace.Core.inner_smul_ofReal_right, HasFDerivAt.arctan, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Real.hasStrictDerivAt_arccos, MDifferentiable.cle_arrowCongr, Unitization.nnnorm_def, Unitization.dist_inr, HasStrictFDerivAt.abs, IsUnit.cfcSqrt, CFC.continuousOn_log, isScalarTower_closedBall_closedBall_closedBall, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Function.locallyFinsuppWithin.logCounting_eval_zero, ProbabilityTheory.IndepFun.integral_comp_mul_comp, Complex.instContinuousStar, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, HasLineDerivAt.tendsto_slope_zero_right, isScalarTower_sphere_closedBall_closedBall, Complex.hasDerivAt_GammaIntegral, PadicInt.norm_lt_one_iff_dvd, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, MeromorphicOn.divisor_natCast, PadicInt.mul_inv, PiTensorProduct.mapL_smul, RCLike.I_mul_I, cfcL_integrable, ContinuousLinearMap.adjointAux_norm, RCLike.toIsStrictOrderedModule, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, ValueDistribution.logCounting_mul_zero_eventuallyLE, ValueDistribution.logCounting_top, hasDerivAtFilter_natCast, Polynomial.isEquivalent_atTop_lead, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.toMatrixOrthonormal_apply_apply, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, LDL.lowerInv_orthogonal, HasStrictFDerivAt.arsinh, HasFDerivWithinAt.exp, ContinuousOn.cfc, summable_mul_of_bigO_atTop, SchwartzMap.fourier_lineDerivOp_eq, AddChar.wInner_cWeight_eq_zero_iff_ne, hasStrictDerivAt_exp_smul_const, RCLike.ofReal_nonneg, ContinuousMap.setOfIdeal_ofSet_of_isOpen, isBoundedBilinearMap_comp, fderivWithin_sin, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, CFC.continuousOn_sqrt, hasStrictDerivAt_add_const_iff, multipliable_one_add_of_summable, RCLike.complexRingEquiv_apply, FormalMultilinearSeries.rightInv_removeZero, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ClosedSubmodule.orthogonal_closure'', hasStrictDerivAt_exp_smul_const', Complex.hasStrictFDerivAt_cpow', Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, ValueDistribution.logCounting_mul_top_eventuallyLE, meromorphicOrderAt_mul_of_ne_zero, hasDerivAtFilter_zero, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, derivWithin_zpow, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, UnitAddTorus.mFourierCoeff_toLp, WeakDual.toStrongDual_inj, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, Asymptotics.IsEquivalent.mul, LinearMap.extendToπ'_apply, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, hasDerivAt_id', Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, ContinuousLinearMap.analyticOn_bilinear, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, fderiv.log, hasStrictFDerivAt_multiset_prod, MDifferentiableAt.clm_postcomp, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, hasDerivAt_abs_neg, coe_innerSL_apply, fderivWithin_finset_prod, inner_eq_zero_of_right, LinearMap.IsSymmetric.inner_map_self_eq_zero, Real.deriv_sqrt_aux, deriv_fderiv, meromorphicNFAt_mul_iff_left, RegularNormedAlgebra.isometry_mul', PadicInt.inv_mul, Matrix.PosSemidef.det_sqrt, multipliable_norm_one_add_of_summable_norm, range_cfcβHom, hasDerivWithinAt_abs, RCLike.toPosMulReflectLT, hasFPowerSeriesOnBall_const, ContDiffMapSupportedIn.seminorm_le_iff, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, PadicInt.fwdDiff_tendsto_zero, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, norm_cfcβ_lt, MeasureTheory.convolution_precompR_apply, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, VectorFourier.fourierIntegral_iteratedFDeriv, InformationTheory.hasDerivAt_klFun, ContinuousMap.toNNReal_algebraMap, InnerProductSpace.nnnorm_rankOne, BoundedContinuousFunction.mem_charPoly, spectrum.gelfandTransform_eq, StarAlgHom.continuous_realContinuousMapOfNNReal, BoundedContinuousFunction.charAlgHom_apply, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, FormalMultilinearSeries.continuousOn_of_finite, Matrix.PosSemidef.trace_eq_zero_iff, Commute.cfc_real, Matrix.gram_zero, ContinuousAlternatingMap.curryLeft_apply_apply, ContinuousLinearMap.flip_smul, logDeriv_fun_pow, MeromorphicOn.divisor_inv, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, Submodule.norm_eq_iInf_iff_inner_eq_zero, HasCompactSupport.hasDerivAt_convolution_right, InnerProductSpace.isSymmetricProjection_rankOne_self, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, MeromorphicOn.divisor_fun_pow, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, MeasureTheory.ConvolutionExistsAt.integrable_swap, Real.volume_eq_stieltjes_id, HasFiniteFPowerSeriesOnBall.eq_partialSum, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, nnnorm_cfcβ_nnreal_lt, CFC.sqrt_eq_rpow, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, AffineMap.hasDerivAt_lineMap, cfcβ_comp_norm, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasDerivWithinAt.norm_sq, NormedSpace.smul_mem_polar, HasGradientAtFilter.hasDerivAtFilter', WeakDual.CharacterSpace.continuousMapEval_bijective, LDL.lowerInv_triangular, CompactlySupportedContinuousMap.coe_toRealLinearMap, HasFPowerSeriesOnBall.fderiv_eq, UpperHalfPlane.zero_form_isBoundedAtImInfty, continuousMap_mem_polynomialFunctions_closure, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, AffineMap.hasDerivWithinAt_lineMap, NumberField.ComplexEmbedding.IsConj.eq, cfc_real_eq_nnreal, ContinuousLinearMap.fderiv_of_bilinear, Matrix.PosSemidef.posSemidef_sqrt, Real.hasDerivWithinAt_arccos_Ici, ContinuousLinearMap.nnnorm_toSpanSingleton, continuousOn_cfc_setProd, ContinuousAlternatingMap.alternatizeUncurryFin_smul, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Complex.hasDerivAt_Gammaβ_one, StarAlgHom.realContinuousMapOfNNReal_apply, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, Submodule.adjoint_subtypeL, IsGreatest.norm_cfc, hasStrictFDerivAt_exp, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, deriv_fun_div, Function.FactorizedRational.mulSupport, RCLike.conj_mul, MeasureTheory.convolution_def, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, Polynomial.toAddCircle.integrable, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MDifferentiableWithinAt.cle_arrowCongr, CStarModule.inner_smul_left_complex, HasFPowerSeriesWithinOnBall.prod, MDifferentiableWithinAt.clm_precomp, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, hasStrictDerivAt_const_add_iff, isBoundedBilinearMap_compMultilinear, sum_mul_eq_sub_integral_mul', hasFDerivAt_norm_rpow, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, iteratedDeriv_fun_id_zero, HasFPowerSeriesOnBall.uniform_geometric_approx, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, summable_jacobiThetaβ_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, MeromorphicOn.divisor_sub_const_self, Unitization.cobounded_eq_aux, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, RCLike.ofReal_mul, Polynomial.div_tendsto_atBot_zero_of_degree_lt, HasFPowerSeriesWithinAt.fderivWithin_eq, isCoveringMap_zpow, RCLike.instContinuousMapUniqueHom, FormalMultilinearSeries.id_comp', ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, derivWithin_fun_div, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, DifferentiableWithinAt.hasDerivWithinAt, ProbabilityTheory.covarianceBilin_zero, CFC.posPart_algebraMap_nnreal, HasFPowerSeriesOnBall.sum, contDiffOn_stereoToFun, fderiv_inverse, SchwartzMap.smulLeftCLM_fun_neg, deriv_pow, range_cfcβ, ContMDiffOn.clm_precomp, contDiffOn_nat_iff_continuousOn_differentiableOn, Matrix.PosSemidef.sqrt_eq_one_iff, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Complex.hasStrictFDerivAt_cpow, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, Filter.EventuallyEq.hasDerivAt_iff, fderiv_pow, InnerProductSpace.rankOne_eq_zero, IsGreatest.nnnorm_cfc, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, RCLike.mul_wInner_left, Convex.toWeakSpace_closure, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, Complex.hasStrictDerivAt_sinh, tsum_pow_div_one_sub_eq_tsum_sigma, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, RCLike.re_eq_norm_of_mul_conj, Bundle.ContMDiffRiemannianMetric.symm, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, InnerProductSpace.inner_right_rankOne_apply, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, HasFDerivAt.pow, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, meromorphicOrderAt_const_natCast, Real.hasDerivAt_qaryEntropy, innerSL_inj, fderivWithin_inv', hasDerivAt_add_const_iff, hasDerivWithinAt_pow, HasFDerivWithinAt.cpow, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, HasFPowerSeriesOnBall.compContinuousLinearMap, HasStrictFDerivAt.const_cpow, MeromorphicOn.divisor_intCast, HasFDerivWithinAt.csinh, RealRMK.rieszMeasure_le_of_eq_one, AnalyticAt.meromorphicOrderAt_nonneg, ContDiffMapSupportedIn.uniformSpace_eq_iInf, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, NormedSpace.inclusionInDoubleDual_norm_le, hasDerivWithinAt_one, deriv_comp_add_const, HasFDerivAt.abs, WeakDual.isCompact_closedBall, RCLike.instMulPosReflectLE, TestFunction.coe_ofSupportedInCLM, PointedContMDiffMap.smul_def, CFC.sqrt_eq_one_iff, HasFDerivWithinAt.abs, continuousSMul_closedBall_ball, InnerProductSpace.rankOne_eq_rankOne_iff_comm, RCLike.ofNat_mul_re, CStarAlgebra.norm_posPart_le, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, HasDerivWithinAt.inner, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, IsGreatest.nnnorm_cfcβ_nnreal, HasFDerivWithinAt.mul_const, UnitAddTorus.mFourier_zero, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, isScalarTower_sphere_sphere_sphere, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, fderiv_mul, StieltjesFunction.measurable_measure, hasDerivAt_ofNat, iteratedFDerivWithin_eq_equiv_comp, CompactlySupportedContinuousMap.toRealLinearMap_apply, Matrix.l2_opNNNorm_mulVec, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, meromorphicOrderAt_id, ContDiffMapSupportedIn.structureMapCLM_zero_apply, FormalMultilinearSeries.mkPiRing_coeff_eq, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, ProbabilityTheory.covarianceBilinDual_zero, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, RealRMK.integral_rieszMeasure, CFC.continuous_abs, LeftInvariantDerivation.map_zero, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, RCLike.I_eq_zero_or_im_I_eq_one, gelfandTransform_map_star, continuousOn_cfc_nnreal, InnerProductSpace.gramSchmidt_orthogonal, ContinuousLinearMap.adjoint_inner_left, fderivWithin_cos, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, InnerProductSpace.gramSchmidt_pairwise_orthogonal, ContinuousLinearMap.isBoundedBilinearMap, HasFPowerSeriesWithinOnBall.sum, Matrix.l2_opNorm_diagonal, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, cfcHom_integral, Asymptotics.isEquivalent_iff_exists_eq_mul, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, MeromorphicOn.divisor_sub_const_of_ne, ContinuousMultilinearMap.ofSubsingletonβα΅’_symm_apply, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, fderivWithin_ccos, hasDerivAt_update, cfc_nnreal_eq_real, ContinuousAlternatingMap.ofSubsingletonLIE_apply, HasStrictFDerivAt.clog, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, FormalMultilinearSeries.compAlongComposition_bound, iteratedDeriv_fun_id, continuousMultilinearCurryRightEquiv_symm_apply, RCLike.uniqueNonUnitalContinuousFunctionalCalculus, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, cfcβ_real_eq_complex, inner_eq_sum_norm_sq_div_four, fderiv_pow_ring, constFormalMultilinearSeries_apply_zero, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, FormalMultilinearSeries.radius_smul_eq, Bundle.ContMDiffRiemannianMetric.pos, HasStrictFDerivAt.sqrt, ContinuousLinearMap.bilinearComp_zero_right, IsContMDiffRiemannianBundle.exists_contMDiff, ContinuousMap.ideal_isMaximal_iff, MeasureTheory.SignedMeasure.singularPart_add, hasDerivAtFilter_add_const_iff, hasDerivAt_jacobiThetaβ_fst, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, IsometricContinuousFunctionalCalculus.toNonUnital, HasStrictFDerivAt.rpow, RCLike.exists_norm_eq_mul_self, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, ContinuousMap.sup_mem_closed_subalgebra, ContinuousLinearMap.adjointAux_apply, Real.hasDerivAt_arcsin, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Submodule.linearEquiv_det_reflection, ProperCone.innerDual_singleton, Complex.hasDerivAt_sinh, RCLike.add_conj, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, CFC.abs_natCast, HasLineDerivAt.tendsto_slope_zero_left, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, tendsto_nhds_iff_meromorphicOrderAt_nonneg, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, RCLike.im_eq_conj_sub, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, LDL.lower_conj_diag, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionβ_apply_apply, hasFDerivAt_list_prod', hasFDerivAt_integral_of_dominated_loc_of_lip', InnerProductSpace.rankOne_def, InnerProductSpace.Core.inner_self_eq_zero, ContinuousLinearMap.coe_flipβα΅’', Finset.norm_prod_one_add_sub_one_le, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.lpNorm_fun_mul_natCast, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, ContinuousLinearMap.norm_smulRight_apply, PadicInt.norm_lt_one_mul, Real.hasStrictDerivAt_cosh, contDiff_iff_continuous_differentiable, hasDerivAt_const, iteratedDerivWithin_comp_three, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', UniformSpace.Completion.norm_toComplL, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, instSMulCommClass_sphere_closedBall_closedBall, HasStrictFDerivAt.ccos, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, Complex.hasDerivAt_Gammaβ_one, Matrix.l2_opNNNorm_conjTranspose, Summable.hasProdUniformlyOn_nat_one_add, Complex.hasStrictDerivAt_const_cpow, RCLike.ofReal_add, ClosedSubmodule.orthogonal_eq_inter, ContinuousMultilinearMap.prodL_apply, Real.hasStrictDerivAt_log, HasFDerivWithinAt.cexp, IsSelfAdjoint.cfc_arg, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, SchwartzMap.smulRightCLM_apply_apply, LinearIsometryEquiv.conjStarAlgEquiv_refl, Matrix.PosSemidef.nonneg, eventually_singleton_add_smul_subset, RCLike.im_mul_ofReal, fderivWithin_fderivWithin_eq_of_eventuallyEq, StrongDual.polarSubmodule_eq_polar, summable_prod_mul_pow, PiTensorProduct.liftEquiv_symm_apply, Matrix.nonneg_iff_posSemidef, TestFunction.coe_ofSupportedInLM, extDerivWithin_fun_smul, RCLike.wInner_zero_right, fourierSubalgebra_separatesPoints, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, MeasureTheory.SignedMeasure.re_toComplexMeasure, Matrix.exp_zsmul, Commute.cfcβHom, Submodule.mem_orthogonal', ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, ContinuousLinearMap.aestronglyMeasurable_compβ, continuousSMul_sphere_closedBall, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, SchwartzMap.smulLeftCLM_const, LinearMap.toMatrix_innerββ_apply, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, Matrix.permMatrix_l2_opNorm_le, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Function.locallyFinsuppWithin.toClosedBall_divisor, PointwiseConvergenceCLM.equivWeakDual_symm_apply, PadicAlgCl.instUniformContinuousConstSMulPadic, hasDerivAt_of_tendstoUniformlyOn, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, Complex.hasFDerivAt_cpow, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, iteratedDerivWithin_zpow, inner_zero_left, ContinuousLinearMap.norm_precompR_le, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, MeasureTheory.lpNorm_fun_natCast_mul, hasStrictDerivAt_finCons', RCLike.neg_iff, isScalarTower_closedBall_ball_ball, Continuous.cfc_nnreal_of_mem_nhdsSet, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, meromorphicNFAt_iff_analyticAt_or, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMapβ'_zero_iff, RCLike.sqrt_eq_real_add_ite, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, WeakDual.isSeqCompact_closedBall, hasStrictDerivAt_finCons, PiTensorProduct.liftEquiv_apply, HasFDerivAt.cexp, Matrix.l2_opNorm_conjTranspose, HasFDerivAt.ccos, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, MultilinearMap.mkContinuousLinear_norm_le, WeakDual.exists_countable_separating, ContinuousLinearMap.deriv_of_bilinear, HasFDerivWithinAt.log, Orientation.areaForm'_apply, HasFDerivAt.clog, innerSLFlip_apply_apply, Continuous.cfcβ_nnreal, ContinuousLinearMap.nnnorm_holder_apply_apply_le, RCLike.ofReal_mul_pos_iff, Polynomial.hasFDerivAt, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Summable.summable_log_norm_one_add, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, ContinuousLinearMap.bilinear_hasTemperateGrowth, UpperHalfPlane.Ο_neg, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, inner_add_left, Submodule.orthogonal_orthogonal_eq_closure, MeromorphicOn.divisor_ofNat, RCLike.toZeroLEOneClass, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Complex.hasDerivAt_cos, contMDiffOn_continuousLinearMapCoordChange, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, Convex.exists_forall_hasDerivWithinAt, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, meromorphicNFOn_mul_iff_left_of_analyticOnNhd, HasFPowerSeriesAt.hasStrictDerivAt, derivWithin_comp_of_eq, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, analyticOrderAt_mul, ContinuousAt.cfcβ_nnreal, ContDiff.smulRight, ContinuousMultilinearMap.flipLinear_apply_apply, tendsto_integral_mul_one_add_inv_smul_sq_pow, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, PadicComplex.isNonarchimedean, LinearMap.hasDerivWithinAt, Real.fourier_fderiv, FormalMultilinearSeries.comp_id, ContinuousMap.adjoin_id_eq_span_one_union, hasFTaylorSeriesUpTo_succ_nat_iff_right, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, HasFDerivWithinAt.norm_sq, CFC.abs_algebraMap, Complex.restrictScalars_one_smulRight, ClosedSubmodule.iInf_orthogonal, Matrix.isHermitian_gram, HasFPowerSeriesOnBall.neg, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, hasStrictDerivAt_abs, Matrix.PosDef.commute_iff, SchwartzMap.fourierInv_lineDerivOp_eq, Bundle.RiemannianMetric.symm, PadicInt.norm_lt_one_add, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, iteratedFDeriv_eq_equiv_comp, Complex.hasStrictDerivAt_log, Unitization.norm_eq_sup, RCLike.nonneg_iff, Real.hasDerivAt_cos, RCLike.ofReal_zero, Matrix.ofLp_toEuclideanCLM, hasFTaylorSeriesUpToOn_succ_nat_iff_right, summable_pow_div_add, hasDerivAtFilter_iff_isLittleO, IsStrictlyPositive.nnrpow, deriv_comp, HasFDerivAt.ccosh, Circle.star_addChar, fderiv_cos, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ContinuousMap.sup_mem_subalgebra_closure, hasDerivAt_exp_smul_const, hasFDerivWithinAt_comp_smul_smul_iff, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, RCLike.instContinuousStar, ProbabilityTheory.hasDerivAt_complexMGF, MeromorphicOn.divisor_fun_zpow, LinearMap.isPositive_toContinuousLinearMap_iff, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', iteratedDeriv_comp_const_smul, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, iteratedDerivWithin_one_div, FormalMultilinearSeries.changeOrigin_eval_of_finite, fderivWithin_fun_pow, iteratedFDerivWithin_two_apply', Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, HasStrictFDerivAt.arctan, RCLike.zero_re, RCLike.inner_tmul_eq, inr_comp_cfcβHom_eq_cfcβAux, InnerProductSpace.gramSchmidt_triangular, CFC.monotoneOn_one_sub_one_add_inv_real, HasFDerivAt.multiset_prod, Matrix.l2_opNNNorm_mul, HasFDerivAt.mul_const, unitary.spectrum_subset_circle, MeasureTheory.integral_prod_mul, iteratedDerivWithin_fun_id, HasFPowerSeriesAt.fderiv_eq, MeromorphicOn.divisor_apply, ContinuousWithinAt.cfcβ_nnreal, nnnorm_cfc_le_iff, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, exists_polynomial_near_continuousMap, RCLike.re_eq_add_conj, continuousMultilinearCurryFin0_apply, ContinuousMap.inf_mem_subalgebra_closure, PiTensorProduct.dualSeminorms_bounded, CommCStarAlgebra.toStarModule, FormalMultilinearSeries.radius_neg, extDeriv_smul, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, Summable.multipliableLocallyUniformlyOn_one_add, ContinuousMap.inf_mem_closed_subalgebra, ValueDistribution.logCounting_mul_top_le, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, fderiv_exp, DoubleCentralizer.algebraMap_snd, WeakDual.polar_def, RCLike.wInner_const_left, fderiv_arctan, ProbabilityTheory.covarianceBilinDual_self_eq_variance, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, hasFiniteFPowerSeriesOnBall_const, iteratedFDerivWithin_succ_apply_left, EuclideanSpace.toLp_single, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, hasStrictFDerivAt_norm_sq, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, ContinuousMultilinearMap.norm_mkPiAlgebra, hasDerivWithinAt_natCast, MeromorphicOn.divisor_fun_mul, MeromorphicOn.divisor_zpow, ContinuousLinearMap.bilinearComp_apply, derivWithin_pow_field, Summable.multipliableLocallyUniformlyOn_nat_one_add, range_cfcβ_nnreal_eq_image_cfcβ_real, RCLike.inner_apply, ClosedSubmodule.mem_orthogonal, Matrix.posDef_iff_eq_conjTranspose_mul_self, Filter.Tendsto.cfcβ_nnreal, WeakDual.CharacterSpace.compContinuousMap_apply, hasDerivAt_id, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, DoubleCentralizer.algebraMap_toProd, RCLike.normSq_mul, Polynomial.isEquivalent_atBot_lead, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, FormalMultilinearSeries.id_comp, fderivWithin.log, ContinuousLinearMap.norm_map_tail_le, deriv_update, HasFPowerSeriesAt.restrictScalars, hasDerivAt_integral_of_dominated_loc_of_deriv_le, HasFDerivWithinAt.sinh, orthonormal_subtype_iff_ite, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, Summable.hasProdLocallyUniformlyOn_one_add, ContinuousLinearMap.instStarModuleId, Polynomial.hasFDerivAt_aeval, continuous_cfcHomSuperset_left, EisensteinSeries.vecMul_SL2_mem_gammaSet, IsUnit.cfcNNRpow, Summable.multipliableUniformlyOn_one_add, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, LeftInvariantDerivation.map_add, Continuous.cfc_of_mem_nhdsSet, norm_fderiv_iteratedFDeriv, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, ProbabilityTheory.covarianceBilinDual_self_nonneg, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, HasFDerivAt.log, Matrix.l2_opNNNorm_def, ValueDistribution.logCounting_top_mul_eventually_le, hasDerivAtFilter_sub_const_iff, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.adjointAux_adjointAux, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, hasDerivAt_exp, LeftInvariantDerivation.coe_add, ContMDiffAt.clm_precomp, Complex.hasDerivAt_logTaylor, inner_zero_right, ProbabilityTheory.covarianceBilin_real_self, ContinuousOn.cfc_nnreal, nnnorm_cfcβ_nnreal_lt_iff, inner_self_eq_zero, Real.hasStrictDerivAt_arsinh, iter_deriv_pow', cfc_integral, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, Orthonormal.inner_right_finsupp, ValueDistribution.characteristic_sub_characteristic_inv, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, inner_product_apply_eigenvector, HasFTaylorSeriesUpToOn.hasFDerivAt, hasStrictFDerivAt_inv, ContinuousLinearMap.flip_add, hasFiniteFPowerSeriesAt_const, VectorFourier.fourierSMulRight_apply, ContinuousLinearMap.isSelfAdjoint_iff', RCLike.exists_norm_mul_eq_self, IsLocalFrameOn.coeff_apply_of_notMem, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, ContinuousMultilinearMap.uncurryRight_apply, WithLp.unitization_nnnorm_inr, nnnorm_cfc_nnreal_lt, InnerProductSpace.Core.inner_smul_ofReal_left, fderiv_inv, derivWithin_comp_mul_left, HasFDerivAt.exp, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, ContinuousLinearMap.bilinearComp_zero, isScalarTower_sphere_sphere_closedBall, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, OrthonormalBasis.inner_eq_zero, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, iteratedDeriv_comp_const_add, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, Submodule.isOrtho_span, IsStrictlyPositive.sqrt, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, HasFiniteFPowerSeriesOnBall.neg, inner_add_add_self, RCLike.complexLinearIsometryEquiv_symm_apply, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, UpperHalfPlane.denom_neg, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, cfcβ_real_eq_nnreal, ProbabilityTheory.instIsProbabilityMeasureCondCDF, fderiv_ccos, InnerProductSpace.Core.inner_sub_sub_self, Meromorphic.fun_mul, nnnorm_cfc_nnreal_le, Matrix.PosSemidef.kronecker, inner_add_right, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, ContinuousLinearMap.le_opNormβ, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, InnerProductSpace.Core.inner_zero_right, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ContinuousLinearMap.norm_uncurryMid, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.uncurryLeft_norm, MeromorphicOn.divisor_restrict, Continuous.cfc_nnreal, hasStrictDerivAt_abs_neg, HasFPowerSeriesOnBall.tendstoUniformlyOn', Pretrivialization.continuousLinearMap.isLinear, HasFPowerSeriesWithinOnBall.const_smul, ContinuousOn.cfc_of_mem_nhdsSet, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, isScalarTower_sphere_sphere_ball, nnnorm_cfc_nnreal_le_iff, HasFPowerSeriesOnBall.sub, ContinuousLinearMap.IsPositive.inner_nonneg_left, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, PadicComplex.instIsScalarTowerPadicPadicAlgCl, MeasureTheory.Integrable.convolution_integrand, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, RCLike.ofNat_mul_im, LinearMap.toMatrixOrthonormal_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, fderivWithin_exp, CFC.sqrt_sq, NormedSpace.vonNBornology_eq, ProbabilityTheory.covarianceBilin_apply_pi, EuclideanSpace.inner_eq_star_dotProduct, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, isCoveringMapOn_npow, NonUnitalCommCStarAlgebra.toStarModule, logDeriv_eq_zero_of_not_differentiableAt, CFC.rpow_sqrt_nnreal, Complex.hasStrictDerivAt_cos, StrongDual.toLpβ_apply, PadicInt.fwdDiff_iter_le_of_forall_le, Valued.integer.coe_span_singleton_eq_closedBall, IsLocalFrameOn.coeff_apply_zero_at, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', HasFDerivWithinAt.rpow_const, fderivWithin_multiset_prod, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, HasFDerivAt.mul, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, MultilinearMap.mkContinuousMultilinear_norm_le', toWeakSpace_closedConvexHull_eq, Unitization.norm_def, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, contDiffOn_inv, ContinuousLinearMap.extendToπ_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, HasFDerivAt.sinh, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, ContinuousMapZero.toContinuousMapHom_toNNReal, Valued.isNonarchimedean_norm, Submodule.inner_left_of_mem_orthogonal, MDifferentiableAt.clm_precomp, ContDiffMapSupportedIn.postcompCLM_apply, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, ProbabilityTheory.covarianceBilin_apply_basisFun, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, ProbabilityTheory.measure_cdf, HasFDerivWithinAt.clog, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, locallyFinsuppWithin.logCounting_divisor, Asymptotics.isTheta_const_mul_right, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, inner_eq_zero_of_left, HasFPowerSeriesWithinAt.prod, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, fourierSubalgebra_coe, FormalMultilinearSeries.leftInv_coeff_one, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, Matrix.toLin_conjTranspose, RCLike.instStarModuleReal, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, Complex.hasStrictDerivAt_sin, hasFPowerSeriesAt_pi_iff, norm_cfcβ_le, hasDerivWithinAt_univ, MulChar.star_apply', ValueDistribution.logCounting_zero_mul_eventually_le, Matrix.PosSemidef.sq_sqrt, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, HasFDerivAt.rpow_const, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, HasFPowerSeriesAt.hasFDerivAt, WeakDual.isClosed_polar, iteratedDerivWithin_pow, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, ContinuousOn.cfcβ_nnreal', Submodule.inner_right_of_mem_orthogonal, LinearMap.mkContinuousβ_norm_le, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, HasStrictFDerivAt.const_rpow, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, InnerProductSpaceable.add_left, RCLike.complexRingEquiv_symm_apply, hasStrictDerivAt_const, RCLike.ofReal_eq_zero, fderiv_finset_prod, CompactlySupportedContinuousMap.toReal_add, deriv_single, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, StrongDual.norm_toLpβ_le, HasFPowerSeriesWithinAt.restrictScalars, Matrix.PosDef.isStrictlyPositive, Asymptotics.IsEquivalent.exists_eq_mul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, ContDiffMapSupportedIn.norm_apply_le_seminorm, RCLike.re_mul_ofReal, nnnorm_cfc_le, PiTensorProduct.mapLMultilinear_apply_apply, iteratedDeriv_comp_two, HasStrictFDerivAt.cos, ContinuousMap.setOfIdeal_eq_compl_singleton, Complex.hasDerivAt_cosh, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, PadicInt.zmodRepr_zero, hasStrictFDerivAt_ringInverse, ContinuousLinearMap.mul_apply', MeromorphicNFOn.zero_set_eq_divisor_support, LinearMap.instStarModuleId, NumberField.inverse_basisMatrix_mulVec_eq_repr, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, HasFDerivWithinAt.arsinh, InnerProductSpace.rankOne_comp_rankOne, MeromorphicOn.circleAverage_log_norm, Real.hasStrictDerivAt_arctan, Matrix.PosSemidef.det_nonneg, CFC.abs_ofNat, parallelogram_law, Submodule.orthogonal_closure', hasDerivAtFilter_finCons', MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Asymptotics.IsTheta.listProd, nnnorm_apply_le_nnnorm_cfc, CFC.negPart_one, StrongDual.toLpβ_of_not_memLp, analyticOrderAt_id, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, BoundedContinuousFunction.instIsBoundedSMul_1, Continuous.cfc, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, deriv_zpow, InnerProductSpace.rankOne_comp, Submodule.mem_orthogonal, StrongDual.mem_polarSubmodule, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, hasFPowerSeriesWithinAt_pi_iff, UnitAddTorus.hasSum_mFourier_series_of_summable, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, hasDerivAt_iff_isLittleO_nhds_zero, inner_smul_right, SchwartzMap.tsupport_smulLeftCLM_subset, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, cfcβHom_real_eq_restrict, CFC.abs_algebraMap_nnreal, EuclideanSpace.ofLp_single, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, UnitAddTorus.mFourierSubalgebra_separatesPoints, RCLike.nonneg_iff_exists_ofReal, InnerProductSpace.isSymmetric_rankOne_self, Commute.cfcHom, Real.hasDerivAt_cosh, HasFDerivAt.sin, continuousMultilinearCurryLeftEquiv_apply, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, cfc_apply_mem_elemental, HasFDerivAt.csin, Complex.hasDerivAt_sin, RCLike.ofReal_nonpos, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, ContinuousLinearMap.intervalIntegral_apply, MeromorphicAt.fun_mul, hasDerivAt_intCast, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcβHom, SchwartzMap.smulLeftCLM_neg, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, CFC.nnnorm_rpow, spectrum.differentiableOn_inverse_one_sub_smul, Continuous.cfcβ_nnreal_of_mem_nhdsSet, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, derivWithin_comp, ContinuousMultilinearMap.changeOriginSeries_support, ContDiffMapSupportedIn.seminorm_apply, OrthogonalFamily.eq_ite, Complex.hasStrictDerivAt_exp, DoubleCentralizer.algebraMap_fst, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, ContinuousLinearMap.adjoint_toSpanSingleton, IsStarNormal.instContinuousFunctionalCalculus, ContinuousLinearMap.toBilinForm_injective, Complex.hasStrictDerivAt_cosh, tsum_prod_pow_eq_tsum_sigma, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, toSpanSingleton_derivWithin, fderiv_norm_smul, PadicComplex.coe_zero, HasFDerivAt.hasFDerivAt_norm_smul, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, deriv_comp_of_eq, HasFiniteFPowerSeriesOnBall.eq_partialSum', cfc_comp_norm, CFC.abs_intCast, apply_le_nnnorm_cfc_nnreal, MeromorphicOn.AnalyticOnNhd.divisor_nonneg, IsBoundedBilinearMap.toContinuousLinearMap_apply, HasFPowerSeriesOnBall.pi, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, HasFPowerSeriesWithinOnBall.fderivWithin_eq, ContinuousMultilinearMap.piβα΅’_symm_apply, integral_coe_re_add_coe_im, RCLike.wInner_one_const_right, Commute.cfc, Matrix.posSemidef_iff_eq_sum_vecMulVec, HasFDerivWithinAt.sqrt, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, SchwartzMap.pairing_continuous_left, Matrix.ofLp_toEuclideanLin_apply, range_cfc_nnreal_eq_image_cfc_real, SchwartzMap.integralCLM_apply, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, hasDerivAt_one, Polynomial.fourierCoeff_toAddCircle_natCast, PadicInt.limNthHom_add, fderivWithin_sqrt, RCLike.norm_sq_re_conj_add, ContinuousMap.spectrum_eq_range, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, innerSLFlip_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, hasDerivAt_const_mul, RCLike.sqrt_neg_I, hasLineDerivAt_iff_tendsto_slope_zero, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, IsSelfAdjoint.commute_cfcβHom, Polynomial.fderivWithin_aeval, fderiv_sinh, inner_eq_ofReal_norm_sq_left_iff, contDiff_nat_iff_continuous_differentiable, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, Polynomial.fderivWithin, HasFDerivWithinAt.const_cpow, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, Polynomial.hasDerivAt, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, ContinuousLinearMap.opNorm_lsmul_le, ProbabilityTheory.covarianceBilin_of_not_memLp, MultilinearMap.mkContinuousMultilinear_norm_le, WeakDual.CharacterSpace.norm_le_norm_one, hasDerivAt_natCast, cfcL_integral, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, Real.fourier_bilin_convolution_eq_integral, Real.hasStrictDerivAt_cos, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_symm_apply, iter_deriv_inv, Matrix.frobenius_norm_mul, Matrix.star_dotProduct_gram_mulVec, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, RCLike.inv_def, MeromorphicOn.fun_mul, RCLike.sqrt_I, HasFPowerSeriesAt.sub, Matrix.PosDef.kronecker, StarAlgHom.realContinuousMapOfNNReal_injective, hasDerivWithinAt_zpow, HasFDerivWithinAt.arctan, OrthogonalFamily.range_linearIsometry, Monotone.deriv_nonneg, fderivWithin_inv, locallyIntegrableOn_mul_sum_Icc, ProbabilityTheory.covarianceBilinDual_comm, ContinuousLinearMap.opNNNorm_mul_flip_apply, HasFDerivWithinAt.rpow, HasFPowerSeriesOnBall.hasFDerivAt, Submodule.IsOrtho.inner_eq, HasMFDerivAt.prod, fderivWithin_csin, ContinuousMultilinearMap.curryMid_apply, norm_cfc_le, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, NNReal.orderIsoRpow_symm_eq, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Matrix.PosSemidef.re_dotProduct_nonneg, ContMDiff.clm_postcomp, instSMulCommClass_sphere_ball_ball, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, CFC.spectrum_abs, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, MDifferentiableWithinAt.clm_postcomp, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, iteratedDeriv_comp_eq_sum_orderedFinpartition, RCLike.ofReal_pos, ContinuousLinearMap.opNorm_mul_apply_le, HasFPowerSeriesAt.tendsto_partialSum, circleAverage_log_norm_factorizedRational, RCLike.wInner_zero_left, deriv_pow_field, ContinuousLinearMap.orthogonal_range, HasFiniteFPowerSeriesAt.add, HasFPowerSeriesAt.hasDerivAt, hasDerivWithinAt_congr_set', Real.instContinuousMapUniqueHom, MeromorphicOn.min_divisor_le_divisor_add, ProbabilityTheory.covarianceBilin_apply, meromorphicOrderAt_pow, instSymmEqInnerOfNat, Polynomial.hasDerivAt_aeval, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, HasFDerivAt.cos, HasFDerivAt.linear_multilinear_comp, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, ContinuousMap.comp_attachBound_mem_closure, MeasureTheory.convolutionExistsAt_iff_integrable_swap, deriv_div, hasDerivAt_norm_rpow, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, PadicInt.valuation_p_pow_mul, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, ContinuousLinearMap.isPositive_iff, Unitization.isUniformEmbedding_addEquiv, ContinuousMultilinearMap.compContinuousLinearMapL_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, InnerProductSpace.Core.inner_add_right, MeromorphicOn.extract_zeros_poles, ContinuousOn.cfc', ContinuousLinearMap.norm_bilinearRestrictScalars, RCLike.inv_pos, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, meromorphicAt_mul_iff_of_ne_zero, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, RCLike.real_smul_ofReal, BoundedContinuousFunction.integral_add_const, cfcβ_norm_sq_nonneg, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, HasFPowerSeriesWithinOnBall.neg, PadicInt.fwdDiff_mahlerSeries, HasFDerivAt.const_rpow, ContinuousLinearMap.bilinearComp_zero_left, ContinuousLinearMap.nnnorm_smulRight_apply, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, hasSum_fourier_series_of_summable, MeromorphicOn.negPart_divisor_add_le_max, IsCoercive.continuousLinearEquivOfBilin_apply, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, hasDerivWithinAt_inter', Complex.hasStrictDerivAt_cpow_const, MDifferentiableOn.clm_precomp, RCLike.I_mul_re, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', PadicInt.pow_p_dvd_int_iff, deriv_comp_mul_left, hasDerivAt_neg, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, hasFTaylorSeriesUpToOn_succ_iff_left, HasCompactSupport.hasDerivAt_convolution_left, Polynomial.hasStrictDerivAt, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, Commute.cfcβ, derivWithin_fun_pow, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, HasMFDerivWithinAt.mul, Bundle.RiemannianMetric.pos, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', CFC.sqrt_eq_cfc, continuousMultilinearCurryRightEquiv_symm_apply', InnerProductSpace.Core.inner_self_of_eq_zero, HasFDerivAt.arsinh, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, UpperHalfPlane.det_J, ContDiffMapSupportedIn.continuousSMul, Real.hasStrictDerivAt_sin, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, BoundedContinuousFunction.add_norm_nonneg, LinearMap.isStarProjection_toContinuousLinearMap_iff, MeromorphicOn.divisor_smul, iteratedDerivWithin_eq_equiv_comp, PadicInt.instNormMulClass, iteratedFDerivWithin_two_apply, extDerivWithin_smul, fderiv_ccosh, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, inner_mul_symm_re_eq_norm, DoubleCentralizer.coe_fst, Filter.Tendsto.cfc_nnreal, HasStrictFDerivAt.cpow, IsSelfAdjoint.instContinuousFunctionalCalculus, CompactlySupportedContinuousMap.toReal_smul, fderiv_fun_mul, Submodule.adjoint_orthogonalProjection, CFC.abs_eq_cfcβ_norm, continuousOn_cfcβ_nnreal, ContinuousMapZero.instCStarRing, iteratedDeriv_comp_add_const, CurveIntegrable.smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, FormalMultilinearSeries.min_radius_le_radius_add, CFC.abs_sq, hasStrictDerivAt_one, ValueDistribution.logCounting_top_mul_le, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, ContinuousLinearMap.closed_range_of_antilipschitz, ProbabilityTheory.uncenteredCovarianceBilin_zero, HasStrictFDerivAt.multiset_prod, LinearMap.IsPositive.inner_nonneg_right, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, InnerProductSpace.inner_gramSchmidtOrthonormalBasis_eq_zero, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, HasFPowerSeriesAt.pi, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', RCLike.mul_im, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, VectorFourier.fourierPowSMulRight_apply, nnnorm_cfc_lt_iff, ContinuousAlternatingMap.prodLIE_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, ValueDistribution.logCounting_pow_zero, hasDerivAt_pow, Submodule.mem_adjoint_iff, inner_eq_zero_symm, Function.FactorizedRational.extractFactor, integrableOn_mul_sum_Icc, PadicInt.mahlerEquiv_apply, Polynomial.div_tendsto_atTop_zero_of_degree_lt, Orthonormal.orthogonalFamily, continuousSMul_closedBall_closedBall, ContinuousLinearMap.opNorm_flip, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, limit_zero_of_norm_tendsto_zero, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, logDeriv_const_mul, IsConformalMap.smul, isCoveringMap_npow, Irreducible.maximalIdeal_eq_closedBall, Complex.instContinuousMapUniqueHom, Real.hasStrictDerivAt_sqrt, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular, PadicInt.norm_add_eq_max_of_ne, Complex.hasDerivAt_Gamma_one, BumpCovering.exists_finset_toPOUFun_eventuallyEq, FormalMultilinearSeries.derivSeries_eq_zero, HilbertBasis.summable_inner_mul_inner, Polynomial.div_tendsto_zero_of_degree_lt, ContinuousLinearMap.isPositive_iff', ContDiffWithinAt.smulRight, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, EisensteinSeries.vecMulSL_gcd, Real.hasDerivAt_tan_of_mem_Ioo, ContinuousLinearMap.star_eq_adjoint, ContinuousMultilinearMap.curryLeft_apply, iteratedDeriv_comp_three, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, CStarAlgebra.isStrictlyPositive_TFAE, continuousOn_cfcβ_setProd, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, fderiv_sqrt, derivWithin_comp_add_const, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, logDeriv_fun_zpow, AlternatingMap.mkContinuousLinear_norm_le, ProperCone.hyperplane_separation_of_notMem, RCLike.ofReal_mul_neg_iff, Unitization.complex_cfcβ_eq_cfc_inr, ContinuousAlternatingMap.curryLeftLI_apply, LDL.diag_eq_lowerInv_conj, deriv_comp_const_add, iteratedDerivWithin_id, RCLike.norm_sq_re_add_conj, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, differentiableAt_iff_comp_add_const, ContinuousLinearMap.norm_compSL_le, ContDiffMapSupportedIn.withSeminorms, MeasureTheory.withDensityα΅₯_smul, CStarAlgebra.norm_negPart_le, cfcβ_nnreal_eq_real, deriv_inner_apply, CFC.sqrt_algebraMap, innerSL_apply, CFC.posPart_algebraMap, hasStrictFDerivAt_list_prod, CFC.sqrt_one, Summable.hasProdLocallyUniformlyOn_nat_one_add, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, hasDerivAtFilter_pi, StrongDual.toLp_apply, ContinuousLinearMap.coe_flipβα΅’, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, CFC.nnrpow_eq_cfcβ_real, hasDerivAtFilter_const_add_iff, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, InnerProductSpaceable.innerProp, instSMulCommClass_closedBall_closedBall_ball, LeftInvariantDerivation.coe_zero, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, ProbabilityTheory.measure_condCDF_Iic, polynomialFunctions.topologicalClosure, FormalMultilinearSeries.changeOrigin_eval, Unitization.nndist_inr, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, iter_deriv_inv_linear_sub, IsSelfAdjoint.adjoint_conj, HasDerivAt.inner, HasFPowerSeriesAt.prod, hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable, ProbabilityTheory.measurable_measure_condCDF, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, MeasureTheory.lpNorm_natCast_mul, AlternatingMap.mkContinuousAlternating_norm_le_max, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, norm_apply_le_norm_cfc, hasDerivAt_finCons', isScalarTower_sphere_ball_ball, iteratedDeriv_id, HasFPowerSeriesWithinAt.add, meromorphicOrderAt_zpow, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, CFC.negPart_def, Profinite.NobelingProof.CC_comp_zero, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, RCLike.mul_re, hasStrictDerivAt_exp_zero_of_radius_pos, LinearMap.isPositive_iff, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, integrable_cfc, MeasureTheory.convolution_mul_swap, ContDiffMapSupportedIn.postcompLM_apply, UnitAddTorus.span_mFourier_closure_eq_top, ContinuousLinearMap.norm_smulRightL_le, MeasureTheory.withDensityα΅₯_smul', analyticOrderAt_mul_eq_top_of_left, hasDerivAtFilter_const, SchwartzMap.tsupport_derivCLM_subset, CFC.sqrt_rpow_nnreal, RCLike.normSq_zero, hasDerivAt_single, WeakDual.Complex.instStarHomClass, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, nnnorm_cfc_nnreal_lt_iff, orthonormal_iff_ite, RCLike.wInner_add_left, FormalMultilinearSeries.radius_prod_eq_min, fderivWithin_mul_const, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, CompactlySupportedContinuousMap.nnrealPart_smul_pos, ContinuousMap.polynomial_comp_attachBound, VectorFourier.norm_fourierSMulRight_le, RCLike.neg_iff_exists_ofReal, derivWithin_div, InnerProductSpace.Core.inner_add_add_self, norm_cfcHom, RCLike.to_complex_nonneg_iff, RCLike.sqrt_zero, ContinuousMultilinearMap.currySum_apply, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, signedDist_apply, Unitization.norm_splitMul_snd_sq, WeakDual.CharacterSpace.equivAlgHom_coe, Valued.toNormedField.setOf_mem_integer_eq_closedBall, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipβα΅’'_symm, EuclideanSpace.inner_toLp_toLp, cfc_real_eq_complex, CFC.norm_rpow, RCLike.im_ofReal_mul, ContinuousMap.toNNReal_neg_one, Matrix.l2_opNNNorm_diagonal, MeromorphicOn.negPart_divisor_add_le_add, HasFiniteFPowerSeriesOnBall.hasFDerivAt, hasStrictDerivAt_zero, HasStrictFDerivAt.sin, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, Complex.hasDerivAt_tan, Matrix.instCStarRing, RCLike.normSq_eq_zero, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, HasFDerivWithinAt.const_rpow, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, hasStrictDerivAt_exp_smul_const_of_mem_ball', Unitization.antilipschitzWith_addEquiv, ContinuousLinearMap.extendToπ'_apply, fderivWithin_cosh, ContinuousLinearMap.isAdjointPair_inner, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, VectorFourier.norm_fourierPowSMulRight_le, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, RCLike.instPosMulReflectLE, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, Padic.norm_rat_le_one_iff_padicValuation_le_one, Unitization.splitMul_injective, ProbabilityTheory.measure_condCDF_univ, Antitone.deriv_nonpos, ContDiffMapSupportedIn.continuous_iff_comp, MonotoneOn.nnnorm_cfc, VectorFourier.norm_fourierSMulRight, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, ContinuousLinearEquiv.coord_norm', deriv_fun_pow, iteratedDerivWithin_comp_eq_sum_orderedFinpartition, ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, HasFPowerSeriesAt.eq_zero_of_eventually, analyticOrderNatAt_mul, hasStrictFDerivAt_inv', ContinuousOn.cfcβ_nnreal, hasDerivAt_mul_const, SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, cfcβ_apply_mem_elemental, CFC.posPart_def, iteratedDeriv_fun_pow_zero, CFC.nnrpow_eq_rpow, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, Complex.hasStrictFDerivAt_log_real, iteratedFDeriv_two_apply, Real.hasStrictDerivAt_tan, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, RCLike.wInner_cWeight_const_right, HasStrictFDerivAt.mul, iter_deriv_inv_linear, sum_mul_eq_sub_sub_integral_mul', Irreducible.maximalIdeal_pow_eq_closedBall_pow, Summable.hasProdUniformlyOn_one_add, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, meromorphicNFAt_mul_iff_right, MDifferentiable.clm_precomp, Real.differentiable_fourierChar_neg_bilinear_left, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, IsSelfAdjoint.commute_cfcβ, FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, continuousMultilinearCurryLeftEquiv_symm_apply, QuotientAddGroup.integral_mul_eq_integral_automorphize_mul, WithLp.unitization_mul, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, polynomialFunctions_closure_eq_top', fderiv_mul_const, fderiv_csinh, Complex.im_eq_zero_iff_isSelfAdjoint, meromorphicOrderAt_of_not_meromorphicAt, iteratedFDeriv_succ_eq_comp_left, ContinuousMapZero.toNNReal_neg_smul, AddChar.wInner_cWeight_eq_boole, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, continuousOn_cfc_nnreal_setProd, PadicInt.limNthHom_mul, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousMap.polynomial_comp_attachBound_mem, range_cfcHom, ContinuousLinearMap.opNorm_mulLeftRight_le, RCLike.re_ofReal_mul, HasFDerivAt.sqrt, ClosedSubmodule.orthogonal_closure, EisensteinSeries.eisSummand_SL2_apply, meromorphicOrderAt_const_intCast, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, CFC.abs_one, InnerProductSpace.add_left, ContDiffMapSupportedIn.structureMapCLM_zero_injective, EuclideanSpace.inner_single_right, sum_mul_eq_sub_integral_mul, ContinuousMultilinearMap.piβα΅’_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, integrableOn_cfc, Matrix.PosSemidef.sqrt_mul_self, ContMDiffWithinAt.clm_precomp, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonβα΅’_apply, continuousOn_cfc, HasFDerivWithinAt.finset_prod, continuousMultilinearCurryFin1_symm_apply, FormalMultilinearSeries.radius_pi_le, Submodule.orthogonal_eq_inter, BoundedContinuousFunction.charMonoidHom_apply, RCLike.normSq_add, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, Asymptotics.IsEquivalent.listProd, MeromorphicOn.mul, hasDerivAt_iff_tendsto, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, setIntegral_re_add_im, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_apply, ContDiffAt.differentiableAt_iteratedFDeriv, MeromorphicNFAt.meromorphicOrderAt_eq_zero_iff, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, HasStrictFDerivAt.cosh, ContDiffOn.smulRight, Polynomial.toAddCircle_X_eq_fourier_one, Real.hasStrictDerivAt_const_rpow, ContinuousLinearMap.norm_adjoint_comp_self, hasDerivWithinAt_intCast, ContMDiff.clm_precomp, fderivWithin_pow, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, instSMulCommClass_sphere_closedBall_ball, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearMap.hasDerivWithinAt, hasStrictFDerivAt_pow, FormalMultilinearSeries.derivSeries_apply_diag, derivWithin_comp_const_add, prod_vanishing_of_summable_norm, Matrix.l2_opNNNorm_conjTranspose_mul_self, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, ContinuousLinearMap.opNorm_lsmul, isCoveringMapOn_zpow, ProbabilityTheory.covarianceBilinDual_of_not_memLp, FormalMultilinearSeries.norm_changeOriginSeriesTerm, fderivWithin_arctan, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Unitization.uniformity_eq_aux, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, hasDerivAt_exp_zero, HasFTaylorSeriesUpTo.zero_eq', MeasureTheory.charFun_map_eq_charFunDual_smul, ProbabilityTheory.gaussianPDFReal_mul, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, Matrix.cstar_norm_def, CStarAlgebra.toStarModule, PointwiseConvergenceCLM.withSeminorms, MeasureTheory.convolution_eq_swap, CFC.isUnit_nnrpow_iff, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, Real.zero_at_infty_vector_fourierIntegral, hasDerivAt_const_add_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, RCLike.conj_eq_re_sub_im, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, fderiv_csin, MeromorphicOn.divisor_def, PadicInt.limNthHom_zero, WeakDual.isSeqCompact_polar, inner_matrix_row_row, HasFTaylorSeriesUpTo.fderiv, CFC.monotoneOn_cfcβ_rpowIntegrandββ, UpperHalfPlane.neg_smul, Int.padicValuation_le_one, ContinuousMap.idealOf_compl_singleton_isMaximal, fderiv_cosh, HasStrictFDerivAt.fun_mul, ContinuousLinearMap.norm_holderL_le, hasFDerivWithinAt_pow, logDeriv_mul_const, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Unitization.lipschitzWith_addEquiv, hasStrictDerivAt_id, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, HasStrictFDerivAt.sinh, HasFDerivAt.cpow, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, Real.hasStrictDerivAt_rpow_const, Matrix.instStarOrderedRing, LinearMap.hasDerivAtFilter, IsStarNormal.instIsometricContinuousFunctionalCalculus, HasFiniteFPowerSeriesOnBall.fderiv_eq, PreInnerProductSpace.Core.add_left, analyticOrderAt_mul_eq_top_of_right, PadicInt.unitCoeff_spec, Complex.hasDerivAt_log_sub_logTaylor, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, ContinuousLinearMap.analyticAt_bilinear, PadicInt.norm_natCast_zmodRepr_eq_iff, ProbabilityTheory.IsGaussian.charFunDual_eq', HasFPowerSeriesAt.hasStrictFDerivAt, inner_sub_sub_self, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, isBoundedLinearMap_continuousMultilinearMap_comp_linear, ContinuousAt.cfc_nnreal, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, hasStrictDerivAt_exp_smul_const_of_mem_ball, Real.hasDerivAt_Gamma_nat, ordinaryHypergeometricSeries_norm_div_succ_norm, hasDerivAt_pi, ContinuousWithinAt.cfc, MeasureTheory.ContinuousMap.inner_toLp, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, hasDerivWithinAt_finCons, WeakDual.CharacterSpace.exists_apply_eq_zero, HasFDerivAt.cosh, exists_continuousLinearEquiv_fderiv_symm_eq, FormalMultilinearSeries.rightInv_coeff, Complex.hasDerivAt_log, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, hasDerivAt_zpow, MeasureTheory.AEStronglyMeasurable.convolution_integrand', WeakDual.CharacterSpace.compContinuousMap_id, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, instSMulCommClass_sphere_sphere_closedBall, ContDiffOn.differentiableOn_iteratedFDerivWithin, EuclideanSpace.single_eq_zero_iff, differentiableAt_iff_comp_const_add, ValueDistribution.log_counting_zero_sub_logCounting_top, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, Asymptotics.IsTheta.mul, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bundle.RiemannianMetric.continuousAt, nnnorm_cfcβ_le, Asymptotics.isTheta_const_mul_left, integral_re_add_im, ContinuousLinearMap.holderL_apply_apply, FormalMultilinearSeries.comp_rightInv_aux2, Real.hasDerivAt_sinh, Polynomial.toAddCircle_C_eq_smul_fourier_zero, isConformalMap_const_smul, Matrix.l2_opNorm_mul, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, norm_innerSL_le, polynomialFunctions_closure_eq_top, VectorFourier.hasFDerivAt_fourierChar_smul, BoundedContinuousFunction.separatesPoints_charPoly, HasStrictFDerivAt.csinh, ContMDiffWithinAt.cle_arrowCongr, HasFDerivWithinAt.cos, ContinuousWithinAt.cfc_nnreal, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, continuousMultilinearCurryRightEquiv_apply, RCLike.norm_le_im_iff_eq_I_mul_norm, RCLike.real_smul_eq_coe_mul, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, nnnorm_cfcβ_nnreal_le, CFC.sqrt_eq_real_sqrt, orthonormal_vecCons_iff, ContinuousAlternatingMap.prodLIE_symm_apply, DifferentiableOn.hasDerivAt, Summable.multipliableUniformlyOn_nat_one_add, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcβ_nnreal, ProbabilityTheory.covarianceBilinDual_of_not_memLp', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, fderivWithin_comp_smul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, instSMulCommClass_closedBall_closedBall_closedBall, ContinuousLinearMap.flipβα΅’_symm, HasFPowerSeriesAt.compContinuousLinearMap, continuousOn_cfcβ_nnreal_setProd, cfcHom_eq_of_isStarNormal, exists_continuousLinearEquiv_fderivWithin_symm_eq, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', MeromorphicAt.meromorphicTrailingCoeffAt_mul, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, hasFDerivAt_exp, EuclideanSpace.single_apply, Polynomial.hasDerivWithinAt, Matrix.PosDef.det_pos, ZSpan.mem_fundamentalDomain, differentiableAt_iff_comp_sub_const, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, MeromorphicOn.divisor_mul, CFC.continuousOn_rpow, ContinuousLinearMap.norm_holder_apply_apply_le, WithLp.unitization_norm_inr, range_cfc, ContinuousLinearMap.hasStrictDerivAt, sum_mul_eq_sub_sub_integral_mul, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, fderivWithin_pow_ring, hasDerivWithinAt_iff_tendsto_slope, constFormalMultilinearSeries_apply_succ, Polynomial.fourierCoeff_toAddCircle, FormalMultilinearSeries.continuousOn, RCLike.wInner_add_right, hasFDerivAt_inv, MonotoneOn.nnnorm_cfcβ, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.fpowerSeries_apply_one, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, derivWithin_pow, BoundedContinuousFunction.char_add_eq_mul, constFormalMultilinearSeries_zero, ValueDistribution.logCounting_inv, HasStrictFDerivAt.mul_const, HilbertBasis.hasSum_inner_mul_inner, Real.hasDerivWithinAt_arccos_Iic, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, ContinuousMultilinearMap.curryFinFinset_apply, ContDiffAt.smulRight, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, FormalMultilinearSeries.changeOriginSeriesTerm_bound, spectrum.subset_circle_of_unitary, spectrum.subset_closedBall_norm, RCLike.I_mul_I_of_nonzero, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, summable_mul_of_bigO_atTop', VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, CFC.nnnorm_nnrpow, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, Function.locallyFinsuppWithin.logCounting_even, HasFTaylorSeriesUpToOn.restrictScalars, ContinuousLinearMap.apply_apply, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, instSMulCommClass_sphere_sphere_ball, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, PiTensorProduct.mapLMultilinear_opNorm, hasDerivWithinAt_inter, hasDerivAt_exp_smul_const_of_mem_ball, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, ContinuousMap.idealOfSet_ofIdeal_eq_closure, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, CFC.norm_nnrpow, WithLp.unitization_isometry_inr, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, HasCompactSupport.convolution_integrand_bound_right, isBigO_norm_restrict_cocompact, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, QuotientGroup.integral_mul_eq_integral_automorphize_mul, Commute.cfcβ_real, ContMDiffAt.cle_arrowCongr, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, ContinuousLinearMap.adjoint_innerSL_apply, HasFDerivAt.rpow, LSeries.hasDerivAt_term, ContDiffMapSupportedIn.structureMapLM_apply, RCLike.normSq_sub, isBoundedLinearMap_prod_multilinear, fderivWithin_fun_mul, Orthonormal.inner_sum, HasCompactSupport.convolution_integrand_bound_right_of_subset, intervalIntegral.integral_mul_const, CFC.complex_exp_eq_normedSpace_exp, HasStrictDerivAt_ofNat, HasFiniteFPowerSeriesAt.comp, ContinuousMap.idealOfSet_isMaximal_iff, hasDerivWithinAt_iff_tendsto, Unitary.path_apply, InnerProductSpace.Core.inner_zero_left, Unitary.spectrum_subset_circle, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, inner_eq_ofReal_norm_sq_right_iff, HasFDerivWithinAt.sin, SchwartzMap.smulLeftCLM_smul, DoubleCentralizer.coe_snd, hasFPowerSeriesAt_iff, HasStrictFDerivAt.exp, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, Matrix.IsHermitian.instContinuousFunctionalCalculus, MeasureTheory.integral_convolution, fderiv_norm_sq_apply, IsSelfAdjoint.commute_cfc, fderiv_sin, cfcHom_apply_mem_elemental, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, ContinuousMultilinearMap.norm_curryMid, cfc_setIntegral, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, Submodule.starProjection_tendsto_closure_iSup, NormedSpace.dual_def, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, MeasureTheory.integral_mul_const, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, ContinuousMap.idealOpensGI_choice, HasMFDerivAt.const_smul, WeakDual.CharacterSpace.instStarHomClass, Int.Matrix.exists_ne_zero_int_vec_norm_le, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulβα΅’, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', Unitization.norm_inr, PadicInt.zmodRepr_eq_zero_iff_dvd, norm_cfc_lt, ContinuousLinearMap.innerSL_apply_comp, inner_vsub_left_eq_zero_symm, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_derivβ, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj, inner_smul_left, Unitization.continuous_inr, MeromorphicAt.meromorphicOrderAt_comp, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, fderivWithin_mul, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, CFC.rpow_eq_cfc_real, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, fderiv_inner_apply, inner_matrix_col_col, Real.hasStrictDerivAt_log_of_pos, HasFDerivWithinAt.fun_mul, ValueDistribution.logCounting_mul_zero_le, RCLike.div_I, OrthonormalBasis.inner_eq_ite, BoundedContinuousFunction.char_mem_charPoly, MeasureTheory.SignedMeasure.im_toComplexMeasure, ContinuousLinearMap.orthogonal_ker, AnalyticAt.hasStrictDerivAt, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, BoxIntegral.unitPartition.tag_mem_smul_span, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, Rat.padicValuation_le_one_iff, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, HasStrictFDerivAt.finset_prod, Continuous.cfcβ_nnreal', Filter.EventuallyEq.hasDerivWithinAt_iff, ProbabilityTheory.instIsProbabilityMeasurecdf, InnerProductSpace.norm_rankOne, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, Asymptotics.IsTheta.const_mul_right, Complex.hasDerivAt_Gamma_nat, HasFDerivAt.const_cpow, hasFDerivAt_integral_of_dominated_loc_of_lip, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, PadicInt.valuation_mul, PiTensorProduct.mapLMultilinear_toFun_apply, HasFDerivWithinAt.cosh, CFC.isUnit_sqrt_iff, Matrix.PosDef.re_dotProduct_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, Unitization.nnnorm_inr, MeasureTheory.SignedMeasure.rnDeriv_add, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Int.Matrix.exists_ne_zero_int_vec_norm_le', HasStrictFDerivAt.rpow_const, Matrix.gram_single, Function.locallyFinsuppWithin.toClosedBall_eval_within, NormedSpace.exp_add, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, Orthonormal.inner_eq_zero, hasDerivWithinAt_sub_const_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, RCLike.zero_im, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, fderiv_inv', ContinuousLinearMapWOT.ext_inner_iff, Matrix.permMatrix_l2_opNorm_eq, norm_inner_div_norm_mul_norm_eq_one_iff, tendsto_zero_geometric_tsum_pnat, CFC.rpow_sqrt, FormalMultilinearSeries.comp_assoc, HasFPowerSeriesWithinAt.comp, Real.hasDerivAt_negMulLog, continuousMultilinearCurryFin1_apply, InnerProductSpace.gramSchmidt_inv_triangular, hasStrictDerivAt_neg, hasFDerivAt_finset_prod, HilbertBasis.finite_spans_dense, nnnorm_cfcβ_lt, RCLike.ofReal_lt_zero
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toNonUnitalNormedRing π | CompOp | 991 mathmath: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, ValueDistribution.logCounting_zero, hasFDerivAt_iff_hasDerivAt, Polynomial.differentiableWithinAt, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, MeasureTheory.lpNorm_conj, TensorProduct.enorm_lid, differentiableAt_comp_neg, Matrix.frobenius_nnnorm_mul, continuousOn_stereoToFun, LeftInvariantDerivation.lift_zero, norm_cfcβHom, RCLike.map_apply, LinearMap.IsSymmetric.inner_map_polarization, LinearMap.coe_toSeminorm, RCLike.ofRealCLM_apply, PadicInt.lift_sub_val_mem_span, LeftInvariantDerivation.leibniz, hasFDerivAt_iff_hasGradientAt, RCLike.reCLM_apply, smooth_barycentric_coord, InnerProductSpace.rankOne_one_left_eq_innerSL, Function.FactorizedRational.divisor, MeromorphicAt.analyticAt, HasFDerivWithinAt.pow, EuclideanSpace.orthonormal_single, meromorphicOrderAt_const_ofNat, AffineMap.hasDerivAtFilter, Matrix.IsHermitian.det_abs, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, differentiableAt_zpow, hasFDerivAt_multiset_prod, smoothSheafCommRing.nonunits_stalk, MeasureTheory.convolution_mul, deriv_mem_iff, Matrix.spectrum_toEuclideanLin, MeasureTheory.lpNorm_fun_div_natCast, Matrix.cstar_nnnorm_def, lp.inner_eq_tsum, OrthonormalBasis.sum_inner_mul_inner, Matrix.l2_opNorm_mulVec, ContinuousLinearMap.hasDerivAtFilter, RCLike.conjCLE_norm, ordinaryHypergeometric_radius_top_of_neg_natβ, LinearMap.polar_eq_iInter, hensels_lemma, MeasureTheory.integral_fintype_prod_volume_eq_pow, BoundedContinuousFunction.char_neg, PadicInt.appr_spec, flip_innerSL_real, Matrix.le_iff, RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, continuousOn_dslope, RCLike.sub_conj, isClosedEmbedding_cfcβAux, deriv_comp_const_sub, LeftInvariantDerivation.coe_derivation, innerSL_apply_apply, RCLike.norm_expect_le, LinearMap.adjoint_innerββ_apply, inner_sum, EuclideanSpace.inner_single_left, EuclideanSpace.basisFun_toBasis, hasDerivAt_neg', ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, HasFDerivAt.fun_mul, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, eqOn_dslope_sub_smul, LeftInvariantDerivation.left_invariant', derivWithin_fderivWithin, RCLike.wInner_sub_right, FormalMultilinearSeries.derivSeries_coeff_one, PadicInt.sub_zmodRepr_mem, MeasureTheory.integral_fintype_prod_eq_prod, derivWithin_comp_const_sub, iteratedDeriv_pow, AffineMap.hasDerivWithinAt, LeftInvariantDerivation.left_invariant, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, EuclideanSpace.basisFun_apply, hasDerivWithinAt_iff_isLittleO, Matrix.PosSemidef.sqrt_eq_zero_iff, Differentiable.fderiv_norm_rpow, RCLike.normSq_neg, MeasureTheory.integral_const_mul, TensorProduct.toLinearEquiv_lidIsometry, OrthonormalBasis.toBasis_singleton, ContDiffOn.inner, AnalyticOnNhd.eval_linearMap', hasStrictFDerivAt_exp_smul_const_of_mem_ball', LinearMap.toMatrixOrthonormal_reindex, MeasureTheory.integral_div, Matrix.IsHermitian.eigenvalues_eq, HasStrictFDerivAt.pow, UnitAddTorus.mFourierSubalgebra_closure_eq_top, mul_comm, iter_deriv_zpow', PadicInt.coe_sum, Matrix.exp_conj', ConvexOn.univ_sSup_of_countable_affine_eq, RCLike.hasSum_ofReal, Matrix.PosSemidef.commute_iff, IsLocalFrameOn.coeff_apply_of_mem, HasFDerivAt.finset_prod, Matrix.exp_neg, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, polynomialFunctions.starClosure_topologicalClosure, innerββ_apply_apply, hasFDerivWithinAt_inv, RCLike.ofReal_balance, smoothSheafCommRing.instLocalRing_stalk, MeasureTheory.L2.inner_def, LinearMap.polar_singleton, intervalIntegral.integral_div, NormedSpace.Dual.toWeakDual_continuous, ContinuousMultilinearMap.norm_smulRightL_le, cfcβ_integral, differentiableAt_comp_add_const, RCLike.ofReal_comp_balance, RCLike.reCLM_norm, cfcβ_setIntegral, RCLike.ofReal_sub, hasDerivAt_iff_isLittleO, HasDerivWithinAt.hasFDerivWithinAt, Polynomial.abs_div_tendsto_atTop_of_degree_gt, Matrix.IsHermitian.eigenvectorUnitary_col_eq, fderiv_eq_deriv_mul, nndist_right_lineMap, ContinuousLinearMap.toSesqForm_apply_coe, Polynomial.differentiableOn_aeval, MeromorphicAt.inv_iff, MeasureTheory.setIntegral_prod_mul, Matrix.toEuclideanLin_apply, iteratedDerivWithin_eq_iteratedFDerivWithin, HasFDerivWithinAt.mul, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, HasFDerivWithinAt.multiset_prod, MeasureTheory.integral_fintype_prod_eq_pow, RCLike.conjCLE_apply, ProbabilityTheory.IndepFun.integral_comp_mul_comp, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, PiTensorProduct.mapL_smul, RCLike.I_mul_I, ValueDistribution.logCounting_top, LeftInvariantDerivation.lift_add, meromorphicOrderAt_ne_top_iff, Pi.counit_eq_adjoint, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.toMatrixOrthonormal_apply_apply, RCLike.instCStarRing, LDL.lowerInv_orthogonal, InnerProductSpace.Core.inner_neg_left, summable_mul_of_bigO_atTop, ContinuousLinearMapWOT.inducingFn_apply, entrywise_sup_norm_bound_of_unitary, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, Finsupp.sum_inner, MeasureTheory.integral_fin_nat_prod_volume_eq_prod, LeftInvariantDerivation.lift_smul, PadicInt.exists_mem_range, contDiffWithinAt_euclidean, Real.fourier_iteratedFDeriv, EulerProduct.eulerProduct_completely_multiplicative, PadicInt.exists_mem_range_of_norm_rat_le_one, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, AntitoneOn.derivWithin_nonpos, LinearMap.extendToπ'_apply, dslope_sub_smul, hasDerivAt_id', Matrix.IsHermitian.eigenvectorUnitary_mulVec, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, MeasureTheory.convolution_lsmul, coe_innerSL_apply, deriv_fderiv, Matrix.PosSemidef.det_sqrt, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, HasDerivAt.differentiableAt, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, TensorProduct.lidIsometry_apply, ContinuousLinearMap.hasDerivAt, PadicInt.fwdDiff_tendsto_zero, EulerProduct.eulerProduct_hasProd, Module.Basis.coe_toOrthonormalBasis_repr, hasGradientAtFilter_iff_isLittleO, hasGradientAt_iff_isLittleO, BoundedContinuousFunction.mem_charPoly, LeftInvariantDerivation.comp_L, AffineMap.differentiableWithinAt, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, LinearMap.trace_eq_sum_inner, MeromorphicOn.divisor_inv, MeromorphicOn.id, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, IsLocalFrameOn.coeff_congr, LinearMap.hasStrictDerivAt, FiniteDimensional.rclike_to_real, HasDerivAtFilter.isBigO_sub_rev, differentiableOn_dslope_of_notMem, RCLike.wInner_neg_right, ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd, NormedSpace.inclusionInDoubleDual_norm_eq, Meromorphic.MeromorphicOn.countable_compl_analyticAt, Matrix.PosSemidef.posSemidef_sqrt, Polynomial.abs_tendsto_atTop_iff, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, EulerProduct.eulerProduct, deriv_id'', hasStrictFDerivAt_exp, ContinuousLinearMap.norm_smulRightL, Function.FactorizedRational.mulSupport, PadicInt.coe_addChar_of_value_at_one, RCLike.summable_ofReal, ContinuousMapZero.integral_apply, HasDerivAt.hasFDerivAt, RCLike.imLm_coe, hasFDerivAt_norm_rpow, Function.FactorizedRational.meromorphicOrderAt_eq, iteratedDeriv_fun_id_zero, MeromorphicOn.divisor_sub_const_self, sum_inner, iteratedDeriv_comp_sub_const, Matrix.linfty_opNNNorm_toMatrix, analyticOrderAt_ne_zero, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, InnerProductSpace.Core.inner_neg_right, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, RCLike.conjCLE_coe, contDiffOn_stereoToFun, Polynomial.abs_tendsto_atTop, LeftInvariantDerivation.evalAt_coe, Matrix.IsHermitian.trace_eq_sum_eigenvalues, hasStrictFDerivAt_exp_smul_const', hasGradientAt_iff_isLittleO_nhds_zero, Matrix.PosSemidef.sqrt_eq_one_iff, Polynomial.differentiable_aeval, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Function.FactorizedRational.finprod_eq_fun, hasDerivAtFilter_neg, tsum_pow_div_one_sub_eq_tsum_sigma, HilbertBasis.hasSum_repr, HasFDerivAt.pow, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, meromorphicOrderAt_const_natCast, innerSL_inj, continuousAt_dslope_same, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, StrongDual.toLp_of_not_memLp, differentiableWithinAt_of_derivWithin_ne_zero, MeromorphicOn.divisor_intCast, TensorProduct.inner_lid_lid, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, NormedSpace.inclusionInDoubleDual_norm_le, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, ConvexOn.sSup_of_countable_affine_eq, RCLike.reCLM_coe, HasDerivWithinAt.inner, DifferentiableAt.inner, HasFDerivWithinAt.mul_const, MeromorphicOn.analyticAt_mem_codiscreteWithin, smoothSheafCommRing.isUnit_stalk_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, FormalMultilinearSeries.coeff_ofScalars, iteratedFDerivWithin_eq_equiv_comp, Matrix.l2_opNNNorm_mulVec, Orthonormal.inner_left_right_finset, meromorphicOrderAt_id, differentiableAt_inv_iff, Finsupp.inner_sum, LinearMap.deriv, contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, HasFDerivWithinAt.inner, EulerProduct.eulerProduct_tprod, fdifferential_apply, LinearMap.extendToπ_apply, Matrix.l2_opNorm_conjTranspose_mul_self, MeromorphicOn.divisor_sub_const_of_ne, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, hasDerivAt_update, inner_neg_right, Orthonormal.isHilbertSum, iteratedDeriv_fun_id, OrthonormalBasis.singleton_apply, inner_eq_sum_norm_sq_div_four, fderiv_pow_ring, Polynomial.abs_tendsto_atBot_iff, integral_conj, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, meromorphicNFAt_inv, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, ProperCone.innerDual_singleton, differentiable_inner, LeftInvariantDerivation.coe_sub, RCLike.im_eq_conj_sub, LDL.lower_conj_diag, hasFDerivAt_list_prod', ArithmeticFunction.IsMultiplicative.eulerProduct_tprod, InnerProductSpace.rankOne_def, Meromorphic.countable_compl_analyticAt, Finset.norm_prod_one_add_sub_one_le, stereoToFun_apply, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.lpNorm_fun_mul_natCast, Polynomial.fderiv_aeval, dslope_sub_smul_of_ne, Module.Basis.equivFunL_symm_apply_repr, iter_deriv_zpow, ClosedSubmodule.orthogonal_eq_inter, hasFDerivWithinAt_iff_hasDerivWithinAt, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, LeftInvariantDerivation.left_invariant'', MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, RCLike.ofReal_neg, contDiff_nat_iff_iteratedDeriv, ContinuousLinearMapWOT.isInducing_inducingFn, EulerProduct.eulerProduct_completely_multiplicative_tprod, summable_prod_mul_pow, RCLike.summable_conj, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, meromorphicOrderAt_inv, hasFDerivAt_exp_smul_const', Matrix.exp_zsmul, LinearMap.toMatrixOrthonormal_symm_apply, RCLike.wInner_sub_left, LinearMap.toMatrix_innerββ_apply, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, PointwiseConvergenceCLM.equivWeakDual_symm_apply, RCLike.wInner_one_eq_inner, AffineMap.hasDerivAt, iteratedDerivWithin_zpow, meromorphicOrderAt_eq_int_iff, dist_lineMap_right, MeasureTheory.lpNorm_fun_natCast_mul, AffineMap.differentiableAt, meromorphicNFAt_iff_analyticAt_or, Matrix.PosSemidef.toLinearMapβ'_zero_iff, RCLike.sqrt_eq_real_add_ite, hasStrictDerivAt_zpow, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, Matrix.instNonnegSpectrumClass, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, innerSLFlip_apply_apply, Polynomial.hasFDerivAt, RCLike.ofReal_finsupp_sum, finrank_euclideanSpace, hasDerivAt_inv, ConvexOn.sSup_of_nat_affine_eq, contMDiff_smul, MeromorphicOn.divisor_ofNat, Function.FactorizedRational.meromorphicNFOn_univ, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, Module.Basis.equivFunL_apply, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, LinearMap.hasDerivWithinAt, Real.fourier_fderiv, MeromorphicOn.inv_iff, ContinuousMap.adjoin_id_eq_span_one_union, meromorphicTrailingCoeffAt_const, instCStarRingReal, HasFDerivWithinAt.norm_sq, ordinaryHypergeometric_radius_top_of_neg_natβ, ContinuousLinearMapWOT.isEmbedding_inducingFn, integral_inner, AnalyticAt.harmonicAt_conj, HasDerivWithinAt.differentiableWithinAt, ZSpan.coe_floor_self, Orthonormal.linearIsometryEquiv_symm_apply_single_one, Matrix.PosDef.commute_iff, RCLike.finrank_le_two, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, dist_homothety_self, iteratedFDeriv_eq_equiv_comp, meromorphicTrailingCoeffAt_inv, MeromorphicAt.id, Matrix.ofLp_toEuclideanCLM, hasDerivAtFilter_iff_isLittleO, NonUnitalCommCStarAlgebra.toCompleteSpace, meromorphicNFOn_inv, logDeriv_apply, iteratedDerivWithin_one_div, RCLike.sqrt_map, PadicInt.mahlerTerm_one, HasStrictDerivAt.hasStrictFDerivAt, RCLike.inner_tmul_eq, HasFDerivAt.multiset_prod, dist_self_homothety, Matrix.l2_opNNNorm_mul, IsLocalFrameOn.eventually_eq_sum_coeff_smul, HasFDerivAt.mul_const, differentiableWithinAt_euclidean, MeasureTheory.integral_prod_mul, Matrix.isPositive_toEuclideanLin_iff, padic_polynomial_dist, ContDiff.inner, HasGradientAt.differentiableAt, NormedSpace.exp_sum, Function.FactorizedRational.analyticAt, PadicInt.zmodRepr_spec, RCLike.wInner_const_left, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, contDiffAt_inv, hasStrictFDerivAt_norm_sq, LinearMap.adjoint_toSpanSingleton, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, HasDerivAtFilter.isBigO_sub, iteratedDeriv_comp_neg, Matrix.posDef_iff_eq_conjTranspose_mul_self, Polynomial.differentiableAt_aeval, hasDerivAt_id, RCLike.hasSum_conj, deriv_update, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, nndist_lineMap_right, Polynomial.hasFDerivAt_aeval, deriv_zpow', LeftInvariantDerivation.map_add, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, HasGradientAtFilter.isBigO_sub, LinearMap.polar_gc, hasDerivAt_exp, contDiffOn_succ_iff_deriv_of_isOpen, LeftInvariantDerivation.coe_add, iter_deriv_pow', cfc_integral, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, EuclideanSpace.basisFun_repr, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, MeromorphicOn.eventually_codiscreteWithin_analyticAt, ArithmeticFunction.IsMultiplicative.eulerProduct, deriv_neg'', OrthonormalBasis.equiv_apply_euclideanSpace, IsLocalFrameOn.coeff_apply_of_notMem, PadicInt.limNthHom_spec, fderiv_inv, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, iteratedDeriv_eq_equiv_comp, HasFDerivWithinAt.hasDerivWithinAt, Matrix.PosSemidef.isUnit_sqrt_iff, hasDerivAt_iff_hasFDerivAt, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, PadicInt.continuous_addChar_of_value_at_one, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, LinearMap.polar_weak_closed, hasGradientAt_iff_tendsto, InnerProductSpace.Core.inner_sub_sub_self, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, fdifferential_comp, RCLike.sqrt_neg_one, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', LeftInvariantDerivation.coe_injective, Matrix.IsHermitian.eigenvectorUnitary_apply, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, fderiv_apply_one_eq_deriv, EulerProduct.eulerProduct_hasProd_mulIndicator, HasFDerivAt.inner, meromorphicTrailingCoeffAt_id_sub_const, LinearMap.toMatrixOrthonormal_apply, OrthogonalFamily.inner_sum, EuclideanSpace.inner_eq_star_dotProduct, NonUnitalCommCStarAlgebra.toStarModule, LeftInvariantDerivation.coe_neg, StrongDual.toLpβ_apply, PadicInt.fwdDiff_iter_le_of_forall_le, Valued.integer.coe_span_singleton_eq_closedBall, Polynomial.differentiableOn, IsLocalFrameOn.coeff_apply_zero_at, Orientation.inner_mul_areaForm_sub', inner_sub_left, AnalyticOnNhd.eval_polynomial, differentiableOn_neg, HasFDerivAt.mul, LinearMap.continuous_of_nonzero_on_open, InnerProductSpace.innerSL_norm, Submodule.det_reflection, deriv_neg', AnalyticAt.of_meromorphicOrderAt_pos, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.hasDerivWithinAt_aeval, contDiffOn_inv, ContinuousLinearMap.extendToπ_apply, Polynomial.hasStrictDerivAt_aeval, differentiableAt_iff_comp_const_sub, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, summable_norm_pow_mul_geometric_div_one_sub, ProbabilityTheory.covarianceBilin_apply_basisFun, hasGradientAt_iff_hasFDerivAt, MeromorphicOn.countable_compl_analyticAt_inter, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, hasFDerivAt_exp_smul_const_of_mem_ball, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, Matrix.exp_conj, Orthonormal.inner_finsupp_eq_sum_left, fderiv_deriv, Matrix.PosSemidef.sq_sqrt, contDiffAt_inner, lp.summable_inner, spec_cfcβAux, DifferentiableOn.inner, hasFDerivAt_exp_smul_const, Differentiable.inner, LeftInvariantDerivation.map_smul, Polynomial.isBoundedUnder_abs_atBot_iff, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, Module.Basis.parallelepiped_eq_map, LinearMap.mem_polar_singleton, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, RCLike.ofRealCLM_norm, Matrix.IsHermitian.eigenvectorUnitary_coe, Complex.sqrt_map, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, MeasureTheory.convolution_lsmul_swap, Matrix.toEuclideanLin_eq_toLin, StrongDual.toLpβ_of_not_memLp, analyticOrderAt_id, Matrix.isHermitian_iff_isSymmetric, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, deriv_zpow, NonUnitalCommCStarAlgebra.toCStarRing, inner_eq_neg_one_iff_of_norm_eq_one, FormalMultilinearSeries.apply_eq_prod_smul_coeff, EuclideanSpace.basisFun_inner, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, differentiableAt_euclidean, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, LeftInvariantDerivation.coe_smul, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, hfdifferential_apply, MeasureTheory.integral_fin_nat_prod_eq_prod, spectrum.differentiableOn_inverse_one_sub_smul, LinearMap.tripolar_eq_polar, RCLike.toIsOrderedAddMonoid, logDeriv_inv, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, differentiableOn_euclidean, RCLike.reLm_coe, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, tsum_prod_pow_eq_tsum_sigma, toSpanSingleton_derivWithin, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, MeromorphicOn.eventually_analyticAt_or_mem_compl, integral_coe_re_add_coe_im, RCLike.wInner_one_const_right, Matrix.posSemidef_iff_eq_sum_vecMulVec, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, MeasureTheory.lpNorm_one, HasStrictFDerivAt.hasStrictDerivAt, EuclideanSpace.inner_basisFun_real, innerSLFlip_apply, fderivWithin_derivWithin, hasDerivAt_const_mul, RCLike.sqrt_neg_I, InnerProductSpace.Core.inner_sub_left, IsLocalFrameOn.eq_iff_coeff, iteratedDeriv_comp_const_sub, Function.RCLike.hasTemperateGrowth_ofReal, PadicInt.instIsAdicCompleteMaximalIdeal, Polynomial.hasDerivAt, RCLike.conj_I, contDiff_inner, Matrix.linfty_opNorm_toMatrix, innerSL_apply_norm, iter_deriv_inv, Matrix.frobenius_norm_mul, Matrix.star_dotProduct_gram_mulVec, RCLike.hasSum_iff, RCLike.sqrt_I, hasDerivWithinAt_zpow, Monotone.deriv_nonneg, locallyIntegrableOn_mul_sum_Icc, innerSL_real_flip, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, TensorProduct.norm_lid, Matrix.instIsOrderedAddMonoid, iteratedDeriv_eq_iteratedFDeriv, iter_deriv_inv', toMatrix_innerSL_apply, Matrix.PosSemidef.re_dotProduct_nonneg, MeasureTheory.lpNorm_div_natCast, Polynomial.isBoundedUnder_abs_atTop_iff, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, lp.hasSum_inner, DoubleCentralizer.coe_eq_algebraMap, deriv_pow_field, deriv_comp_neg, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, PadicInt.norm_sub_modPart, inner_sub_right, HasFDerivAt.hasDerivAt, LeftInvariantDerivation.map_sub, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, BoundedContinuousFunction.star_mem_range_charAlgHom, MeromorphicOn.extract_zeros_poles, cfcβAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, norm_deriv_eq_norm_fderiv, PadicInt.fwdDiff_mahlerSeries, deriv_id, MeasureTheory.L2.mem_L1_inner, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, differentiable_neg, RCLike.wInner_neg_left, hasDerivAt_neg, PadicInt.continuous_multichoose, Polynomial.hasStrictDerivAt, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, HilbertBasis.repr_self, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, ContDiffWithinAt.inner, ContinuousMapZero.instCStarRing, hasFDerivWithinAt_iff_hasGradientWithinAt, Polynomial.abs_tendsto_atBot, HasStrictFDerivAt.multiset_prod, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, Matrix.toEuclideanLin_apply_piLp_toLp, Matrix.linfty_opNorm_eq_opNorm, RCLike.ofReal_tsum, hasDerivAt_pow, contDiff_succ_iff_deriv, Submodule.mem_adjoint_iff, PadicInt.norm_sub_zmodRepr_lt_one, Function.FactorizedRational.extractFactor, integrableOn_mul_sum_Icc, PadicInt.mahlerEquiv_apply, LinearMap.isSymmetric_iff_sesqForm, hasDerivWithinAt_derivWithin_iff, hasStrictDerivAt_exp, Irreducible.maximalIdeal_eq_closedBall, intervalIntegral.integral_smul_const, Polynomial.deriv, HilbertBasis.summable_inner_mul_inner, HasDerivAtFilter.isEquivalent_sub, AffineMap.differentiableOn, Polynomial.hasFDerivWithinAt_aeval, fourierSubalgebra_closure_eq_top, derivWithin_comp_add_const, hasStrictDerivAt_inv, Polynomial.contDiff_aeval, RCLike.wInner_one_const_left, LinearMap.continuous_of_isClosed_ker, LDL.diag_eq_lowerInv_conj, differentiableAt_iff_comp_add_const, LinearMap.polar_isClosed, innerββ_apply, deriv_inner_apply, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, Polynomial.abs_isBoundedUnder_iff, StrongDual.toLp_apply, LinearMap.continuous_iff_isClosed_ker, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, LinearMap.toSeminorm_ball_zero, iter_deriv_inv_linear_sub, RCLike.imCLM_coe, UnitAddTorus.mFourierBasis_repr, HasDerivAt.inner, LinearMap.toSeminorm_apply, LeftInvariantDerivation.toDerivation_injective, MeasureTheory.lpNorm_natCast_mul, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, iteratedDeriv_id, MeasureTheory.BoundedContinuousFunction.inner_toLp, MeasureTheory.integral_fintype_prod_volume_eq_prod, MeasureTheory.convolution_mul_swap, ContinuousLinearMap.norm_smulRightL_le, analyticOrderAt_eq_zero, hasDerivAt_single, SchwartzMap.integral_smul_laplacian_right_eq_left, RCLike.re_le_neg_norm_iff_eq_neg_norm, OrthonormalBasis.coe_equiv_euclideanSpace, RCLike.wInner_one_eq_sum, NonUnitalCommCStarAlgebra.toSMulCommClass, integral_ofReal, Polynomial.differentiableWithinAt_aeval, signedDist_apply, EuclideanSpace.inner_toLp_toLp, ordinaryHypergeometric_radius_top_of_neg_natβ, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, FormalMultilinearSeries.coeff_iterate_fslope, PadicInt.continuousAddCharEquiv_symm_apply, ContinuousLinearMap.extendToπ'_apply, derivWithin_comp_sub_const, IsLocalFrameOn.coeff_eq_of_eq, ContinuousLinearMap.isAdjointPair_inner, AddChar.linearIndependent, Antitone.deriv_nonpos, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, differentiable_tsum', Polynomial.differentiable, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, LinearMap.mem_span_iff_bound, hasFDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_mul_const, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, iteratedDeriv_fun_pow_zero, hasStrictFDerivAt_exp_smul_const, RCLike.instNormSMulClassInt, ContDiffAt.inner, RCLike.wInner_cWeight_const_right, HasStrictFDerivAt.mul, iter_deriv_inv_linear, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, ContinuousMap.elemental_id_eq_top, dist_right_lineMap, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, innerββ_apply_coe, PiLp.inner_apply, differentiableAt_of_deriv_ne_zero, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, meromorphicOrderAt_const_intCast, LinearMap.toSeminormFamily_apply, hasGradientWithinAt_iff_tendsto, EuclideanSpace.inner_single_right, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, HasFDerivWithinAt.finset_prod, Submodule.orthogonal_eq_inter, hasDerivAt_iff_tendsto, ProbabilityTheory.iIndepFun.integral_prod_comp, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, sub_smul_dslope, setIntegral_re_add_im, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, MeasureTheory.lpNorm_one', Matrix.toEuclideanLin_eq_toLin_orthonormal, LinearPMap.mem_adjoint_domain_iff, differentiableWithinAt_zpow, RCLike.intervalIntegral_ofReal, contDiffOn_infty_iff_deriv_of_isOpen, ContinuousMultilinearMap.norm_smulRight, LeftInvariantDerivation.commutator_apply, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, OrthonormalBasis.coe_singleton, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, hasStrictFDerivAt_pow, derivWithin_comp_const_add, AnalyticOn.eval_polynomial, prod_vanishing_of_summable_norm, Matrix.l2_opNNNorm_conjTranspose_mul_self, coe_innerββ_apply, hasDerivAt_exp_zero, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, instFieldContMDiffRing, hasGradientWithinAt_iff_isLittleO, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, RCLike.conj_eq_re_sub_im, DFinsupp.inner_sum, inner_matrix_row_row, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, LinearMap.polar_mem_iff, hasDerivWithinAt_inv, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, hasStrictDerivAt_id, HasGradientAt.fderiv_apply, deriv_neg, integral_re, LeftInvariantDerivation.ext_iff, MeromorphicOn.countable_compl_analyticAt, Polynomial.hasFDerivWithinAt, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, hasStrictDerivAt_iff_hasStrictFDerivAt, ConvexOn.exists_affine_le_of_lt, MeasureTheory.integral_prod_smul, inner_sub_sub_self, innerSL_apply_coe, HasStrictFDerivAt.inner, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, differentiableAt_dslope_of_ne, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, hasDerivAt_zpow, EuclideanSpace.single_eq_zero_iff, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, Matrix.IsHermitian.mulVec_eigenvectorBasis, ValueDistribution.log_counting_zero_sub_logCounting_top, Matrix.l2_opNorm_def, Matrix.toEuclideanLin_toLp, integral_re_add_im, ZSpan.coe_fract_self, LeftInvariantDerivation.toFun_eq_coe, Matrix.l2_opNorm_mul, norm_innerSL_le, BoundedContinuousFunction.separatesPoints_charPoly, AffineMap.deriv, SchwartzMap.integral_smul_deriv_right_eq_neg_left, AnalyticOnNhd.eval_continuousLinearMap', PadicInt.instIsAddTorsionFree, HasGradientWithinAt.hasFDerivWithinAt, hasFDerivAt_exp, RCLike.hasSum_conj', MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, differentiableAt_iff_comp_sub_const, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support, LinearMap.polar_mem, LinearMap.isAdjointPair_inner, AnalyticOnNhd.eval_mvPolynomial, ContinuousLinearMap.hasStrictDerivAt, hasFDerivAt_inv, DifferentiableWithinAt.inner, ContinuousLinearMap.smulRightL_apply_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasDerivAtFilter.isTheta_sub, ValueDistribution.logCounting_inv, HasStrictFDerivAt.mul_const, HilbertBasis.hasSum_inner_mul_inner, fderivInnerCLM_apply, ConvexOn.sSup_affine_eq, nndist_self_homothety, RCLike.I_mul_I_of_nonzero, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, summable_mul_of_bigO_atTop', RCLike.span_one_I, hasFPowerSeriesAt_iff', MeasureTheory.eLpNorm_conj, DFinsupp.sum_inner, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, differentiableAt_comp_sub_const, smooth_functions_tower, RCLike.ofReal_sum, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, LinearMap.mem_span_iff_continuous, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, AnalyticOnNhd.eval_continuousLinearMap, ContinuousLinearMap.adjoint_innerSL_apply, RCLike.normSq_sub, nndist_homothety_self, Orthonormal.inner_sum, intervalIntegral.integral_mul_const, Filter.IsBoundedUnder.isLittleO_sub_self_inv, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, LeftInvariantDerivation.coeFnAddMonoidHom_apply, RCLike.sqrt_neg_of_nonneg, hasDerivWithinAt_iff_tendsto, MeasureTheory.condExpL2_const_inner, PadicInt.existsUnique_mem_range, ContinuousLinearMap.norm_smulRightL_apply, PadicInt.toZMod_spec, differentiableAt_iff_comp_neg, hasFPowerSeriesAt_iff, contDiff_euclidean, fderiv_norm_sq_apply, RCLike.imCLM_apply, hasStrictDerivAt_pow, Derivation.evalAt_apply, derivWithin_mem_iff, RCLike.conj_neg_I, ConvexOn.univ_sSup_of_nat_affine_eq, cfc_setIntegral, RCLike.inv_I, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, HasFDerivAtFilter.hasDerivAtFilter, MeasureTheory.integral_mul_const, fderiv_norm_sq, NonUnitalCommCStarAlgebra.toIsScalarTower, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, ContinuousLinearMap.toSesqForm_apply_norm_le, HilbertBasis.hasSum_repr_symm, inner_neg_left, differentiableWithinAt_Ioi_iff_Ici, integral_im, differentiableOn_zpow, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Function.FactorizedRational.meromorphicNFOn, fderiv_inner_apply, contDiff_one_iff_deriv, inner_matrix_col_col, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, derivWithin_comp_neg, HasFDerivWithinAt.fun_mul, RCLike.div_I, BoundedContinuousFunction.char_mem_charPoly, iter_deriv_pow, HasStrictFDerivAt.finset_prod, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, Matrix.PosDef.re_dotProduct_pos, fderiv_eq_smul_deriv, hasStrictFDerivAt_exp_smul_const_of_mem_ball, InnerProductSpace.Core.inner_sub_right, PadicInt.addChar_of_value_at_one_def, deriv_comp_sub_const, tendsto_zero_geometric_tsum_pnat, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod
|
toNonUnitalSeminormedCommRing π | CompOp | 2 mathmath: nnnorm_cfcβHom, ContinuousMapZero.elemental_eq_top
|
| Name | Category | Theorems |
|---|
induced π | CompOp | β |
toMetricSpace π | CompOp | 71 mathmath: Unitization.isometry_inr, continuous_cfcβHomSuperset_left, norm_cfcβHom, ContinuousWithinAt.cfcβ, nnnorm_cfcβ_nnreal_le_iff, nnnorm_cfcβ_lt_iff, CFC.nnnorm_sqrt, ContinuousOn.cfcβ', IsGreatest.nnnorm_cfcβ, ContinuousLinearMap.isometry_mul_flip, CFC.continuousOn_sqrt, norm_cfcβ_lt, antilipschitzWith_mul_right, IsGreatest.norm_cfcβ, nnnorm_cfcβ_nnreal_lt, Continuous.cfcβ_of_mem_nhdsSet, Continuous.cfcβ, continuousOn_cfcβ, CStarAlgebra.norm_posPart_le, IsGreatest.nnnorm_cfcβ_nnreal, CFC.continuous_abs, nnnorm_apply_le_nnnorm_cfcβ, norm_cfcβ_lt_iff, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Continuous.cfcβ_nnreal, ContinuousAt.cfcβ_nnreal, Filter.Tendsto.cfcβ, NonUnitalCommCStarAlgebra.toCompleteSpace, ContinuousWithinAt.cfcβ_nnreal, CFC.continuousOn_nnrpow, Filter.Tendsto.cfcβ_nnreal, nnnorm_cfcβ_nnreal_lt_iff, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, norm_cfcβ_le, ContinuousOn.cfcβ_nnreal', nnnorm_cfcβHom, Continuous.cfcβ_nnreal_of_mem_nhdsSet, ContinuousOn.cfcβ, ContinuousOn.cfcβ_of_mem_nhdsSet, antilipschitzWith_mul_left, dist_eq, Continuous.cfcβ', NonUnitalStarAlgHom.isometry, ContinuousAt.cfcβ, nnnorm_cfcβ_le_iff, continuousOn_cfcβ_nnreal, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, NonUnitalCStarAlgebra.toCompleteSpace, continuousOn_cfcβ_setProd, CStarAlgebra.norm_negPart_le, Dilation.mulRight_toFun, Unitization.antilipschitzWith_addEquiv, ContinuousOn.cfcβ_nnreal, norm_apply_le_norm_cfcβ, Dilation.mulLeft_toFun, Unitization.lipschitzWith_addEquiv, nnnorm_cfcβ_le, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, nnnorm_cfcβ_nnreal_le, apply_le_nnnorm_cfcβ_nnreal, continuousOn_cfcβ_nnreal_setProd, CFC.norm_sqrt, MonotoneOn.nnnorm_cfcβ, CFC.nnnorm_nnrpow, norm_cfcβ_le_iff, CFC.norm_nnrpow, WithLp.unitization_isometry_inr, StarAlgEquiv.isometry, Continuous.cfcβ_nnreal', nnnorm_cfcβ_lt
|
toNonUnitalRing π | CompOp | 204 mathmath: CStarAlgebra.preimage_inr_Icc_zero_one, norm_cfcβHom, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, DoubleCentralizer.star_snd, CFC.monotoneOn_one_sub_one_add_inv, NonUnitalCStarAlgebra.toStarModule, Matrix.IsHermitian.det_abs, CFC.monotone_nnrpow, CStarAlgebra.inr_mem_Icc_iff_norm_le, Unitization.real_cfcβ_eq_cfc_inr, DoubleCentralizer.natCast_fst, isClosedEmbedding_cfcβAux, Unitization.splitMul_apply, DoubleCentralizer.nnnorm_def', Matrix.PosSemidef.sqrt_eq_zero_iff, WithCStarModule.prod_norm_sq, CStarModule.innerSL_apply, NonUnitalNormedCommRing.mul_comm, CStarAlgebra.span_nonneg_inter_unitBall, WithCStarModule.inner_def, RCLike.nonUnitalContinuousFunctionalCalculus, CStarMatrix.toCLM_injective, CStarRing.norm_mul_self_le, CStarMatrix.instStarOrderedRing, Unitization.nnnorm_def, Unitization.instStarOrderedRing, DoubleCentralizer.norm_def', CStarMatrix.norm_def', WithLp.unitization_algebraMap, CStarMatrix.inner_toCLM_conjTranspose_left, Prod.cstarRing, CFC.continuousOn_sqrt, PositiveLinearMap.preGNS_norm_def, DoubleCentralizer.central, Matrix.PosSemidef.det_sqrt, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, norm_cfcβ_lt, Filter.IsIncreasingApproximateUnit.toIsApproximateUnit, antilipschitzWith_mul_right, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, nnnorm_cfcβ_nnreal_lt, Matrix.PosSemidef.posSemidef_sqrt, Filter.IsIncreasingApproximateUnit.eventually_nonneg, continuousOn_cfcβ, Unitization.cobounded_eq_aux, Matrix.PosSemidef.sqrt_eq_one_iff, CStarRing.norm_star_mul_self', Matrix.PosSemidef.sqrt_sq, Unitization.splitMul_injective_of_clm_mul_injective, CStarRing.MulOpposite.instMulOpposite, PositiveLinearMap.preGNS_inner_def, CStarAlgebra.instNonnegSpectrumClassComplexNonUnital, DoubleCentralizer.add_fst, quasispectrum.isCompact, cfcβAux_id, CStarAlgebra.norm_posPart_le, CStarAlgebra.span_nonneg_inter_unitClosedBall, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, CFC.continuous_abs, coe_ringEquiv_lpBCF, integral_const_mul_of_integrable, selfAdjoint.unitarySelfAddISMul_coe, CStarRing.star_mul_self_eq_zero_iff, IsometricContinuousFunctionalCalculus.toNonUnital, lp.infty_coeFn_mul, DoubleCentralizer.star_fst, normRingNorm_toFun, CStarAlgebra.instNonnegSpectrumClass, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Filter.IsIncreasingApproximateUnit.eventually_isSelfAdjoint, DoubleCentralizer.add_snd, CStarModule.norm_inner_le, Matrix.instNonnegSpectrumClass, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, CStarMatrix.toCLM_apply_single, Unitization.norm_eq_sup, CStarMatrix.toCLM_apply_eq_sum, WithCStarModule.pi_norm, inr_comp_cfcβHom_eq_cfcβAux, CFC.monotoneOn_one_sub_one_add_inv_real, CFC.continuousOn_nnrpow, DoubleCentralizer.algebraMap_snd, upperHemicontinuous_quasispectrum, CStarMatrix.toCLM_apply, DoubleCentralizer.algebraMap_toProd, DoubleCentralizer.instIsCentralScalar, mem_compactlySupported, PositiveLinearMap.gnsStarAlgHom_apply, WithCStarModule.pi_inner, ContinuousMap.instCStarRing, CStarRing.norm_star_mul_self, Matrix.PosSemidef.isUnit_sqrt_iff, WithCStarModule.prod_norm, CStarMatrix.mul_entry_mul_eq_inner_toCLM, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, CStarModule.norm_sq_eq, ZeroAtInftyContinuousMap.instCStarRing, NonUnitalCommCStarAlgebra.toStarModule, WithCStarModule.inner_single_right, Unitization.norm_def, selfAdjoint.star_coe_unitarySelfAddISMul, DoubleCentralizer.coeHom_apply, WithLp.unitizationAlgEquiv_symm_apply_ofLp, norm_cfcβ_le, Matrix.PosSemidef.sq_sqrt, spec_cfcβAux, ContinuousLinearMap.instNonnegSpectrumClassRealId, Unitization.nnreal_cfcβ_eq_cfc_inr, CStarModule.norm_eq_csSup, Matrix.PosSemidef.inv_sqrt, CStarRing.norm_self_mul_star, upperHemicontinuous_quasispectrum_nnreal, nnnorm_cfcβHom, CFC.nnrpow_le_nnrpow, DoubleCentralizer.algebraMap_fst, CStarAlgebra.span_nonneg_inter_closedBall, CStarAlgebra.isClosed_nonneg, Unitization.instCStarRing, norm_mul_le, integral_mul_const_of_integrable, antilipschitzWith_mul_left, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, dist_eq, Filter.IsIncreasingApproximateUnit.eventually_star_eq, CFC.norm_abs, Memβp.infty_mul, Unitization.isUniformEmbedding_addEquiv, cfcβAux_mem_range_inr, Unitization.nnnorm_eq_sup, CStarModule.inner_mul_inner_swap_le, CFC.monotone_sqrt, quasispectrum.isCompact_nnreal, CStarAlgebra.instNonnegSpectrumClass', norm_cfcβ_one_sub_one_add_inv_lt_one, continuousOn_cfcβ_nnreal, Unitization.instNormOneClass, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, WithCStarModule.inner_single_left, CStarAlgebra.directedOn_nonneg_ball, PositiveLinearMap.leftMulMapPreGNS_mul_eq_comp, continuousOn_cfcβ_setProd, Unitization.complex_cfcβ_eq_cfc_inr, Filter.comap_mul_left_cobounded, CStarAlgebra.norm_negPart_le, NonUnitalCStarAlgebra.toIsScalarTower, CStarRing.to_normedStarGroup, CFC.sqrt_le_sqrt, Dilation.mulRight_toFun, CStarModule.continuous_inner, PositiveLinearMap.instStarHomClassOfLinearMapClassComplexOfOrderHomClass, CStarAlgebra.spectralOrderedRing, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, NonUnitalCommCStarAlgebra.toSMulCommClass, Unitization.norm_splitMul_snd_sq, DoubleCentralizer.natCast_snd, Unitization.antilipschitzWith_addEquiv, coe_ringEquiv_lpBCF_symm, Unitization.splitMul_injective, CStarAlgebra.inr_mem_Icc_iff_nnnorm_le, WithCStarModule.pi_norm_sq, WithLp.unitization_mul, DoubleCentralizer.instStarModule, CStarRing.nnnorm_self_mul_star, Matrix.PosSemidef.sqrt_mul_self, CStarMatrix.instCStarRing, Filter.comap_mul_right_cobounded, CStarAlgebra.span_nonneg_inter_ball, CStarAlgebra.isBasis_nonneg_sections, Unitization.uniformity_eq_aux, CFC.monotoneOn_cfcβ_rpowIntegrandββ, Dilation.mulLeft_toFun, Unitization.lipschitzWith_addEquiv, WithLp.unitizationAlgEquiv_apply, CStarAlgebra.instNonnegSpectrumClassComplexUnital, CStarAlgebra.hasBasis_approximateUnit, quasispectrum.instCompactSpaceNNReal, nnnorm_cfcβ_le, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, nnnorm_cfcβ_nnreal_le, continuousOn_cfcβ_nnreal_setProd, WithCStarModule.prod_inner, CStarRing.mul_star_self_eq_zero_iff, NonUnitalCStarAlgebra.toSMulCommClass, CStarRing.nnnorm_star_mul_self, NormedRing.toRingNorm_apply, Matrix.PosDef.posDef_sqrt, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, ContinuousMap.idealOfSet_ofIdeal_eq_closure, le_iff_norm_sqrt_mul_rpow, CStarAlgebra.exists_sum_four_nonneg, PositiveLinearMap.preGNS_norm_sq, NonUnitalCommCStarAlgebra.toIsScalarTower, Unitization.inr_nonneg_iff, CStarMatrix.norm_def, DoubleCentralizer.add_toProd, CFC.abs_eq_zero_iff, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, CStarMatrix.inner_toCLM_conjTranspose_right, quasispectrum.instCompactSpace, CStarMatrix.toCLM_apply_single_apply, DoubleCentralizer.toProdMulOppositeHom_apply, Unitization.cfcβ_eq_cfc_inr, le_iff_norm_sqrt_mul_sqrt_inv, nnnorm_cfcβ_lt
|
toNonUnitalSeminormedRing π | CompOp | 486 mathmath: CStarAlgebra.preimage_inr_Icc_zero_one, nnnorm_inv, MeasureTheory.eLpNormEssSup_const_smul_le, NormedSpace.exp_continuous, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, norm_cfcβHom, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, IsStarNormal.spectralRadius_eq_nnnorm, DoubleCentralizer.star_snd, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, MeasureTheory.eLpNormEssSup_const_smul, CFC.monotoneOn_one_sub_one_add_inv, hasStrictFDerivAt_list_prod_finRange', NonUnitalCStarAlgebra.toStarModule, nnnorm_cfc_lt, PositiveLinearMap.apply_le_of_isSelfAdjoint, Filter.Tendsto.exp, BoundedContinuousFunction.algebraMap_apply, CFC.monotone_nnrpow, Matrix.cstar_nnnorm_def, egauge_prod_mk, DoubleCentralizer.intCast_snd, DoubleCentralizer.range_toProdMulOpposite, integrableOn_cfc', Unitary.mem_pathComponentOne_iff, Unitization.real_cfcβ_eq_cfc_inr, norm_iteratedFDeriv_mul_le, DoubleCentralizer.natCast_fst, isClosedEmbedding_cfcβAux, Unitization.splitMul_apply, DoubleCentralizer.nnnorm_def', deriv_mul_const_field, DoubleCentralizer.zero_snd, selfAdjoint.expUnitaryPathToOne_apply, CFC.nnnorm_sqrt, selfAdjoint.norm_sq_expUnitary_sub_one, StarAlgebra.elemental.characterSpaceToSpectrum_coe, differentiableWithinAt_inv, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, CFC.exp_log, NormedSpace.exp_series_hasSum_exp', ContinuousLinearMap.isometry_mul_flip, WithCStarModule.prod_norm_sq, CStarModule.innerSL_apply, egauge_add_add_le, CStarAlgebra.span_nonneg_inter_unitBall, MeasureTheory.integrable_const_mul_iff, ContinuousLinearMap.opNorm_mul_flip_apply, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum, WithCStarModule.inner_def, DoubleCentralizer.pow_snd, gelfandStarTransform_naturality, RCLike.nonUnitalContinuousFunctionalCalculus, DoubleCentralizer.nnnorm_snd, egauge_univ, CStarAlgebra.tendsto_mul_left_iff_tendsto_mul_right, CStarAlgebra.mem_Icc_iff_nnnorm_le_one, compactlySupported_eq_top_of_isCompact, Function.update_exp, CStarMatrix.toCLM_injective, formalMultilinearSeries_geometric_apply_norm_le, NormedSpace.map_exp, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, NonUnitalStarAlgHom.nnnorm_apply_le, ContinuousLinearMap.opNorm_mul, DoubleCentralizer.smul_toProd, egauge_zero_zero, DoubleCentralizer.toProdMulOpposite_injective, DoubleCentralizer.norm_fst_eq_snd, Unitization.nnnorm_def, Unitization.dist_inr, Unitization.instStarOrderedRing, NormedSpace.exp_hasFPowerSeriesOnBall, NormedSpace.expSeries_summable, BoundedContinuousFunction.coe_toContinuousMapStarβ, cfcL_integrable, DoubleCentralizer.norm_def', CStarMatrix.norm_def', IsGreatest.nnnorm_cfc_nnreal, Quaternion.linearIsometryEquivTuple_symm_apply, WithLp.unitization_algebraMap, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, CStarMatrix.inner_toCLM_conjTranspose_left, hasStrictDerivAt_exp_smul_const, CFC.continuousOn_sqrt, DoubleCentralizer.norm_def, hasStrictDerivAt_exp_smul_const', egauge_univ_pi, nnnorm_div, PositiveLinearMap.preGNS_norm_def, PositiveLinearMap.leftMulMapPreGNS_apply, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Matrix.exp_add_of_commute, DoubleCentralizer.central, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, CompletelyPositiveMap.instLinearMapClassComplex, hasFDerivAt_ringInverse, norm_cfcβ_lt, Filter.IsIncreasingApproximateUnit.toIsApproximateUnit, antilipschitzWith_mul_right, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, differentiableWithinAt_pow, NormedSpace.norm_expSeries_summable, DoubleCentralizer.nnnorm_def, nnnorm_cfcβ_nnreal_lt, nndist_inv_invβ, CStarAlgebra.nnnorm_le_iff_of_nonneg, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, deriv_const_mul_field', Unitary.expUnitary_eq_mul_inv, continuousOn_cfcβ, infEDist_smulβ, DoubleCentralizer.neg_snd, Unitization.cobounded_eq_aux, NormedSpace.expSeries_hasSum_exp, WeakDual.CharacterSpace.homeoEval_naturality, CStarAlgebra.instOrderClosedTopology, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', DoubleCentralizer.range_toProd, IsGreatest.nnnorm_cfc, egauge_le_one, ContinuousMap.isUnit_iff_forall_isUnit, selfAdjoint.nnnorm_pow_two_pow, PositiveLinearMap.preGNS_inner_def, CStarAlgebra.instNonnegSpectrumClassComplexNonUnital, MeasureTheory.Measure.hausdorffMeasure_smulβ, DoubleCentralizer.add_fst, quasispectrum.isCompact, derivWithin_div_const, spectrum.gelfand_formula, iteratedFDerivWithin_smul_const_apply, cfcβAux_id, le_egauge_smul_left, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, compactlySupported_eq_top, CStarAlgebra.norm_posPart_le, NormedSpace.exp_continuousMap_eq, CStarAlgebra.span_nonneg_inter_unitClosedBall, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, CFC.continuous_abs, DoubleCentralizer.smul_fst, coe_ringEquiv_lpBCF, egauge_pi, selfAdjoint.unitarySelfAddISMul_coe, Filter.IsIncreasingApproximateUnit.eventually_nnnorm, deriv_const_mul_field, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', Matrix.exp_nsmul, IsometricContinuousFunctionalCalculus.toNonUnital, AlgHom.instContinuousLinearMapClassOfAlgHomClass, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, PositiveLinearMap.toPreGNS_ofPreGNS, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, PositiveLinearMap.exists_norm_apply_le, DoubleCentralizer.star_fst, IsSelfAdjoint.nnnorm_mul_self, hasFDerivAt_exp_smul_const', compactlySupported_eq_top_iff, CStarAlgebra.instNonnegSpectrumClass, Matrix.exp_sum_of_commute, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, hasFDerivWithinAt_pow', DoubleCentralizer.add_snd, CStarModule.norm_inner_le, infEdist_smulβ, DoubleCentralizer.norm_snd, DoubleCentralizer.nnnorm_fst, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, hasFDerivAt_list_prod_finRange', NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, CStarMatrix.toCLM_apply_single, Unitization.norm_eq_sup, CStarMatrix.toCLM_apply_eq_sum, differentiableOn_pow, hasDerivAt_exp_smul_const, NormedSpace.algebraMap_exp_comm, WithCStarModule.pi_norm, LinearIsometryEquiv.toSpanUnitSingleton_apply, derivWithin_mul_const_field, inr_comp_cfcβHom_eq_cfcβAux, CFC.monotoneOn_one_sub_one_add_inv_real, NormedSpace.expSeries_radius_eq_top, DoubleCentralizer.neg_toProd, MeasureTheory.integrable_mul_const_iff, nnnorm_cfc_le_iff, CStarMatrix.ofMatrix_eq_ofMatrixL, CStarAlgebra.nnnorm_le_one_iff_of_nonneg, CFC.continuousOn_nnrpow, DoubleCentralizer.algebraMap_snd, MeasureTheory.eLpNorm_const_smul_le', NormedSpace.invOf_exp, DoubleCentralizer.one_snd, fderiv_pow_ring', upperHemicontinuous_quasispectrum, WeakDual.CharacterSpace.compContinuousMap_apply, CStarMatrix.toCLM_apply, DoubleCentralizer.algebraMap_toProd, DoubleCentralizer.instIsCentralScalar, NormedSpace.exp_units_conj', spectrum.hasDerivAt_resolvent, mem_compactlySupported, selfAdjoint.realPart_unitarySelfAddISMul, PositiveLinearMap.gnsStarAlgHom_apply, DoubleCentralizer.pow_toProd, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, WithLp.unitization_nnnorm_inr, nnnorm_cfc_nnreal_lt, NonUnitalStarAlgHom.nnnorm_map, Units.nnnorm_pos, HasMFDerivWithinAt.mul', WithCStarModule.pi_inner, ContinuousMap.instCStarRing, le_egauge_smul_right, WithCStarModule.prod_norm, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, DoubleCentralizer.zero_fst, nnnorm_cfc_nnreal_le, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, CStarMatrix.mul_entry_mul_eq_inner_toCLM, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, NormedSpace.exp_hasFPowerSeriesAt_zero, nnnorm_cfc_nnreal_le_iff, CStarModule.norm_sq_eq, BoundedContinuousFunction.instCStarRing, ZeroAtInftyContinuousMap.instCStarRing, expUnitary_argSelfAdjoint, NonUnitalCommCStarAlgebra.toStarModule, NormedSpace.exp_nsmul, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, formalMultilinearSeries_geometric_eq_ofScalars, hasFDerivAt_exp_zero, DoubleCentralizer.nnnorm_fst_eq_snd, WithCStarModule.inner_single_right, Unitization.norm_def, selfAdjoint.star_coe_unitarySelfAddISMul, MeasureTheory.eLpNorm_const_smul_le, argSelfAdjoint_expUnitary, egauge_le_of_smul_mem, hasStrictFDerivAt_pow', DoubleCentralizer.one_fst, DoubleCentralizer.coeHom_apply, WithLp.unitizationAlgEquiv_symm_apply_ofLp, MeasureTheory.eLpNorm'_const_smul, norm_cfcβ_le, spec_cfcβAux, hasFDerivAt_exp_smul_const, hasStrictFDerivAt_list_prod_attach', DoubleCentralizer.sub_fst, nnnorm_cfc_le, Unitization.nnreal_cfcβ_eq_cfc_inr, hasStrictFDerivAt_ringInverse, integrable_cfc', Prod.fst_exp, CStarModule.norm_eq_csSup, nnnorm_apply_le_nnnorm_cfc, DoubleCentralizer.pow_fst, IsometricContinuousFunctionalCalculus.spectrum_le, IsSelfAdjoint.spectralRadius_eq_nnnorm, MeasureTheory.eLpNorm_const_smul, iteratedFDeriv_smul_const_apply, CStarRing.instRegularNormedAlgebra, upperHemicontinuous_quasispectrum_nnreal, differentiable_pow, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, CStarAlgebra.conjugate_le_norm_smul', WStarAlgebra.exists_predual, nnnorm_cfcβHom, ContinuousLinearMap.opNNNorm_mul, differentiableOn_inverse, CFC.nnnorm_rpow, spectrum.differentiableOn_inverse_one_sub_smul, CFC.nnrpow_le_nnrpow, Matrix.exp_units_conj', DoubleCentralizer.algebraMap_fst, CStarAlgebra.span_nonneg_inter_closedBall, CStarAlgebra.isClosed_nonneg, apply_le_nnnorm_cfc_nnreal, Unitization.instCStarRing, AlgHom.coe_toContinuousLinearMap, CStarAlgebra.star_left_conjugate_le_norm_smul, hasFDerivAt_pow', WeakDual.CharacterSpace.norm_le_norm_one, MemHolder.nnHolderNorm_smul, hasStrictFDerivAt_exp_zero, antilipschitzWith_mul_left, ContinuousLinearMap.opNNNorm_mul_flip_apply, egauge_eq_zero_iff, DoubleCentralizer.mul_fst, BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, PositiveLinearMap.ofPreGNS_toPreGNS, CStarMatrix.normedSpaceCore, ediam_smulβ, CFC.norm_abs, spectrum.exp_mem_exp, Unitization.isUniformEmbedding_addEquiv, differentiableWithinAt_inverse, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, cfcβAux_mem_range_inr, Unitization.nnnorm_eq_sup, DoubleCentralizer.zero_toProd, CStarModule.inner_mul_inner_swap_le, NormedSpace.exp_smul, DilationEquiv.smulTorsor_ratio, CFC.monotone_sqrt, quasispectrum.isCompact_nnreal, nnnorm_commutator_sub_one_le, CStarAlgebra.instNonnegSpectrumClass', CStarAlgebra.conjugate_le_norm_smul, DoubleCentralizer.norm_fst, BoundedContinuousFunction.coe_toContinuousMapβ, DoubleCentralizer.coe_fst, norm_cfcβ_one_sub_one_add_inv_lt_one, continuousOn_cfcβ_nnreal, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, nnnorm_cfc_lt_iff, spectrum.spectralRadius_le_nnnorm, WithCStarModule.inner_single_left, CStarAlgebra.directedOn_nonneg_ball, MeasureTheory.eLpNorm'_const_smul_le, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, continuousOn_cfcβ_setProd, Unitization.complex_cfcβ_eq_cfc_inr, Filter.comap_mul_left_cobounded, BoundedContinuousFunction.toContinuousMapβ_apply, CStarAlgebra.norm_negPart_le, NormedSpace.continuousOn_exp, Matrix.isUnit_exp, unitary.expUnitary_eq_mul_inv, PositiveLinearMap.norm_apply_le_of_nonneg, Unitization.nndist_inr, NonUnitalCStarAlgebra.toIsScalarTower, CStarRing.to_normedStarGroup, CFC.sqrt_le_sqrt, DoubleCentralizer.natCast_toProd, CStarModule.continuous_inner, integrable_cfc, DoubleCentralizer.one_toProd, NormedSpace.expSeries_radius_pos, StarAlgEquiv.nnnorm_map, nnnorm_cfc_nnreal_lt_iff, NormedSpace.algebraMap_exp_comm_of_mem_ball, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, NonUnitalCommCStarAlgebra.toSMulCommClass, Unitization.norm_splitMul_snd_sq, WeakDual.CharacterSpace.equivAlgHom_coe, spectrum.le_nnnorm_of_mem, DoubleCentralizer.natCast_snd, CompletelyPositiveMap.map_cstarMatrix_nonneg', CStarMatrix.uniformEmbedding_ofMatrix, coe_ringEquiv_lpBCF_symm, Unitization.splitMul_injective, MeasureTheory.eLpNorm'_const_smul_le', Polynomial.cauchyBound_X_add_C, CStarAlgebra.inr_mem_Icc_iff_nnnorm_le, MeasureTheory.Lp.smul_assoc, DoubleCentralizer.sub_snd, MonotoneOn.nnnorm_cfc, norm_iteratedFDerivWithin_mul_le, WithCStarModule.pi_norm_sq, hasStrictFDerivAt_inv', hasStrictFDerivAt_exp_smul_const, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, WithLp.unitization_mul, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, CStarAlgebra.star_right_conjugate_le_norm_smul, CStarRing.nnnorm_self_mul_star, Polynomial.cauchyBound_X_sub_C, DoubleCentralizer.intCast_fst, nnnorm_cfcHom, integrableOn_cfc, NormedSpace.exp_add_of_commute, WeakDual.CharacterSpace.equivAlgHom_symm_coe, CStarAlgebra.nnnorm_le_nnnorm_of_nonneg_of_le, hasStrictFDerivAt_list_prod', Prod.snd_exp, Filter.comap_mul_right_cobounded, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, NormedSpace.isUnit_exp, CStarAlgebra.span_nonneg_inter_ball, CFC.log_exp, ContinuousLinearMap.opNorm_lsmul, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, Unitization.uniformity_eq_aux, CFC.monotoneOn_cfcβ_rpowIntegrandββ, Quaternion.linearIsometryEquivTuple_apply, coe_algEquiv_lpBCF_symm, WithLp.unitizationAlgEquiv_apply, egauge_smul_right, NormedSpace.exp_analytic, differentiableAt_inv, NormedSpace.exp_sum_of_commute, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, CStarAlgebra.instNonnegSpectrumClassComplexUnital, hasFDerivAt_inv', Matrix.exp_units_conj, CStarAlgebra.hasBasis_approximateUnit, quasispectrum.instCompactSpaceNNReal, NormedSpace.exp_units_conj, WeakDual.CharacterSpace.compContinuousMap_id, differentiableAt_inverse, nnnorm_cfcβ_le, BoundedContinuousFunction.separatesPoints_charPoly, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, nnnorm_cfcβ_nnreal_le, enorm_inv, HasMFDerivAt.mul', nnnorm_zpow, continuousOn_cfcβ_nnreal_setProd, cfcHom_eq_of_isStarNormal, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, eHolderNorm_smul, NormedSpace.exp_mem_unitary_of_mem_skewAdjoint, deriv_mul_const_field', CFC.norm_sqrt, WithLp.unitization_nnnorm_def, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, DoubleCentralizer.toProdHom_apply, DoubleCentralizer.mul_snd, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, Ring.inverse_exp, WithCStarModule.prod_inner, one_le_nnnorm_one, unitary.mem_pathComponentOne_iff, derivWithin_const_mul_field, CFC.nnnorm_nnrpow, egauge_zero_right, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, NonUnitalCStarAlgebra.toSMulCommClass, CStarRing.nnnorm_star_mul_self, DoubleCentralizer.intCast_toProd, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, continuousFunctionalCalculus_map_id, CFC.norm_nnrpow, coe_algEquiv_lpBCF, CStarAlgebra.nnnorm_le_natCast_iff_of_nonneg, hasFDerivAt_list_prod_attach', CStarAlgebra.span_unitary, CFC.complex_exp_eq_normedSpace_exp, le_iff_norm_sqrt_mul_rpow, DoubleCentralizer.smul_snd, deriv_div_const, CStarAlgebra.nnnorm_mem_spectrum_of_nonneg, CStarAlgebra.exists_sum_four_nonneg, DoubleCentralizer.coe_snd, PositiveLinearMap.preGNS_norm_sq, differentiableOn_inv, MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, Ideal.IsMaximal.closure_eq, egauge_le_of_smul_mem_of_ne, WeakDual.CharacterSpace.instStarHomClass, NonUnitalCommCStarAlgebra.toIsScalarTower, egauge_pi', Pi.exp_def, CStarMatrix.norm_def, Unitization.continuous_inr, Polynomial.IsRoot.norm_lt_cauchyBound, DoubleCentralizer.add_toProd, CFC.abs_eq_zero_iff, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, MeasureTheory.eLpNormEssSup_const_smul_le', IsSelfAdjoint.nnnorm_pow_two_pow, DoubleCentralizer.neg_fst, CStarMatrix.inner_toCLM_conjTranspose_right, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, Unitization.nnnorm_inr, quasispectrum.instCompactSpace, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, CStarMatrix.toCLM_apply_single_apply, DoubleCentralizer.toProdMulOppositeHom_apply, selfAdjoint.joined_one_expUnitary, Unitization.cfcβ_eq_cfc_inr, le_iff_norm_sqrt_mul_sqrt_inv, fderiv_inv', egauge_smul_left, Pi.coe_exp, nnnorm_cfcβ_lt
|
toNorm π | CompOp | 63 mathmath: norm_cfcβHom, CStarMatrix.norm_entry_le_norm, IsSelfAdjoint.norm_mul_self, StarAlgEquiv.norm_map, CStarAlgebra.inr_mem_Icc_iff_norm_le, exist_norm_eq, WithCStarModule.prod_norm_sq, CStarModule.innerSL_apply, ContinuousLinearMap.opNorm_mul_flip_apply, NonUnitalIsometricContinuousFunctionalCalculus.norm_quasispectrum_le, WithCStarModule.inner_def, CStarRing.norm_mul_self_le, CStarMatrix.inner_toCLM_conjTranspose_left, norm_cfcβ_lt, IsGreatest.norm_cfcβ, Filter.IsIncreasingApproximateUnit.eventually_norm, CStarRing.norm_star_mul_self', CStarAlgebra.norm_posPart_le, PositiveLinearMap.exists_norm_apply_le, norm_cfcβ_lt_iff, CStarModule.norm_inner_le, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, WithCStarModule.pi_norm, norm_lt_iff_of_compactlySupported, WithCStarModule.pi_inner, CStarRing.norm_star_mul_self, WithCStarModule.prod_norm, NonUnitalStarAlgHom.norm_map, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, CStarMatrix.mul_entry_mul_eq_inner_toCLM, WithLp.unitization_norm_def, CStarModule.norm_sq_eq, WithCStarModule.inner_single_right, norm_cfcβ_le, CStarModule.norm_eq_csSup, CStarRing.norm_self_mul_star, CStarAlgebra.conjugate_le_norm_smul', CStarAlgebra.norm_le_norm_of_nonneg_of_le, CStarAlgebra.star_left_conjugate_le_norm_smul, norm_mul_le, dist_eq, CFC.norm_abs, CStarModule.inner_mul_inner_swap_le, CStarAlgebra.conjugate_le_norm_smul, norm_cfcβ_one_sub_one_add_inv_lt_one, WithCStarModule.inner_single_left, CStarAlgebra.norm_negPart_le, CStarModule.continuous_inner, WithCStarModule.pi_norm_sq, CStarAlgebra.star_right_conjugate_le_norm_smul, norm_apply_le_norm_cfcβ, CStarAlgebra.isBasis_nonneg_sections, norm_lt_iff_of_nonempty_compactlySupported, CStarAlgebra.hasBasis_approximateUnit, CFC.norm_sqrt, WithLp.unitization_norm_inr, NonUnitalStarAlgHom.norm_apply_le, WithCStarModule.prod_inner, norm_cfcβ_le_iff, CFC.norm_nnrpow, CStarAlgebra.exists_sum_four_nonneg, Unitization.norm_inr, CStarMatrix.inner_toCLM_conjTranspose_right
|
toNormedAddCommGroup π | CompOp | 1356 mathmath: Unitary.openPartialHomeomorph_source, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, ValueDistribution.logCounting_zero, hasFDerivAt_iff_hasDerivAt, Polynomial.differentiableWithinAt, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, MeasureTheory.lpNorm_conj, TensorProduct.enorm_lid, differentiableAt_comp_neg, HasStrictFDerivAt.fun_mul', Matrix.frobenius_nnnorm_mul, continuousOn_stereoToFun, LeftInvariantDerivation.lift_zero, hasSum_geometric_of_norm_lt_one, norm_cfcβHom, RCLike.map_apply, LinearMap.IsSymmetric.inner_map_polarization, LinearMap.coe_toSeminorm, CStarRing.norm_unitary_smul, DoubleCentralizer.star_snd, RCLike.ofRealCLM_apply, PowerSeries.IsRestricted.smul, PadicInt.lift_sub_val_mem_span, NormedRing.inverse_one_sub_norm, LeftInvariantDerivation.leibniz, hasFDerivAt_iff_hasGradientAt, RCLike.reCLM_apply, smooth_barycentric_coord, NormedSpace.exp_zsmul, CFC.monotoneOn_one_sub_one_add_inv, hasStrictFDerivAt_list_prod_finRange', InnerProductSpace.rankOne_one_left_eq_innerSL, ContMDiffMap.coeFnAlgHom_apply, Function.FactorizedRational.divisor, iteratedDerivWithin_const_mul_field, nnnorm_cfcβ_nnreal_le_iff, MeromorphicAt.analyticAt, HasFDerivWithinAt.pow, EuclideanSpace.orthonormal_single, meromorphicOrderAt_const_ofNat, AffineMap.hasDerivAtFilter, PositiveLinearMap.apply_le_of_isSelfAdjoint, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, differentiableAt_zpow, hasFDerivAt_multiset_prod, BoundedContinuousFunction.algebraMap_apply, geom_series_mul_shift, CFC.monotone_nnrpow, smoothSheafCommRing.nonunits_stalk, MeasureTheory.convolution_mul, deriv_mem_iff, Matrix.spectrum_toEuclideanLin, MeasureTheory.lpNorm_fun_div_natCast, Matrix.cstar_nnnorm_def, hasSum_choose_mul_geometric_of_norm_lt_one, tsum_coe_mul_geometric_of_norm_lt_one', lp.inner_eq_tsum, OrthonormalBasis.sum_inner_mul_inner, Matrix.l2_opNorm_mulVec, ContinuousLinearMap.hasDerivAtFilter, DoubleCentralizer.intCast_snd, DoubleCentralizer.range_toProdMulOpposite, RCLike.conjCLE_norm, ordinaryHypergeometric_radius_top_of_neg_natβ, Unitary.mem_pathComponentOne_iff, LinearMap.polar_eq_iInter, hensels_lemma, MeasureTheory.integral_fintype_prod_volume_eq_pow, Unitization.real_cfcβ_eq_cfc_inr, PadicInt.appr_spec, Matrix.le_iff, RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, DoubleCentralizer.natCast_fst, analyticOnNhd_inverse, continuousOn_dslope, RCLike.sub_conj, isClosedEmbedding_cfcβAux, deriv_comp_const_sub, LeftInvariantDerivation.coe_derivation, innerSL_apply_apply, RCLike.norm_expect_le, LinearMap.adjoint_innerββ_apply, inner_sum, EuclideanSpace.inner_single_left, EuclideanSpace.basisFun_toBasis, hasDerivAt_neg', ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, DoubleCentralizer.nnnorm_def', tendsto_smul_comp_nat_floor_of_tendsto_mul, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, HasFDerivAt.fun_mul, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, eqOn_dslope_sub_smul, deriv_mul_const_field, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', selfAdjoint.expUnitaryPathToOne_apply, NormedRing.inverse_add_norm_diff_nth_order, Unitary.continuousOn_argSelfAdjoint, derivWithin_fderivWithin, RCLike.wInner_sub_right, FormalMultilinearSeries.derivSeries_coeff_one, PadicInt.sub_zmodRepr_mem, tsum_choose_mul_geometric_of_norm_lt_one', MeasureTheory.integral_fintype_prod_eq_prod, derivWithin_comp_const_sub, iteratedDeriv_pow, hasSum_coe_mul_geometric_of_norm_lt_one', AffineMap.hasDerivWithinAt, LeftInvariantDerivation.left_invariant, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, EuclideanSpace.basisFun_apply, tsum_coe_mul_geometric_of_norm_lt_one, hasDerivWithinAt_iff_isLittleO, Differentiable.fderiv_norm_rpow, RCLike.normSq_neg, MeasureTheory.integral_const_mul, iteratedDeriv_div_const, differentiableWithinAt_inv, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, TensorProduct.toLinearEquiv_lidIsometry, NormedSpace.exp_series_hasSum_exp', ContinuousLinearMap.isometry_mul_flip, OrthonormalBasis.toBasis_singleton, ContDiffOn.inner, AnalyticOnNhd.eval_linearMap', HasStrictFDerivAt.mul', CStarModule.innerSL_apply, LinearMap.toMatrixOrthonormal_reindex, MeasureTheory.integral_div, Matrix.IsHermitian.eigenvalues_eq, HasStrictFDerivAt.pow, iter_deriv_zpow', PadicInt.coe_sum, Matrix.exp_conj', CStarAlgebra.span_nonneg_inter_unitBall, HasStrictFDerivAt.const_mul, ConvexOn.univ_sSup_of_countable_affine_eq, RCLike.hasSum_ofReal, Matrix.PosSemidef.commute_iff, IsLocalFrameOn.coeff_apply_of_mem, HasFDerivAt.finset_prod, Matrix.exp_neg, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, polynomialFunctions.starClosure_topologicalClosure, innerββ_apply_apply, WithCStarModule.inner_def, hasFDerivWithinAt_inv, DoubleCentralizer.pow_snd, RCLike.ofReal_balance, smoothSheafCommRing.instLocalRing_stalk, MeasureTheory.L2.inner_def, LinearMap.polar_singleton, intervalIntegral.integral_div, NormedSpace.Dual.toWeakDual_continuous, HasFDerivWithinAt.const_mul, CStarMatrix.instIsUniformAddGroup, ContinuousMultilinearMap.norm_smulRightL_le, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, tsum_geometric_of_norm_lt_one, cfcβ_integral, DoubleCentralizer.nnnorm_snd, differentiableAt_comp_add_const, RCLike.ofReal_comp_balance, RCLike.reCLM_norm, cfcβ_setIntegral, CStarMatrix.toCLM_injective, formalMultilinearSeries_geometric_apply_norm_le, RCLike.ofReal_sub, hasDerivAt_iff_isLittleO, HasDerivWithinAt.hasFDerivWithinAt, Polynomial.abs_div_tendsto_atTop_of_degree_gt, Matrix.IsHermitian.eigenvectorUnitary_col_eq, fderiv_eq_deriv_mul, nndist_right_lineMap, ContinuousLinearMap.toSesqForm_apply_coe, Polynomial.differentiableOn_aeval, NormedRing.inverse_one_sub_nth_order, ordinaryHypergeometricSeries_radius_eq_one, MeromorphicAt.inv_iff, MeasureTheory.setIntegral_prod_mul, Matrix.toEuclideanLin_apply, iteratedDerivWithin_eq_iteratedFDerivWithin, HasFDerivWithinAt.mul, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, HasFDerivWithinAt.multiset_prod, ContinuousLinearMap.opNorm_mul, MeasureTheory.integral_fintype_prod_eq_pow, DoubleCentralizer.smul_toProd, DoubleCentralizer.toProdMulOpposite_injective, RCLike.conjCLE_apply, DoubleCentralizer.norm_fst_eq_snd, Unitization.nnnorm_def, ProbabilityTheory.IndepFun.integral_comp_mul_comp, NormedSpace.exp_hasFPowerSeriesOnBall, NormedSpace.expSeries_summable, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, lp.inftyCStarRing, PiTensorProduct.mapL_smul, BoundedContinuousFunction.coe_toContinuousMapStarβ, RCLike.I_mul_I, DoubleCentralizer.norm_def', CStarMatrix.norm_def', ValueDistribution.logCounting_top, LeftInvariantDerivation.lift_add, binomialSeries_radius_eq_one, meromorphicOrderAt_ne_top_iff, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.toMatrixOrthonormal_apply_apply, LDL.lowerInv_orthogonal, InnerProductSpace.Core.inner_neg_left, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, HasStrictFDerivAt.list_prod', summable_mul_of_bigO_atTop, ContinuousLinearMapWOT.inducingFn_apply, entrywise_sup_norm_bound_of_unitary, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, CStarMatrix.inner_toCLM_conjTranspose_left, hasStrictDerivAt_exp_smul_const, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, Finsupp.sum_inner, MeasureTheory.integral_fin_nat_prod_volume_eq_prod, LeftInvariantDerivation.lift_smul, geom_series_succ, DoubleCentralizer.norm_def, PadicInt.exists_mem_range, contDiffWithinAt_euclidean, hasStrictDerivAt_exp_smul_const', Real.fourier_iteratedFDeriv, uniqueDiffWithinAt_iff_accPt, EulerProduct.eulerProduct_completely_multiplicative, PositiveLinearMap.preGNS_norm_def, PositiveLinearMap.leftMulMapPreGNS_apply, tsum_geometric_le_of_norm_lt_one, PadicInt.exists_mem_range_of_norm_rat_le_one, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, AntitoneOn.derivWithin_nonpos, LinearMap.extendToπ'_apply, dslope_sub_smul, hasDerivAt_id', Matrix.IsHermitian.eigenvectorUnitary_mulVec, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, MeasureTheory.convolution_lsmul, coe_innerSL_apply, deriv_fderiv, summable_mul_of_summable_norm, DoubleCentralizer.central, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, HasDerivAt.differentiableAt, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, TensorProduct.lidIsometry_apply, Unitary.openPartialHomeomorph_symm_apply, ContinuousLinearMap.hasDerivAt, PadicInt.fwdDiff_tendsto_zero, CompletelyPositiveMap.instLinearMapClassComplex, EulerProduct.eulerProduct_hasProd, Module.Basis.coe_toOrthonormalBasis_repr, hasGradientAtFilter_iff_isLittleO, hasGradientAt_iff_isLittleO, LeftInvariantDerivation.comp_L, AffineMap.differentiableWithinAt, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, LinearMap.trace_eq_sum_inner, MeromorphicOn.divisor_inv, MeromorphicOn.id, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, Unitary.norm_sub_one_lt_two_iff, differentiableWithinAt_pow, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, tsum_mul_tsum_of_summable_norm, IsLocalFrameOn.coeff_congr, nnnorm_cfcβ_nnreal_lt, LinearMap.hasStrictDerivAt, FiniteDimensional.rclike_to_real, HasDerivAtFilter.isBigO_sub_rev, differentiableOn_dslope_of_notMem, RCLike.wInner_neg_right, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd, NormedSpace.inclusionInDoubleDual_norm_eq, Meromorphic.MeromorphicOn.countable_compl_analyticAt, Polynomial.abs_tendsto_atTop_iff, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, EulerProduct.eulerProduct, deriv_id'', hasStrictFDerivAt_exp, IsSelfAdjoint.neg_algebraMap_norm_le_self, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, mul_neg_geom_series, deriv_const_mul_field', Function.FactorizedRational.mulSupport, PadicInt.coe_addChar_of_value_at_one, RCLike.summable_ofReal, ContinuousMapZero.integral_apply, HasDerivAt.hasFDerivAt, RCLike.imLm_coe, hasFDerivAt_norm_rpow, Function.FactorizedRational.meromorphicOrderAt_eq, iteratedDeriv_fun_id_zero, unitary.norm_sub_eq, DoubleCentralizer.neg_snd, MeromorphicOn.divisor_sub_const_self, sum_inner, iteratedDeriv_comp_sub_const, Matrix.linfty_opNNNorm_toMatrix, NormedSpace.expSeries_hasSum_exp, analyticOrderAt_ne_zero, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, InnerProductSpace.Core.inner_neg_right, norm_commutator_sub_one_le, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, RCLike.conjCLE_coe, contDiffOn_stereoToFun, Polynomial.abs_tendsto_atTop, Units.instIsManifoldModelWithCornersSelf, LeftInvariantDerivation.evalAt_coe, Matrix.IsHermitian.trace_eq_sum_eigenvalues, selfAdjoint.expUnitary_zero, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', hasGradientAt_iff_isLittleO_nhds_zero, analyticAt_smul, Polynomial.differentiable_aeval, DoubleCentralizer.range_toProd, hasDerivAt_deriv_iff, Unitization.splitMul_injective_of_clm_mul_injective, Function.FactorizedRational.finprod_eq_fun, hasDerivAtFilter_neg, tsum_pow_div_one_sub_eq_tsum_sigma, HilbertBasis.hasSum_repr, HasFDerivAt.pow, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, meromorphicOrderAt_const_natCast, innerSL_inj, continuousAt_dslope_same, PositiveLinearMap.preGNS_inner_def, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, StrongDual.toLp_of_not_memLp, DoubleCentralizer.add_fst, differentiableWithinAt_of_derivWithin_ne_zero, MeromorphicOn.divisor_intCast, TensorProduct.inner_lid_lid, derivWithin_div_const, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, NormedSpace.inclusionInDoubleDual_norm_le, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, Real.fourier_mul_convolution_eq, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, ConvexOn.sSup_of_countable_affine_eq, MeasureTheory.Integrable.toL1_smul, RCLike.reCLM_coe, HasDerivWithinAt.inner, DifferentiableAt.inner, MeasureTheory.condExp_ofNat, IsGreatest.nnnorm_cfcβ_nnreal, HasFDerivWithinAt.mul_const, MeromorphicOn.analyticAt_mem_codiscreteWithin, CStarAlgebra.span_nonneg_inter_unitClosedBall, smoothSheafCommRing.isUnit_stalk_iff, FormalMultilinearSeries.coeff_ofScalars, iteratedFDerivWithin_eq_equiv_comp, summable_norm_sum_mul_range_of_summable_norm, Matrix.l2_opNNNorm_mulVec, Orthonormal.inner_left_right_finset, meromorphicOrderAt_id, differentiableAt_inv_iff, Finsupp.inner_sum, LinearMap.deriv, contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, HasFDerivWithinAt.inner, DoubleCentralizer.smul_fst, selfAdjoint.continuous_expUnitary, EulerProduct.eulerProduct_tprod, fdifferential_apply, LinearMap.extendToπ_apply, coe_ringEquiv_lpBCF, Matrix.l2_opNorm_conjTranspose_mul_self, MeromorphicOn.divisor_sub_const_of_ne, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, integral_const_mul_of_integrable, hasDerivAt_update, inner_neg_right, Orthonormal.isHilbertSum, iteratedDeriv_fun_id, OrthonormalBasis.singleton_apply, inner_eq_sum_norm_sq_div_four, fderiv_pow_ring, Polynomial.abs_tendsto_atBot_iff, deriv_const_mul_field, integral_conj, Matrix.exp_nsmul, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, meromorphicNFAt_inv, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, ProperCone.innerDual_singleton, differentiable_inner, LeftInvariantDerivation.coe_sub, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, RCLike.im_eq_conj_sub, LDL.lower_conj_diag, hasFDerivAt_list_prod', lp.infty_coeFn_mul, ArithmeticFunction.IsMultiplicative.eulerProduct_tprod, InnerProductSpace.rankOne_def, Meromorphic.countable_compl_analyticAt, SchwartzMap.integral_mul_laplacian_right_eq_left, Finset.norm_prod_one_add_sub_one_le, stereoToFun_apply, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.lpNorm_fun_mul_natCast, Polynomial.fderiv_aeval, dslope_sub_smul_of_ne, Module.Basis.equivFunL_symm_apply_repr, iter_deriv_zpow, Units.instLieGroupModelWithCornersSelf, ClosedSubmodule.orthogonal_eq_inter, PositiveLinearMap.toPreGNS_ofPreGNS, hasFDerivWithinAt_iff_hasDerivWithinAt, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, LeftInvariantDerivation.left_invariant'', NormedSpace.expSeries_summable', MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, RCLike.ofReal_neg, contDiff_nat_iff_iteratedDeriv, Unitary.norm_sub_one_sq_eq, ContinuousLinearMapWOT.isInducing_inducingFn, PositiveLinearMap.exists_norm_apply_le, EulerProduct.eulerProduct_completely_multiplicative_tprod, DoubleCentralizer.star_fst, summable_prod_mul_pow, RCLike.summable_conj, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, meromorphicOrderAt_inv, normRingNorm_toFun, hasFDerivAt_exp_smul_const', Matrix.exp_zsmul, LinearMap.toMatrixOrthonormal_symm_apply, RCLike.wInner_sub_left, LinearMap.toMatrix_innerββ_apply, Matrix.exp_sum_of_commute, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, PointwiseConvergenceCLM.equivWeakDual_symm_apply, RCLike.wInner_one_eq_inner, AffineMap.hasDerivAt, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, iteratedDerivWithin_zpow, meromorphicOrderAt_eq_int_iff, dist_lineMap_right, hasFDerivWithinAt_pow', MeasureTheory.lpNorm_fun_natCast_mul, AffineMap.differentiableAt, meromorphicNFAt_iff_analyticAt_or, Matrix.PosSemidef.toLinearMapβ'_zero_iff, MeasureTheory.Lp.smul_zero, RCLike.sqrt_eq_real_add_ite, DoubleCentralizer.add_snd, hasStrictDerivAt_zpow, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, innerSLFlip_apply_apply, Continuous.cfcβ_nnreal, Polynomial.hasFDerivAt, RCLike.ofReal_finsupp_sum, finrank_euclideanSpace, hasDerivAt_inv, DoubleCentralizer.norm_snd, ConvexOn.sSup_of_nat_affine_eq, contMDiff_smul, MeromorphicOn.divisor_ofNat, DoubleCentralizer.nnnorm_fst, MeasureTheory.Lp.norm_smul_le, Function.FactorizedRational.meromorphicNFOn_univ, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, Module.Basis.equivFunL_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, ContinuousAt.cfcβ_nnreal, hasFDerivAt_list_prod_finRange', contDiffOn_euclidean, HasGradientAt.hasFDerivAt, LinearMap.hasDerivWithinAt, summable_choose_mul_geometric_of_norm_lt_one, CStarMatrix.toCLM_apply_single, Real.fourier_fderiv, MeromorphicOn.inv_iff, ContinuousMap.adjoin_id_eq_span_one_union, one_memβp_infty, meromorphicTrailingCoeffAt_const, HasFDerivWithinAt.norm_sq, ordinaryHypergeometric_radius_top_of_neg_natβ, ContinuousLinearMapWOT.isEmbedding_inducingFn, integral_inner, Asymptotics.continuousAt_iff_isLittleO, HasDerivWithinAt.differentiableWithinAt, ZSpan.coe_floor_self, Orthonormal.linearIsometryEquiv_symm_apply_single_one, Matrix.PosDef.commute_iff, RCLike.finrank_le_two, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, dist_homothety_self, iteratedFDeriv_eq_equiv_comp, meromorphicTrailingCoeffAt_inv, Unitization.norm_eq_sup, MeromorphicAt.id, Matrix.ofLp_toEuclideanCLM, hasDerivAtFilter_iff_isLittleO, NormedSpace.expSeries_div_summable, CStarMatrix.toCLM_apply_eq_sum, summable_descFactorial_mul_geometric_of_norm_lt_one, differentiableOn_pow, tsum_choose_mul_geometric_of_norm_lt_one, hasDerivAt_exp_smul_const, WithCStarModule.pi_norm, meromorphicNFOn_inv, derivWithin_mul_const_field, logDeriv_apply, iteratedDerivWithin_one_div, RCLike.sqrt_map, PadicInt.mahlerTerm_one, HasStrictDerivAt.hasStrictFDerivAt, RCLike.inner_tmul_eq, inr_comp_cfcβHom_eq_cfcβAux, CFC.monotoneOn_one_sub_one_add_inv_real, HasFDerivAt.multiset_prod, dist_self_homothety, Matrix.l2_opNNNorm_mul, IsLocalFrameOn.eventually_eq_sum_coeff_smul, lp.infty_coeFn_pow, HasFDerivAt.mul_const, NormedSpace.expSeries_radius_eq_top, differentiableWithinAt_euclidean, MeasureTheory.integral_prod_mul, DoubleCentralizer.neg_toProd, Matrix.isPositive_toEuclideanLin_iff, ContinuousWithinAt.cfcβ_nnreal, padic_polynomial_dist, ContDiff.inner, CStarMatrix.ofMatrix_eq_ofMatrixL, HasGradientAt.differentiableAt, NormedSpace.exp_sum, Function.FactorizedRational.analyticAt, HasFDerivWithinAt.mul_const', PadicInt.zmodRepr_spec, DoubleCentralizer.algebraMap_snd, CStarMatrix.instIsTopologicalAddGroup, RCLike.wInner_const_left, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, NormedSpace.invOf_exp, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, contDiffAt_inv, hasStrictFDerivAt_norm_sq, LinearMap.adjoint_toSpanSingleton, DoubleCentralizer.one_snd, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, algebraMap_memβp_infty, fderiv_pow_ring', HasDerivAtFilter.isBigO_sub, iteratedDeriv_comp_neg, unitary.two_mul_one_sub_le_norm_sub_one_sq, NormedRing.inverse_one_sub, Matrix.posDef_iff_eq_conjTranspose_mul_self, Polynomial.differentiableAt_aeval, PowerSeries.IsRestricted.neg, Filter.Tendsto.cfcβ_nnreal, hasDerivAt_id, contDiff_smul_const, CStarMatrix.toCLM_apply, DoubleCentralizer.algebraMap_toProd, RCLike.hasSum_conj, deriv_update, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, nndist_lineMap_right, Polynomial.hasFDerivAt_aeval, DoubleCentralizer.instIsCentralScalar, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, deriv_zpow', LeftInvariantDerivation.map_add, binomialSeries_radius_eq_top_of_nat, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, HasGradientAtFilter.isBigO_sub, spectrum.hasDerivAt_resolvent, LinearMap.polar_gc, hasDerivAt_exp, contDiffOn_succ_iff_deriv_of_isOpen, LeftInvariantDerivation.coe_add, MeasureTheory.Lp.add_smul, nnnorm_cfcβ_nnreal_lt_iff, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', cfc_integral, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, EuclideanSpace.basisFun_repr, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, MeasureTheory.Integrable.toL1_smul', MeromorphicOn.eventually_codiscreteWithin_analyticAt, ArithmeticFunction.IsMultiplicative.eulerProduct, deriv_neg'', DoubleCentralizer.pow_toProd, OrthonormalBasis.equiv_apply_euclideanSpace, NormedRing.inverse_add_norm_diff_second_order, IsLocalFrameOn.coeff_apply_of_notMem, PadicInt.limNthHom_spec, fderiv_inv, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, HasFDerivAt.fun_pow', Unitary.openPartialHomeomorph_target, iteratedDeriv_eq_equiv_comp, WithCStarModule.pi_inner, HasFDerivWithinAt.hasDerivWithinAt, hasDerivAt_iff_hasFDerivAt, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, PadicInt.continuous_addChar_of_value_at_one, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, LinearMap.polar_weak_closed, hasGradientAt_iff_tendsto, InnerProductSpace.Core.inner_sub_sub_self, DoubleCentralizer.zero_fst, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, fdifferential_comp, CStarMatrix.mul_entry_mul_eq_inner_toCLM, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, RCLike.sqrt_neg_one, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', LeftInvariantDerivation.coe_injective, NormedSpace.exp_hasFPowerSeriesAt_zero, Matrix.IsHermitian.eigenvectorUnitary_apply, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, fderiv_apply_one_eq_deriv, EulerProduct.eulerProduct_hasProd_mulIndicator, HasFDerivAt.inner, meromorphicTrailingCoeffAt_id_sub_const, LinearMap.toMatrixOrthonormal_apply, OrthogonalFamily.inner_sum, EuclideanSpace.inner_eq_star_dotProduct, HasFDerivAt.const_mul, LeftInvariantDerivation.coe_neg, StrongDual.toLpβ_apply, NormedSpace.exp_nsmul, PadicInt.fwdDiff_iter_le_of_forall_le, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, Valued.integer.coe_span_singleton_eq_closedBall, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Polynomial.differentiableOn, hasSum_geom_series_inverse, IsLocalFrameOn.coeff_apply_zero_at, Orientation.inner_mul_areaForm_sub', inner_sub_left, AnalyticOnNhd.eval_polynomial, differentiableOn_neg, HasFDerivAt.mul, LinearMap.continuous_of_nonzero_on_open, hasSum_coe_mul_geometric_of_norm_lt_one, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, DoubleCentralizer.nnnorm_fst_eq_snd, Unitization.norm_def, Submodule.det_reflection, deriv_neg', AnalyticAt.of_meromorphicOrderAt_pos, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.hasDerivWithinAt_aeval, contDiffOn_inv, hasSum_choose_mul_geometric_of_norm_lt_one', ContinuousLinearMap.extendToπ_apply, hasStrictFDerivAt_pow', Polynomial.hasStrictDerivAt_aeval, DoubleCentralizer.one_fst, CFC.log_pow', differentiableAt_iff_comp_const_sub, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ProbabilityTheory.covarianceBilin_apply_basisFun, hasGradientAt_iff_hasFDerivAt, MeromorphicOn.countable_compl_analyticAt_inter, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, Matrix.exp_conj, Orthonormal.inner_finsupp_eq_sum_left, fderiv_deriv, MeasureTheory.Lp.coeFn_lpSMul, contDiffAt_inner, lp.summable_inner, spec_cfcβAux, hasSum_sum_range_mul_of_summable_norm, DifferentiableOn.inner, ContinuousOn.cfcβ_nnreal', hasFDerivAt_exp_smul_const, Differentiable.inner, lp.infty_coeFn_one, LeftInvariantDerivation.map_smul, Polynomial.isBoundedUnder_abs_atBot_iff, hasStrictFDerivAt_list_prod_attach', deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, DoubleCentralizer.sub_fst, Module.Basis.parallelepiped_eq_map, hasFPowerSeriesOnBall_inv_one_sub, LinearMap.mem_polar_singleton, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational, Unitization.nnreal_cfcβ_eq_cfc_inr, hasFPowerSeriesOnBall_inverse_one_sub, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, RCLike.ofRealCLM_norm, Matrix.IsHermitian.eigenvectorUnitary_coe, Complex.sqrt_map, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, MeasureTheory.convolution_lsmul_swap, Matrix.toEuclideanLin_eq_toLin, DoubleCentralizer.pow_fst, StrongDual.toLpβ_of_not_memLp, analyticOrderAt_id, Matrix.isHermitian_iff_isSymmetric, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, deriv_zpow, inner_eq_neg_one_iff_of_norm_eq_one, FormalMultilinearSeries.apply_eq_prod_smul_coeff, EuclideanSpace.basisFun_inner, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, differentiableAt_euclidean, geom_series_mul_one_add, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, LeftInvariantDerivation.coe_smul, differentiable_pow, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, CStarAlgebra.conjugate_le_norm_smul', hfdifferential_apply, ContinuousLinearMap.opNNNorm_mul, differentiableOn_inverse, MeasureTheory.integral_fin_nat_prod_eq_prod, spectrum.differentiableOn_inverse_one_sub_smul, Continuous.cfcβ_nnreal_of_mem_nhdsSet, CFC.nnrpow_le_nnrpow, LinearMap.tripolar_eq_polar, RCLike.toIsOrderedAddMonoid, logDeriv_inv, Matrix.exp_units_conj', ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, lp.infty_coeFn_intCast, DoubleCentralizer.algebraMap_fst, differentiableOn_euclidean, RCLike.reLm_coe, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, tsum_prod_pow_eq_tsum_sigma, CStarAlgebra.span_nonneg_inter_closedBall, toSpanSingleton_derivWithin, MeasureTheory.Lp.zero_smul, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, MeromorphicOn.eventually_analyticAt_or_mem_compl, integral_coe_re_add_coe_im, RCLike.wInner_one_const_right, AlgHom.coe_toContinuousLinearMap, Matrix.posSemidef_iff_eq_sum_vecMulVec, HasFDerivWithinAt.pow', ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, MeasureTheory.lpNorm_one, HasStrictFDerivAt.hasStrictDerivAt, EuclideanSpace.inner_basisFun_real, innerSLFlip_apply, intCast_memβp_infty, fderivWithin_derivWithin, hasDerivAt_const_mul, RCLike.sqrt_neg_I, HasFDerivAt.list_prod', InnerProductSpace.Core.inner_sub_left, CStarAlgebra.star_left_conjugate_le_norm_smul, hasFDerivAt_pow', MeasureTheory.Lp.smul_def, IsLocalFrameOn.eq_iff_coeff, iteratedDeriv_comp_const_sub, Function.RCLike.hasTemperateGrowth_ofReal, PadicInt.instIsAdicCompleteMaximalIdeal, Polynomial.hasDerivAt, MeasureTheory.Lp.smul_neg, RCLike.conj_I, Unitary.two_mul_one_sub_le_norm_sub_one_sq, contDiff_inner, Matrix.linfty_opNorm_toMatrix, innerSL_apply_norm, iter_deriv_inv, Matrix.frobenius_norm_mul, Matrix.star_dotProduct_gram_mulVec, hasStrictFDerivAt_exp_zero, RCLike.hasSum_iff, formalMultilinearSeries_geometric_radius, integral_mul_const_of_integrable, AccPt.uniqueDiffWithinAt, RCLike.sqrt_I, hasDerivWithinAt_zpow, Monotone.deriv_nonneg, locallyIntegrableOn_mul_sum_Icc, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, TensorProduct.norm_lid, Matrix.instIsOrderedAddMonoid, Summable.mul_tendsto_const, iteratedDeriv_eq_iteratedFDeriv, iter_deriv_inv', toMatrix_innerSL_apply, analyticOn_inv, DoubleCentralizer.mul_fst, Matrix.PosSemidef.re_dotProduct_nonneg, MeasureTheory.lpNorm_div_natCast, Polynomial.isBoundedUnder_abs_atTop_iff, BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MeasureTheory.Lp.smul_comm, lp.infty_coeFn_natCast, PositiveLinearMap.ofPreGNS_toPreGNS, lp.hasSum_inner, CStarMatrix.normedSpaceCore, deriv_pow_field, deriv_comp_neg, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, MeasureTheory.Lp.smul_add, contDiff_mul, PadicInt.norm_sub_modPart, inner_sub_right, HasFDerivAt.hasDerivAt, LeftInvariantDerivation.map_sub, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, differentiableWithinAt_inverse, NormedSpace.exp_neg, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, MeromorphicOn.extract_zeros_poles, cfcβAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, Unitization.nnnorm_eq_sup, norm_deriv_eq_norm_fderiv, PadicInt.fwdDiff_mahlerSeries, DoubleCentralizer.zero_toProd, deriv_id, CStarModule.inner_mul_inner_swap_le, MeasureTheory.L2.mem_L1_inner, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, NormedSpace.exp_smul, differentiable_neg, RCLike.wInner_neg_left, hasDerivAt_neg, PadicInt.continuous_multichoose, Polynomial.hasStrictDerivAt, Unitary.norm_sub_eq, CFC.monotone_sqrt, contDiff_smul, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, HilbertBasis.repr_self, nnnorm_commutator_sub_one_le, CStarAlgebra.conjugate_le_norm_smul, summable_geometric_iff_norm_lt_one, DoubleCentralizer.norm_fst, summable_pow_mul_geometric_of_norm_lt_one, BoundedContinuousFunction.coe_toContinuousMapβ, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, NormedSpace.expSeries_div_hasSum_exp, DoubleCentralizer.coe_fst, iteratedDeriv_mul_const_field, ContDiffWithinAt.inner, norm_cfcβ_one_sub_one_add_inv_lt_one, HasFDerivAt.pow', continuousOn_cfcβ_nnreal, Units.val_oneSub, HasStrictFDerivAt.pow', hasFDerivWithinAt_iff_hasGradientWithinAt, Polynomial.abs_tendsto_atBot, tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm, HasStrictFDerivAt.multiset_prod, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, Matrix.toEuclideanLin_apply_piLp_toLp, Matrix.linfty_opNorm_eq_opNorm, RCLike.ofReal_tsum, hasDerivAt_pow, contDiff_succ_iff_deriv, Submodule.mem_adjoint_iff, NormedRing.inverse_add_norm_diff_first_order, PadicInt.norm_sub_zmodRepr_lt_one, Function.FactorizedRational.extractFactor, integrableOn_mul_sum_Icc, PadicInt.mahlerEquiv_apply, LinearMap.isSymmetric_iff_sesqForm, hasDerivWithinAt_derivWithin_iff, hasStrictDerivAt_exp, HasStrictFDerivAt.mul_const', Irreducible.maximalIdeal_eq_closedBall, CFC.log_pow, intervalIntegral.integral_smul_const, MeasureTheory.Lp.neg_smul, Polynomial.deriv, HilbertBasis.summable_inner_mul_inner, HasDerivAtFilter.isEquivalent_sub, AffineMap.differentiableOn, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, Polynomial.hasFDerivWithinAt_aeval, selfAdjoint.val_re_map_spectrum, derivWithin_comp_add_const, hasStrictDerivAt_inv, Polynomial.contDiff_aeval, RCLike.wInner_one_const_left, LinearMap.continuous_of_isClosed_ker, Unitization.complex_cfcβ_eq_cfc_inr, LDL.diag_eq_lowerInv_conj, differentiableAt_iff_comp_add_const, HasFDerivWithinAt.fun_mul', BoundedContinuousFunction.toContinuousMapβ_apply, LinearMap.polar_isClosed, innerββ_apply, deriv_inner_apply, NormedSpace.continuousOn_exp, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, Polynomial.abs_isBoundedUnder_iff, StrongDual.toLp_apply, LinearMap.continuous_iff_isClosed_ker, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, PositiveLinearMap.norm_apply_le_of_nonneg, LinearMap.toSeminorm_ball_zero, iter_deriv_inv_linear_sub, RCLike.imCLM_coe, lp.instNormOneClassSubtypePreLpMemAddSubgroupTopENNRealOfNonempty, UnitAddTorus.mFourierBasis_repr, HasDerivAt.inner, LinearMap.toSeminorm_apply, CFC.sqrt_le_sqrt, LeftInvariantDerivation.toDerivation_injective, MeasureTheory.lpNorm_natCast_mul, DoubleCentralizer.natCast_toProd, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, iteratedDeriv_id, MeasureTheory.BoundedContinuousFunction.inner_toLp, HasFDerivWithinAt.fun_pow', MeasureTheory.integral_fintype_prod_volume_eq_prod, MeasureTheory.convolution_mul_swap, ContinuousLinearMap.norm_smulRightL_le, DoubleCentralizer.one_toProd, NormedSpace.expSeries_radius_pos, analyticOrderAt_eq_zero, hasDerivAt_single, SchwartzMap.integral_smul_laplacian_right_eq_left, analyticAt_mul, RCLike.re_le_neg_norm_iff_eq_neg_norm, OrthonormalBasis.coe_equiv_euclideanSpace, RCLike.wInner_one_eq_sum, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, HasFDerivAt.mul_const', integral_ofReal, analyticAt_inv, Polynomial.differentiableWithinAt_aeval, contDiffAt_ringInverse, signedDist_apply, Unitization.norm_splitMul_snd_sq, geom_series_mul_neg, HasStrictFDerivAt.fun_pow', EuclideanSpace.inner_toLp_toLp, DoubleCentralizer.natCast_snd, ordinaryHypergeometric_radius_top_of_neg_natβ, Units.contMDiff_val, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, FormalMultilinearSeries.coeff_iterate_fslope, PadicInt.continuousAddCharEquiv_symm_apply, ContinuousLinearMap.extendToπ'_apply, derivWithin_comp_sub_const, CompletelyPositiveMap.map_cstarMatrix_nonneg', IsLocalFrameOn.coeff_eq_of_eq, ContinuousLinearMap.isAdjointPair_inner, AddChar.linearIndependent, coe_ringEquiv_lpBCF_symm, Unitization.splitMul_injective, Antitone.deriv_nonpos, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, MeasureTheory.Lp.smul_assoc, differentiable_tsum', DoubleCentralizer.sub_snd, analyticAt_inverse_one_sub, Polynomial.differentiable, unitary.norm_sub_one_lt_two_iff, WithCStarModule.pi_norm_sq, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, LinearMap.mem_span_iff_bound, ContinuousOn.cfcβ_nnreal, hasDerivAt_mul_const, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, analyticAt_inv_one_sub, iteratedDeriv_const_mul_field, iteratedDeriv_fun_pow_zero, hasStrictFDerivAt_exp_smul_const, RCLike.instNormSMulClassInt, ContDiffAt.inner, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, RCLike.wInner_cWeight_const_right, HasStrictFDerivAt.mul, iter_deriv_inv_linear, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, ContinuousMap.elemental_id_eq_top, WithLp.unitization_mul, hasDerivAt_exp_smul_const', dist_right_lineMap, DoubleCentralizer.instStarModule, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, CStarAlgebra.star_right_conjugate_le_norm_smul, innerββ_apply_coe, PiLp.inner_apply, MeasureTheory.Lp.neg_smul_neg, summable_geometric_of_norm_lt_one, differentiableAt_of_deriv_ne_zero, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, DoubleCentralizer.intCast_fst, meromorphicOrderAt_const_intCast, LinearMap.toSeminormFamily_apply, hasGradientWithinAt_iff_tendsto, EuclideanSpace.inner_single_right, unitary.norm_sub_one_sq_eq, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, NormedRing.inverse_one_sub_nth_order', HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', Submodule.orthogonal_eq_inter, hasDerivAt_iff_tendsto, ProbabilityTheory.iIndepFun.integral_prod_comp, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, sub_smul_dslope, setIntegral_re_add_im, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, MeasureTheory.lpNorm_one', Matrix.toEuclideanLin_eq_toLin_orthonormal, summable_norm_sum_mul_antidiagonal_of_summable_norm, LinearPMap.mem_adjoint_domain_iff, unitary.norm_argSelfAdjoint_le_pi, differentiableWithinAt_zpow, RCLike.intervalIntegral_ofReal, contDiffOn_infty_iff_deriv_of_isOpen, ContinuousMultilinearMap.norm_smulRight, CStarAlgebra.span_nonneg_inter_ball, LeftInvariantDerivation.commutator_apply, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, OrthonormalBasis.coe_singleton, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, hasStrictFDerivAt_pow, derivWithin_comp_const_add, AnalyticOn.eval_polynomial, prod_vanishing_of_summable_norm, Matrix.l2_opNNNorm_conjTranspose_mul_self, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, coe_innerββ_apply, NormedRing.inverse_add_nth_order, analyticOnNhd_inv, hasDerivAt_exp_zero, Unitary.norm_argSelfAdjoint_le_pi, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, instFieldContMDiffRing, hasGradientWithinAt_iff_isLittleO, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, RCLike.conj_eq_re_sub_im, DFinsupp.inner_sum, inner_matrix_row_row, CFC.monotoneOn_cfcβ_rpowIntegrandββ, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, coe_algEquiv_lpBCF_symm, LinearMap.polar_mem_iff, hasDerivWithinAt_inv, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, hasStrictDerivAt_id, HasFDerivWithinAt.mul', HasGradientAt.fderiv_apply, deriv_neg, integral_re, LeftInvariantDerivation.ext_iff, MeromorphicOn.countable_compl_analyticAt, Polynomial.hasFDerivWithinAt, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, NormedSpace.exp_analytic, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, differentiableAt_inv, NormedSpace.exp_sum_of_commute, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, hasStrictDerivAt_iff_hasStrictFDerivAt, ConvexOn.exists_affine_le_of_lt, MeasureTheory.integral_prod_smul, inner_sub_sub_self, innerSL_apply_coe, Unitary.openPartialHomeomorph_apply, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, HasStrictFDerivAt.inner, Unitary.argSelfAdjoint_coe, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, Matrix.exp_units_conj, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, differentiableAt_dslope_of_ne, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, hasDerivAt_zpow, tangentConeAt_eq_univ, EuclideanSpace.single_eq_zero_iff, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, Matrix.IsHermitian.mulVec_eigenvectorBasis, ValueDistribution.log_counting_zero_sub_logCounting_top, differentiableAt_inverse, Matrix.l2_opNorm_def, Matrix.toEuclideanLin_toLp, integral_re_add_im, ZSpan.coe_fract_self, LeftInvariantDerivation.toFun_eq_coe, Matrix.l2_opNorm_mul, norm_innerSL_le, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, CStarAlgebra.exists_sum_four_unitary, nnnorm_cfcβ_nnreal_le, AffineMap.deriv, SchwartzMap.integral_smul_deriv_right_eq_neg_left, apply_le_nnnorm_cfcβ_nnreal, AnalyticOnNhd.eval_continuousLinearMap', PadicInt.instIsAddTorsionFree, continuousOn_cfcβ_nnreal_setProd, HasGradientWithinAt.hasFDerivWithinAt, hasFDerivAt_exp, deriv_mul_const_field', RCLike.hasSum_conj', MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, differentiableAt_iff_comp_sub_const, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support, LinearMap.polar_mem, LinearMap.isAdjointPair_inner, AnalyticOnNhd.eval_mvPolynomial, ContinuousLinearMap.hasStrictDerivAt, hasFDerivAt_inv, DifferentiableWithinAt.inner, DoubleCentralizer.toProdHom_apply, DoubleCentralizer.mul_snd, MonotoneOn.nnnorm_cfcβ, ContinuousLinearMap.smulRightL_apply_apply, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', HasDerivAtFilter.isTheta_sub, ValueDistribution.logCounting_inv, Ring.inverse_exp, HasStrictFDerivAt.mul_const, HilbertBasis.hasSum_inner_mul_inner, fderivInnerCLM_apply, ConvexOn.sSup_affine_eq, unitary.mem_pathComponentOne_iff, nndist_self_homothety, RCLike.I_mul_I_of_nonzero, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, summable_mul_of_bigO_atTop', derivWithin_const_mul_field, RCLike.span_one_I, hasFPowerSeriesAt_iff', analyticAt_inverse, DFinsupp.sum_inner, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, HasFDerivAt.mul', DoubleCentralizer.intCast_toProd, differentiableAt_comp_sub_const, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, smooth_functions_tower, RCLike.ofReal_sum, finrank_euclideanSpace_fin, coe_algEquiv_lpBCF, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, hasFDerivAt_list_prod_attach', iteratedDerivWithin_mul_const_field, geom_series_eq_inverse, LinearMap.mem_span_iff_continuous, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, AnalyticOnNhd.eval_continuousLinearMap, ContinuousLinearMap.adjoint_innerSL_apply, CStarAlgebra.span_unitary, binomialSeries_radius_ge_one, RCLike.normSq_sub, nndist_homothety_self, Orthonormal.inner_sum, intervalIntegral.integral_mul_const, Filter.IsBoundedUnder.isLittleO_sub_self_inv, DoubleCentralizer.smul_snd, deriv_div_const, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, LeftInvariantDerivation.coeFnAddMonoidHom_apply, RCLike.sqrt_neg_of_nonneg, hasDerivWithinAt_iff_tendsto, MeasureTheory.condExpL2_const_inner, SpectrumRestricts.nnreal_iff_nnnorm, PadicInt.existsUnique_mem_range, ContinuousLinearMap.norm_smulRightL_apply, CStarAlgebra.exists_sum_four_nonneg, PadicInt.toZMod_spec, differentiableAt_iff_comp_neg, DoubleCentralizer.coe_snd, hasFPowerSeriesAt_iff, isUnit_one_sub_of_norm_lt_one, one_le_formalMultilinearSeries_geometric_radius, contDiff_euclidean, fderiv_norm_sq_apply, RCLike.imCLM_apply, hasStrictDerivAt_pow, Derivation.evalAt_apply, derivWithin_mem_iff, PositiveLinearMap.preGNS_norm_sq, RCLike.conj_neg_I, ConvexOn.univ_sSup_of_nat_affine_eq, cfc_setIntegral, differentiableOn_inv, RCLike.inv_I, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, HasFDerivAtFilter.hasDerivAtFilter, MeasureTheory.integral_mul_const, fderiv_norm_sq, tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, ContinuousLinearMap.toSesqForm_apply_norm_le, HilbertBasis.hasSum_repr_symm, CStarMatrix.norm_def, inner_neg_left, differentiableWithinAt_Ioi_iff_Ici, integral_im, differentiableOn_zpow, selfAdjoint.expUnitary_coe, DoubleCentralizer.add_toProd, intervalIntegral.integral_const_mul, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Function.FactorizedRational.meromorphicNFOn, fderiv_inner_apply, contDiff_one_iff_deriv, inner_matrix_col_col, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, derivWithin_comp_neg, HasFDerivWithinAt.fun_mul, RCLike.div_I, iter_deriv_pow, HasStrictFDerivAt.finset_prod, Continuous.cfcβ_nnreal', ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, DoubleCentralizer.neg_fst, CStarMatrix.inner_toCLM_conjTranspose_right, Matrix.PosDef.re_dotProduct_pos, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, fderiv_eq_smul_deriv, CStarMatrix.toCLM_apply_single_apply, DoubleCentralizer.toProdMulOppositeHom_apply, InnerProductSpace.Core.inner_sub_right, Unitization.cfcβ_eq_cfc_inr, PadicInt.addChar_of_value_at_one_def, deriv_comp_sub_const, HasFDerivWithinAt.list_prod', fderiv_inv', unitary.continuousOn_argSelfAdjoint, tendsto_zero_geometric_tsum_pnat, natCast_memβp_infty, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod
|
| Name | Category | Theorems |
|---|
induced π | CompOp | β |
toNonUnitalCommRing π | CompOp | 4 mathmath: Submodule.Quotient.instIsBoundedSMul, StrongDual.dualPairing_separatingLeft, TrivSqZeroExt.instL1IsBoundedSMul, PiLp.basis_toMatrix_basisFun_mul
|
toNonUnitalSeminormedRing π | CompOp | 2141 mathmath: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, hasFDerivAt_iff_hasDerivAt, iteratedDeriv_scomp_two, Real.differentiableOn_arcosh, isEquivalent_descFactorial, Real.hasDerivAt_arccos, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, HasSum.exp, BoundedContinuousFunction.tietze_extension_step, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, InformationTheory.integrable_klFun_rnDeriv_iff, Polynomial.differentiableWithinAt, MeasureTheory.Integrable.integral_norm_prod_right, Seminorm.isBounded_const, isConformalMap_conj, MeasureTheory.eLpNorm'_norm, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, HasStrictFDerivAt.isLittleOTVS, Bundle.ContMDiffRiemannianMetric.isVonNBounded, NormedSpace.isBounded_polar_of_mem_nhds_zero, TensorProduct.enorm_lid, differentiableAt_comp_neg, Real.integrableOn_rpowIntegrandββ_Ioi, Matrix.frobenius_nnnorm_mul, HasMFDerivAt.mul, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, MonotoneOn.intervalIntegral_slope_le, ProbabilityTheory.isGaussian_iff_gaussian_charFun, Real.differentiable_arctan, RCLike.map_apply, Real.differentiableAt_mulExpNegMulSq, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, Complex.restrictScalars_one_smulRight', IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, HasFDerivWithinAt.ccos, InnerProductSpace.toLinearIsometry_toDual, RCLike.ofRealCLM_apply, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, Real.hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, Complex.linearEquiv_det_conjLIE, Ideal.toCharacterSpace_apply_eq_zero_of_mem, hasFDerivAt_iff_hasGradientAt, RCLike.reCLM_apply, NumberField.Units.finrank_eq_rank, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, InnerProductSpace.rankOne_one_left_eq_innerSL, ConvexOn.rightDeriv_le_slope_of_mem_interior, ContinuousMap.abs_mem_subalgebra_closure, hasDerivAt_sqrt_mul_log, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, HasStrictFDerivAt.csin, Polynomial.isEquivalent_atBot_div, ZSpan.volume_real_fundamentalDomain, ContinuousLinearMap.opNorm_bound_of_ball_bound, Complex.ofRealCLM_coe, Complex.kahler, RightDerivMeasurableAux.D_subset_differentiable_set, Complex.areaForm, WeakDual.isCompact_polar, finrank_real_complex_fact', EuclideanSpace.orthonormal_single, Real.deriv_negMulLog, Real.hasDerivAt_sigmoid, AffineMap.hasDerivAtFilter, Matrix.IsHermitian.det_abs, RCLike.ofRealLI_apply, deriv_abs, differentiableAt_zpow, hasFDerivAt_multiset_prod, Stirling.factorial_isEquivalent_stirling, ProbabilityTheory.covarianceBilinDual_apply', Real.nnnorm_deriv_mulExpNegMulSq_le_one, OrthonormalBasis.repr_injective, Real.deriv_binEntropy, MeasureTheory.convolution_mul, Complex.ofRealLI_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, deriv_mem_iff, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, integrableOn_exp_mul_Iic, ProbabilityTheory.IsGaussian.integrable_dual, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, norm_iteratedFDerivWithin_smul_le, Matrix.cstar_nnnorm_def, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Real.hasStrictDerivAt_rpow_const_of_ne, StrongDual.polarSubmodule_eq_setOf, ContinuousMap.attachBound_apply_coe, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, ContinuousLinearMap.hasDerivAtFilter, fderivWithin_csinh, span_fourier_closure_eq_top, PeriodPair.basis_one, RCLike.conjCLE_norm, HasDerivWithinAt.complexToReal_fderiv', Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, ContDiffBump.integrable, WeakDual.isClosed_image_polar_of_mem_nhds, ZLattice.covolume_eq_det_inv, ContinuousLinearMap.integral_apply, circleIntegrable_iff, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', MeasureTheory.MemLp.const_inner, not_integrableOn_Ioi_cpow, MeasureTheory.AEStronglyMeasurable.memLp_truncation, Real.fderiv_fourierChar_neg_bilinear_right_apply, intervalIntegral.fderiv_integral_of_tendsto_ae, flip_innerSL_real, LipschitzWith.memLp_lineDeriv, differentiableWithinAt_abs_pos, continuousOn_dslope, ProbabilityTheory.integrable_preCDF, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, isClosedEmbedding_cfcβAux, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, AddChar.wInner_cWeight_self, AddCircle.coe_real_preimage_closedBall_eq_iUnion, innerSL_apply_apply, MeasureTheory.Integrable.norm_integral_condExpKernel, LinearMap.adjoint_innerββ_apply, Real.differentiable_sinh, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, hasDerivAt_neg', AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, nnnorm_cfcβ_lt_iff, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, LeftInvariantDerivation.left_invariant', Int.enorm_natCast, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, derivWithin_fderivWithin, ContDiffBump.integrable_normed, ProbabilityTheory.uncenteredCovarianceBilin_apply, Real.deriv_log, ContDiff.differentiable_deriv_two, FormalMultilinearSeries.derivSeries_coeff_one, Complex.ofRealCLM_norm, Matrix.spectrum_toLpLin, contMDiff_neg_sphere, HasDerivAt.comp_ofReal, not_differentiableAt_norm_zero, rotation_injective, BoxIntegral.unitPartition.mem_smul_span_iff, SchwartzMap.bilinLeftCLM_apply, InnerProductSpace.toDual_symm_apply, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, HasGradientAt.hasDerivAt', SmoothBumpCovering.exists_immersion_euclidean, AffineMap.hasDerivWithinAt, LeftInvariantDerivation.left_invariant, MeasureTheory.pdf.IsUniform.mul_pdf_integrable, ProbabilityTheory.integrable_toReal_condExpKernel, Bundle.RiemannianMetric.isVonNBounded, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, IsGreatest.nnnorm_cfcβ, Complex.convexHull_reProdIm, Complex.conjLIE_apply, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, hasDerivAt_exp_zero_of_radius_pos, egauge_ball_le_of_one_lt_norm, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasStrictFDerivAt_iff_isLittleOTVS, not_IntegrableOn_Ioi_inv, ContinuousMap.continuousMap_mem_subalgebra_closure_of_separatesPoints, Matrix.PosSemidef.sqrt_eq_zero_iff, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, lintegral_fderiv_lineMap_eq_edist, UnitAddTorus.mFourierSubalgebra_coe, signedDist_right_congr, TensorProduct.toLinearEquiv_lidIsometry, Real.differentiableOn_arcsin, AnalyticOnNhd.eval_linearMap', MeasureTheory.MemLp.integrable_norm_rpow', Complex.hasStrictFDerivAt_exp_real, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.parallelepiped_basisFun, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, monomial_has_deriv_aux, MeasureTheory.hasFiniteIntegral_prod_iff', Real.vector_fourierIntegral_eq_integral_exp_smul, MeasureTheory.MemLp.norm_rpow, nndist_midpoint_right, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, Asymptotics.isLittleOTVS_prodMk_left, NNReal.enorm_eq, iter_deriv_zpow', differentiableWithinAt_abs, Matrix.exp_conj', Real.deriv_arccos, Real.hasStrictDerivAt_sinh, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, LocallyBoundedVariationOn.ae_differentiableWithinAt, ConvexOn.univ_sSup_of_countable_affine_eq, integrableOn_exp_Iic, cfcβHom_nnreal_eq_restrict, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, IsLocalFrameOn.coeff_apply_of_mem, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, IsLocalMax.fderiv_eq_zero, Matrix.exp_neg, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, polynomialFunctions.starClosure_topologicalClosure, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerββ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, differentiableAt_sigmoid, OrthonormalBasis.repr_self, iteratedDeriv_scomp_three, Real.integrable_prod_sub, HasFDerivWithinAt.csin, MeasureTheory.eLpNorm_mono_real, Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, Icc_isBoundaryPoint_bot, mellin_convergent_zero_of_isBigO, deriv_abs_neg, ProbabilityTheory.evariance_lt_top_iff_memLp, Real.differentiableWithinAt_arccos_Ici, gelfandStarTransform_naturality, gelfandStarTransform_apply_apply, HarmonicAt.analyticAt_complex_partial, integrableOn_Ioi_rpow_of_lt, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, NormedSpace.Dual.toWeakDual_continuous, signedDist_left_congr, NormedField.exists_lt_nnnorm_lt, exists_deriv_eq_zero, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, ContinuousMultilinearMap.norm_smulRightL_le, NormedField.exists_nnnorm_lt_one, differentiableAt_comp_add_const, integrableOn_Ioi_norm_cpow_of_lt, QuadraticForm.equivalent_signType_weighted_sum_squared, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, SchwartzMap.integral_fourierInv_smul_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, signedDist_triangle, Real.hasDerivAt_arcosh, ConvexOn.monotoneOn_rightDeriv, enorm_fderiv_norm_rpow_le, LocallyBoundedVariationOn.ae_differentiableAt, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, fderiv_eq_deriv_mul, nndist_right_lineMap, Orientation.abs_volumeForm_apply_of_orthonormal, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, Polynomial.differentiableOn_aeval, NumberField.mixedEmbedding.negAt_apply_snd, fderivWithin_ccosh, Real.GammaIntegral_convergent, Matrix.toEuclideanLin_apply, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, fourier_norm, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, Real.hasStrictDerivAt_arccos, RCLike.conjCLE_apply, MeasureTheory.integrable_norm_rpow_iff, Complex.reCLM_nnnorm, Unitization.nnnorm_def, isScalarTower_closedBall_closedBall_closedBall, nndist_left_lineMap, Euclidean.closedBall_eq_image, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, isScalarTower_sphere_closedBall_closedBall, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, Complex.deriv_ofReal_cpow_const, PiTensorProduct.mapL_smul, MeasureTheory.L1.setToL1_smul_left, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, MeasureTheory.eLpNorm_norm, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, Real.norm_deriv_mulExpNegMulSq_le_one, Quaternion.linearIsometryEquivTuple_symm_apply, Polynomial.isEquivalent_atTop_lead, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, MeasureTheory.charFun_apply_real, Orientation.areaForm_to_volumeForm, Icc_isInteriorPoint_interior, VectorFourier.fourierIntegral_continuousLinearMap_apply, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, Real.not_continuousAt_deriv_mul_log_zero, integrable_one_add_norm, ProbabilityTheory.integrable_condCDF, HasFDerivAtFilter.isThetaTVS_sub, integrableOn_add_rpow_Ioi_of_lt, InformationTheory.klDiv_eq_top_iff, SchwartzMap.fourier_lineDerivOp_eq, LinearMap.isBigOTVS_rev_comp, AddChar.wInner_cWeight_eq_zero_iff_ne, NormedField.exists_one_lt_enorm, ContinuousLinearMapWOT.inducingFn_apply, Orientation.areaForm_neg_orientation, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, Monotone.ae_differentiableAt, mfderivWithin_comp_projIcc_one, contDiffWithinAt_euclidean, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, AddCircle.norm_div_natCast, InnerProductSpace.toDualMap_apply_apply, Orientation.kahler_eq_zero_iff, BoundedContinuousFunction.integral_const_sub, signedDist_apply_apply, Real.differentiableAt_rpow_const_of_ne, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, WeakDual.toStrongDual_inj, IccLeftChart_extend_interior_pos, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, Orientation.areaForm_swap, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, hasDerivAt_id', integrableOn_Ioi_cpow_iff, Bundle.ContinuousRiemannianMetric.symm, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, MeasureTheory.MemLp.inner_const, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, Complex.sameRay_of_arg_eq, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, Real.deriv_sqrt_aux, deriv_fderiv, HasStrictDerivAt.real_of_complex, Matrix.PosSemidef.det_sqrt, Real.deriv_rpow_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, HasDerivAt.differentiableAt, DifferentiableWithinAt.dist, MeasureTheory.integrable_thickenedIndicator, NormedField.exists_nnnorm_lt, hasDerivWithinAt_abs, MeasureTheory.integrable_of_tendsto, TensorProduct.lidIsometry_apply, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ContinuousLinearMap.hasDerivAt, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Complex.reCLM_coe, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, MeasureTheory.eLpNorm_ofReal, Real.deriv_sinh, NormedField.exists_lt_enorm, Module.Basis.coe_toOrthonormalBasis_repr, Filter.HasBasis.isLittleOTVS_iff, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, Matrix.linfty_opNNNorm_eq_opNNNorm, VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, InformationTheory.hasDerivAt_klFun, integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, Orientation.kahler_comp_rightAngleRotation, Seminorm.ball_smul, ae_differentiableAt_norm, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, HasGradientWithinAt.differentiableWithinAt, MeasureTheory.memLp_haarAddCircle_iff, NumberField.Units.instZLattice_unitLattice, HasFDerivAt.isBigOTVS_sub, hasDerivWithinAt_neg, Orientation.volumeForm_zero_pos, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, ProbabilityTheory.complexMGF_mul_I, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, IsLocalFrameOn.coeff_congr, ProbabilityTheory.Kernel.integrable_densityProcess, NumberField.Units.span_basisOfIsMaxRank, LinearMap.hasStrictDerivAt, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, FiniteDimensional.rclike_to_real, Complex.equivRealProdCLM_symm_apply, HasDerivWithinAt.norm_sq, NormedSpace.smul_mem_polar, HasGradientAtFilter.hasDerivAtFilter', CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, IsLocalExtr.fderiv_eq_zero, NumberField.Units.basisOfIsMaxRank_apply, Real.differentiableOn_rpow_const, MeasureTheory.MemLp.integrable_norm_pow, NormedField.denseRange_nnnorm, Asymptotics.IsLittleOTVS.zero, ContinuousLinearMap.flip_mul, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, PeriodPair.basis_zero, MeasureTheory.Integrable.norm_integral_condDistrib, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, ContinuousLinearMap.nnnorm_toSpanSingleton, InformationTheory.leftDeriv_klFun, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Asymptotics.isLittleOTVS_fun_neg_left, deriv_id'', AddCircle.exists_norm_nsmul_le, isEquivalent_choose, Asymptotics.isBigOTVS_iff_smallSets, OrthonormalBasis.coe_ofRepr, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MeasureTheory.Integrable.integral_norm_comp, EuclideanSpace.nnnorm_single, ProbabilityTheory.differentiableAt_mgf, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, RCLike.conjLIE_apply, Complex.orthonormalBasisOneI_repr_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Complex.differentiable_exp, Polynomial.toAddCircle.integrable, RCLike.imLm_coe, Real.differentiable_cos, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, isAddFundamentalDomain_Ioc, norm_cauchyPowerSeries_le, hasFDerivAt_norm_rpow, intervalIntegral.integrableOn_Ioo_rpow_iff, Asymptotics.isEquivalent_nat_ceil, summable_jacobiThetaβ_term_fderiv_iff, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, AddCircle.norm_coe_mul, Asymptotics.isBigOTVS_fun_neg_left, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Matrix.linfty_opNNNorm_toMatrix, Asymptotics.isBigOTVS_fun_neg_right, hasDerivAt_abs_rpow, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, signedDist_eq_zero_of_orthogonal, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, ProbabilityTheory.memLp_of_mem_interior_integrableExpSet, ZSpan.volume_fundamentalDomain, FormalMultilinearSeries.coeff_eq_zero, ProbabilityTheory.covarianceBilin_zero, RCLike.conjCLE_coe, contDiffOn_stereoToFun, LeftInvariantDerivation.evalAt_coe, AddCircle.norm_half_period_eq, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, Matrix.PosSemidef.sqrt_eq_one_iff, Real.deriv_Gamma_nat, GaussianFourier.integrable_cexp_neg_mul_sum_add, Complex.hasStrictFDerivAt_cpow, MeasureTheory.integrable_add_iff_of_nonneg, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, Polynomial.differentiable_aeval, IsGreatest.nnnorm_cfc, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Convex.toWeakSpace_closure, hasDerivAtFilter_neg, integrable_rpow_neg_one_add_norm_sq, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, Bundle.ContMDiffRiemannianMetric.symm, HilbertBasis.hasSum_repr, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, Asymptotics.isBigOTVS_iff_isBigO, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, hasDerivWithinAt_pow, HasFDerivWithinAt.cpow, MeasureTheory.lintegral_nnnorm_condExpL2_le, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, AffineSubspace.signedInfDist_eq_signedDist_of_mem, HasStrictFDerivAt.const_cpow, Finset.nnnorm_prod_le', differentiableWithinAt_of_derivWithin_ne_zero, one_mem_posTangentConeAt_iff_mem_closure, HasFDerivWithinAt.csinh, Real.integrable_sinc, RealRMK.rieszMeasure_le_of_eq_one, TensorProduct.inner_lid_lid, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, NormedSpace.inclusionInDoubleDual_norm_le, not_IntegrableOn_Ici_inv, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, MeasureTheory.memLp_two_iff_integrable_sq, WeakDual.isCompact_closedBall, Affine.Simplex.signedInfDist_apply_self, ConvexOn.sSup_of_countable_affine_eq, Real.differentiableAt_rpow_of_ne, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, RCLike.reCLM_coe, ProbabilityTheory.gaussianReal_map_linearMap, InnerProductSpace.toDual_apply, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', HasDerivWithinAt.inner, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, DifferentiableAt.inner, HarmonicAt.differentiableAt_complex_partial, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, NormedSpace.exp_continuousMap_eq, Seminorm.comp_smul, isScalarTower_sphere_sphere_sphere, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', Real.deriv_inv_log, ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, Asymptotics.IsLittleO.isLittleOTVS, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, iteratedFDerivWithin_eq_equiv_comp, CompactlySupportedContinuousMap.toRealLinearMap_apply, DifferentiableAt.isBigOTVS_sub, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, MeasureTheory.Integrable.integral_norm_prod_left, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, differentiableAt_inv_iff, AddCircle.instIsUnifLocDoublingMeasureRealVolume, ProbabilityTheory.covarianceBilinDual_zero, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, RealRMK.integral_rieszMeasure, LinearMap.deriv, RCLike.nnnorm_nnratCast, contDiff_iff_iteratedDeriv, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, EuclideanSpace.instIsManifoldSphere, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, Real.isEquivalent_sin, InnerProductSpace.toDualMap_apply, Real.differentiable_exp, ProbabilityTheory.differentiableOn_mgf, Real.abs_mulExpNegMulSq_comp_le_norm, nnnorm_algebraMap, fdifferential_apply, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, Asymptotics.isEquivalent_iff_exists_eq_mul, MeasureTheory.Integrable.integral_norm_condExpKernel, Real.differentiableAt_cos, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, innerβ_apply, Asymptotics.isBigOTVS_congr, ProbabilityTheory.complexMGF_id_mul_I, fderivWithin_ccos, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, ModularGroup.lcRow0Extend_apply, Asymptotics.isBigOTVS_neg_right, Real.deriv_log', hasDerivAt_update, HasStrictFDerivAt.clog, nnnorm_apply_le_nnnorm_cfcβ, Real.one_div_sub_hasFPowerSeriesOnBall_zero, ProbabilityTheory.integrable_condVar, OrthonormalBasis.equiv_apply, Seminorm.bound_of_continuous, fderiv_pow_ring, Bundle.ContMDiffRiemannianMetric.pos, HasDerivWithinAt.complexToReal_fderiv, signedDist_triangle_left, IsContMDiffRiemannianBundle.exists_contMDiff, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, Real.deriv2_binEntropy, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, InnerProductSpace.toDual_apply_apply, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, contMDiff_subtype_coe_Icc, Real.hasDerivAt_arcsin, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, ProperCone.innerDual_singleton, RCLike.nnnorm_ofNat, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, differentiable_inner, Real.hasDerivAt_tan, hasFDerivAt_list_prod', InnerProductSpace.rankOne_def, Real.deriv_tan_sub_id, AddCircle.volume_closedBall, Real.leftDeriv_mul_log, stereoToFun_apply, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, Real.differentiableAt_Gamma, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, orthogonalBilin_innerβ, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, ConvexOn.real_univ_sSup_of_countable_affine_eq, NumberField.mixedEmbedding.mem_span_latticeBasis, ProbabilityTheory.evariance_eq_top_iff, Module.Basis.equivFunL_symm_apply_repr, OrthonormalBasis.repr_apply_apply, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, HasStrictFDerivAt.ccos, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, MeasureTheory.lintegral_ofReal_ne_top_iff_integrable, BoundedContinuousFunction.neg_norm_le_apply, gradient_eq_deriv', QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ClosedSubmodule.orthogonal_eq_inter, Chebyshev.integrableOn_theta_div_id_mul_log_sq, Orientation.kahler_neg_orientation, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, MonotoneOn.intervalIntegrable_slope, nndist_left_midpoint, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', intervalIntegral.integrableOn_Ioo_cpow_iff, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, Real.differentiableOn_mul_log, MeasureTheory.setToFun_smul_left, InformationTheory.klDiv_def, HasDerivAt.complexToReal_fderiv', hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.Integrable.norm_integral_condKernel, RCLike.abs_wInner_le, contDiff_nat_iff_iteratedDeriv, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, ProbabilityTheory.memLp_id_gaussianReal', fderiv_norm_smul_neg, HasDerivAt.complexToReal_fderiv, ContinuousLinearMapWOT.isInducing_inducingFn, integrableOn_Ioi_deriv_ofReal_cpow, Real.deriv_mulExpNegMulSq, StrongDual.polarSubmodule_eq_polar, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, Asymptotics.isLittleOTVS_fun_neg_right, Complex.isEquivalent_sinh, hasFDerivAt_exp_smul_const', dense_differentiableAt_norm, MeasureTheory.SignedMeasure.re_toComplexMeasure, Matrix.exp_zsmul, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, MonotoneOn.intervalIntegral_deriv_mem_uIcc, NumberField.mixedEmbedding.volume_preserving_negAt, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, Real.deriv_qaryEntropy, Real.deriv_arctan, monotoneOn_deriv_descPochhammer_eval, SchwartzMap.smulLeftCLM_const, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, mellin_convergent_top_of_isBigO, LinearMap.toMatrix_innerββ_apply, PointwiseConvergenceCLM.equivWeakDual_symm_apply, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, MeasureTheory.ComplexMeasure.integrable_rnDeriv, RCLike.wInner_one_eq_inner, NumberField.mixedEmbedding.negAt_apply_isComplex, ProbabilityTheory.hasFiniteIntegral_compProd_iff', AffineMap.hasDerivAt, Complex.hasFDerivAt_cpow, Complex.differentiableAt_exp, ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, not_integrableOn_Ioi_rpow, AffineMap.differentiableAt, isScalarTower_closedBall_ball_ball, Matrix.PosSemidef.toLinearMapβ'_zero_iff, Polynomial.rootSet_derivative_subset_convexHull_rootSet, WeakDual.isSeqCompact_closedBall, HasFDerivAt.ccos, MeasureTheory.Measure.integrable_measure_prodMk_left, has_antideriv_at_fourier_neg, Real.differentiableAt_log_iff, hasStrictDerivAt_zpow, norm_iteratedFDerivWithin_prod_le, UnitAddTorus.mFourier_norm, Matrix.instNonnegSpectrumClass, LinearIsometry.toSpanSingleton_apply, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, DifferentiableAt.norm_sq, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, HasFDerivAt.clog, innerSLFlip_apply_apply, Polynomial.hasFDerivAt, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, finrank_euclideanSpace, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, IsContinuousRiemannianBundle.exists_continuous, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, NormedField.exists_enorm_lt, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', MeasureTheory.MemLp.integrable_norm_rpow, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, nndist_midpoint_left, intervalIntegral.integral_hasStrictFDerivAt, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, MeasureTheory.IntegrableAtFilter.norm, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, Module.Basis.equivFunL_apply, inner_map_complex, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, tendsto_integral_mul_one_add_inv_smul_sq_pow, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, LinearMap.hasDerivWithinAt, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, Real.fourier_fderiv, ContinuousMap.adjoin_id_eq_span_one_union, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, Seminorm.const_isBounded, MeasureTheory.integrable_prod_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, HasFDerivWithinAt.norm_sq, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, differentiableAt_abs_neg, Asymptotics.isLittleOTVS_iff_smallSets, BoundedContinuousFunction.apply_le_norm, hasDerivAt_fourier_neg, ProbabilityTheory.isGaussian_gaussianReal, norm_fderiv_norm_rpow_le, StrongDual.dualPairing_separatingLeft, deriv_abs_zero, HasDerivWithinAt.differentiableWithinAt, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, nndist_midpoint_midpoint_le', Polynomial.Chebyshev.integrable_measureT, SchwartzMap.fourierInv_lineDerivOp_eq, RCLike.finrank_le_two, Bundle.RiemannianMetric.symm, MeasureTheory.integral_charFun_Icc, iteratedFDeriv_eq_equiv_comp, linear_isometry_complex, Real.hasDerivAt_cos, Matrix.ofLp_toEuclideanCLM, AffineSubspace.signedInfDist_eq_const_of_mem, ProbabilityTheory.HasSubgaussianMGF.integrable, HasFDerivAt.ccosh, ContinuousMap.sup_mem_subalgebra_closure, AddCircle.exists_norm_eq_of_isOfFinAddOrder, Asymptotics.isBigOTVS_neg_left, exists_dual_vector, nndist_center_homothety, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, Differentiable.norm_rpow, DifferentiableWithinAt.isBigOTVS_sub, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, Real.differentiableWithinAt_arcsin_Ici, AddChar.wInner_cWeight_eq_one_iff_eq, logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, InformationTheory.klDiv_ne_top_iff, RCLike.sqrt_map, MeasureTheory.integrable_conv_iff, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, PadicInt.mahlerTerm_one, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, rotationOf_rotation, IsMIntegralCurveAt.hasMFDerivAt, SpectrumRestricts.real_iff, IsLocalFrameOn.eventually_eq_sum_coeff_smul, differentiableWithinAt_euclidean, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, deriv_abs_pos, Matrix.isPositive_toEuclideanLin_iff, nnnorm_cfc_le_iff, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, exists_polynomial_near_continuousMap, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, HasGradientAt.differentiableAt, ContinuousMap.inf_mem_subalgebra_closure, NormedSpace.exp_sum, Real.differentiableAt_cosh, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, ProbabilityTheory.integral_linearMap_gaussianReal, AddCircle.coe_real_preimage_closedBall_inter_eq, Real.nnnorm_mul_toNNReal, Polynomial.hermite_eq_deriv_gaussian', MeasureTheory.integrable_of_integral_eq_one, MeasureTheory.integrable_norm_iff, WeakDual.polar_def, MeasureTheory.integrable_toReal_of_lintegral_ne_top, RCLike.wInner_const_left, ProbabilityTheory.covarianceBilinDual_self_eq_variance, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, MeasureTheory.integrable_smul_const, Orientation.areaForm_comp_linearIsometryEquiv, NormedField.exists_one_lt_nnnorm, hasStrictFDerivAt_norm_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', LinearMap.adjoint_toSpanSingleton, ContDiff.differentiable_iteratedDeriv, ContinuousMultilinearMap.norm_mkPiAlgebra, Real.deriv_exp, NumberField.canonicalEmbedding.nnnorm_eq, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, QuasispectrumRestricts.real_iff, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, RCLike.inner_apply, NormedField.exists_enorm_lt_one, Polynomial.differentiableAt_aeval, WeakDual.CharacterSpace.compContinuousMap_apply, hasDerivAt_id, Real.hasDerivAt_rpow_const, Real.toNNReal_mul_nnnorm, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, MeasureTheory.Integrable.re_im_iff, Polynomial.isEquivalent_atBot_lead, differentiableAt_norm_smul, deriv_update, MeasureTheory.HasFiniteIntegral.norm, Real.iter_deriv_exp, Real.differentiable_iteratedDeriv_cos, nndist_lineMap_right, Polynomial.hasFDerivAt_aeval, Differentiable.norm_sq, exists_dual_vector'', deriv_zpow', RCLike.norm_wInner_le, ProbabilityTheory.IsGaussian.memLp_dual, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Asymptotics.isLittleOTVS_map, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, hasDerivAt_exp, contDiffOn_succ_iff_deriv_of_isOpen, signedDist_lineMap_left, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, Real.tendsto_rightDeriv_mul_log_atTop, Real.hasStrictDerivAt_arsinh, iter_deriv_pow', MeasureTheory.Integrable.integral_norm_compProd, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, Asymptotics.isLittleOTVS_iff_isLittleO, integrable_rpow_mul_exp_neg_mul_sq, EuclideanSpace.basisFun_repr, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, RCLike.realLinearIsometryEquiv_symm_apply, hasStrictFDerivAt_inv, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, InformationTheory.klDiv_eq_integral_klFun, LinearIsometry.coe_toSpanSingleton, MeasureTheory.hasFiniteIntegral_iff_ofReal, integrable_mul_exp_neg_mul_sq, VectorFourier.fourierSMulRight_apply, deriv_neg'', UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, IsLocalFrameOn.coeff_apply_of_notMem, ProbabilityTheory.evariance_def', Seminorm.closedBall_smul, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, fderiv_inv, Complex.orthonormalBasisOneI_repr_symm_apply, Manifold.riemannianEDist_def, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, isScalarTower_sphere_sphere_closedBall, signedDist_anticomm, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, UnitAddTorus.hasSum_mFourier_series_L2, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Orientation.areaForm_comp_rightAngleRotation, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, modelWithCornersEuclideanHalfSpace_zero, UnitAddCircle.mem_approxAddOrderOf_iff, ContinuousLinearMap.norm_extendToπ'_bound, MeasureTheory.hausdorffMeasure_homothety_image, Real.differentiableAt_arctan, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, spectralNorm_smul, Asymptotics.isEquivalent_of_tendsto_one, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, HasGradientWithinAt.fderivWithin_apply, differentiableWithinAt_abs_neg, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, ProbabilityTheory.integrable_exp_mul_gaussianReal, WeakDual.isClosed_closedBall, MeasureTheory.integrable_add_iff_of_nonpos, hasDerivAt_fourier, fderiv_ccos, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Real.rightDeriv_mul_log, ProbabilityTheory.Kernel.integrable_density, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, ProbabilityTheory.hasFiniteIntegral_prodMk_left, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, nnnorm_inner_le_nnnorm, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ProbabilityTheory.hasFiniteIntegral_comp_iff', IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, fderiv_apply_one_eq_deriv, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, isScalarTower_sphere_sphere_ball, IsUltrametricDist.algNormOfAlgEquiv_apply, integrableOn_exp_mul_complex_Iic, AddCircle.norm_coe_eq_abs_iff, HasFDerivAt.inner, MeasureTheory.L2.eLpNorm_inner_lt_top, ProbabilityTheory.integrable_pow_of_mem_interior_integrableExpSet, deriv_circleMap, ProbabilityTheory.exp_neg_integrableOn_Ioc, ProbabilityTheory.deriv_mgf, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, MeasureTheory.hasFiniteIntegral_norm_iff, MeasureTheory.Integrable.norm_integral_condDistrib_map, OrthonormalBasis.sum_repr_symm, StrongDual.toLpβ_apply, Orientation.kahler_apply_self, IsPrimitiveRoot.nnnorm_eq_one, Real.differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, ProbabilityTheory.hasFiniteIntegral_comp_iff, Complex.conjCLE_nnorm, Polynomial.differentiableOn, HasStrictDerivAt.complexToReal_fderiv', IsLocalFrameOn.coeff_apply_zero_at, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, egauge_ball_one_le_of_one_lt_norm, differentiableOn_neg, Asymptotics.isBigOTVS_pi, LinearMap.continuous_of_nonzero_on_open, MeasureTheory.HasFiniteIntegral.of_mem_Icc, ConvexOn.real_univ_sSup_affine_eq, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, AddCircle.closedBall_eq_univ_of_half_period_le, toWeakSpace_closedConvexHull_eq, ConvexOn.monotoneOn_leftDeriv, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, deriv_neg', Orientation.kahler_rotation_left', Real.differentiable_sin, hasFDerivAtFilter_iff_isLittleOTVS, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.hasDerivWithinAt_aeval, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, rotation_trans, integrableOn_Ioi_rpow_iff, Real.eulerMascheroniConstant_eq_neg_deriv, Real.not_differentiableAt_inv_log_zero, Orientation.abs_areaForm_le, Real.deriv_mul_log, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, ContinuousLinearMap.norm_extendToπ', integrableOn_rpow_mul_exp_neg_rpow, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, differentiableAt_iff_comp_const_sub, MeasureTheory.Integrable.integral_norm_condDistrib, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, signedDist_neg, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, Complex.restrictScalars_toSpanSingleton, integrableOn_exp_mul_Ioi, Orientation.normSq_kahler, ProbabilityTheory.IsCondKernelCDF.integrable, Complex.UnitDisc.mk_neg, HasFDerivWithinAt.clog, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, ProbabilityTheory.integrable_of_mem_integrableExpSet, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, hasFDerivAt_exp_smul_const_of_mem_ball, Real.differentiableAt_tan, Real.differentiable_cosh, NumberField.mixedEmbedding.negAt_symm, fourierSubalgebra_coe, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ProbabilityTheory.integrable_compProd_iff, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, Complex.inner, cfcHom_nnreal_eq_restrict, fderiv_deriv, Asymptotics.isLittleOTVS_neg_right, MeasureTheory.MemLp.norm_rpow_div, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, signedDist_vsub_self_rev, coord_norm', Int.Matrix.one_le_norm_A_of_ne_zero, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, OrthonormalBasis.measurePreserving_repr_symm, spectrum.exists_nnnorm_eq_spectralRadius_of_nonempty, WeakDual.isClosed_polar, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, spec_cfcβAux, MeasureTheory.measureReal_abs_gt_le_integral_charFun, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, EuclideanSpace.piLpCongrLeft_single, hasFDerivAt_exp_smul_const, Differentiable.inner, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Real.hasDerivAt_log, oneTangentSpaceIcc_def, IccRightChart_extend_top_mem_frontier, rotationOf_coe, NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, Module.Basis.parallelepiped_eq_map, MeasureTheory.tendsto_eLpNorm_condExp, iteratedDeriv_comp_two, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, signedDist_self, MeasureTheory.MemLp.norm, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, integrable_inv_one_add_sq, Complex.sqrt_map, signedDist_vsub_self, MeasureTheory.SignedMeasure.rnDeriv_smul, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, signedDist_smul, MeasureTheory.eLpNorm_mono_ae_real, TemperedDistribution.fourierTransform_apply, Real.hasStrictDerivAt_arctan, ZLattice.volume_image_eq_volume_div_covolume, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Real.map_linearMap_volume_pi_eq_smul_volume_pi, nnnorm_apply_le_nnnorm_cfc, Matrix.toEuclideanLin_eq_toLin, StrongDual.toLpβ_of_not_memLp, isConformalMap_complex_linear_conj, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, ProbabilityTheory.memLp_id_gaussianReal, intervalIntegral.differentiable_integral_of_continuous, deriv_zpow, LipschitzWith.locallyIntegrable_lineDeriv, AddCircle.norm_neg_period, SmoothBumpCovering.embeddingPiTangent_injOn, MeasureTheory.memLp_norm_rpow_iff, StrongDual.mem_polarSubmodule, exists_dual_vector', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Orientation.kahler_rightAngleRotation_left, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, UnitAddTorus.hasSum_mFourier_series_of_summable, Real.hasDerivAt_mulExpNegMulSq, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, cfcβHom_real_eq_restrict, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, Real.differentiableOn_arccos, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, IsLocalMin.deriv_eq_zero, Real.hasDerivAt_cosh, Real.tendsto_deriv_mul_log_atTop, Orientation.abs_areaForm_of_orthogonal, LipschitzOnWith.ae_differentiableWithinAt_real, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, UnitAddCircle.norm_eq, HasFPowerSeriesAt.deriv, innerβ_apply_apply, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, HasFDerivAt.csin, MeasureTheory.eLpNorm_norm_rpow, Asymptotics.IsBigOTVS.rfl, Asymptotics.IsLittleOTVS.bot, ContinuousLinearMap.isBigOTVS_comp, PadicAlgCl.valuation_def, hfdifferential_apply, MeasureTheory.Integrable.inner_const, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, Real.hasDerivAt_fourierChar, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, Orientation.kahler_rotation_left, nnnorm_cfcβHom, SchwartzMap.smulLeftCLM_neg, Complex.conjCLE_enorm, Real.differentiableWithinAt_arccos_Iic, spectrum.differentiableOn_inverse_one_sub_smul, Asymptotics.isBigOTVS_fun_comm, mdifferentiableWithinAt_comp_projIcc_iff, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Orientation.inner_sq_add_areaForm_sq, Real.enorm_exp_I_mul_ofReal_sub_one_le, signedDist_smul_of_neg, MeasureTheory.lpNorm_const_smul, differentiableOn_euclidean, RCLike.reLm_coe, nnnorm_fderiv_norm_rpow_le, differentiableAt_abs_pos, ContinuousLinearMap.adjoint_toSpanSingleton, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, ContinuousLinearMap.toBilinForm_injective, integrableOn_exp_neg_Ioi, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, toSpanSingleton_derivWithin, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, RCLike.nnnorm_conj, SchwartzMap.integral_fourier_mul_eq, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, range_mfderiv_coe_sphere, MeasureTheory.integrable_prod_iff', RCLike.wInner_one_const_right, hahnEmbedding_isOrderedModule_rat, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Affine.Simplex.sign_signedInfDist_touchpoint_empty, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, signedDist_vadd_right_swap, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, Real.differentiable_mulExpNegMulSq, ContinuousMap.neg_norm_le_apply, AddCircle.coe_real_preimage_closedBall_period_zero, integrable_of_isBigO_exp_neg, nnnorm_algebraMap', Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, Complex.conjCLE_apply, NormedSpace.polar_ball, Valued.integer.exists_nnnorm_lt_one, Real.not_DifferentiableAt_log_mul_zero, innerSLFlip_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, iccLeftChart_extend_zero, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, hasDerivAt_const_mul, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, Euclidean.ball_eq_preimage, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, norm_iteratedFDeriv_prod_le, SchwartzMap.lineDerivOp_fourierInv_eq, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, HasFDerivWithinAt.const_cpow, IsLocalFrameOn.eq_iff_coeff, Polynomial.hasDerivAt, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, OrthonormalBasis.repr_symm_single, MeasureTheory.hasFiniteIntegral_toReal_iff, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, interior_range_modelWithCornersEuclideanHalfSpace, WeakDual.CharacterSpace.norm_le_norm_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, AddCircle.addWellApproximable_ae_empty_or_univ, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.hasStrictDerivAt_cos, IntervalIntegrable.intervalIntegrable_slope, iter_deriv_inv, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, integrableOn_Ioi_cpow_of_lt, Differentiable.dist, EulerSine.antideriv_cos_comp_const_mul, ProbabilityTheory.condVar_of_sigmaFinite, RightDerivMeasurableAux.differentiable_set_eq_D, hasDerivWithinAt_zpow, mellin_convergent_iff_norm, Monotone.deriv_nonneg, Orientation.kahler_mul, innerSL_real_flip, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, RCLike.nnnorm_two, ProbabilityTheory.iteratedDeriv_two_cgf, measurableSet_of_differentiableWithinAt_Ioi, TensorProduct.norm_lid, Real.differentiable_iteratedDeriv_sin, ProbabilityTheory.deriv_mgf_zero, MeasureTheory.charFun_eq_charFunDual_toDualMap, HasMFDerivAt.prod, fderivWithin_csin, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sigmoid, ProperCone.dual_dual_flip, flip_innerβ, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, MeasureTheory.LocallyIntegrableOn.norm, HasStrictFDerivAt.isBigOTVS_sub, Orientation.volumeForm_robust', instSMulCommClass_sphere_ball_ball, PiLp.basis_toMatrix_basisFun_mul, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, EulerSine.antideriv_sin_comp_const_mul, signedDist_vadd_left, Diffeology.IsPlot.contDiff, ModularGroup.tendsto_lcRow0, ProbabilityTheory.integrable_kernel_prodMk_left, NormedSpace.sInter_polar_eq_closedBall, ProbabilityTheory.deriv_cgf, Complex.imCLM_coe, isBoundedBilinearMap_inner, intervalIntegral.integral_hasFDerivWithinAt, deriv_pow_field, SmoothBumpCovering.embeddingPiTangent_injective, ProbabilityTheory.memLp_tilted_mul, HasFPowerSeriesAt.hasDerivAt, Int.nnnorm_coe_units, ProbabilityTheory.covarianceBilin_apply, ContinuousLinearMap.isThetaTVS_comp, Polynomial.hasDerivAt_aeval, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivAt_gronwallBound, ContinuousMap.comp_attachBound_mem_closure, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, hasDerivAt_ofReal_cpow_const, hasDerivAt_norm_rpow, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, NumberField.mixedEmbedding.latticeBasis_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, TemperedDistribution.fourierInv_apply, cfcβAux_mem_range_inr, Ideal.Quotient.norm_mk_lt, ContinuousMap.adjoin_id_eq_span_one_add, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, ProbabilityTheory.covarianceBilin_map, Unitization.nnnorm_eq_sup, AffineSubspace.signedInfDist_singleton, norm_deriv_eq_norm_fderiv, ContinuousMap.apply_le_norm, MeasureTheory.AEStronglyMeasurable.integrable_truncation, AkraBazziRecurrence.differentiableAt_smoothingFn, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, hasSum_fourier_series_of_summable, Real.deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, integrableOn_Ioi_exp_neg_mul_sq_iff, Orientation.volumeForm_zero_neg, BoundedContinuousFunction.nnnorm_coeFn_eq, Real.differentiableAt_binEntropy, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, Real.hasDerivAt_arctan', Orientation.areaForm_map, Real.enorm_rpow_of_nonneg, Asymptotics.isEquivalent_iff_tendsto_one, differentiable_neg, hasDerivAt_neg, ProbabilityTheory.integrable_of_mem_interior_integrableExpSet, deriv_bernoulliFun, NNReal.nnnorm_eq, det_fderivPiPolarCoordSymm, Polynomial.hasStrictDerivAt, Real.deriv2_qaryEntropy, Real.differentiableAt_exp, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.commMap_apply_of_isReal, ZSpan.fundamentalDomain_pi_basisFun, AffineMap.hasStrictDerivAt, LipschitzWith.ae_differentiableAt_of_real, InnerProductSpace.toLinearMap_rankOne, Seminorm.finset_sup_smul, MeasureTheory.Measure.integrable_comp_iff, HasMFDerivWithinAt.mul, Bundle.RiemannianMetric.pos, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, HilbertBasis.repr_self, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, BoundedContinuousFunction.add_norm_nonneg, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, Complex.equivRealProdCLM_symm_apply_re, HasFDerivAtFilter.isLittleOTVS, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, MeasureTheory.L2.integrable_inner, MeasureTheory.hasFiniteIntegral_prod_iff, nnnorm_cfcβ_le_iff, MeasureTheory.charFun_map_mul, fderiv_ccosh, HasStrictFDerivAt.cpow, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, BoundedContinuousFunction.norm_sub_nonneg, NumberField.mixedEmbedding.latticeBasis_repr_apply, Filter.HasBasis.isBigOTVS_iff, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, DifferentiableWithinAt.norm_sq, ContinuousMapZero.instCStarRing, SchwartzMap.integral_fourierInv_mul_eq, hasFDerivWithinAt_iff_hasGradientWithinAt, Real.fourierIntegral_continuousLinearMap_apply', signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, Real.differentiable_fourierChar, VectorFourier.fourierPowSMulRight_apply, mul_comm, Matrix.linfty_opNorm_eq_opNorm, nnnorm_cfc_lt_iff, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, Real.deriv_cos', isBigO_deriv_rpow_const_atTop, hasDerivAt_pow, contDiff_succ_iff_deriv, DifferentiableOn.dist, Real.deriv_rpow_const', NumberField.mixedEmbedding.normAtPlace_negAt, Orthonormal.orthogonalFamily, Real.differentiableAt_arcosh, IsLocalMaxOn.fderivWithin_eq_zero, AlternatingMap.measure_def, MeasureTheory.Integrable.of_mem_Icc, LinearMap.isSymmetric_iff_sesqForm, hasDerivWithinAt_derivWithin_iff, hasStrictDerivAt_exp, Complex.isometryOfOrthonormal_apply, Complex.sameRay_iff, AddCircle.norm_le_half_period, Real.hasStrictDerivAt_sqrt, Polynomial.deriv, Int.nnnorm_natCast, Real.hasDerivAt_tan_of_mem_Ioo, contMDiffOn_comp_projIcc_iff, NumberField.mixedEmbedding.finrank, SchwartzMap.integral_fourier_smul_eq, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, Polynomial.hasFDerivWithinAt_aeval, Orientation.inner_rightAngleRotation_right, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, ProbabilityTheory.HasSubgaussianMGF.memLp, LinearMap.continuous_of_isClosed_ker, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Orientation.volumeForm_apply_le, differentiableAt_iff_comp_add_const, RCLike.nnnorm_nnqsmul, ProbabilityTheory.Kernel.eLpNorm_density_le, NumberField.mixedEmbedding.negAt_apply_norm_isReal, innerββ_apply, HasFDerivWithinAt.isBigOTVS_sub, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, hasStrictFDerivAt_list_prod, UnitAddCircle.mem_addWellApproximable_iff, div_le_egauge_ball, StrongDual.toLp_apply, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, contDiff_infty_iff_deriv, LinearMap.toSeminorm_ball_zero, Complex.nnnorm_intCast, Real.differentiableAt_negMulLog, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Orientation.inner_rightAngleRotationAuxβ_left, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasDerivAt.inner, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', Orientation.areaForm_apply_self, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Real.differentiable_fourierChar_neg_bilinear_right, Complex.conjCLE_norm, ProbabilityTheory.variance_linearMap_gaussianReal, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, MeasureTheory.SignedMeasure.integrable_rnDeriv, AffineSubspace.signedInfDist_def, isScalarTower_sphere_ball_ball, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, MeasureTheory.BoundedContinuousFunction.inner_toLp, exists_extension_norm_eq, ProbabilityTheory.integrable_exp_mul_of_le, hasStrictDerivAt_exp_zero_of_radius_pos, NormedSpace.closedBall_inv_subset_polar_closedBall, MeasureTheory.convolution_mul_swap, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, ContinuousLinearMap.norm_smulRightL_le, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, Complex.imCLM_enorm, SchwartzMap.tsupport_derivCLM_subset, hasDerivAt_single, OrthonormalBasis.coe_toBasis_repr_apply, det_rotation, RCLike.enorm_conj, PadicInt.norm_mahler_eq, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, hasStrictDerivAt_exp_of_mem_ball, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, AlternatingMap.measure_parallelepiped, norm_cfcHom, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Affine.Simplex.signedInfDist_affineCombination, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, WeakDual.CharacterSpace.equivAlgHom_coe, AddCircle.norm_eq, le_egauge_ball_one, not_integrableOn_Ici_inv, Matrix.l2_opNNNorm_diagonal, Int.toNat_add_toNat_neg_eq_nnnorm, spectrum.exists_nnnorm_eq_spectralRadius, HasFDerivAt.hasGradientAt, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Real.differentiableAt_sinh, ContinuousLinearMap.isBigOTVS_fun_comp, NormedField.denselyOrdered_range_nnnorm, signedDist_eq_dist_iff_vsub_mem_span, Real.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, exp_neg_integrableOn_Ioi, MeasureTheory.Integrable.const_inner, rotation_symm, IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, VectorFourier.norm_fourierPowSMulRight_le, Complex.equivRealProdCLM_symm_apply_im, AddChar.linearIndependent, integrable_exp_neg_mul_sq_iff, nndist_homothety_center, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Antitone.deriv_nonpos, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, differentiable_tsum', VectorFourier.norm_fourierSMulRight, Polynomial.differentiable, ContinuousLinearEquiv.coord_norm', GaussianFourier.integrable_cexp_neg_sum_mul_add, ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, differentiableOn_abs, ProbabilityTheory.hasDerivAt_mgf, HasFPowerSeriesAt.eq_zero_of_eventually, div_le_egauge_closedBall, LinearMap.mem_span_iff_bound, ProbabilityTheory.integrable_toReal_condDistrib, hasFDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_mul_const, SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, Probability.integrable_cauchyPDFReal, MeasureTheory.integrable_toReal_iff, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, SchwartzMap.fourier_fderivCLM_eq, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, hasStrictFDerivAt_exp_smul_const, integrableOn_rpow_mul_exp_neg_mul_sq, Complex.hasStrictFDerivAt_log_real, Asymptotics.isBigOTVS_map, Real.hasStrictDerivAt_tan, RCLike.wInner_cWeight_const_right, SimpleGraph.isEquivalent_extremalNumber, Real.nnnorm_rpow_of_nonneg, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, iter_deriv_inv_linear, ProbabilityTheory.deriv_cgf_zero, AffineMap.differentiable, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, DifferentiableAt.norm, Real.differentiable_fourierChar_neg_bilinear_left, fderiv_norm_smul_pos, MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore, Real.hasDerivAt_arctan, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Finset.nnnorm_prod_le, WeakDual.CharacterSpace.compContinuousMap_comp, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, EuclideanSpace.nnnorm_eq, innerββ_apply_coe, RCLike.nnnorm_natCast, fderiv_csinh, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, range_modelWithCornersEuclideanHalfSpace, ContinuousMapZero.toNNReal_neg_smul, AddChar.wInner_cWeight_eq_boole, differentiableAt_of_deriv_ne_zero, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, TemperedDistribution.fourier_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, IsLocalMin.fderiv_eq_zero, Real.differentiableAt_qaryEntropy, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Submodule.orthogonal_eq_inter, ContinuousLinearMap.lsmul_flip_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, norm_iteratedFDeriv_smul_le, integrable_exp_neg_mul_sq, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, LinearPMap.mem_adjoint_domain_iff, differentiableWithinAt_zpow, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, CircleIntegrable.out, nnnorm_prod, AddCircle.closedBall_ae_eq_ball, contDiffOn_infty_iff_deriv_of_isOpen, SchwartzMap.integrable_pow_mul, MeasureTheory.memLp_of_bounded, ContinuousMultilinearMap.norm_smulRight, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearMap.hasDerivWithinAt, hasStrictFDerivAt_pow, NormedSpace.polar_closedBall, ContinuousMapZero.toNNReal_smul, integrable_mulExpNegMulSq_comp, integrable_cexp_quadratic, AffineSubspace.signedInfDist_apply_self, coe_innerββ_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, ModularGroup.lcRow0_apply, hasDerivAt_exp_zero, deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, MeasureTheory.integrable_withDensity_iff, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PeriodPair.indep, Module.Basis.opNorm_le, ContMDiff.codRestrict_sphere, Real.differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, SchwartzMap.smulLeftCLM_apply, MeasureTheory.Integrable.norm, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, fderiv_csin, AddCircle.norm_eq', WeakDual.isSeqCompact_polar, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.intervalIntegrable_charFun, ProbabilityTheory.integrable_rpow_of_mem_interior_integrableExpSet, hasFDerivWithinAt_pow, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, NormedField.valuation_apply, hasDerivWithinAt_inv, Asymptotics.isBigOTVS_prodMk_left, hasStrictDerivAt_id, instNonemptySeedRatReal, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, deriv_neg, abs_signedDist_le_dist, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, HasFDerivAt.cpow, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, LinearMap.hasDerivAtFilter, intervalIntegral.integral_hasFDerivAt, MeasureTheory.memLp_norm_iff, integrable_mul_cexp_neg_mul_sq, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.GammaIntegral_convergent, MeasureTheory.hausdorffMeasure_homothety_preimage, HasFPowerSeriesAt.locally_zero_iff, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, AffineSubspace.signedInfDist_apply_of_mem, hasDerivAt_exp_of_mem_ball, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, differentiableAt_abs, ConvexOn.real_sSup_of_nat_affine_eq, ProbabilityTheory.IsRatCondKernelCDF.integrable, Ideal.Quotient.norm_mk_le, ProbabilityTheory.charFun_gaussianReal, WeakDual.CharacterSpace.exists_apply_eq_zero, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, DifferentiableOn.norm, Complex.map_isometryOfOrthonormal, hasDerivAt_zpow, TemperedDistribution.fourierTransformInv_apply, WeakDual.CharacterSpace.compContinuousMap_id, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, MeasureTheory.MemLp.integrable_norm_pow', Matrix.l2_opNorm_def, signedDist_apply_linear, Real.differentiableAt_sin, RCLike.wInner_nonneg, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, parallelepiped_orthonormalBasis_one_dim, Complex.reCLM_enorm, MeasureTheory.integrable_mconv_iff, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, Polynomial.toAddCircle_C_eq_smul_fourier_zero, norm_innerSL_le, MeasureTheory.eLpNorm'_norm_rpow, VectorFourier.hasFDerivAt_fourierChar_smul, integrable_cexp_quadratic', Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, HasStrictFDerivAt.csinh, InformationTheory.not_differentiableAt_klFun_zero, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, Real.exists_extension_norm_eq, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sin, AffineMap.deriv, SmoothBumpCovering.embeddingPiTangent_coe, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ProbabilityTheory.covarianceBilinDual_of_not_memLp', PadicComplex.nnnorm_extends, SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', UnitAddTorus.span_mFourierLp_closure_eq_top, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, MeasureTheory.Integrable.integral_norm_condKernel, Complex.nnnorm_eq_one_of_pow_eq_one, ProbabilityTheory.integrable_gaussianPDFReal, Asymptotics.IsBigOTVS.refl, expNegInvGlue.differentiable_polynomial_eval_inv_mul, cfcHom_eq_of_isStarNormal, HasGradientWithinAt.hasFDerivWithinAt, hasFDerivAt_exp, Orientation.volumeForm_comp_linearIsometryEquiv, Pi.orthonormalBasis_repr, Polynomial.hasDerivWithinAt, differentiableAt_iff_comp_sub_const, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, NumberField.Units.basisOfIsMaxRank_fundSystem, LinearMap.isAdjointPair_inner, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, AnalyticOnNhd.eval_mvPolynomial, WithLp.unitization_nnnorm_def, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Affine.Simplex.signedInfDist_apply_of_ne, ContinuousLinearMap.hasStrictDerivAt, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, signedDist_left_lineMap, hasFDerivAt_inv, Real.deriv_mul_log_zero, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, IccRightChart_extend_top, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Asymptotics.IsBigO.isBigOTVS, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, measurableSet_of_differentiableWithinAt_Ici, fderivInnerCLM_apply, ConvexOn.sSup_affine_eq, nndist_self_homothety, boundary_Icc, deriv_sqrt_mul_log', Asymptotics.isLittleOTVS_sup, Real.differentiableAt_binEntropy_iff_ne_zero_one, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, SchwartzMap.integrable_pow_mul_iteratedFDeriv, Real.fderiv_fourierChar_neg_bilinear_left_apply, Real.deriv_tan, isConformalMap_iff_is_complex_or_conj_linear, Asymptotics.isEquivalent_of_tendsto_one', RCLike.span_one_I, Asymptotics.isThetaTVS_iff_isTheta, Real.exists_measure_rpow_eq_integral, Real.fourierIntegral_continuousMultilinearMap_apply', HasGradientAtFilter.hasDerivAtFilter, AddCircle.norm_eq_of_zero, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, MeasureTheory.eLpNorm_conj, ProbabilityTheory.integrable_comp_iff, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, integrable_cexp_neg_mul_sq, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, differentiableAt_comp_sub_const, finrank_euclideanSpace_fin, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, le_egauge_closedBall_one, InformationTheory.deriv_klFun, boundary_product, differentiable_sigmoid, LinearMap.mem_span_iff_continuous, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, NormedField.exists_lt_nnnorm, Asymptotics.isBigOTVS_comm, OrthonormalBasis.repr_reindex, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, AnalyticOnNhd.eval_continuousLinearMap, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, Asymptotics.isLittleOTVS_pi, ProbabilityTheory.integral_tilted_mul_self, integrableOn_Ioi_deriv_norm_ofReal_cpow, integrable_of_le_of_pow_mul_le, nndist_homothety_self, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, Complex.det_conjLIE, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, RCLike.realLinearIsometryEquiv_apply, ProbabilityTheory.mgf_pos_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, ContinuousLinearMap.norm_smulRightL_apply, Asymptotics.IsThetaTVS.rfl, Orientation.areaForm_rightAngleRotation_left, Differentiable.norm, SchwartzMap.smulLeftCLM_smul, differentiableAt_iff_comp_neg, NumberField.mixedEmbedding.disjoint_negAt_plusPart, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, DifferentiableAt.dist, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, ConvexOn.univ_sSup_of_nat_affine_eq, Icc_isBoundaryPoint_top, ConvexOn.slope_le_leftDeriv_of_mem_interior, NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, NumberField.house_eq_sup', fderiv_norm_sq, Seminorm.smul_le_smul, WeakDual.CharacterSpace.instStarHomClass, Int.Matrix.exists_ne_zero_int_vec_norm_le, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', Real.integrableOn_rpowIntegrandββ_Ici, ModularGroup.smul_eq_lcRow0_add, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, hasDerivAt_abs_pos, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', differentiableWithinAt_Ioi_iff_Ici, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, HasCompactSupport.hasFDerivAt_convolution_left, Complex.isEquivalent_sin, differentiableOn_zpow, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, MeasureTheory.integrable_rnDeriv_mul_log_iff, TemperedDistribution.smulLeftCLM_apply_apply, integrableAtFilter_rpow_atTop_iff, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, nndist_lineMap_left, Orientation.inner_mul_areaForm_sub, fderiv_inner_apply, contDiff_one_iff_deriv, deriv2_sqrt_mul_log, Real.hasStrictDerivAt_log_of_pos, contMDiffOn_projIcc, MeasureTheory.SignedMeasure.im_toComplexMeasure, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, MeasureTheory.pdf.hasFiniteIntegral_mul, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, parallelepiped_single, contMDiff_circleExp, Quaternion.nnnorm_coe, Real.deriv2_negMulLog, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Urysohns.CU.lim_eq_midpoint, MeasureTheory.Measure.integrable_pow_neg_integrablePower, HasFDerivAt.const_cpow, norm_jacobiThetaβ_term_fderiv_le, fderiv_eq_smul_deriv, integrableOn_rpow_mul_exp_neg_mul_rpow, MeasureTheory.Measure.integrable_toReal_rnDeriv, Real.isEquivalent_sinh, Int.Matrix.exists_ne_zero_int_vec_norm_le', intervalIntegral.differentiableOn_integral_of_continuous, hasStrictFDerivAt_exp_smul_const_of_mem_ball, differentiable_circleMap, integrableOn_exp_mul_complex_Ioi, NormedSpace.exp_add, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Complex.restrictScalars_toSpanSingleton', Real.differentiableAt_negMulLog_iff, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, BoundedContinuousFunction.integrable_of_nnreal, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, IsLocalMinOn.fderivWithin_eq_zero, Real.deriv2_mul_log, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, Orientation.abs_volumeForm_apply_le, Complex.conjLIE_symm, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding', deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, Affine.Simplex.signedInfDist_incenter, ProbabilityTheory.integrable_rpow_mul_exp_of_mem_interior_integrableExpSet
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| Name | Category | Theorems |
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induced π | CompOp | β |
toNonUnitalRing π | CompOp | 59 mathmath: ContinuousLinearMap.mulLeftRight_isBoundedBilinear, Unitization.splitMul_apply, BoundedContinuousFunction.instSMulCommClass_1, mulRight_bound, Metric.unitBall.instContinuousMul, BoundedContinuousFunction.instSMulCommClass_2, ContinuousLinearMap.opNorm_mul, Matrix.linfty_opNNNorm_mulVec, PositiveLinearMap.leftMulMapPreGNS_apply, ContinuousLinearMap.mulLeftRight_apply, nnnorm_mul_le, norm_mul_le, RegularNormedAlgebra.isometry_mul', nnnorm_mulβ_le, hasFDerivAt_ringInverse, ContinuousLinearMap.opNorm_mul_apply, fderiv_inverse, fderivWithin_inv', norm_mulβ_le, instBoundedMul, dist_eq, Metric.unitClosedBall.coe_mul, BoundedContinuousFunction.instIsScalarTower_1, NonUnitalAlgHom.coe_Lmul, Unitization.norm_eq_sup, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, Metric.unitBall.instIsLeftCancelMulZero, toIsTopologicalRing, ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.isometry_mul, isBoundedSMul, hasStrictFDerivAt_ringInverse, ContinuousLinearMap.mul_apply', isBoundedSMulOpposite, Matrix.linfty_opNorm_mulVec, ContinuousLinearMap.opNNNorm_mul, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, Matrix.linfty_opNNNorm_mul, toContinuousMul, Matrix.linfty_opNorm_mul, ContinuousLinearMap.opNorm_mul_apply_le, Metric.unitBall.coe_mul, Unitization.nnnorm_eq_sup, Metric.unitBall.instIsRightCancelMulZero, DoubleCentralizer.coe_fst, NonUnitalSeminormedCommRing.mul_comm, hasStrictFDerivAt_inv', Metric.unitClosedBall.instContinuousMul, norm_mul_le, ContinuousLinearMap.opNorm_mulLeftRight_le, Metric.unitBall.instIsCancelMulZero, hasFDerivAt_inv', nnnorm_mul_le_of_le, SeminormedRing.toRingSeminorm_apply, norm_mul_le_of_le, ContinuousLinearMap.opNNNorm_mul_apply, mulLeft_bound, ContinuousLinearMap.coe_mulβα΅’, fderiv_inv'
|
toNorm π | CompOp | 12 mathmath: mulRight_bound, norm_mul_le, ContinuousLinearMap.opNorm_mul_apply, norm_mulβ_le, dist_eq, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, Matrix.linfty_opNorm_mulVec, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, Matrix.linfty_opNormOneClass, ContinuousLinearMap.opNorm_mul_apply_le, norm_mul_le, mulLeft_bound
|
toPseudoMetricSpace π | CompOp | 244 mathmath: CStarAlgebra.preimage_inr_Icc_zero_one, integrableOn_cfcβ', cfcβL_integral, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcβHom, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, DoubleCentralizer.star_snd, CFC.monotoneOn_one_sub_one_add_inv, nnnorm_cfcβ_nnreal_le_iff, CFC.monotone_nnrpow, DoubleCentralizer.intCast_snd, DoubleCentralizer.range_toProdMulOpposite, Unitization.real_cfcβ_eq_cfc_inr, DoubleCentralizer.natCast_fst, isClosedEmbedding_cfcβAux, Unitization.splitMul_apply, DoubleCentralizer.nnnorm_def', nnnorm_cfcβ_lt_iff, DoubleCentralizer.zero_snd, CFC.nnnorm_sqrt, IsGreatest.nnnorm_cfcβ, BoundedContinuousFunction.instSMulCommClass_1, CStarModule.innerSL_apply, CStarAlgebra.span_nonneg_inter_unitBall, Metric.unitBall.instContinuousMul, DoubleCentralizer.pow_snd, RCLike.nonUnitalContinuousFunctionalCalculus, cfcβ_integral, DoubleCentralizer.nnnorm_snd, CStarAlgebra.tendsto_mul_left_iff_tendsto_mul_right, compactlySupported_eq_top_of_isCompact, cfcβ_setIntegral, CStarMatrix.toCLM_injective, BoundedContinuousFunction.instSMulCommClass_2, ContinuousLinearMap.opNorm_mul, DoubleCentralizer.smul_toProd, DoubleCentralizer.toProdMulOpposite_injective, DoubleCentralizer.norm_fst_eq_snd, Unitization.nnnorm_def, Unitization.dist_inr, DoubleCentralizer.norm_def', CStarMatrix.norm_def', WithLp.unitization_algebraMap, CStarMatrix.inner_toCLM_conjTranspose_left, CFC.continuousOn_sqrt, DoubleCentralizer.norm_def, PositiveLinearMap.preGNS_norm_def, PositiveLinearMap.leftMulMapPreGNS_apply, ContinuousLinearMap.mulLeftRight_apply, RegularNormedAlgebra.isometry_mul', DoubleCentralizer.central, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, CompletelyPositiveMap.instLinearMapClassComplex, hasFDerivAt_ringInverse, norm_cfcβ_lt, Filter.IsIncreasingApproximateUnit.toIsApproximateUnit, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, IsGreatest.norm_cfcβ, DoubleCentralizer.nnnorm_def, nnnorm_cfcβ_nnreal_lt, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, cfcβHom_integral, ContinuousLinearMap.opNorm_mul_apply, continuousOn_cfcβ, DoubleCentralizer.neg_snd, Unitization.cobounded_eq_aux, CStarAlgebra.instOrderClosedTopology, fderiv_inverse, DoubleCentralizer.range_toProd, PositiveLinearMap.preGNS_inner_def, fderivWithin_inv', DoubleCentralizer.add_fst, instBoundedMul, cfcβAux_id, dist_eq, compactlySupported_eq_top, CStarAlgebra.norm_posPart_le, IsGreatest.nnnorm_cfcβ_nnreal, CStarAlgebra.span_nonneg_inter_unitClosedBall, CFC.continuous_abs, DoubleCentralizer.smul_fst, coe_ringEquiv_lpBCF, nnnorm_apply_le_nnnorm_cfcβ, Metric.unitClosedBall.coe_mul, BoundedContinuousFunction.instIsScalarTower_1, integrable_cfcβ, PositiveLinearMap.toPreGNS_ofPreGNS, NonUnitalAlgHom.coe_Lmul, PositiveLinearMap.exists_norm_apply_le, DoubleCentralizer.star_fst, norm_cfcβ_lt_iff, compactlySupported_eq_top_iff, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, DoubleCentralizer.add_snd, DoubleCentralizer.norm_snd, DoubleCentralizer.nnnorm_fst, CStarMatrix.toCLM_apply_single, Unitization.norm_eq_sup, CStarMatrix.toCLM_apply_eq_sum, WithCStarModule.pi_norm, inr_comp_cfcβHom_eq_cfcβAux, CFC.monotoneOn_one_sub_one_add_inv_real, DoubleCentralizer.neg_toProd, CStarMatrix.ofMatrix_eq_ofMatrixL, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, DoubleCentralizer.algebraMap_snd, DoubleCentralizer.one_snd, upperHemicontinuous_quasispectrum, Metric.unitBall.instIsLeftCancelMulZero, CStarMatrix.toCLM_apply, DoubleCentralizer.algebraMap_toProd, toIsTopologicalRing, DoubleCentralizer.instIsCentralScalar, mem_compactlySupported, nnnorm_cfcβ_nnreal_lt_iff, PositiveLinearMap.gnsStarAlgHom_apply, DoubleCentralizer.pow_toProd, WithCStarModule.pi_inner, ContinuousMap.instCStarRing, DoubleCentralizer.zero_fst, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, CStarMatrix.mul_entry_mul_eq_inner_toCLM, ContinuousLinearMap.opNorm_mul_le, BoundedContinuousFunction.instCStarRing, ZeroAtInftyContinuousMap.instCStarRing, ContinuousLinearMap.isometry_mul, DoubleCentralizer.sub_toProd, DoubleCentralizer.nnnorm_fst_eq_snd, Unitization.norm_def, DoubleCentralizer.one_fst, DoubleCentralizer.coeHom_apply, integrableOn_cfcβ, norm_cfcβ_le, spec_cfcβAux, integrable_cfcβ', DoubleCentralizer.sub_fst, Unitization.nnreal_cfcβ_eq_cfc_inr, isBoundedSMul, hasStrictFDerivAt_ringInverse, ContinuousLinearMap.mul_apply', isBoundedSMulOpposite, DoubleCentralizer.pow_fst, upperHemicontinuous_quasispectrum_nnreal, CStarAlgebra.conjugate_le_norm_smul', nnnorm_cfcβHom, ContinuousLinearMap.opNNNorm_mul, CFC.nnrpow_le_nnrpow, DoubleCentralizer.algebraMap_fst, CStarAlgebra.span_nonneg_inter_closedBall, CStarAlgebra.isClosed_nonneg, CStarAlgebra.star_left_conjugate_le_norm_smul, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, toContinuousMul, DoubleCentralizer.mul_fst, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, PositiveLinearMap.ofPreGNS_toPreGNS, ContinuousLinearMap.opNorm_mul_apply_le, CStarMatrix.normedSpaceCore, Metric.unitBall.coe_mul, CFC.norm_abs, Unitization.isUniformEmbedding_addEquiv, cfcβAux_mem_range_inr, Unitization.nnnorm_eq_sup, DoubleCentralizer.zero_toProd, CStarModule.inner_mul_inner_swap_le, Metric.unitBall.instIsRightCancelMulZero, CFC.monotone_sqrt, CStarAlgebra.conjugate_le_norm_smul, DoubleCentralizer.norm_fst, nnnorm_cfcβ_le_iff, DoubleCentralizer.coe_fst, norm_cfcβ_one_sub_one_add_inv_lt_one, continuousOn_cfcβ_nnreal, CStarAlgebra.directedOn_nonneg_ball, continuousOn_cfcβ_setProd, Unitization.complex_cfcβ_eq_cfc_inr, Filter.comap_mul_left_cobounded, CStarAlgebra.norm_negPart_le, Unitization.nndist_inr, CFC.sqrt_le_sqrt, DoubleCentralizer.natCast_toProd, CStarModule.continuous_inner, DoubleCentralizer.one_toProd, Unitization.norm_splitMul_snd_sq, DoubleCentralizer.natCast_snd, CompletelyPositiveMap.map_cstarMatrix_nonneg', CStarMatrix.uniformEmbedding_ofMatrix, coe_ringEquiv_lpBCF_symm, Unitization.splitMul_injective, DoubleCentralizer.sub_snd, WithCStarModule.pi_norm_sq, cfcβ_setIntegral', hasStrictFDerivAt_inv', CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, Metric.unitClosedBall.instContinuousMul, WithLp.unitization_mul, DoubleCentralizer.instStarModule, CStarAlgebra.star_right_conjugate_le_norm_smul, norm_apply_le_norm_cfcβ, ContinuousLinearMap.opNorm_mulLeftRight_le, DoubleCentralizer.intCast_fst, Filter.comap_mul_right_cobounded, Metric.unitBall.instIsCancelMulZero, CStarAlgebra.span_nonneg_inter_ball, ContinuousMapZero.elemental_eq_top, Unitization.uniformity_eq_aux, CFC.monotoneOn_cfcβ_rpowIntegrandββ, cfcβL_integrable, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, hasFDerivAt_inv', CStarAlgebra.hasBasis_approximateUnit, nnnorm_cfcβ_le, nnnorm_cfcβ_nnreal_le, apply_le_nnnorm_cfcβ_nnreal, continuousOn_cfcβ_nnreal_setProd, CFC.norm_sqrt, DoubleCentralizer.toProdHom_apply, DoubleCentralizer.mul_snd, MonotoneOn.nnnorm_cfcβ, ContinuousLinearMap.opNNNorm_mul_apply, CFC.nnnorm_nnrpow, DoubleCentralizer.intCast_toProd, norm_cfcβ_le_iff, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, CFC.norm_nnrpow, DoubleCentralizer.smul_snd, CStarAlgebra.exists_sum_four_nonneg, DoubleCentralizer.coe_snd, PositiveLinearMap.preGNS_norm_sq, ContinuousLinearMap.coe_mulβα΅’, CStarMatrix.norm_def, Unitization.continuous_inr, DoubleCentralizer.add_toProd, CFC.abs_eq_zero_iff, DoubleCentralizer.neg_fst, CStarMatrix.inner_toCLM_conjTranspose_right, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, CStarMatrix.toCLM_apply_single_apply, DoubleCentralizer.toProdMulOppositeHom_apply, Unitization.cfcβ_eq_cfc_inr, fderiv_inv', cfcβ_integral', nnnorm_cfcβ_lt
|
toSeminormedAddCommGroup π | CompOp | 2560 mathmath: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, hasFDerivAt_iff_hasDerivAt, iteratedDeriv_scomp_two, Real.differentiableOn_arcosh, isEquivalent_descFactorial, Real.hasDerivAt_arccos, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, BoundedContinuousFunction.tietze_extension_step, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, InformationTheory.integrable_klFun_rnDeriv_iff, Polynomial.differentiableWithinAt, nnnorm_inv, MeasureTheory.Integrable.integral_norm_prod_right, Seminorm.isBounded_const, isConformalMap_conj, MeasureTheory.eLpNorm'_norm, MeasureTheory.eLpNormEssSup_const_smul_le, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, HasStrictFDerivAt.isLittleOTVS, Bundle.ContMDiffRiemannianMetric.isVonNBounded, NormedSpace.isBounded_polar_of_mem_nhds_zero, TensorProduct.enorm_lid, differentiableAt_comp_neg, Real.integrableOn_rpowIntegrandββ_Ioi, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, Matrix.frobenius_nnnorm_mul, HasMFDerivAt.mul, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, MonotoneOn.intervalIntegral_slope_le, RingHom.compLeftContinuousBounded_apply_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, Real.differentiable_arctan, norm_cfcβHom, List.nnnorm_prod, RCLike.map_apply, Real.differentiableAt_mulExpNegMulSq, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, Complex.restrictScalars_one_smulRight', IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, IsStarNormal.spectralRadius_eq_nnnorm, DoubleCentralizer.star_snd, HasFDerivWithinAt.ccos, InnerProductSpace.toLinearIsometry_toDual, RCLike.ofRealCLM_apply, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, Real.hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, Complex.linearEquiv_det_conjLIE, Ideal.toCharacterSpace_apply_eq_zero_of_mem, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, hasFDerivAt_iff_hasGradientAt, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, MeasureTheory.eLpNormEssSup_const_smul, RCLike.reCLM_apply, NumberField.Units.finrank_eq_rank, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, CFC.monotoneOn_one_sub_one_add_inv, hasStrictFDerivAt_list_prod_finRange', InnerProductSpace.rankOne_one_left_eq_innerSL, ConvexOn.rightDeriv_le_slope_of_mem_interior, NonUnitalCStarAlgebra.toStarModule, hasDerivAt_sqrt_mul_log, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, HasStrictFDerivAt.csin, Polynomial.isEquivalent_atBot_div, ZSpan.volume_real_fundamentalDomain, ContinuousLinearMap.opNorm_bound_of_ball_bound, Complex.ofRealCLM_coe, Complex.kahler, RightDerivMeasurableAux.D_subset_differentiable_set, Complex.areaForm, WeakDual.isCompact_polar, finrank_real_complex_fact', EuclideanSpace.orthonormal_single, Real.deriv_negMulLog, Real.hasDerivAt_sigmoid, AffineMap.hasDerivAtFilter, PositiveLinearMap.apply_le_of_isSelfAdjoint, Matrix.IsHermitian.det_abs, RCLike.ofRealLI_apply, deriv_abs, differentiableAt_zpow, hasFDerivAt_multiset_prod, Stirling.factorial_isEquivalent_stirling, ProbabilityTheory.covarianceBilinDual_apply', BoundedContinuousFunction.algebraMap_apply, Real.nnnorm_deriv_mulExpNegMulSq_le_one, OrthonormalBasis.repr_injective, Real.deriv_binEntropy, CFC.monotone_nnrpow, Complex.ofRealLI_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, deriv_mem_iff, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, integrableOn_exp_mul_Iic, ProbabilityTheory.IsGaussian.integrable_dual, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, norm_iteratedFDerivWithin_smul_le, Matrix.cstar_nnnorm_def, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, egauge_prod_mk, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Real.hasStrictDerivAt_rpow_const_of_ne, StrongDual.polarSubmodule_eq_setOf, ContinuousMap.attachBound_apply_coe, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, ContinuousLinearMap.hasDerivAtFilter, fderivWithin_csinh, DoubleCentralizer.intCast_snd, span_fourier_closure_eq_top, PeriodPair.basis_one, DoubleCentralizer.range_toProdMulOpposite, RCLike.conjCLE_norm, HasDerivWithinAt.complexToReal_fderiv', Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, ContDiffBump.integrable, WeakDual.isClosed_image_polar_of_mem_nhds, ZLattice.covolume_eq_det_inv, ContinuousLinearMap.integral_apply, Unitary.mem_pathComponentOne_iff, circleIntegrable_iff, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', MeasureTheory.MemLp.const_inner, not_integrableOn_Ioi_cpow, MeasureTheory.AEStronglyMeasurable.memLp_truncation, Real.fderiv_fourierChar_neg_bilinear_right_apply, Unitization.real_cfcβ_eq_cfc_inr, norm_iteratedFDeriv_mul_le, intervalIntegral.fderiv_integral_of_tendsto_ae, flip_innerSL_real, LipschitzWith.memLp_lineDeriv, DoubleCentralizer.natCast_fst, differentiableWithinAt_abs_pos, continuousOn_dslope, ProbabilityTheory.integrable_preCDF, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, isClosedEmbedding_cfcβAux, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, AddChar.wInner_cWeight_self, AddCircle.coe_real_preimage_closedBall_eq_iUnion, innerSL_apply_apply, MeasureTheory.Integrable.norm_integral_condExpKernel, LinearMap.adjoint_innerββ_apply, Real.differentiable_sinh, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, hasDerivAt_neg', AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, DoubleCentralizer.nnnorm_def', ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, deriv_mul_const_field, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', Int.enorm_natCast, selfAdjoint.expUnitaryPathToOne_apply, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, derivWithin_fderivWithin, CFC.nnnorm_sqrt, List.nnnorm_prod_le', ContDiffBump.integrable_normed, ProbabilityTheory.uncenteredCovarianceBilin_apply, Real.deriv_log, selfAdjoint.norm_sq_expUnitary_sub_one, ContDiff.differentiable_deriv_two, FormalMultilinearSeries.derivSeries_coeff_one, Complex.ofRealCLM_norm, Matrix.spectrum_toLpLin, contMDiff_neg_sphere, HasDerivAt.comp_ofReal, not_differentiableAt_norm_zero, ContinuousLinearMap.opNorm_lsmul_apply_le, StarAlgebra.elemental.characterSpaceToSpectrum_coe, rotation_injective, BoxIntegral.unitPartition.mem_smul_span_iff, SchwartzMap.bilinLeftCLM_apply, InnerProductSpace.toDual_symm_apply, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, HasGradientAt.hasDerivAt', SmoothBumpCovering.exists_immersion_euclidean, AffineMap.hasDerivWithinAt, LeftInvariantDerivation.left_invariant, MeasureTheory.pdf.IsUniform.mul_pdf_integrable, ProbabilityTheory.integrable_toReal_condExpKernel, Bundle.RiemannianMetric.isVonNBounded, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, Complex.convexHull_reProdIm, exist_norm_eq, Complex.conjLIE_apply, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, hasDerivAt_exp_zero_of_radius_pos, BoundedContinuousFunction.instSMulCommClass_1, egauge_ball_le_of_one_lt_norm, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasStrictFDerivAt_iff_isLittleOTVS, not_IntegrableOn_Ioi_inv, Matrix.PosSemidef.sqrt_eq_zero_iff, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, lintegral_fderiv_lineMap_eq_edist, UnitAddTorus.mFourierSubalgebra_coe, signedDist_right_congr, differentiableWithinAt_inv, TensorProduct.toLinearEquiv_lidIsometry, Real.differentiableOn_arcsin, ContinuousLinearMap.isometry_mul_flip, AnalyticOnNhd.eval_linearMap', MeasureTheory.MemLp.integrable_norm_rpow', Complex.hasStrictFDerivAt_exp_real, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, WithCStarModule.prod_norm_sq, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.parallelepiped_basisFun, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, CStarModule.innerSL_apply, monomial_has_deriv_aux, MeasureTheory.hasFiniteIntegral_prod_iff', Real.vector_fourierIntegral_eq_integral_exp_smul, MeasureTheory.MemLp.norm_rpow, nndist_midpoint_right, egauge_add_add_le, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, Asymptotics.isLittleOTVS_prodMk_left, NNReal.enorm_eq, nndist_smulβ, iter_deriv_zpow', differentiableWithinAt_abs, CStarAlgebra.span_nonneg_inter_unitBall, Real.deriv_arccos, Real.hasStrictDerivAt_sinh, MeasureTheory.integrable_const_mul_iff, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, LocallyBoundedVariationOn.ae_differentiableWithinAt, ContinuousLinearMap.opNorm_mul_flip_apply, ConvexOn.univ_sSup_of_countable_affine_eq, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum, integrableOn_exp_Iic, cfcβHom_nnreal_eq_restrict, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, IsLocalFrameOn.coeff_apply_of_mem, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, IsLocalMax.fderiv_eq_zero, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, polynomialFunctions.starClosure_topologicalClosure, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerββ_apply_apply, WithCStarModule.inner_def, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, differentiableAt_sigmoid, DoubleCentralizer.pow_snd, OrthonormalBasis.repr_self, iteratedDeriv_scomp_three, Real.integrable_prod_sub, HasFDerivWithinAt.csin, MeasureTheory.eLpNorm_mono_real, norm_sub_mul_le', Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, Icc_isBoundaryPoint_bot, mellin_convergent_zero_of_isBigO, deriv_abs_neg, ProbabilityTheory.evariance_lt_top_iff_memLp, Real.differentiableWithinAt_arccos_Ici, gelfandStarTransform_naturality, gelfandStarTransform_apply_apply, RCLike.nonUnitalContinuousFunctionalCalculus, HarmonicAt.analyticAt_complex_partial, integrableOn_Ioi_rpow_of_lt, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, NormedSpace.Dual.toWeakDual_continuous, signedDist_left_congr, NormedField.exists_lt_nnnorm_lt, exists_deriv_eq_zero, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, ContinuousMultilinearMap.norm_smulRightL_le, NormedField.exists_nnnorm_lt_one, DoubleCentralizer.nnnorm_snd, egauge_univ, differentiableAt_comp_add_const, integrableOn_Ioi_norm_cpow_of_lt, CStarAlgebra.mem_Icc_iff_nnnorm_le_one, QuadraticForm.equivalent_signType_weighted_sum_squared, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, SchwartzMap.integral_fourierInv_smul_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, signedDist_triangle, Real.hasDerivAt_arcosh, ConvexOn.monotoneOn_rightDeriv, CStarMatrix.toCLM_injective, enorm_fderiv_norm_rpow_le, formalMultilinearSeries_geometric_apply_norm_le, LocallyBoundedVariationOn.ae_differentiableAt, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, BoundedContinuousFunction.instSMulCommClass_2, fderiv_eq_deriv_mul, nndist_right_lineMap, Orientation.abs_volumeForm_apply_of_orthonormal, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, Polynomial.differentiableOn_aeval, NumberField.mixedEmbedding.negAt_apply_snd, fderivWithin_ccosh, Real.GammaIntegral_convergent, nnnorm_algebraMap_nnreal, NonUnitalStarAlgHom.nnnorm_apply_le, Matrix.toEuclideanLin_apply, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, fourier_norm, ContinuousLinearMap.opNorm_mul, DoubleCentralizer.smul_toProd, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, egauge_zero_zero, Real.hasStrictDerivAt_arccos, DoubleCentralizer.toProdMulOpposite_injective, RCLike.conjCLE_apply, MeasureTheory.integrable_norm_rpow_iff, isBoundedBilinearMap_mul, Complex.reCLM_nnnorm, DoubleCentralizer.norm_fst_eq_snd, Unitization.nnnorm_def, Matrix.linfty_opNNNorm_mulVec, isScalarTower_closedBall_closedBall_closedBall, nndist_left_lineMap, Unitization.instStarOrderedRing, Euclidean.closedBall_eq_image, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, isScalarTower_sphere_closedBall_closedBall, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, Complex.deriv_ofReal_cpow_const, PiTensorProduct.mapL_smul, BoundedContinuousFunction.coe_toContinuousMapStarβ, DoubleCentralizer.norm_def', MeasureTheory.L1.setToL1_smul_left, CStarMatrix.norm_def', IsGreatest.nnnorm_cfc_nnreal, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, MeasureTheory.eLpNorm_norm, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, Real.norm_deriv_mulExpNegMulSq_le_one, Quaternion.linearIsometryEquivTuple_symm_apply, Polynomial.isEquivalent_atTop_lead, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, MeasureTheory.charFun_apply_real, Orientation.areaForm_to_volumeForm, Icc_isInteriorPoint_interior, VectorFourier.fourierIntegral_continuousLinearMap_apply, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, Real.not_continuousAt_deriv_mul_log_zero, integrable_one_add_norm, ProbabilityTheory.integrable_condCDF, HasFDerivAtFilter.isThetaTVS_sub, integrableOn_add_rpow_Ioi_of_lt, InformationTheory.klDiv_eq_top_iff, SchwartzMap.fourier_lineDerivOp_eq, LinearMap.isBigOTVS_rev_comp, AddChar.wInner_cWeight_eq_zero_iff_ne, NormedField.exists_one_lt_enorm, ContinuousLinearMapWOT.inducingFn_apply, CStarMatrix.inner_toCLM_conjTranspose_left, Orientation.areaForm_neg_orientation, hasStrictDerivAt_exp_smul_const, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, CFC.continuousOn_sqrt, Monotone.ae_differentiableAt, mfderivWithin_comp_projIcc_one, DoubleCentralizer.norm_def, contDiffWithinAt_euclidean, hasStrictDerivAt_exp_smul_const', SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, egauge_univ_pi, Real.fourier_iteratedFDeriv, nnnorm_div, SchwartzMap.smulLeftCLM_real_smul, AddCircle.norm_div_natCast, InnerProductSpace.toDualMap_apply_apply, Orientation.kahler_eq_zero_iff, PositiveLinearMap.preGNS_norm_def, PositiveLinearMap.leftMulMapPreGNS_apply, BoundedContinuousFunction.integral_const_sub, signedDist_apply_apply, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Real.differentiableAt_rpow_const_of_ne, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, WeakDual.toStrongDual_inj, IccLeftChart_extend_interior_pos, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, Orientation.areaForm_swap, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, hasDerivAt_id', nnnorm_mul_le, integrableOn_Ioi_cpow_iff, Bundle.ContinuousRiemannianMetric.symm, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, MeasureTheory.MemLp.inner_const, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, Complex.sameRay_of_arg_eq, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, Real.deriv_sqrt_aux, deriv_fderiv, RegularNormedAlgebra.isometry_mul', HasStrictDerivAt.real_of_complex, DoubleCentralizer.central, Matrix.PosSemidef.det_sqrt, Real.deriv_rpow_const, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, HasDerivAt.differentiableAt, DifferentiableWithinAt.dist, MeasureTheory.integrable_thickenedIndicator, NormedField.exists_nnnorm_lt, hasDerivWithinAt_abs, MeasureTheory.integrable_of_tendsto, TensorProduct.lidIsometry_apply, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ContinuousLinearMap.hasDerivAt, nnnorm_mulβ_le, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Complex.reCLM_coe, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, CompletelyPositiveMap.instLinearMapClassComplex, MeasureTheory.eLpNorm_ofReal, Real.deriv_sinh, NormedField.exists_lt_enorm, Module.Basis.coe_toOrthonormalBasis_repr, hasFDerivAt_ringInverse, norm_cfcβ_lt, Filter.HasBasis.isLittleOTVS_iff, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, Matrix.linfty_opNNNorm_eq_opNNNorm, VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, InformationTheory.hasDerivAt_klFun, integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, Orientation.kahler_comp_rightAngleRotation, Seminorm.ball_smul, ae_differentiableAt_norm, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, HasGradientWithinAt.differentiableWithinAt, MeasureTheory.memLp_haarAddCircle_iff, NumberField.Units.instZLattice_unitLattice, antilipschitzWith_mul_right, HasFDerivAt.isBigOTVS_sub, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, hasDerivWithinAt_neg, Orientation.volumeForm_zero_pos, differentiableWithinAt_pow, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, ProbabilityTheory.complexMGF_mul_I, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, IsLocalFrameOn.coeff_congr, ProbabilityTheory.Kernel.integrable_densityProcess, NumberField.Units.span_basisOfIsMaxRank, nnnorm_cfcβ_nnreal_lt, LinearMap.hasStrictDerivAt, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, FiniteDimensional.rclike_to_real, Complex.equivRealProdCLM_symm_apply, nndist_inv_invβ, CStarAlgebra.nnnorm_le_iff_of_nonneg, HasDerivWithinAt.norm_sq, NormedSpace.smul_mem_polar, HasGradientAtFilter.hasDerivAtFilter', nnnorm_smul, List.nnnorm_prod_le, CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, IsLocalExtr.fderiv_eq_zero, NumberField.Units.basisOfIsMaxRank_apply, Real.differentiableOn_rpow_const, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, MeasureTheory.MemLp.integrable_norm_pow, RingHomIsometric.enorm_map, NormedField.denseRange_nnnorm, Asymptotics.IsLittleOTVS.zero, ContinuousLinearMap.flip_mul, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, PeriodPair.basis_zero, MeasureTheory.Integrable.norm_integral_condDistrib, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, ContinuousLinearMap.nnnorm_toSpanSingleton, InformationTheory.leftDeriv_klFun, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Asymptotics.isLittleOTVS_fun_neg_left, deriv_id'', AddCircle.exists_norm_nsmul_le, isEquivalent_choose, Asymptotics.isBigOTVS_iff_smallSets, OrthonormalBasis.coe_ofRepr, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MeasureTheory.Integrable.integral_norm_comp, EuclideanSpace.nnnorm_single, ProbabilityTheory.differentiableAt_mgf, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, deriv_const_mul_field', RCLike.conjLIE_apply, Complex.orthonormalBasisOneI_repr_apply, Unitary.expUnitary_eq_mul_inv, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Complex.differentiable_exp, NormedAlgebra.exists_isMinOn_norm_sub_smul, Polynomial.toAddCircle.integrable, RCLike.imLm_coe, Real.differentiable_cos, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, continuousOn_cfcβ, infEDist_smulβ, isAddFundamentalDomain_Ioc, norm_cauchyPowerSeries_le, hasFDerivAt_norm_rpow, ContinuousLinearMap.lsmul_flip_inj, intervalIntegral.integrableOn_Ioo_rpow_iff, Asymptotics.isEquivalent_nat_ceil, DoubleCentralizer.neg_snd, summable_jacobiThetaβ_term_fderiv_iff, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, AddCircle.norm_coe_mul, Asymptotics.isBigOTVS_fun_neg_left, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Matrix.linfty_opNNNorm_toMatrix, Asymptotics.isBigOTVS_fun_neg_right, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, hasDerivAt_abs_rpow, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, signedDist_eq_zero_of_orthogonal, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, ProbabilityTheory.memLp_of_mem_interior_integrableExpSet, ZSpan.volume_fundamentalDomain, FormalMultilinearSeries.coeff_eq_zero, ProbabilityTheory.covarianceBilin_zero, RCLike.conjCLE_coe, contDiffOn_stereoToFun, LeftInvariantDerivation.evalAt_coe, fderiv_inverse, AddCircle.norm_half_period_eq, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, Matrix.PosSemidef.sqrt_eq_one_iff, Real.deriv_Gamma_nat, GaussianFourier.integrable_cexp_neg_mul_sum_add, Complex.hasStrictFDerivAt_cpow, MeasureTheory.integrable_add_iff_of_nonneg, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, Polynomial.differentiable_aeval, DoubleCentralizer.range_toProd, IsGreatest.nnnorm_cfc, egauge_le_one, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Convex.toWeakSpace_closure, hasDerivAtFilter_neg, integrable_rpow_neg_one_add_norm_sq, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, Bundle.ContMDiffRiemannianMetric.symm, selfAdjoint.nnnorm_pow_two_pow, HilbertBasis.hasSum_repr, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, Asymptotics.isBigOTVS_iff_isBigO, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, PositiveLinearMap.preGNS_inner_def, hasDerivWithinAt_pow, CStarAlgebra.instNonnegSpectrumClassComplexNonUnital, MeasureTheory.Measure.hausdorffMeasure_smulβ, HasFDerivWithinAt.cpow, MeasureTheory.lintegral_nnnorm_condExpL2_le, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, DoubleCentralizer.add_fst, AffineSubspace.signedInfDist_eq_signedDist_of_mem, HasStrictFDerivAt.const_cpow, Finset.nnnorm_prod_le', differentiableWithinAt_of_derivWithin_ne_zero, one_mem_posTangentConeAt_iff_mem_closure, HasFDerivWithinAt.csinh, quasispectrum.isCompact, Real.integrable_sinc, RealRMK.rieszMeasure_le_of_eq_one, TensorProduct.inner_lid_lid, derivWithin_div_const, spectrum.gelfand_formula, Matrix.piLp_ofLp_toEuclideanLin, iteratedFDerivWithin_smul_const_apply, cfcβAux_id, NormedSpace.inclusionInDoubleDual_norm_le, not_IntegrableOn_Ici_inv, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, le_egauge_smul_left, MeasureTheory.memLp_two_iff_integrable_sq, WeakDual.isCompact_closedBall, Affine.Simplex.signedInfDist_apply_self, ConvexOn.sSup_of_countable_affine_eq, Real.differentiableAt_rpow_of_ne, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, RCLike.reCLM_coe, ProbabilityTheory.gaussianReal_map_linearMap, InnerProductSpace.toDual_apply, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, CStarAlgebra.norm_posPart_le, OrthonormalBasis.tensorProduct_repr_tmul_apply', nnnorm_natAbs, HasDerivWithinAt.inner, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, DifferentiableAt.inner, HarmonicAt.differentiableAt_complex_partial, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Seminorm.comp_smul, isScalarTower_sphere_sphere_sphere, MeasureTheory.hasFDerivAt_convolution_right_with_param, CStarAlgebra.span_nonneg_inter_unitClosedBall, ProbabilityTheory.IsGaussian.charFun_eq', Real.deriv_inv_log, ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, Asymptotics.IsLittleO.isLittleOTVS, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, iteratedFDerivWithin_eq_equiv_comp, CompactlySupportedContinuousMap.toRealLinearMap_apply, DifferentiableAt.isBigOTVS_sub, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, MeasureTheory.Integrable.integral_norm_prod_left, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, differentiableAt_inv_iff, AddCircle.instIsUnifLocDoublingMeasureRealVolume, ProbabilityTheory.covarianceBilinDual_zero, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, RealRMK.integral_rieszMeasure, LinearMap.deriv, RCLike.nnnorm_nnratCast, CFC.continuous_abs, contDiff_iff_iteratedDeriv, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, EuclideanSpace.instIsManifoldSphere, DoubleCentralizer.smul_fst, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, Real.isEquivalent_sin, InnerProductSpace.toDualMap_apply, Real.differentiable_exp, ProbabilityTheory.differentiableOn_mgf, Real.abs_mulExpNegMulSq_comp_le_norm, nnnorm_algebraMap, fdifferential_apply, nnnorm_pow, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, Asymptotics.isEquivalent_iff_exists_eq_mul, coe_ringEquiv_lpBCF, MeasureTheory.Integrable.integral_norm_condExpKernel, egauge_pi, Real.differentiableAt_cos, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, innerβ_apply, Asymptotics.isBigOTVS_congr, ProbabilityTheory.complexMGF_id_mul_I, fderivWithin_ccos, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, ModularGroup.lcRow0Extend_apply, Asymptotics.isBigOTVS_neg_right, Real.deriv_log', hasDerivAt_update, HasStrictFDerivAt.clog, Real.one_div_sub_hasFPowerSeriesOnBall_zero, ProbabilityTheory.integrable_condVar, OrthonormalBasis.equiv_apply, Seminorm.bound_of_continuous, fderiv_pow_ring, ContinuousLinearMap.lsmul_apply, nnnorm_pow_le, selfAdjoint.unitarySelfAddISMul_coe, Bundle.ContMDiffRiemannianMetric.pos, HasDerivWithinAt.complexToReal_fderiv, signedDist_triangle_left, Filter.IsIncreasingApproximateUnit.eventually_nnnorm, IsContMDiffRiemannianBundle.exists_contMDiff, deriv_const_mul_field, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, Real.deriv2_binEntropy, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, IsometricContinuousFunctionalCalculus.toNonUnital, InnerProductSpace.toDual_apply_apply, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, contMDiff_subtype_coe_Icc, Real.hasDerivAt_arcsin, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, BoundedContinuousFunction.instIsScalarTower_1, ProperCone.innerDual_singleton, RCLike.nnnorm_ofNat, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, differentiable_inner, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, Real.hasDerivAt_tan, hasFDerivAt_list_prod', InnerProductSpace.rankOne_def, Real.deriv_tan_sub_id, AddCircle.volume_closedBall, Real.leftDeriv_mul_log, stereoToFun_apply, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, Real.differentiableAt_Gamma, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, orthogonalBilin_innerβ, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, ConvexOn.real_univ_sSup_of_countable_affine_eq, NumberField.mixedEmbedding.mem_span_latticeBasis, ProbabilityTheory.evariance_eq_top_iff, Module.Basis.equivFunL_symm_apply_repr, OrthonormalBasis.repr_apply_apply, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, HasStrictFDerivAt.ccos, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, MeasureTheory.lintegral_ofReal_ne_top_iff_integrable, BoundedContinuousFunction.neg_norm_le_apply, gradient_eq_deriv', QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ClosedSubmodule.orthogonal_eq_inter, Chebyshev.integrableOn_theta_div_id_mul_log_sq, PositiveLinearMap.toPreGNS_ofPreGNS, Orientation.kahler_neg_orientation, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, MonotoneOn.intervalIntegrable_slope, nndist_left_midpoint, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, intervalIntegral.integrableOn_Ioo_cpow_iff, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, Real.differentiableOn_mul_log, MeasureTheory.setToFun_smul_left, InformationTheory.klDiv_def, HasDerivAt.complexToReal_fderiv', hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.Integrable.norm_integral_condKernel, RCLike.abs_wInner_le, contDiff_nat_iff_iteratedDeriv, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, RingHomIsometric.nnnorm_map, ProbabilityTheory.memLp_id_gaussianReal', fderiv_norm_smul_neg, HasDerivAt.complexToReal_fderiv, ContinuousLinearMapWOT.isInducing_inducingFn, integrableOn_Ioi_deriv_ofReal_cpow, PositiveLinearMap.exists_norm_apply_le, DoubleCentralizer.star_fst, Real.deriv_mulExpNegMulSq, StrongDual.polarSubmodule_eq_polar, IsSelfAdjoint.nnnorm_mul_self, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, Asymptotics.isLittleOTVS_fun_neg_right, Complex.isEquivalent_sinh, hasFDerivAt_exp_smul_const', dense_differentiableAt_norm, MeasureTheory.SignedMeasure.re_toComplexMeasure, CStarAlgebra.instNonnegSpectrumClass, FormalMultilinearSeries.ofScalars_norm_le, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, MonotoneOn.intervalIntegral_deriv_mem_uIcc, NumberField.mixedEmbedding.volume_preserving_negAt, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, Real.deriv_qaryEntropy, Real.deriv_arctan, monotoneOn_deriv_descPochhammer_eval, SchwartzMap.smulLeftCLM_const, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, mellin_convergent_top_of_isBigO, LinearMap.toMatrix_innerββ_apply, PointwiseConvergenceCLM.equivWeakDual_symm_apply, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, MeasureTheory.ComplexMeasure.integrable_rnDeriv, RCLike.wInner_one_eq_inner, NumberField.mixedEmbedding.negAt_apply_isComplex, ProbabilityTheory.hasFiniteIntegral_compProd_iff', AffineMap.hasDerivAt, Complex.hasFDerivAt_cpow, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Complex.differentiableAt_exp, hasFDerivWithinAt_pow', ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, not_integrableOn_Ioi_rpow, AffineMap.differentiableAt, isScalarTower_closedBall_ball_ball, Matrix.PosSemidef.toLinearMapβ'_zero_iff, Polynomial.rootSet_derivative_subset_convexHull_rootSet, WeakDual.isSeqCompact_closedBall, DoubleCentralizer.add_snd, HasFDerivAt.ccos, MeasureTheory.Measure.integrable_measure_prodMk_left, has_antideriv_at_fourier_neg, Real.differentiableAt_log_iff, hasStrictDerivAt_zpow, norm_iteratedFDerivWithin_prod_le, UnitAddTorus.mFourier_norm, CStarModule.norm_inner_le, Matrix.instNonnegSpectrumClass, LinearIsometry.toSpanSingleton_apply, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, DifferentiableAt.norm_sq, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, HasFDerivAt.clog, innerSLFlip_apply_apply, Polynomial.hasFDerivAt, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, finrank_euclideanSpace, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, infEdist_smulβ, IsContinuousRiemannianBundle.exists_continuous, DoubleCentralizer.norm_snd, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, NormedField.exists_enorm_lt, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', MeasureTheory.MemLp.integrable_norm_rpow, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, nndist_midpoint_left, DoubleCentralizer.nnnorm_fst, intervalIntegral.integral_hasStrictFDerivAt, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, MeasureTheory.IntegrableAtFilter.norm, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, Module.Basis.equivFunL_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, inner_map_complex, hasFDerivAt_list_prod_finRange', ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, tendsto_integral_mul_one_add_inv_smul_sq_pow, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, LinearMap.hasDerivWithinAt, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, CStarMatrix.toCLM_apply_single, Real.fourier_fderiv, ContinuousMap.nnnorm_smul_const, ContinuousMap.adjoin_id_eq_span_one_union, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, Seminorm.const_isBounded, MeasureTheory.integrable_prod_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, HasFDerivWithinAt.norm_sq, IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, differentiableAt_abs_neg, Asymptotics.isLittleOTVS_iff_smallSets, BoundedContinuousFunction.apply_le_norm, hasDerivAt_fourier_neg, ProbabilityTheory.isGaussian_gaussianReal, norm_fderiv_norm_rpow_le, StrongDual.dualPairing_separatingLeft, deriv_abs_zero, HasDerivWithinAt.differentiableWithinAt, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, nndist_midpoint_midpoint_le', Polynomial.Chebyshev.integrable_measureT, SchwartzMap.fourierInv_lineDerivOp_eq, RCLike.finrank_le_two, Bundle.RiemannianMetric.symm, MeasureTheory.integral_charFun_Icc, iteratedFDeriv_eq_equiv_comp, linear_isometry_complex, Unitization.norm_eq_sup, Real.hasDerivAt_cos, Matrix.ofLp_toEuclideanCLM, AffineSubspace.signedInfDist_eq_const_of_mem, ProbabilityTheory.HasSubgaussianMGF.integrable, CStarMatrix.toCLM_apply_eq_sum, HasFDerivAt.ccosh, differentiableOn_pow, hasDerivAt_exp_smul_const, AddCircle.exists_norm_eq_of_isOfFinAddOrder, Asymptotics.isBigOTVS_neg_left, WithCStarModule.pi_norm, exists_dual_vector, nndist_center_homothety, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, Differentiable.norm_rpow, DifferentiableWithinAt.isBigOTVS_sub, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, LinearIsometryEquiv.toSpanUnitSingleton_apply, derivWithin_mul_const_field, Real.differentiableWithinAt_arcsin_Ici, AddChar.wInner_cWeight_eq_one_iff_eq, logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, InformationTheory.klDiv_ne_top_iff, RCLike.sqrt_map, MeasureTheory.integrable_conv_iff, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, PadicInt.mahlerTerm_one, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, inr_comp_cfcβHom_eq_cfcβAux, rotationOf_rotation, CFC.monotoneOn_one_sub_one_add_inv_real, IsMIntegralCurveAt.hasMFDerivAt, SpectrumRestricts.real_iff, IsLocalFrameOn.eventually_eq_sum_coeff_smul, differentiableWithinAt_euclidean, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, DoubleCentralizer.neg_toProd, MeasureTheory.integrable_mul_const_iff, deriv_abs_pos, Matrix.isPositive_toEuclideanLin_iff, nnnorm_cfc_le_iff, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, exists_polynomial_near_continuousMap, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, CStarMatrix.ofMatrix_eq_ofMatrixL, HasGradientAt.differentiableAt, Real.differentiableAt_cosh, CStarAlgebra.nnnorm_le_one_iff_of_nonneg, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, ProbabilityTheory.integral_linearMap_gaussianReal, AddCircle.coe_real_preimage_closedBall_inter_eq, Real.nnnorm_mul_toNNReal, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, Polynomial.hermite_eq_deriv_gaussian', DoubleCentralizer.algebraMap_snd, MeasureTheory.integrable_of_integral_eq_one, MeasureTheory.integrable_norm_iff, WeakDual.polar_def, MeasureTheory.integrable_toReal_of_lintegral_ne_top, RCLike.wInner_const_left, ProbabilityTheory.covarianceBilinDual_self_eq_variance, MeasureTheory.eLpNorm_const_smul_le', RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, MeasureTheory.integrable_smul_const, Orientation.areaForm_comp_linearIsometryEquiv, NormedField.exists_one_lt_nnnorm, hasStrictFDerivAt_norm_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', LinearMap.adjoint_toSpanSingleton, DoubleCentralizer.one_snd, ContDiff.differentiable_iteratedDeriv, ContinuousMultilinearMap.norm_mkPiAlgebra, Real.deriv_exp, NumberField.canonicalEmbedding.nnnorm_eq, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, fderiv_pow_ring', QuasispectrumRestricts.real_iff, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, nnnorm_intCast_abs, RCLike.inner_apply, NormedField.exists_enorm_lt_one, upperHemicontinuous_quasispectrum, Polynomial.differentiableAt_aeval, WeakDual.CharacterSpace.compContinuousMap_apply, hasDerivAt_id, Real.hasDerivAt_rpow_const, CStarMatrix.toCLM_apply, Real.toNNReal_mul_nnnorm, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, MeasureTheory.Integrable.re_im_iff, Polynomial.isEquivalent_atBot_lead, differentiableAt_norm_smul, deriv_update, MeasureTheory.HasFiniteIntegral.norm, Real.iter_deriv_exp, Real.differentiable_iteratedDeriv_cos, nndist_lineMap_right, edist_smulβ, Polynomial.hasFDerivAt_aeval, Differentiable.norm_sq, DoubleCentralizer.instIsCentralScalar, exists_dual_vector'', deriv_zpow', RCLike.norm_wInner_le, ProbabilityTheory.IsGaussian.memLp_dual, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Asymptotics.isLittleOTVS_map, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, norm_lt_iff_of_compactlySupported, spectrum.hasDerivAt_resolvent, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, hasDerivAt_exp, contDiffOn_succ_iff_deriv_of_isOpen, signedDist_lineMap_left, selfAdjoint.realPart_unitarySelfAddISMul, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, Real.tendsto_rightDeriv_mul_log_atTop, Real.hasStrictDerivAt_arsinh, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', MeasureTheory.Integrable.integral_norm_compProd, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, Asymptotics.isLittleOTVS_iff_isLittleO, integrable_rpow_mul_exp_neg_mul_sq, EuclideanSpace.basisFun_repr, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, RCLike.realLinearIsometryEquiv_symm_apply, hasStrictFDerivAt_inv, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, InformationTheory.klDiv_eq_integral_klFun, LinearIsometry.coe_toSpanSingleton, MeasureTheory.hasFiniteIntegral_iff_ofReal, integrable_mul_exp_neg_mul_sq, VectorFourier.fourierSMulRight_apply, deriv_neg'', DoubleCentralizer.pow_toProd, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, IsLocalFrameOn.coeff_apply_of_notMem, ProbabilityTheory.evariance_def', Seminorm.closedBall_smul, WithLp.unitization_nnnorm_inr, nnnorm_cfc_nnreal_lt, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, fderiv_inv, Complex.orthonormalBasisOneI_repr_symm_apply, NonUnitalStarAlgHom.nnnorm_map, Manifold.riemannianEDist_def, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, isScalarTower_sphere_sphere_closedBall, signedDist_anticomm, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, Units.nnnorm_pos, HasMFDerivWithinAt.mul', UnitAddTorus.hasSum_mFourier_series_L2, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, WithCStarModule.pi_inner, Orientation.areaForm_comp_rightAngleRotation, ContinuousMap.instCStarRing, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, modelWithCornersEuclideanHalfSpace_zero, UnitAddCircle.mem_approxAddOrderOf_iff, ContinuousLinearMap.norm_extendToπ'_bound, MeasureTheory.hausdorffMeasure_homothety_image, Real.differentiableAt_arctan, le_egauge_smul_right, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, spectralNorm_smul, Asymptotics.isEquivalent_of_tendsto_one, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, HasGradientWithinAt.fderivWithin_apply, differentiableWithinAt_abs_neg, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, WithCStarModule.prod_norm, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, ProbabilityTheory.integrable_exp_mul_gaussianReal, WeakDual.isClosed_closedBall, MeasureTheory.integrable_add_iff_of_nonpos, hasDerivAt_fourier, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, fderiv_ccos, DoubleCentralizer.zero_fst, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Real.rightDeriv_mul_log, ProbabilityTheory.Kernel.integrable_density, nnnorm_cfc_nnreal_le, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, ProbabilityTheory.hasFiniteIntegral_prodMk_left, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, fdifferential_comp, CStarMatrix.mul_entry_mul_eq_inner_toCLM, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, nnnorm_inner_le_nnnorm, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ProbabilityTheory.hasFiniteIntegral_comp_iff', IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, fderiv_apply_one_eq_deriv, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, isScalarTower_sphere_sphere_ball, IsUltrametricDist.algNormOfAlgEquiv_apply, nnnorm_cfc_nnreal_le_iff, integrableOn_exp_mul_complex_Iic, AddCircle.norm_coe_eq_abs_iff, HasFDerivAt.inner, MeasureTheory.L2.eLpNorm_inner_lt_top, CStarModule.norm_sq_eq, ProbabilityTheory.integrable_pow_of_mem_interior_integrableExpSet, deriv_circleMap, ProbabilityTheory.exp_neg_integrableOn_Ioc, ProbabilityTheory.deriv_mgf, ZeroAtInftyContinuousMap.instCStarRing, expUnitary_argSelfAdjoint, ContinuousLinearMap.isometry_mul, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, MeasureTheory.hasFiniteIntegral_norm_iff, NonUnitalCommCStarAlgebra.toStarModule, MeasureTheory.Integrable.norm_integral_condDistrib_map, OrthonormalBasis.sum_repr_symm, StrongDual.toLpβ_apply, Orientation.kahler_apply_self, IsPrimitiveRoot.nnnorm_eq_one, Real.differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, ProbabilityTheory.hasFiniteIntegral_comp_iff, Complex.conjCLE_nnorm, Polynomial.differentiableOn, HasStrictDerivAt.complexToReal_fderiv', IsLocalFrameOn.coeff_apply_zero_at, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, egauge_ball_one_le_of_one_lt_norm, differentiableOn_neg, Asymptotics.isBigOTVS_pi, LinearMap.continuous_of_nonzero_on_open, MeasureTheory.HasFiniteIntegral.of_mem_Icc, ConvexOn.real_univ_sSup_affine_eq, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, DoubleCentralizer.nnnorm_fst_eq_snd, AddCircle.closedBall_eq_univ_of_half_period_le, toWeakSpace_closedConvexHull_eq, WithCStarModule.inner_single_right, ConvexOn.monotoneOn_leftDeriv, Unitization.norm_def, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, selfAdjoint.star_coe_unitarySelfAddISMul, deriv_neg', Orientation.kahler_rotation_left', Real.differentiable_sin, hasFDerivAtFilter_iff_isLittleOTVS, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, MeasureTheory.eLpNorm_const_smul_le, Polynomial.hasDerivWithinAt_aeval, argSelfAdjoint_expUnitary, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, rotation_trans, integrableOn_Ioi_rpow_iff, Real.eulerMascheroniConstant_eq_neg_deriv, Real.not_differentiableAt_inv_log_zero, Orientation.abs_areaForm_le, Real.deriv_mul_log, egauge_le_of_smul_mem, hasStrictFDerivAt_pow', isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, DoubleCentralizer.one_fst, ContinuousLinearMap.norm_extendToπ', integrableOn_rpow_mul_exp_neg_rpow, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, differentiableAt_iff_comp_const_sub, MeasureTheory.Integrable.integral_norm_condDistrib, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, DoubleCentralizer.coeHom_apply, signedDist_neg, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, Complex.restrictScalars_toSpanSingleton, integrableOn_exp_mul_Ioi, Orientation.normSq_kahler, ProbabilityTheory.IsCondKernelCDF.integrable, Complex.UnitDisc.mk_neg, HasFDerivWithinAt.clog, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, ProbabilityTheory.integrable_of_mem_integrableExpSet, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, hasFDerivAt_exp_smul_const_of_mem_ball, Real.differentiableAt_tan, Real.differentiable_cosh, NumberField.mixedEmbedding.negAt_symm, fourierSubalgebra_coe, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ProbabilityTheory.integrable_compProd_iff, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, Complex.inner, cfcHom_nnreal_eq_restrict, fderiv_deriv, WithLp.unitizationAlgEquiv_symm_apply_ofLp, MeasureTheory.eLpNorm'_const_smul, norm_cfcβ_le, Asymptotics.isLittleOTVS_neg_right, MeasureTheory.MemLp.norm_rpow_div, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, signedDist_vsub_self_rev, coord_norm', Int.Matrix.one_le_norm_A_of_ne_zero, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, OrthonormalBasis.measurePreserving_repr_symm, spectrum.exists_nnnorm_eq_spectralRadius_of_nonempty, WeakDual.isClosed_polar, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, spec_cfcβAux, MeasureTheory.measureReal_abs_gt_le_integral_charFun, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, EuclideanSpace.piLpCongrLeft_single, hasFDerivAt_exp_smul_const, Differentiable.inner, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Real.hasDerivAt_log, oneTangentSpaceIcc_def, IccRightChart_extend_top_mem_frontier, hasStrictFDerivAt_list_prod_attach', rotationOf_coe, NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, DoubleCentralizer.sub_fst, Module.Basis.parallelepiped_eq_map, MeasureTheory.tendsto_eLpNorm_condExp, iteratedDeriv_comp_two, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, signedDist_self, MeasureTheory.MemLp.norm, Unitization.nnreal_cfcβ_eq_cfc_inr, isBoundedSMul, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, integrable_inv_one_add_sq, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, signedDist_vsub_self, ContinuousLinearMap.mul_apply', MeasureTheory.SignedMeasure.rnDeriv_smul, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, signedDist_smul, MeasureTheory.eLpNorm_mono_ae_real, TemperedDistribution.fourierTransform_apply, Real.hasStrictDerivAt_arctan, ZLattice.volume_image_eq_volume_div_covolume, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Real.map_linearMap_volume_pi_eq_smul_volume_pi, CStarModule.norm_eq_csSup, nnnorm_apply_le_nnnorm_cfc, Matrix.toEuclideanLin_eq_toLin, DoubleCentralizer.pow_fst, IsometricContinuousFunctionalCalculus.spectrum_le, nnnorm_pow_le', StrongDual.toLpβ_of_not_memLp, isConformalMap_complex_linear_conj, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, IsSelfAdjoint.spectralRadius_eq_nnnorm, hasStrictFDerivAt_finset_prod, ProbabilityTheory.memLp_id_gaussianReal, intervalIntegral.differentiable_integral_of_continuous, Matrix.linfty_opNorm_mulVec, deriv_zpow, LipschitzWith.locallyIntegrable_lineDeriv, AddCircle.norm_neg_period, SmoothBumpCovering.embeddingPiTangent_injOn, MeasureTheory.memLp_norm_rpow_iff, StrongDual.mem_polarSubmodule, exists_dual_vector', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Orientation.kahler_rightAngleRotation_left, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, MeasureTheory.eLpNorm_const_smul, UnitAddTorus.hasSum_mFourier_series_of_summable, Real.hasDerivAt_mulExpNegMulSq, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, cfcβHom_real_eq_restrict, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, iteratedFDeriv_smul_const_apply, Real.differentiableOn_arccos, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, IsLocalMin.deriv_eq_zero, Real.hasDerivAt_cosh, Real.tendsto_deriv_mul_log_atTop, Orientation.abs_areaForm_of_orthogonal, LipschitzOnWith.ae_differentiableWithinAt_real, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, UnitAddCircle.norm_eq, HasFPowerSeriesAt.deriv, upperHemicontinuous_quasispectrum_nnreal, innerβ_apply_apply, differentiable_pow, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, HasFDerivAt.csin, MeasureTheory.eLpNorm_norm_rpow, Asymptotics.IsBigOTVS.rfl, CStarAlgebra.conjugate_le_norm_smul', Asymptotics.IsLittleOTVS.bot, ContinuousLinearMap.isBigOTVS_comp, PadicAlgCl.valuation_def, hfdifferential_apply, MeasureTheory.Integrable.inner_const, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, Real.hasDerivAt_fourierChar, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, Orientation.kahler_rotation_left, nnnorm_cfcβHom, SchwartzMap.smulLeftCLM_neg, ContinuousLinearMap.opNNNorm_mul, differentiableOn_inverse, Complex.conjCLE_enorm, Real.differentiableWithinAt_arccos_Iic, CFC.nnnorm_rpow, spectrum.differentiableOn_inverse_one_sub_smul, CFC.nnrpow_le_nnrpow, Asymptotics.isBigOTVS_fun_comm, mdifferentiableWithinAt_comp_projIcc_iff, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Orientation.inner_sq_add_areaForm_sq, Real.enorm_exp_I_mul_ofReal_sub_one_le, signedDist_smul_of_neg, MeasureTheory.lpNorm_const_smul, DoubleCentralizer.algebraMap_fst, differentiableOn_euclidean, RCLike.reLm_coe, nnnorm_fderiv_norm_rpow_le, differentiableAt_abs_pos, TrivSqZeroExt.nnnorm_def, ContinuousLinearMap.adjoint_toSpanSingleton, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, hasStrictFDerivAt_exp_zero_of_radius_pos, ContinuousLinearMap.toBilinForm_injective, integrableOn_exp_neg_Ioi, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, CStarAlgebra.span_nonneg_inter_closedBall, toSpanSingleton_derivWithin, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, RCLike.nnnorm_conj, SchwartzMap.integral_fourier_mul_eq, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, apply_le_nnnorm_cfc_nnreal, Unitization.instCStarRing, range_mfderiv_coe_sphere, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, MeasureTheory.integrable_prod_iff', RCLike.wInner_one_const_right, AlgHom.coe_toContinuousLinearMap, hahnEmbedding_isOrderedModule_rat, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Affine.Simplex.sign_signedInfDist_touchpoint_empty, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, signedDist_vadd_right_swap, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, Real.differentiable_mulExpNegMulSq, ContinuousMap.neg_norm_le_apply, AddCircle.coe_real_preimage_closedBall_period_zero, integrable_of_isBigO_exp_neg, nnnorm_algebraMap', Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, Complex.conjCLE_apply, NormedSpace.polar_ball, Valued.integer.exists_nnnorm_lt_one, Real.not_DifferentiableAt_log_mul_zero, innerSLFlip_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, iccLeftChart_extend_zero, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, hasDerivAt_const_mul, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, Euclidean.ball_eq_preimage, CStarAlgebra.star_left_conjugate_le_norm_smul, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, norm_iteratedFDeriv_prod_le, hasFDerivAt_pow', SchwartzMap.lineDerivOp_fourierInv_eq, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, HasFDerivWithinAt.const_cpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, Matrix.linfty_opNNNorm_mul, Polynomial.hasDerivAt, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, ContinuousLinearMap.opNorm_lsmul_le, OrthonormalBasis.repr_symm_single, MeasureTheory.hasFiniteIntegral_toReal_iff, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, interior_range_modelWithCornersEuclideanHalfSpace, WeakDual.CharacterSpace.norm_le_norm_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, AddCircle.addWellApproximable_ae_empty_or_univ, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.hasStrictDerivAt_cos, IntervalIntegrable.intervalIntegrable_slope, MemHolder.nnHolderNorm_smul, iter_deriv_inv, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, hasStrictFDerivAt_exp_zero, integrableOn_Ioi_cpow_of_lt, Differentiable.dist, EulerSine.antideriv_cos_comp_const_mul, ProbabilityTheory.condVar_of_sigmaFinite, instENormSMulClass, RightDerivMeasurableAux.differentiable_set_eq_D, hasDerivWithinAt_zpow, mellin_convergent_iff_norm, Monotone.deriv_nonneg, antilipschitzWith_mul_left, Orientation.kahler_mul, innerSL_real_flip, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, RCLike.nnnorm_two, ProbabilityTheory.iteratedDeriv_two_cgf, ContinuousLinearMap.opNNNorm_mul_flip_apply, measurableSet_of_differentiableWithinAt_Ioi, TensorProduct.norm_lid, Real.differentiable_iteratedDeriv_sin, ProbabilityTheory.deriv_mgf_zero, MeasureTheory.charFun_eq_charFunDual_toDualMap, egauge_eq_zero_iff, HasMFDerivAt.prod, fderivWithin_csin, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sigmoid, ProperCone.dual_dual_flip, flip_innerβ, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, MeasureTheory.LocallyIntegrableOn.norm, HasStrictFDerivAt.isBigOTVS_sub, TrivSqZeroExt.nnnorm_inl, DoubleCentralizer.mul_fst, Orientation.volumeForm_robust', BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, Matrix.linfty_opNorm_mul, instSMulCommClass_sphere_ball_ball, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, PiLp.basis_toMatrix_basisFun_mul, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, isBoundedBilinearMap_smul, EulerSine.antideriv_sin_comp_const_mul, signedDist_vadd_left, Diffeology.IsPlot.contDiff, ModularGroup.tendsto_lcRow0, ProbabilityTheory.integrable_kernel_prodMk_left, NormedSpace.sInter_polar_eq_closedBall, ProbabilityTheory.deriv_cgf, PositiveLinearMap.ofPreGNS_toPreGNS, Complex.imCLM_coe, isBoundedBilinearMap_inner, ContinuousLinearMap.opNorm_mul_apply_le, CStarMatrix.normedSpaceCore, intervalIntegral.integral_hasFDerivWithinAt, deriv_pow_field, SmoothBumpCovering.embeddingPiTangent_injective, ProbabilityTheory.memLp_tilted_mul, HasFPowerSeriesAt.hasDerivAt, Int.nnnorm_coe_units, ProbabilityTheory.covarianceBilin_apply, ContinuousLinearMap.isThetaTVS_comp, Polynomial.hasDerivAt_aeval, ediam_smulβ, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivAt_gronwallBound, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, hasDerivAt_ofReal_cpow_const, CFC.norm_abs, hasDerivAt_norm_rpow, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, NumberField.mixedEmbedding.latticeBasis_apply, differentiableWithinAt_inverse, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, TemperedDistribution.fourierInv_apply, cfcβAux_mem_range_inr, Ideal.Quotient.norm_mk_lt, ContinuousMap.adjoin_id_eq_span_one_add, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, ProbabilityTheory.covarianceBilin_map, Unitization.nnnorm_eq_sup, AffineSubspace.signedInfDist_singleton, norm_deriv_eq_norm_fderiv, ContinuousMap.apply_le_norm, DoubleCentralizer.zero_toProd, MeasureTheory.AEStronglyMeasurable.integrable_truncation, AkraBazziRecurrence.differentiableAt_smoothingFn, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, SchwartzMap.fderivCLM_fourier_eq, CStarModule.inner_mul_inner_swap_le, Bundle.ContinuousRiemannianMetric.pos, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, hasSum_fourier_series_of_summable, Real.deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, integrableOn_Ioi_exp_neg_mul_sq_iff, Orientation.volumeForm_zero_neg, BoundedContinuousFunction.nnnorm_coeFn_eq, Real.differentiableAt_binEntropy, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', Orientation.areaForm_map, Real.enorm_rpow_of_nonneg, Asymptotics.isEquivalent_iff_tendsto_one, differentiable_neg, hasDerivAt_neg, ProbabilityTheory.integrable_of_mem_interior_integrableExpSet, deriv_bernoulliFun, NNReal.nnnorm_eq, det_fderivPiPolarCoordSymm, Polynomial.hasStrictDerivAt, DilationEquiv.smulTorsor_ratio, Real.deriv2_qaryEntropy, Real.differentiableAt_exp, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, CFC.monotone_sqrt, NumberField.mixedEmbedding.commMap_apply_of_isReal, ZSpan.fundamentalDomain_pi_basisFun, AffineMap.hasStrictDerivAt, LipschitzWith.ae_differentiableAt_of_real, InnerProductSpace.toLinearMap_rankOne, Seminorm.finset_sup_smul, MeasureTheory.Measure.integrable_comp_iff, quasispectrum.isCompact_nnreal, HasMFDerivWithinAt.mul, Bundle.RiemannianMetric.pos, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, HilbertBasis.repr_self, nnnorm_commutator_sub_one_le, CStarAlgebra.instNonnegSpectrumClass', CStarAlgebra.conjugate_le_norm_smul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, DoubleCentralizer.norm_fst, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, BoundedContinuousFunction.coe_toContinuousMapβ, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, BoundedContinuousFunction.add_norm_nonneg, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, Complex.equivRealProdCLM_symm_apply_re, HasFDerivAtFilter.isLittleOTVS, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, MeasureTheory.L2.integrable_inner, MeasureTheory.hasFiniteIntegral_prod_iff, IsUltrametricDist.nnnorm_intCast_le_one, MeasureTheory.charFun_map_mul, fderiv_ccosh, DoubleCentralizer.coe_fst, HasStrictFDerivAt.cpow, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, norm_cfcβ_one_sub_one_add_inv_lt_one, BoundedContinuousFunction.norm_sub_nonneg, NumberField.mixedEmbedding.latticeBasis_repr_apply, Filter.HasBasis.isBigOTVS_iff, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, continuousOn_cfcβ_nnreal, DifferentiableWithinAt.norm_sq, ContinuousMapZero.instCStarRing, SchwartzMap.integral_fourierInv_mul_eq, hasFDerivWithinAt_iff_hasGradientWithinAt, Real.fourierIntegral_continuousLinearMap_apply', IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, Real.differentiable_fourierChar, VectorFourier.fourierPowSMulRight_apply, Matrix.linfty_opNorm_eq_opNorm, nnnorm_cfc_lt_iff, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, spectrum.spectralRadius_le_nnnorm, Real.deriv_cos', isBigO_deriv_rpow_const_atTop, hasDerivAt_pow, contDiff_succ_iff_deriv, WithCStarModule.inner_single_left, DifferentiableOn.dist, Real.deriv_rpow_const', NumberField.mixedEmbedding.normAtPlace_negAt, Orthonormal.orthogonalFamily, Real.differentiableAt_arcosh, IsLocalMaxOn.fderivWithin_eq_zero, AlternatingMap.measure_def, MeasureTheory.Integrable.of_mem_Icc, nnnormHom_apply, LinearMap.isSymmetric_iff_sesqForm, hasDerivWithinAt_derivWithin_iff, hasStrictDerivAt_exp, Complex.isometryOfOrthonormal_apply, Complex.sameRay_iff, MeasureTheory.eLpNorm'_const_smul_le, AddCircle.norm_le_half_period, Real.hasStrictDerivAt_sqrt, Polynomial.deriv, Int.nnnorm_natCast, Real.hasDerivAt_tan_of_mem_Ioo, contMDiffOn_comp_projIcc_iff, NumberField.mixedEmbedding.finrank, SchwartzMap.integral_fourier_smul_eq, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, Polynomial.hasFDerivWithinAt_aeval, Orientation.inner_rightAngleRotation_right, continuousOn_cfcβ_setProd, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, ProbabilityTheory.HasSubgaussianMGF.memLp, LinearMap.continuous_of_isClosed_ker, Unitization.complex_cfcβ_eq_cfc_inr, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Orientation.volumeForm_apply_le, differentiableAt_iff_comp_add_const, BoundedContinuousFunction.toContinuousMapβ_apply, RCLike.nnnorm_nnqsmul, nnnorm_commutator_units_sub_one_le, ProbabilityTheory.Kernel.eLpNorm_density_le, CStarAlgebra.norm_negPart_le, NumberField.mixedEmbedding.negAt_apply_norm_isReal, innerββ_apply, HasFDerivWithinAt.isBigOTVS_sub, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, hasStrictFDerivAt_list_prod, UnitAddCircle.mem_addWellApproximable_iff, div_le_egauge_ball, StrongDual.toLp_apply, IsUltrametricDist.nnnorm_natCast_le_one, unitary.expUnitary_eq_mul_inv, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, contDiff_infty_iff_deriv, PositiveLinearMap.norm_apply_le_of_nonneg, LinearMap.toSeminorm_ball_zero, Complex.nnnorm_intCast, Real.differentiableAt_negMulLog, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, NonUnitalCStarAlgebra.toIsScalarTower, Orientation.inner_rightAngleRotationAuxβ_left, CStarRing.to_normedStarGroup, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasDerivAt.inner, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', Orientation.areaForm_apply_self, CFC.sqrt_le_sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, ProbabilityTheory.hasFiniteIntegral_compProd_iff, DoubleCentralizer.natCast_toProd, Real.differentiable_fourierChar_neg_bilinear_right, Complex.conjCLE_norm, ProbabilityTheory.variance_linearMap_gaussianReal, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, MeasureTheory.SignedMeasure.integrable_rnDeriv, AffineSubspace.signedInfDist_def, isScalarTower_sphere_ball_ball, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, MeasureTheory.BoundedContinuousFunction.inner_toLp, exists_extension_norm_eq, CStarModule.continuous_inner, ProbabilityTheory.integrable_exp_mul_of_le, hasStrictDerivAt_exp_zero_of_radius_pos, NormedSpace.closedBall_inv_subset_polar_closedBall, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, ContinuousLinearMap.norm_smulRightL_le, DoubleCentralizer.one_toProd, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, Complex.imCLM_enorm, StarAlgEquiv.nnnorm_map, SchwartzMap.tsupport_derivCLM_subset, hasDerivAt_single, OrthonormalBasis.coe_toBasis_repr_apply, det_rotation, RCLike.enorm_conj, PadicInt.norm_mahler_eq, nnnorm_cfc_nnreal_lt_iff, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, hasStrictDerivAt_exp_of_mem_ball, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, AlternatingMap.measure_parallelepiped, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, NonUnitalCommCStarAlgebra.toSMulCommClass, norm_cfcHom, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, norm_commutator_units_sub_one_le, Affine.Simplex.signedInfDist_affineCombination, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, WeakDual.CharacterSpace.equivAlgHom_coe, AddCircle.norm_eq, le_egauge_ball_one, spectrum.le_nnnorm_of_mem, not_integrableOn_Ici_inv, DoubleCentralizer.natCast_snd, Matrix.l2_opNNNorm_diagonal, Int.toNat_add_toNat_neg_eq_nnnorm, spectrum.exists_nnnorm_eq_spectralRadius, HasFDerivAt.hasGradientAt, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Real.differentiableAt_sinh, ContinuousLinearMap.isBigOTVS_fun_comp, NormedField.denselyOrdered_range_nnnorm, signedDist_eq_dist_iff_vsub_mem_span, Real.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, exp_neg_integrableOn_Ioi, MeasureTheory.Integrable.const_inner, hasStrictDerivAt_exp_smul_const_of_mem_ball', rotation_symm, CompletelyPositiveMap.map_cstarMatrix_nonneg', IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, VectorFourier.norm_fourierPowSMulRight_le, Complex.equivRealProdCLM_symm_apply_im, AddChar.linearIndependent, coe_ringEquiv_lpBCF_symm, integrable_exp_neg_mul_sq_iff, nndist_homothety_center, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Unitization.splitMul_injective, MeasureTheory.eLpNorm'_const_smul_le', Polynomial.cauchyBound_X_add_C, Antitone.deriv_nonpos, CStarAlgebra.inr_mem_Icc_iff_nnnorm_le, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, MeasureTheory.Lp.smul_assoc, differentiable_tsum', DoubleCentralizer.sub_snd, MonotoneOn.nnnorm_cfc, norm_iteratedFDerivWithin_mul_le, VectorFourier.norm_fourierSMulRight, Polynomial.differentiable, ContinuousLinearEquiv.coord_norm', GaussianFourier.integrable_cexp_neg_sum_mul_add, ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, differentiableOn_abs, WithCStarModule.pi_norm_sq, ProbabilityTheory.hasDerivAt_mgf, HasFPowerSeriesAt.eq_zero_of_eventually, div_le_egauge_closedBall, hasStrictFDerivAt_inv', LinearMap.mem_span_iff_bound, ProbabilityTheory.integrable_toReal_condDistrib, hasFDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_mul_const, SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, Probability.integrable_cauchyPDFReal, MeasureTheory.integrable_toReal_iff, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, SchwartzMap.fourier_fderivCLM_eq, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, hasStrictFDerivAt_exp_smul_const, integrableOn_rpow_mul_exp_neg_mul_sq, Complex.hasStrictFDerivAt_log_real, Asymptotics.isBigOTVS_map, Real.hasStrictDerivAt_tan, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, RCLike.wInner_cWeight_const_right, SimpleGraph.isEquivalent_extremalNumber, Real.nnnorm_rpow_of_nonneg, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, iter_deriv_inv_linear, ProbabilityTheory.deriv_cgf_zero, AffineMap.differentiable, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, DifferentiableAt.norm, Real.differentiable_fourierChar_neg_bilinear_left, fderiv_norm_smul_pos, MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore, Real.hasDerivAt_arctan, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Finset.nnnorm_prod_le, WithLp.unitization_mul, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, EuclideanSpace.nnnorm_eq, CStarAlgebra.star_right_conjugate_le_norm_smul, innerββ_apply_coe, RCLike.nnnorm_natCast, fderiv_csinh, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, ContinuousMap.norm_smul_const, range_modelWithCornersEuclideanHalfSpace, ContinuousMapZero.toNNReal_neg_smul, AddChar.wInner_cWeight_eq_boole, CStarRing.nnnorm_self_mul_star, differentiableAt_of_deriv_ne_zero, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, ContinuousLinearMap.opNorm_mulLeftRight_le, Polynomial.cauchyBound_X_sub_C, DoubleCentralizer.intCast_fst, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, TemperedDistribution.fourier_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, enorm_pow, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, IsLocalMin.fderiv_eq_zero, CStarAlgebra.nnnorm_le_nnnorm_of_nonneg_of_le, hasStrictFDerivAt_list_prod', Real.differentiableAt_qaryEntropy, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Submodule.orthogonal_eq_inter, ContinuousLinearMap.lsmul_flip_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, norm_iteratedFDeriv_smul_le, integrable_exp_neg_mul_sq, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, LinearPMap.mem_adjoint_domain_iff, differentiableWithinAt_zpow, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, CircleIntegrable.out, nnnorm_prod, AddCircle.closedBall_ae_eq_ball, contDiffOn_infty_iff_deriv_of_isOpen, SchwartzMap.integrable_pow_mul, MeasureTheory.memLp_of_bounded, ContinuousMultilinearMap.norm_smulRight, hasFDerivAt_exp_zero_of_radius_pos, CStarAlgebra.span_nonneg_inter_ball, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearMap.hasDerivWithinAt, hasStrictFDerivAt_pow, NormedSpace.polar_closedBall, ContinuousMapZero.toNNReal_smul, integrable_mulExpNegMulSq_comp, integrable_cexp_quadratic, AffineSubspace.signedInfDist_apply_self, ContinuousLinearMap.opNorm_lsmul, coe_innerββ_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, ModularGroup.lcRow0_apply, hasDerivAt_exp_zero, deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, MeasureTheory.integrable_withDensity_iff, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PeriodPair.indep, Module.Basis.opNorm_le, ContMDiff.codRestrict_sphere, Real.differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, SchwartzMap.smulLeftCLM_apply, MeasureTheory.Integrable.norm, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, fderiv_csin, AddCircle.norm_eq', WeakDual.isSeqCompact_polar, CFC.monotoneOn_cfcβ_rpowIntegrandββ, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.intervalIntegrable_charFun, ProbabilityTheory.integrable_rpow_of_mem_interior_integrableExpSet, hasFDerivWithinAt_pow, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, coe_algEquiv_lpBCF_symm, NormedField.valuation_apply, hasDerivWithinAt_inv, Asymptotics.isBigOTVS_prodMk_left, hasStrictDerivAt_id, instNonemptySeedRatReal, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, deriv_neg, abs_signedDist_le_dist, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, HasFDerivAt.cpow, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Complex.isometryOfOrthonormal_symm_apply, WithLp.unitizationAlgEquiv_apply, Real.hasStrictDerivAt_rpow_const, egauge_smul_right, LinearMap.hasDerivAtFilter, intervalIntegral.integral_hasFDerivAt, MeasureTheory.memLp_norm_iff, differentiableAt_inv, integrable_mul_cexp_neg_mul_sq, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.GammaIntegral_convergent, MeasureTheory.hausdorffMeasure_homothety_preimage, HasFPowerSeriesAt.locally_zero_iff, norm_sub_mul_le, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', norm_lt_iff_of_nonempty_compactlySupported, RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, AffineSubspace.signedInfDist_apply_of_mem, hasDerivAt_exp_of_mem_ball, hasStrictDerivAt_exp_smul_const_of_mem_ball, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, CStarAlgebra.instNonnegSpectrumClassComplexUnital, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, differentiableAt_abs, ConvexOn.real_sSup_of_nat_affine_eq, hasFDerivAt_inv', ProbabilityTheory.IsRatCondKernelCDF.integrable, Ideal.Quotient.norm_mk_le, ProbabilityTheory.charFun_gaussianReal, WeakDual.CharacterSpace.exists_apply_eq_zero, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, DifferentiableOn.norm, Complex.map_isometryOfOrthonormal, quasispectrum.instCompactSpaceNNReal, hasDerivAt_zpow, TemperedDistribution.fourierTransformInv_apply, WeakDual.CharacterSpace.compContinuousMap_id, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, MeasureTheory.MemLp.integrable_norm_pow', differentiableAt_inverse, Matrix.l2_opNorm_def, signedDist_apply_linear, Real.differentiableAt_sin, RCLike.wInner_nonneg, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, parallelepiped_orthonormalBasis_one_dim, Complex.reCLM_enorm, MeasureTheory.integrable_mconv_iff, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, Polynomial.toAddCircle_C_eq_smul_fourier_zero, norm_innerSL_le, MeasureTheory.eLpNorm'_norm_rpow, VectorFourier.hasFDerivAt_fourierChar_smul, integrable_cexp_quadratic', Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, HasStrictFDerivAt.csinh, InformationTheory.not_differentiableAt_klFun_zero, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, Real.exists_extension_norm_eq, nnnorm_cfcβ_nnreal_le, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sin, AffineMap.deriv, SmoothBumpCovering.embeddingPiTangent_coe, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ProbabilityTheory.covarianceBilinDual_of_not_memLp', PadicComplex.nnnorm_extends, enorm_inv, SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', UnitAddTorus.span_mFourierLp_closure_eq_top, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, MeasureTheory.Integrable.integral_norm_condKernel, Complex.nnnorm_eq_one_of_pow_eq_one, HasMFDerivAt.mul', nnnorm_zpow, ProbabilityTheory.integrable_gaussianPDFReal, Asymptotics.IsBigOTVS.refl, expNegInvGlue.differentiable_polynomial_eval_inv_mul, continuousOn_cfcβ_nnreal_setProd, cfcHom_eq_of_isStarNormal, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, eHolderNorm_smul, HasGradientWithinAt.hasFDerivWithinAt, hasFDerivAt_exp, Orientation.volumeForm_comp_linearIsometryEquiv, Pi.orthonormalBasis_repr, deriv_mul_const_field', Polynomial.hasDerivWithinAt, differentiableAt_iff_comp_sub_const, CFC.norm_sqrt, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, NumberField.Units.basisOfIsMaxRank_fundSystem, LinearMap.isAdjointPair_inner, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, AnalyticOnNhd.eval_mvPolynomial, WithLp.unitization_nnnorm_def, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Affine.Simplex.signedInfDist_apply_of_ne, ContinuousLinearMap.hasStrictDerivAt, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, signedDist_left_lineMap, hasFDerivAt_inv, Real.deriv_mul_log_zero, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, DoubleCentralizer.toProdHom_apply, DoubleCentralizer.mul_snd, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, IccRightChart_extend_top, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Asymptotics.IsBigO.isBigOTVS, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, WithCStarModule.prod_inner, measurableSet_of_differentiableWithinAt_Ici, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, one_le_nnnorm_one, ConvexOn.sSup_affine_eq, unitary.mem_pathComponentOne_iff, nndist_self_homothety, boundary_Icc, deriv_sqrt_mul_log', Asymptotics.isLittleOTVS_sup, Real.differentiableAt_binEntropy_iff_ne_zero_one, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, derivWithin_const_mul_field, CFC.nnnorm_nnrpow, SchwartzMap.integrable_pow_mul_iteratedFDeriv, Real.fderiv_fourierChar_neg_bilinear_left_apply, Real.deriv_tan, isConformalMap_iff_is_complex_or_conj_linear, Asymptotics.isEquivalent_of_tendsto_one', RCLike.span_one_I, egauge_zero_right, Asymptotics.isThetaTVS_iff_isTheta, Real.exists_measure_rpow_eq_integral, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, Real.fourierIntegral_continuousMultilinearMap_apply', HasGradientAtFilter.hasDerivAtFilter, AddCircle.norm_eq_of_zero, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, MeasureTheory.eLpNorm_conj, hasDerivAt_exp_smul_const_of_mem_ball, ProbabilityTheory.integrable_comp_iff, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, NonUnitalCStarAlgebra.toSMulCommClass, CStarRing.nnnorm_star_mul_self, DoubleCentralizer.intCast_toProd, Matrix.PosDef.posDef_sqrt, integrable_cexp_neg_mul_sq, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, differentiableAt_comp_sub_const, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, finrank_euclideanSpace_fin, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, CFC.norm_nnrpow, coe_algEquiv_lpBCF, CStarAlgebra.nnnorm_le_natCast_iff_of_nonneg, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', InformationTheory.deriv_klFun, boundary_product, differentiable_sigmoid, LinearMap.mem_span_iff_continuous, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, NormedField.exists_lt_nnnorm, Asymptotics.isBigOTVS_comm, OrthonormalBasis.repr_reindex, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, AnalyticOnNhd.eval_continuousLinearMap, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, Asymptotics.isLittleOTVS_pi, ProbabilityTheory.integral_tilted_mul_self, integrableOn_Ioi_deriv_norm_ofReal_cpow, CStarAlgebra.span_unitary, integrable_of_le_of_pow_mul_le, nndist_homothety_self, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, le_iff_norm_sqrt_mul_rpow, DoubleCentralizer.smul_snd, deriv_div_const, Complex.det_conjLIE, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, CStarAlgebra.nnnorm_mem_spectrum_of_nonneg, RCLike.realLinearIsometryEquiv_apply, ProbabilityTheory.mgf_pos_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, ContinuousLinearMap.norm_smulRightL_apply, Asymptotics.IsThetaTVS.rfl, Orientation.areaForm_rightAngleRotation_left, Differentiable.norm, CStarAlgebra.exists_sum_four_nonneg, SchwartzMap.smulLeftCLM_smul, differentiableAt_iff_comp_neg, DoubleCentralizer.coe_snd, NumberField.mixedEmbedding.disjoint_negAt_plusPart, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, DifferentiableAt.dist, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, PositiveLinearMap.preGNS_norm_sq, ConvexOn.univ_sSup_of_nat_affine_eq, differentiableOn_inv, Icc_isBoundaryPoint_top, ConvexOn.slope_le_leftDeriv_of_mem_interior, ContinuousMultilinearMap.norm_mkPiAlgebraFin, hasFDerivAt_exp_of_mem_ball, MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, egauge_le_of_smul_mem_of_ne, NumberField.house_eq_sup', fderiv_norm_sq, Seminorm.smul_le_smul, WeakDual.CharacterSpace.instStarHomClass, NonUnitalCommCStarAlgebra.toIsScalarTower, Int.Matrix.exists_ne_zero_int_vec_norm_le, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, ContinuousLinearMap.coe_mulβα΅’, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', Real.integrableOn_rpowIntegrandββ_Ici, egauge_pi', ModularGroup.smul_eq_lcRow0_add, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, hasDerivAt_abs_pos, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', CStarMatrix.norm_def, differentiableWithinAt_Ioi_iff_Ici, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, Polynomial.IsRoot.norm_lt_cauchyBound, HasCompactSupport.hasFDerivAt_convolution_left, Complex.isEquivalent_sin, differentiableOn_zpow, HolderWith.smul_iff, DoubleCentralizer.add_toProd, CFC.abs_eq_zero_iff, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, MeasureTheory.integrable_rnDeriv_mul_log_iff, TemperedDistribution.smulLeftCLM_apply_apply, integrableAtFilter_rpow_atTop_iff, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, nndist_lineMap_left, Orientation.inner_mul_areaForm_sub, fderiv_inner_apply, contDiff_one_iff_deriv, MeasureTheory.eLpNormEssSup_const_smul_le', deriv2_sqrt_mul_log, Real.hasStrictDerivAt_log_of_pos, FormalMultilinearSeries.ofScalars_norm, contMDiffOn_projIcc, MeasureTheory.SignedMeasure.im_toComplexMeasure, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, MeasureTheory.pdf.hasFiniteIntegral_mul, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, IsSelfAdjoint.nnnorm_pow_two_pow, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, parallelepiped_single, contMDiff_circleExp, Quaternion.nnnorm_coe, Real.deriv2_negMulLog, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Urysohns.CU.lim_eq_midpoint, MeasureTheory.Measure.integrable_pow_neg_integrablePower, HasFDerivAt.const_cpow, DoubleCentralizer.neg_fst, CStarMatrix.inner_toCLM_conjTranspose_right, norm_jacobiThetaβ_term_fderiv_le, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, Unitization.nnnorm_inr, quasispectrum.instCompactSpace, fderiv_eq_smul_deriv, integrableOn_rpow_mul_exp_neg_mul_rpow, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, CStarMatrix.toCLM_apply_single_apply, MeasureTheory.Measure.integrable_toReal_rnDeriv, Real.isEquivalent_sinh, Int.Matrix.exists_ne_zero_int_vec_norm_le', intervalIntegral.differentiableOn_integral_of_continuous, hasStrictFDerivAt_exp_smul_const_of_mem_ball, differentiable_circleMap, DoubleCentralizer.toProdMulOppositeHom_apply, selfAdjoint.joined_one_expUnitary, integrableOn_exp_mul_complex_Ioi, Unitization.cfcβ_eq_cfc_inr, le_iff_norm_sqrt_mul_sqrt_inv, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Complex.restrictScalars_toSpanSingleton', Real.differentiableAt_negMulLog_iff, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, fderiv_inv', BoundedContinuousFunction.integrable_of_nnreal, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, IsLocalMinOn.fderivWithin_eq_zero, Real.deriv2_mul_log, egauge_smul_left, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, Orientation.abs_volumeForm_apply_le, Complex.conjLIE_symm, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding', deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, Affine.Simplex.signedInfDist_incenter, ProbabilityTheory.integrable_rpow_mul_exp_of_mem_interior_integrableExpSet
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| Name | Category | Theorems |
|---|
induced π | CompOp | β |
toCommRing π | CompOp | 160 mathmath: LinearMap.subset_bipolar, HasSum.exp, NormedSpace.isBounded_polar_of_mem_nhds_zero, contDiffAt_prod', MeasureTheory.Integrable.fin_nat_prod, Finset.analyticOnNhd_prod, MDifferentiableAt.prod, HasFDerivWithinAt.pow, hasFDerivAt_multiset_prod, HasStrictDerivAt.pow, HasDerivAt.fun_finset_prod, LinearMap.polar_eq_iInter, deriv_fun_finset_prod, fderiv_multiset_prod, AnalyticOnNhd.eval_linearMap', fderiv_fun_pow, HasStrictFDerivAt.pow, MeasureTheory.MemLp.prod, HasFDerivAt.finset_prod, Matrix.exp_neg, gelfandStarTransform_naturality, LinearMap.polar_singleton, gelfandStarTransform_apply_apply, ContinuousMultilinearMap.norm_mkPiAlgebra_le, DifferentiableAt.fun_finset_prod, gelfandTransform_bijective, NormedSpace.isClosed_polar, HasFDerivWithinAt.multiset_prod, RingHomIsometric.starRingEnd, multipliable_one_add_of_summable, hasStrictFDerivAt_multiset_prod, fderivWithin_finset_prod, HasDerivAt.pow, EulerProduct.eulerProduct_hasProd, spectrum.gelfandTransform_eq, HasDerivAt.fun_pow, contDiffOn_prod', HasDerivWithinAt.fun_finset_prod, NormedSpace.smul_mem_polar, EulerProduct.eulerProduct, gelfandStarTransform_symm_apply, Finset.analyticWithinAt_fun_prod, contDiffWithinAt_prod', contDiffOn_prod, hasStrictFDerivAt_exp_smul_const', deriv_pow, fderiv_pow, HasFDerivAt.pow, Finset.analyticWithinAt_prod, Finset.nnnorm_prod_le', AnalyticOnNhd.eval_linearMap, NormedSpace.polar_ball_subset_closedBall_div, gelfandTransform_map_star, EulerProduct.eulerProduct_tprod, fderiv_pow_ring, hasFDerivAt_list_prod', Finset.norm_prod_one_add_sub_one_le, MeasureTheory.MemLp.prod', Summable.hasProdUniformlyOn_nat_one_add, MeasureTheory.Integrable.fintype_prod_dep, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, hasFDerivAt_exp_smul_const', Matrix.exp_zsmul, MDifferentiableOn.prod, HasStrictDerivAt.fun_finset_prod, norm_iteratedFDerivWithin_prod_le, AnalyticOnNhd.aeval_mvPolynomial, fderivWithin_fun_pow, HasFDerivAt.multiset_prod, NormedSpace.exp_sum, Summable.multipliableLocallyUniformlyOn_one_add, ContinuousMultilinearMap.norm_mkPiAlgebra, contDiffAt_prod, Summable.multipliableLocallyUniformlyOn_nat_one_add, DifferentiableWithinAt.finset_prod, Summable.hasProdLocallyUniformlyOn_one_add, Summable.multipliableUniformlyOn_one_add, hasFDerivAt_pow, LinearMap.polar_gc, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, LinearMap.polar_weak_closed, EulerProduct.eulerProduct_hasProd_mulIndicator, AnalyticOnNhd.eval_polynomial, fderivWithin_multiset_prod, Finset.norm_prod_le', StrongDual.polar_univ, DifferentiableOn.finset_prod, DifferentiableOn.fun_finset_prod, hasFDerivAt_exp_smul_const, fderiv_finset_prod, LinearMap.mem_polar_singleton, hasStrictFDerivAt_finset_prod, LinearMap.polar_eq_biInter_preimage, LinearMap.tripolar_eq_polar, contDiff_prod', norm_iteratedFDeriv_prod_le, Finset.analyticAt_prod, derivWithin_fun_finset_prod, HasDerivWithinAt.fun_pow, HasDerivWithinAt.finset_prod, HasMFDerivAt.prod, Finset.analyticOn_fun_prod, Differentiable.fun_finset_prod, NormedSpace.sInter_polar_eq_closedBall, deriv_finset_prod, contDiffWithinAt_prod, derivWithin_fun_pow, StrongDual.zero_mem_polar, ContinuousMapZero.instCStarRing, HasStrictFDerivAt.multiset_prod, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, HasDerivWithinAt.pow, LinearMap.polar_isClosed, Summable.hasProdLocallyUniformlyOn_nat_one_add, StrongDual.polar_empty, DifferentiableWithinAt.fun_finset_prod, analyticAt_finprod, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, MeasureTheory.Integrable.fintype_prod, derivWithin_finset_prod, AnalyticAt.aeval_mvPolynomial, deriv_fun_pow, hasStrictFDerivAt_exp_smul_const, Summable.hasProdUniformlyOn_one_add, DifferentiableAt.finset_prod, gelfandTransform_isometry, Finset.nnnorm_prod_le, HasStrictDerivAt.finset_prod, StrongDual.polar_zero, HasFDerivWithinAt.finset_prod, StrongDual.mem_polar_iff, Differentiable.finset_prod, HasDerivAt.finset_prod, fderivWithin_pow, hasStrictFDerivAt_pow, AnalyticOn.eval_polynomial, prod_vanishing_of_summable_norm, hasFDerivWithinAt_pow, LinearMap.polar_mem_iff, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, StrongDual.polar_singleton, Finset.norm_prod_le, StrongDual.mem_polar_singleton, Summable.multipliableUniformlyOn_nat_one_add, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', LinearMap.polar_mem, fderivWithin_pow_ring, derivWithin_pow, MDifferentiable.prod, Finset.analyticAt_fun_prod, AnalyticOnNhd.eval_continuousLinearMap, StrongDual.polar_nonempty, contDiff_prod, Finset.analyticOnNhd_fun_prod, MDifferentiableWithinAt.prod, Finset.analyticOn_prod, HasStrictFDerivAt.finset_prod, hasFDerivAt_finset_prod, HasStrictDerivAt.fun_pow
|
toNonUnitalNormedCommRing π | CompOp | 2808 mathmath: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, ValueDistribution.logCounting_zero, hasFDerivAt_iff_hasDerivAt, LinearMap.IsSymmetric.clm_adjoint_eq, Real.hasDerivAt_arccos, InnerProductSpace.Core.inner_smul_right, HasStrictFDerivAt.log, continuousSMul_sphere_ball, WithLp.prod_inner_apply, fderiv_iteratedFDeriv, Polynomial.differentiableWithinAt, RCLike.sqrt_eq_ite, FormalMultilinearSeries.comp_rightInv_aux1, tendsto_zero_iff_meromorphicOrderAt_pos, Unitization.isometry_inr, LinearMap.mkContinuousβ_norm_le', ContinuousMultilinearMap.norm_mkPiRing, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, Bundle.ContMDiffRiemannianMetric.isVonNBounded, MeasureTheory.lpNorm_conj, TensorProduct.enorm_lid, InnerProductSpace.Core.inner_add_left, differentiableAt_comp_neg, ProbabilityTheory.cdf_measure_stieltjesFunction, continuous_cfcβHomSuperset_left, hasDerivWithinAt_Iio_iff_Iic, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, LinearMap.mkContinuousβ_apply, Matrix.frobenius_nnnorm_mul, RCLike.pos_iff_exists_ofReal, TensorProduct.inner_tmul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, Orthonormal.inner_left_finsupp, LeftInvariantDerivation.lift_zero, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcβHom, logDeriv_const, RCLike.map_apply, MDifferentiableOn.clm_postcomp, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuousβ, LinearMap.IsSymmetric.inner_map_polarization, hasDerivWithinAt_add_const_iff, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, HasFDerivWithinAt.ccos, RCLike.ofRealCLM_apply, PadicInt.lift_sub_val_mem_span, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, hasStrictDerivAt_intCast, cfcβ_norm_nonneg, Complex.linearEquiv_det_conjLIE, LeftInvariantDerivation.leibniz, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.convolution_eq_right', Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, RCLike.reCLM_apply, smooth_barycentric_coord, cfcβHom_apply_mem_elemental, curveIntegral_smul, CFC.abs_eq_cfc_norm, inner_vsub_right_eq_zero_symm, CFC.sqrt_eq_one_iff', Filter.Tendsto.cfc, CFC.posPart_one, InnerProductSpace.rankOne_one_left_eq_innerSL, ContinuousMap.abs_mem_subalgebra_closure, Function.FactorizedRational.divisor, NonUnitalCStarAlgebra.toStarModule, hasDerivAt_sqrt_mul_log, HasFiniteFPowerSeriesAt.neg, HasStrictFDerivAt.csin, Polynomial.isEquivalent_atBot_div, nnnorm_cfcβ_nnreal_le_iff, ContinuousLinearMap.map_add_add, MeromorphicAt.analyticAt, HasFDerivWithinAt.pow, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, WeakDual.isCompact_polar, nnnorm_cfc_lt, EuclideanSpace.orthonormal_single, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, Real.hasDerivAt_sigmoid, meromorphicOrderAt_const_ofNat, Asymptotics.IsTheta.const_mul_left, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, LinearMap.IsPositive.ne_zero_iff, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, differentiableAt_zpow, hasFDerivAt_multiset_prod, MDifferentiableAt.cle_arrowCongr, ProbabilityTheory.covarianceBilinDual_apply', spectrum.subset_closedBall_norm_mul, continuousSMul_sphere_sphere, RCLike.re_add_im, CFC.posPart_natCast, hasFTaylorSeriesUpToOn_top_iff_right, smoothSheafCommRing.nonunits_stalk, MeasureTheory.convolution_mul, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, deriv_mem_iff, Matrix.spectrum_toEuclideanLin, FormalMultilinearSeries.radius_pi_eq_iInf, CFC.tendsto_cfc_rpow_sub_one_log, MeasureTheory.lpNorm_fun_div_natCast, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, Padic.withValUniformEquiv_norm_le_one_iff, tendsto_cobounded_iff_meromorphicOrderAt_neg, Real.hasStrictDerivAt_rpow_const_of_ne, lp.inner_eq_tsum, StrongDual.polarSubmodule_eq_setOf, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, CFC.sq_sqrt, RCLike.star_def, OrthonormalBasis.sum_inner_mul_inner, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, meromorphicOrderAt_const, ContinuousLinearMap.hasDerivAtFilter, fderivWithin_csinh, span_fourier_closure_eq_top, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, RCLike.conjCLE_norm, ordinaryHypergeometric_radius_top_of_neg_natβ, HasFPowerSeriesOnBall.add, WeakDual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.integral_apply, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', hensels_lemma, Padic.AddValuation.map_one, MeasureTheory.integral_fintype_prod_volume_eq_pow, Real.fderiv_fourierChar_neg_bilinear_right_apply, BoundedContinuousFunction.char_neg, Unitization.real_cfcβ_eq_cfc_inr, PadicInt.appr_spec, flip_innerSL_real, Matrix.le_iff, norm_cfc_lt_iff, hasFPowerSeriesOnBall_pi_iff, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, continuousOn_dslope, ContDiffMapSupportedIn.structureMapCLM_apply, RCLike.sub_conj, iteratedFDerivWithin_succ_eq_comp_right, NumberField.mem_maximalRealSubfield_iff, HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', SchwartzMap.lineDerivOp_fourier_eq, RCLike.pos_iff, PadicInt.valuation_zero, deriv_comp_const_sub, LeftInvariantDerivation.coe_derivation, innerSL_apply_apply, RCLike.norm_expect_le, HasFPowerSeriesWithinOnBall.restrictScalars, CFC.abs_eq_cfcβ_coe_norm, LinearMap.adjoint_innerββ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, inner_sum, EuclideanSpace.inner_single_left, HasFTaylorSeriesUpTo.hasFDerivAt, EuclideanSpace.basisFun_toBasis, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Submodule.orthogonalProjectionFn_inner_eq_zero, hasDerivAt_neg', Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContMDiffOn.clm_postcomp, inner_eq_norm_mul_iff, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, eqOn_dslope_sub_smul, ContinuousLinearMap.IsPositive.inner_nonneg_right, LeftInvariantDerivation.left_invariant', selfAdjoint.expUnitaryPathToOne_apply, hasDerivAt_bernoulliFun, derivWithin_fderivWithin, CFC.nnnorm_sqrt, RCLike.wInner_sub_right, MultilinearMap.mkContinuousMultilinear_apply, ProbabilityTheory.uncenteredCovarianceBilin_apply, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, PadicInt.nthHom_zero, FormalMultilinearSeries.derivSeries_coeff_one, Polynomial.isCoveringMapOn_eval, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, PadicInt.sub_zmodRepr_mem, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, BoxIntegral.unitPartition.mem_smul_span_iff, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, ContinuousMap.setOfIdeal_ofSet_eq_interior, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, MeasureTheory.integral_fintype_prod_eq_prod, HasGradientAt.hasDerivAt', derivWithin_comp_const_sub, iteratedDeriv_pow, Int.padicValuation_lt_one_iff, AffineMap.hasDerivWithinAt, MeromorphicOn.divisor_const, LeftInvariantDerivation.left_invariant, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, EuclideanSpace.basisFun_apply, instSMulCommClass_sphere_sphere_sphere, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, PadicInt.nonarchimedean, NormedSpace.toIsBoundedSMul, ContinuousAt.cfc, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, Submodule.isOrtho_iff_inner_eq, Complex.hasStrictDerivAt_tan, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, curveIntegralFun_smul, ClosedSubmodule.mem_orthogonal', CFC.sqrt_rpow, hasDerivWithinAt_iff_isLittleO, ContinuousAlternatingMap.piLIE_apply_apply, PreInnerProductSpace.Core.smul_left, Matrix.PosSemidef.sqrt_eq_zero_iff, Differentiable.fderiv_norm_rpow, RCLike.normSq_neg, UnitAddTorus.mFourierSubalgebra_coe, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, hasDerivWithinAt_zero, RCLike.toStarOrderedRing, MeasureTheory.integral_const_mul, FormalMultilinearSeries.hasSum_of_finite, hasDerivAtFilter_ofNat, RCLike.is_real_TFAE, FormalMultilinearSeries.changeOriginSeries_summable_auxβ, curveIntegrable_smul_iff, ContinuousMap.toNNReal_neg_algebraMap, TensorProduct.toLinearEquiv_lidIsometry, HasFPowerSeriesOnBall.restrictScalars, ContinuousLinearMap.isometry_mul_flip, UpperHalfPlane.num_neg, OrthonormalBasis.toBasis_singleton, ContDiffOn.inner, PadicInt.zmodRepr_mul, AnalyticOnNhd.eval_linearMap', HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, contDiffOn_iff_continuousOn_differentiableOn, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, monomial_has_deriv_aux, LinearIsometryEquiv.conjStarAlgEquiv_apply, LinearMap.toMatrixOrthonormal_reindex, PiTensorProduct.projectiveSeminormAux_smul, MeasureTheory.integral_div, MeasureTheory.ConvolutionExistsAt.integrable, CompactlySupportedContinuousMap.nnrealPart_smul_neg, cfc_complex_eq_real, HasStrictFDerivAt.pow, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, norm_cfc_le_iff, fderivWithin_sinh, RCLike.mul_conj, iter_deriv_zpow', PadicInt.coe_sum, Matrix.exp_conj', hasLineDerivAt_iff_isLittleO_nhds_zero, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, HasFiniteFPowerSeriesOnBall.sum, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, ConvexOn.univ_sSup_of_countable_affine_eq, RCLike.hasSum_ofReal, CFC.negPart_algebraMap, InnerProductSpace.inner_left_rankOne_apply, Matrix.PosSemidef.commute_iff, cfcβHom_nnreal_eq_restrict, TestFunction.toBoundedContinuousFunctionCLM_apply, IsLocalFrameOn.coeff_apply_of_mem, HasFDerivAt.finset_prod, ENNReal.orderIsoRpow_symm_apply, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, Matrix.exp_neg, HasSum.hasSum_at_zero, HasFPowerSeriesAt.add, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, ContinuousAlternatingMap.curryLeft_smul, polynomialFunctions.starClosure_topologicalClosure, antideriv_bernoulliFun, innerββ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, ContMDiffAt.clm_postcomp, RCLike.ofReal_balance, ContMDiffWithinAt.clm_postcomp, hasDerivWithinAt_pi, smoothSheafCommRing.instLocalRing_stalk, Real.integrable_prod_sub, HasFDerivWithinAt.csin, PadicAlgCl.isNonarchimedean, ContinuousLinearMap.eq_adjoint_iff, MeasureTheory.L2.inner_def, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RCLike.nonpos_iff, RCLike.nonpos_iff_exists_ofReal, Polynomial.div_tendsto_zero_iff_degree_lt, RCLike.wInner_of_isEmpty, Real.volume_val, Continuous.cfc', OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Int.padicValuation_eq_one_iff, HasFPowerSeriesAt.comp, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, LinearMap.polar_singleton, FormalMultilinearSeries.sum_of_finite, HasFTaylorSeriesUpToOn.zero_eq', intervalIntegral.integral_div, NormedSpace.Dual.toWeakDual_continuous, PadicInt.le_valuation_add, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMultilinearMap.norm_smulRightL_le, ContinuousLinearMap.precompL_apply, differentiableAt_comp_add_const, IsSelfAdjoint.adjoint_eq, RCLike.ofReal_comp_balance, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, Real.hasDerivAt_arcosh, FormalMultilinearSeries.radius_le_smul, MDifferentiable.clm_postcomp, ContinuousLinearMap.isPositive_self_comp_adjoint, RCLike.ofReal_sub, LinearMap.adjoint_toContinuousLinearMap, hasDerivAt_iff_isLittleO, Polynomial.toAddCircle_X_pow_eq_fourier, HasDerivWithinAt.hasFDerivWithinAt, Polynomial.abs_div_tendsto_atTop_of_degree_gt, Continuous.cfc_nnreal', hasFPowerSeriesAt_const, fderiv_eq_deriv_mul, Submodule.starProjection_inner_eq_zero, nndist_right_lineMap, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, FormalMultilinearSeries.radius_compNeg, Polynomial.differentiableOn_aeval, LinearIsometryEquiv.adjoint_eq_symm, extDeriv_fun_smul, fderivWithin_ccosh, ContinuousAlternatingMap.toAlternatingMap_curryLeft, MeromorphicAt.inv_iff, MeasureTheory.setIntegral_prod_mul, Matrix.toEuclideanLin_apply, iteratedDerivWithin_eq_iteratedFDerivWithin, HasFDerivWithinAt.mul, LinearMap.IsPositive.isPositive_smul_iff, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, RCLike.im_eq_zero_iff_isSelfAdjoint, HasFDerivWithinAt.multiset_prod, ContinuousLinearMap.opNorm_mul, MeasureTheory.integral_fintype_prod_eq_pow, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, InnerProductSpace.Core.inner_smul_ofReal_right, HasFDerivAt.arctan, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Real.hasStrictDerivAt_arccos, RCLike.conjCLE_apply, MDifferentiable.cle_arrowCongr, Unitization.nnnorm_def, Unitization.dist_inr, HasStrictFDerivAt.abs, IsUnit.cfcSqrt, CFC.continuousOn_log, isScalarTower_closedBall_closedBall_closedBall, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Function.locallyFinsuppWithin.logCounting_eval_zero, ProbabilityTheory.IndepFun.integral_comp_mul_comp, Complex.instContinuousStar, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, HasLineDerivAt.tendsto_slope_zero_right, isScalarTower_sphere_closedBall_closedBall, Complex.hasDerivAt_GammaIntegral, PadicInt.norm_lt_one_iff_dvd, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, PadicInt.mul_inv, PiTensorProduct.mapL_smul, RCLike.I_mul_I, ContinuousLinearMap.adjointAux_norm, RCLike.toIsStrictOrderedModule, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, ValueDistribution.logCounting_top, LeftInvariantDerivation.lift_add, hasDerivAtFilter_natCast, Polynomial.isEquivalent_atTop_lead, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, Pi.counit_eq_adjoint, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.toMatrixOrthonormal_apply_apply, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, RCLike.instCStarRing, LDL.lowerInv_orthogonal, HasStrictFDerivAt.arsinh, InnerProductSpace.Core.inner_neg_left, HasFDerivWithinAt.exp, ContinuousOn.cfc, summable_mul_of_bigO_atTop, SchwartzMap.fourier_lineDerivOp_eq, AddChar.wInner_cWeight_eq_zero_iff_ne, ContinuousLinearMapWOT.inducingFn_apply, entrywise_sup_norm_bound_of_unitary, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, hasStrictDerivAt_exp_smul_const, RCLike.ofReal_nonneg, ContinuousMap.setOfIdeal_ofSet_of_isOpen, isBoundedBilinearMap_comp, fderivWithin_sin, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, CFC.continuousOn_sqrt, hasStrictDerivAt_add_const_iff, Finsupp.sum_inner, MeasureTheory.integral_fin_nat_prod_volume_eq_prod, multipliable_one_add_of_summable, LeftInvariantDerivation.lift_smul, RCLike.complexRingEquiv_apply, FormalMultilinearSeries.rightInv_removeZero, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ClosedSubmodule.orthogonal_closure'', PadicInt.exists_mem_range, contDiffWithinAt_euclidean, hasStrictDerivAt_exp_smul_const', Complex.hasStrictFDerivAt_cpow', Real.fourier_iteratedFDeriv, EulerProduct.eulerProduct_completely_multiplicative, hasDerivAtFilter_zero, PadicInt.exists_mem_range_of_norm_rat_le_one, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, UnitAddTorus.mFourierCoeff_toLp, WeakDual.toStrongDual_inj, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, Asymptotics.IsEquivalent.mul, LinearMap.extendToπ'_apply, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, dslope_sub_smul, hasDerivAt_id', Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, ContinuousLinearMap.analyticOn_bilinear, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, fderiv.log, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, MeasureTheory.convolution_lsmul, MDifferentiableAt.clm_postcomp, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, hasDerivAt_abs_neg, coe_innerSL_apply, inner_eq_zero_of_right, LinearMap.IsSymmetric.inner_map_self_eq_zero, Real.deriv_sqrt_aux, deriv_fderiv, RegularNormedAlgebra.isometry_mul', PadicInt.inv_mul, Matrix.PosSemidef.det_sqrt, multipliable_norm_one_add_of_summable_norm, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, hasDerivWithinAt_abs, RCLike.toPosMulReflectLT, hasFPowerSeriesOnBall_const, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, TensorProduct.lidIsometry_apply, ContDiffMapSupportedIn.seminorm_le_iff, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, PadicInt.fwdDiff_tendsto_zero, Module.Basis.coe_toOrthonormalBasis_repr, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, norm_cfcβ_lt, hasGradientAtFilter_iff_isLittleO, MeasureTheory.convolution_precompR_apply, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, VectorFourier.fourierIntegral_iteratedFDeriv, hasGradientAt_iff_isLittleO, InformationTheory.hasDerivAt_klFun, ContinuousMap.toNNReal_algebraMap, InnerProductSpace.nnnorm_rankOne, BoundedContinuousFunction.mem_charPoly, StarAlgHom.continuous_realContinuousMapOfNNReal, BoundedContinuousFunction.charAlgHom_apply, LeftInvariantDerivation.comp_L, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, FormalMultilinearSeries.continuousOn_of_finite, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, Commute.cfc_real, LinearMap.trace_eq_sum_inner, Matrix.gram_zero, ContinuousAlternatingMap.curryLeft_apply_apply, ContinuousLinearMap.flip_smul, MeromorphicOn.divisor_inv, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, Submodule.norm_eq_iInf_iff_inner_eq_zero, MeromorphicOn.id, InnerProductSpace.isSymmetricProjection_rankOne_self, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, MeasureTheory.ConvolutionExistsAt.integrable_swap, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, Real.volume_eq_stieltjes_id, HasFiniteFPowerSeriesOnBall.eq_partialSum, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, IsLocalFrameOn.coeff_congr, nnnorm_cfcβ_nnreal_lt, CFC.sqrt_eq_rpow, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, AffineMap.hasDerivAt_lineMap, cfcβ_comp_norm, FiniteDimensional.rclike_to_real, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasDerivWithinAt.norm_sq, NormedSpace.smul_mem_polar, HasGradientAtFilter.hasDerivAtFilter', WeakDual.CharacterSpace.continuousMapEval_bijective, LDL.lowerInv_triangular, CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, HasFPowerSeriesOnBall.fderiv_eq, RCLike.wInner_neg_right, UpperHalfPlane.zero_form_isBoundedAtImInfty, continuousMap_mem_polynomialFunctions_closure, NormedSpace.inclusionInDoubleDual_norm_eq, Meromorphic.MeromorphicOn.countable_compl_analyticAt, AffineMap.hasDerivWithinAt_lineMap, NumberField.ComplexEmbedding.IsConj.eq, cfc_real_eq_nnreal, ContinuousLinearMap.fderiv_of_bilinear, Matrix.PosSemidef.posSemidef_sqrt, Real.hasDerivWithinAt_arccos_Ici, ContinuousLinearMap.nnnorm_toSpanSingleton, continuousOn_cfc_setProd, Polynomial.abs_tendsto_atTop_iff, ContinuousAlternatingMap.alternatizeUncurryFin_smul, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Complex.hasDerivAt_Gammaβ_one, StarAlgHom.realContinuousMapOfNNReal_apply, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, deriv_id'', HasFTaylorSeriesUpToOn.hasFDerivWithinAt, Submodule.adjoint_subtypeL, IsGreatest.norm_cfc, hasStrictFDerivAt_exp, ContinuousLinearMap.opNorm_mul_apply, ContinuousLinearMap.norm_smulRightL, Function.FactorizedRational.mulSupport, PadicInt.coe_addChar_of_value_at_one, RCLike.summable_ofReal, RCLike.conj_mul, MeasureTheory.convolution_def, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, HasDerivAt.hasFDerivAt, Polynomial.toAddCircle.integrable, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MDifferentiableWithinAt.cle_arrowCongr, RCLike.imLm_coe, HasFPowerSeriesWithinOnBall.prod, MDifferentiableWithinAt.clm_precomp, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, hasStrictDerivAt_const_add_iff, isBoundedBilinearMap_compMultilinear, hasFDerivAt_norm_rpow, Function.FactorizedRational.meromorphicOrderAt_eq, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, iteratedDeriv_fun_id_zero, HasFPowerSeriesOnBall.uniform_geometric_approx, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, summable_jacobiThetaβ_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, MeromorphicOn.divisor_sub_const_self, Unitization.cobounded_eq_aux, sum_inner, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, RCLike.ofReal_mul, Polynomial.div_tendsto_atBot_zero_of_degree_lt, iteratedDeriv_comp_sub_const, HasFPowerSeriesWithinAt.fderivWithin_eq, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, RCLike.instContinuousMapUniqueHom, FormalMultilinearSeries.id_comp', ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, analyticOrderAt_ne_zero, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, InnerProductSpace.Core.inner_neg_right, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, ProbabilityTheory.covarianceBilin_zero, CFC.posPart_algebraMap_nnreal, RCLike.conjCLE_coe, HasFPowerSeriesOnBall.sum, contDiffOn_stereoToFun, Polynomial.abs_tendsto_atTop, LeftInvariantDerivation.evalAt_coe, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', range_cfcβ, ContMDiffOn.clm_precomp, hasGradientAt_iff_isLittleO_nhds_zero, contDiffOn_nat_iff_continuousOn_differentiableOn, Matrix.PosSemidef.sqrt_eq_one_iff, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Complex.hasStrictFDerivAt_cpow, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, Filter.EventuallyEq.hasDerivAt_iff, InnerProductSpace.rankOne_eq_zero, Polynomial.differentiable_aeval, IsGreatest.nnnorm_cfc, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, RCLike.mul_wInner_left, Convex.toWeakSpace_closure, Function.FactorizedRational.finprod_eq_fun, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, Complex.hasStrictDerivAt_sinh, tsum_pow_div_one_sub_eq_tsum_sigma, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, RCLike.re_eq_norm_of_mul_conj, Bundle.ContMDiffRiemannianMetric.symm, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, HasFDerivAt.pow, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, meromorphicOrderAt_const_natCast, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, fderivWithin_inv', hasDerivAt_add_const_iff, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, HasFDerivWithinAt.cpow, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, HasFPowerSeriesOnBall.compContinuousLinearMap, HasStrictFDerivAt.const_cpow, differentiableWithinAt_of_derivWithin_ne_zero, MeromorphicOn.divisor_intCast, HasFDerivWithinAt.csinh, RealRMK.rieszMeasure_le_of_eq_one, TensorProduct.inner_lid_lid, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Matrix.piLp_ofLp_toEuclideanLin, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, NormedSpace.inclusionInDoubleDual_norm_le, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, hasDerivWithinAt_one, deriv_comp_add_const, HasFDerivAt.abs, WeakDual.isCompact_closedBall, RCLike.instMulPosReflectLE, ConvexOn.sSup_of_countable_affine_eq, TestFunction.coe_ofSupportedInCLM, PointedContMDiffMap.smul_def, CFC.sqrt_eq_one_iff, RCLike.reCLM_coe, HasFDerivWithinAt.abs, continuousSMul_closedBall_ball, InnerProductSpace.rankOne_eq_rankOne_iff_comm, RCLike.ofNat_mul_re, CStarAlgebra.norm_posPart_le, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, HasDerivWithinAt.inner, DifferentiableAt.inner, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, IsGreatest.nnnorm_cfcβ_nnreal, HasFDerivWithinAt.mul_const, UnitAddTorus.mFourier_zero, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, isScalarTower_sphere_sphere_sphere, MeromorphicOn.analyticAt_mem_codiscreteWithin, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, smoothSheafCommRing.isUnit_stalk_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, FormalMultilinearSeries.coeff_ofScalars, StieltjesFunction.measurable_measure, hasDerivAt_ofNat, iteratedFDerivWithin_eq_equiv_comp, CompactlySupportedContinuousMap.toRealLinearMap_apply, Matrix.l2_opNNNorm_mulVec, Orthonormal.inner_left_right_finset, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, meromorphicOrderAt_id, ContDiffMapSupportedIn.structureMapCLM_zero_apply, FormalMultilinearSeries.mkPiRing_coeff_eq, differentiableAt_inv_iff, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, ProbabilityTheory.covarianceBilinDual_zero, RealRMK.integral_rieszMeasure, Finsupp.inner_sum, LinearMap.deriv, CFC.continuous_abs, contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, HasFDerivWithinAt.inner, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, RCLike.I_eq_zero_or_im_I_eq_one, continuousOn_cfc_nnreal, InnerProductSpace.gramSchmidt_orthogonal, ContinuousLinearMap.adjoint_inner_left, fderivWithin_cos, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, InnerProductSpace.gramSchmidt_pairwise_orthogonal, ContinuousLinearMap.isBoundedBilinearMap, fdifferential_apply, HasFPowerSeriesWithinOnBall.sum, Matrix.l2_opNorm_diagonal, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, Asymptotics.isEquivalent_iff_exists_eq_mul, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, MeromorphicOn.divisor_sub_const_of_ne, ContinuousMultilinearMap.ofSubsingletonβα΅’_symm_apply, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, fderivWithin_ccos, hasDerivAt_update, cfc_nnreal_eq_real, inner_neg_right, ContinuousAlternatingMap.ofSubsingletonLIE_apply, HasStrictFDerivAt.clog, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, FormalMultilinearSeries.compAlongComposition_bound, iteratedDeriv_fun_id, OrthonormalBasis.singleton_apply, continuousMultilinearCurryRightEquiv_symm_apply, RCLike.uniqueNonUnitalContinuousFunctionalCalculus, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, cfcβ_real_eq_complex, inner_eq_sum_norm_sq_div_four, fderiv_pow_ring, constFormalMultilinearSeries_apply_zero, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, FormalMultilinearSeries.radius_smul_eq, Bundle.ContMDiffRiemannianMetric.pos, HasStrictFDerivAt.sqrt, Polynomial.abs_tendsto_atBot_iff, ContinuousLinearMap.bilinearComp_zero_right, IsContMDiffRiemannianBundle.exists_contMDiff, ContinuousMap.ideal_isMaximal_iff, MeasureTheory.SignedMeasure.singularPart_add, integral_conj, hasDerivAtFilter_add_const_iff, hasDerivAt_jacobiThetaβ_fst, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, IsometricContinuousFunctionalCalculus.toNonUnital, meromorphicNFAt_inv, HasStrictFDerivAt.rpow, RCLike.exists_norm_eq_mul_self, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousMap.sup_mem_closed_subalgebra, ContinuousLinearMap.adjointAux_apply, Real.hasDerivAt_arcsin, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Submodule.linearEquiv_det_reflection, ProperCone.innerDual_singleton, Complex.hasDerivAt_sinh, RCLike.add_conj, differentiable_inner, LeftInvariantDerivation.coe_sub, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, CFC.abs_natCast, HasLineDerivAt.tendsto_slope_zero_left, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, tendsto_nhds_iff_meromorphicOrderAt_nonneg, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, RCLike.im_eq_conj_sub, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, LDL.lower_conj_diag, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionβ_apply_apply, hasFDerivAt_list_prod', hasFDerivAt_integral_of_dominated_loc_of_lip', InnerProductSpace.rankOne_def, InnerProductSpace.Core.inner_self_eq_zero, Meromorphic.countable_compl_analyticAt, ContinuousLinearMap.coe_flipβα΅’', Finset.norm_prod_one_add_sub_one_le, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.lpNorm_fun_mul_natCast, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, ContinuousLinearMap.norm_smulRight_apply, PadicInt.norm_lt_one_mul, Real.hasStrictDerivAt_cosh, contDiff_iff_continuous_differentiable, hasDerivAt_const, dslope_sub_smul_of_ne, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, UniformSpace.Completion.norm_toComplL, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, instSMulCommClass_sphere_closedBall_closedBall, HasStrictFDerivAt.ccos, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, Complex.hasDerivAt_Gammaβ_one, Matrix.l2_opNNNorm_conjTranspose, Summable.hasProdUniformlyOn_nat_one_add, Complex.hasStrictDerivAt_const_cpow, RCLike.ofReal_add, ClosedSubmodule.orthogonal_eq_inter, ContinuousMultilinearMap.prodL_apply, Real.hasStrictDerivAt_log, HasFDerivWithinAt.cexp, hasFDerivWithinAt_iff_hasDerivWithinAt, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, LeftInvariantDerivation.left_invariant'', SchwartzMap.smulRightCLM_apply_apply, LinearIsometryEquiv.conjStarAlgEquiv_refl, MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, RCLike.ofReal_neg, Matrix.PosSemidef.nonneg, contDiff_nat_iff_iteratedDeriv, eventually_singleton_add_smul_subset, RCLike.im_mul_ofReal, ContinuousLinearMapWOT.isInducing_inducingFn, fderivWithin_fderivWithin_eq_of_eventuallyEq, EulerProduct.eulerProduct_completely_multiplicative_tprod, StrongDual.polarSubmodule_eq_polar, summable_prod_mul_pow, PiTensorProduct.liftEquiv_symm_apply, Matrix.nonneg_iff_posSemidef, RCLike.summable_conj, TestFunction.coe_ofSupportedInLM, meromorphicOrderAt_inv, extDerivWithin_fun_smul, RCLike.wInner_zero_right, fourierSubalgebra_separatesPoints, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, hasFDerivAt_exp_smul_const', MeasureTheory.SignedMeasure.re_toComplexMeasure, Matrix.exp_zsmul, Commute.cfcβHom, Submodule.mem_orthogonal', ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, ContinuousLinearMap.aestronglyMeasurable_compβ, continuousSMul_sphere_closedBall, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, SchwartzMap.smulLeftCLM_const, RCLike.wInner_sub_left, LinearMap.toMatrix_innerββ_apply, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, Matrix.permMatrix_l2_opNorm_le, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Function.locallyFinsuppWithin.toClosedBall_divisor, PointwiseConvergenceCLM.equivWeakDual_symm_apply, PadicAlgCl.instUniformContinuousConstSMulPadic, hasDerivAt_of_tendstoUniformlyOn, RCLike.wInner_one_eq_inner, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, Complex.hasFDerivAt_cpow, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, iteratedDerivWithin_zpow, inner_zero_left, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, dist_lineMap_right, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, MeasureTheory.lpNorm_fun_natCast_mul, AffineMap.differentiableAt, hasStrictDerivAt_finCons', RCLike.neg_iff, isScalarTower_closedBall_ball_ball, Continuous.cfc_nnreal_of_mem_nhdsSet, meromorphicNFAt_iff_analyticAt_or, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMapβ'_zero_iff, RCLike.sqrt_eq_real_add_ite, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, WeakDual.isSeqCompact_closedBall, hasStrictDerivAt_finCons, PiTensorProduct.liftEquiv_apply, HasFDerivAt.cexp, Matrix.l2_opNorm_conjTranspose, HasFDerivAt.ccos, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, Matrix.instNonnegSpectrumClass, MultilinearMap.mkContinuousLinear_norm_le, WeakDual.exists_countable_separating, HasFDerivWithinAt.log, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, HasFDerivAt.clog, innerSLFlip_apply_apply, Continuous.cfcβ_nnreal, ContinuousLinearMap.nnnorm_holder_apply_apply_le, RCLike.ofReal_mul_pos_iff, Polynomial.hasFDerivAt, RCLike.ofReal_finsupp_sum, finrank_euclideanSpace, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Summable.summable_log_norm_one_add, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, ContinuousLinearMap.bilinear_hasTemperateGrowth, UpperHalfPlane.Ο_neg, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, ConvexOn.sSup_of_nat_affine_eq, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, inner_add_left, Submodule.orthogonal_orthogonal_eq_closure, contMDiff_smul, MeromorphicOn.divisor_ofNat, RCLike.toZeroLEOneClass, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Complex.hasDerivAt_cos, contMDiffOn_continuousLinearMapCoordChange, Function.FactorizedRational.meromorphicNFOn_univ, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, Module.Basis.equivFunL_apply, ContinuousAt.cfcβ_nnreal, ContinuousMultilinearMap.flipLinear_apply_apply, tendsto_integral_mul_one_add_inv_smul_sq_pow, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, PadicComplex.isNonarchimedean, LinearMap.hasDerivWithinAt, Real.fourier_fderiv, MeromorphicOn.inv_iff, FormalMultilinearSeries.comp_id, ContinuousMap.adjoin_id_eq_span_one_union, hasFTaylorSeriesUpTo_succ_nat_iff_right, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, meromorphicTrailingCoeffAt_const, instCStarRingReal, HasFDerivWithinAt.norm_sq, CFC.abs_algebraMap, ordinaryHypergeometric_radius_top_of_neg_natβ, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, ClosedSubmodule.iInf_orthogonal, Matrix.isHermitian_gram, integral_inner, HasFPowerSeriesOnBall.neg, AnalyticAt.harmonicAt_conj, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, ZSpan.coe_floor_self, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, hasStrictDerivAt_abs, Matrix.PosDef.commute_iff, SchwartzMap.fourierInv_lineDerivOp_eq, RCLike.finrank_le_two, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Bundle.RiemannianMetric.symm, PadicInt.norm_lt_one_add, dist_homothety_self, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, iteratedFDeriv_eq_equiv_comp, Complex.hasStrictDerivAt_log, meromorphicTrailingCoeffAt_inv, Unitization.norm_eq_sup, RCLike.nonneg_iff, MeromorphicAt.id, Real.hasDerivAt_cos, RCLike.ofReal_zero, Matrix.ofLp_toEuclideanCLM, hasFTaylorSeriesUpToOn_succ_nat_iff_right, summable_pow_div_add, hasDerivAtFilter_iff_isLittleO, IsStrictlyPositive.nnrpow, HasFDerivAt.ccosh, Circle.star_addChar, fderiv_cos, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ContinuousMap.sup_mem_subalgebra_closure, hasDerivAt_exp_smul_const, hasFDerivWithinAt_comp_smul_smul_iff, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, RCLike.instContinuousStar, ProbabilityTheory.hasDerivAt_complexMGF, LinearMap.isPositive_toContinuousLinearMap_iff, meromorphicNFOn_inv, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, iteratedDerivWithin_one_div, FormalMultilinearSeries.changeOrigin_eval_of_finite, RCLike.sqrt_map, iteratedFDerivWithin_two_apply', PadicInt.mahlerTerm_one, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, HasStrictFDerivAt.arctan, HasStrictDerivAt.hasStrictFDerivAt, RCLike.zero_re, RCLike.inner_tmul_eq, InnerProductSpace.gramSchmidt_triangular, CFC.monotoneOn_one_sub_one_add_inv_real, HasFDerivAt.multiset_prod, dist_self_homothety, Matrix.l2_opNNNorm_mul, IsLocalFrameOn.eventually_eq_sum_coeff_smul, HasFDerivAt.mul_const, differentiableWithinAt_euclidean, unitary.spectrum_subset_circle, MeasureTheory.integral_prod_mul, HasFPowerSeriesAt.fderiv_eq, MeromorphicOn.divisor_apply, Matrix.isPositive_toEuclideanLin_iff, ContinuousWithinAt.cfcβ_nnreal, padic_polynomial_dist, nnnorm_cfc_le_iff, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, exists_polynomial_near_continuousMap, RCLike.re_eq_add_conj, continuousMultilinearCurryFin0_apply, ContDiff.inner, HasGradientAt.differentiableAt, ContinuousMap.inf_mem_subalgebra_closure, PiTensorProduct.dualSeminorms_bounded, NormedSpace.exp_sum, CommCStarAlgebra.toStarModule, FormalMultilinearSeries.radius_neg, Function.FactorizedRational.analyticAt, extDeriv_smul, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, Summable.multipliableLocallyUniformlyOn_one_add, ContinuousMap.inf_mem_closed_subalgebra, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, PadicInt.zmodRepr_spec, fderiv_exp, DoubleCentralizer.algebraMap_snd, WeakDual.polar_def, RCLike.wInner_const_left, fderiv_arctan, ProbabilityTheory.covarianceBilinDual_self_eq_variance, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, hasFiniteFPowerSeriesOnBall_const, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, contDiffAt_inv, iteratedFDerivWithin_succ_apply_left, EuclideanSpace.toLp_single, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, hasStrictFDerivAt_norm_sq, LinearMap.adjoint_toSpanSingleton, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, ContinuousMultilinearMap.norm_mkPiAlgebra, hasDerivWithinAt_natCast, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, ContinuousLinearMap.bilinearComp_apply, Summable.multipliableLocallyUniformlyOn_nat_one_add, iteratedDeriv_comp_neg, range_cfcβ_nnreal_eq_image_cfcβ_real, RCLike.inner_apply, ClosedSubmodule.mem_orthogonal, Matrix.posDef_iff_eq_conjTranspose_mul_self, Polynomial.differentiableAt_aeval, Filter.Tendsto.cfcβ_nnreal, WeakDual.CharacterSpace.compContinuousMap_apply, hasDerivAt_id, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, DoubleCentralizer.algebraMap_toProd, RCLike.normSq_mul, RCLike.hasSum_conj, Polynomial.isEquivalent_atBot_lead, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, FormalMultilinearSeries.id_comp, fderivWithin.log, ContinuousLinearMap.norm_map_tail_le, deriv_update, HasFPowerSeriesAt.restrictScalars, hasDerivAt_integral_of_dominated_loc_of_deriv_le, HasFDerivWithinAt.sinh, orthonormal_subtype_iff_ite, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, Summable.hasProdLocallyUniformlyOn_one_add, ContinuousLinearMap.instStarModuleId, nndist_lineMap_right, Polynomial.hasFDerivAt_aeval, continuous_cfcHomSuperset_left, EisensteinSeries.vecMul_SL2_mem_gammaSet, IsUnit.cfcNNRpow, Summable.multipliableUniformlyOn_one_add, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, LeftInvariantDerivation.map_add, Continuous.cfc_of_mem_nhdsSet, norm_fderiv_iteratedFDeriv, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, ProbabilityTheory.covarianceBilinDual_self_nonneg, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, HasFDerivAt.log, Matrix.l2_opNNNorm_def, HasGradientAtFilter.isBigO_sub, hasDerivAtFilter_sub_const_iff, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.adjointAux_adjointAux, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, LinearMap.polar_gc, hasDerivAt_exp, contDiffOn_succ_iff_deriv_of_isOpen, LeftInvariantDerivation.coe_add, ContMDiffAt.clm_precomp, Complex.hasDerivAt_logTaylor, inner_zero_right, ProbabilityTheory.covarianceBilin_real_self, ContinuousOn.cfc_nnreal, nnnorm_cfcβ_nnreal_lt_iff, inner_self_eq_zero, Real.hasStrictDerivAt_arsinh, iter_deriv_pow', cfc_integral, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, Orthonormal.inner_right_finsupp, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, ValueDistribution.characteristic_sub_characteristic_inv, EuclideanSpace.basisFun_repr, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, inner_product_apply_eigenvector, HasFTaylorSeriesUpToOn.hasFDerivAt, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, ContinuousLinearMap.flip_add, hasFiniteFPowerSeriesAt_const, MeromorphicOn.eventually_codiscreteWithin_analyticAt, VectorFourier.fourierSMulRight_apply, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', OrthonormalBasis.equiv_apply_euclideanSpace, RCLike.exists_norm_mul_eq_self, IsLocalFrameOn.coeff_apply_of_notMem, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, PadicInt.limNthHom_spec, ContinuousMultilinearMap.uncurryRight_apply, WithLp.unitization_nnnorm_inr, nnnorm_cfc_nnreal_lt, InnerProductSpace.Core.inner_smul_ofReal_left, fderiv_inv, derivWithin_comp_mul_left, HasFDerivAt.exp, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, ContinuousLinearMap.bilinearComp_zero, isScalarTower_sphere_sphere_closedBall, iteratedDeriv_eq_equiv_comp, OrthonormalBasis.inner_eq_zero, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, iteratedDeriv_comp_const_add, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, Submodule.isOrtho_span, IsStrictlyPositive.sqrt, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, HasFDerivWithinAt.hasDerivWithinAt, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, hasDerivAt_iff_hasFDerivAt, HasFiniteFPowerSeriesOnBall.neg, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, inner_add_add_self, RCLike.complexLinearIsometryEquiv_symm_apply, PadicInt.continuous_addChar_of_value_at_one, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, norm_derivWithin_eq_norm_fderivWithin, UpperHalfPlane.denom_neg, differentiableWithinAt_dslope_of_ne, LinearMap.polar_weak_closed, hasGradientAt_iff_tendsto, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, cfcβ_real_eq_nnreal, ProbabilityTheory.instIsProbabilityMeasureCondCDF, fderiv_ccos, InnerProductSpace.Core.inner_sub_sub_self, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, nnnorm_cfc_nnreal_le, Matrix.PosSemidef.kronecker, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, inner_add_right, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, fdifferential_comp, ContinuousOn.cfcβ_nnreal_of_mem_nhdsSet, RCLike.sqrt_neg_one, ContinuousLinearMap.le_opNormβ, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, InnerProductSpace.Core.inner_zero_right, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ContinuousLinearMap.norm_uncurryMid, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, LeftInvariantDerivation.coe_injective, ContinuousLinearMap.uncurryLeft_norm, MeromorphicOn.divisor_restrict, Continuous.cfc_nnreal, hasStrictDerivAt_abs_neg, HasFPowerSeriesOnBall.tendstoUniformlyOn', Pretrivialization.continuousLinearMap.isLinear, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, ContinuousOn.cfc_of_mem_nhdsSet, fderiv_apply_one_eq_deriv, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, isScalarTower_sphere_sphere_ball, nnnorm_cfc_nnreal_le_iff, HasFPowerSeriesOnBall.sub, ContinuousLinearMap.IsPositive.inner_nonneg_left, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, meromorphicTrailingCoeffAt_id_sub_const, PadicComplex.instIsScalarTowerPadicPadicAlgCl, MeasureTheory.Integrable.convolution_integrand, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, RCLike.ofNat_mul_im, LinearMap.toMatrixOrthonormal_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, fderivWithin_exp, CFC.sqrt_sq, OrthogonalFamily.inner_sum, NormedSpace.vonNBornology_eq, ProbabilityTheory.covarianceBilin_apply_pi, EuclideanSpace.inner_eq_star_dotProduct, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, isCoveringMapOn_npow, NonUnitalCommCStarAlgebra.toStarModule, CFC.rpow_sqrt_nnreal, LeftInvariantDerivation.coe_neg, Complex.hasStrictDerivAt_cos, StrongDual.toLpβ_apply, PadicInt.fwdDiff_iter_le_of_forall_le, Valued.integer.coe_span_singleton_eq_closedBall, Polynomial.differentiableOn, IsLocalFrameOn.coeff_apply_zero_at, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, inner_sub_left, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', AnalyticOnNhd.eval_polynomial, HasFDerivWithinAt.rpow_const, differentiableOn_neg, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, HasFDerivAt.mul, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, LinearMap.continuous_of_nonzero_on_open, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, MultilinearMap.mkContinuousMultilinear_norm_le', toWeakSpace_closedConvexHull_eq, Unitization.norm_def, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, Submodule.det_reflection, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, deriv_neg', FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, contDiffOn_inv, ContinuousLinearMap.extendToπ_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, HasFDerivAt.sinh, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, ContinuousMapZero.toContinuousMapHom_toNNReal, Valued.isNonarchimedean_norm, Submodule.inner_left_of_mem_orthogonal, differentiableAt_iff_comp_const_sub, MDifferentiableAt.clm_precomp, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, ContDiffMapSupportedIn.postcompCLM_apply, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, ProbabilityTheory.covarianceBilin_apply_basisFun, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, ProbabilityTheory.measure_cdf, HasFDerivWithinAt.clog, hasGradientAt_iff_hasFDerivAt, MeromorphicOn.countable_compl_analyticAt_inter, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, locallyFinsuppWithin.logCounting_divisor, Asymptotics.isTheta_const_mul_right, hasFDerivAt_exp_smul_const_of_mem_ball, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, inner_eq_zero_of_left, HasFPowerSeriesWithinAt.prod, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, fourierSubalgebra_coe, FormalMultilinearSeries.leftInv_coeff_one, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, Matrix.toLin_conjTranspose, RCLike.instStarModuleReal, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, fderiv_deriv, Complex.hasStrictDerivAt_sin, hasFPowerSeriesAt_pi_iff, norm_cfcβ_le, hasDerivWithinAt_univ, MulChar.star_apply', Matrix.PosSemidef.sq_sqrt, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, HasFDerivAt.rpow_const, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, contDiffAt_inner, HasFPowerSeriesAt.hasFDerivAt, lp.summable_inner, WeakDual.isClosed_polar, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, ContinuousOn.cfcβ_nnreal', Submodule.inner_right_of_mem_orthogonal, hasFDerivAt_exp_smul_const, Differentiable.inner, LinearMap.mkContinuousβ_norm_le, LeftInvariantDerivation.map_smul, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, HasStrictFDerivAt.const_rpow, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, InnerProductSpaceable.add_left, RCLike.complexRingEquiv_symm_apply, Polynomial.isBoundedUnder_abs_atBot_iff, hasStrictDerivAt_const, RCLike.ofReal_eq_zero, CompactlySupportedContinuousMap.toReal_add, deriv_single, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, HasFPowerSeriesWithinAt.restrictScalars, Matrix.PosDef.isStrictlyPositive, Module.Basis.parallelepiped_eq_map, Asymptotics.IsEquivalent.exists_eq_mul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, ContDiffMapSupportedIn.norm_apply_le_seminorm, RCLike.re_mul_ofReal, nnnorm_cfc_le, PiTensorProduct.mapLMultilinear_apply_apply, HasStrictFDerivAt.cos, LinearMap.mem_polar_singleton, ContinuousMap.setOfIdeal_eq_compl_singleton, Complex.hasDerivAt_cosh, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, RCLike.ofRealCLM_norm, PadicInt.zmodRepr_zero, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, ContinuousLinearMap.mul_apply', MeromorphicNFOn.zero_set_eq_divisor_support, LinearMap.instStarModuleId, NumberField.inverse_basisMatrix_mulVec_eq_repr, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, HasFDerivWithinAt.arsinh, InnerProductSpace.rankOne_comp_rankOne, MeasureTheory.convolution_lsmul_swap, MeromorphicOn.circleAverage_log_norm, Real.hasStrictDerivAt_arctan, Matrix.PosSemidef.det_nonneg, CFC.abs_ofNat, parallelogram_law, Submodule.orthogonal_closure', hasDerivAtFilter_finCons', MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Asymptotics.IsTheta.listProd, nnnorm_apply_le_nnnorm_cfc, CFC.negPart_one, Matrix.toEuclideanLin_eq_toLin, StrongDual.toLpβ_of_not_memLp, analyticOrderAt_id, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, BoundedContinuousFunction.instIsBoundedSMul_1, Continuous.cfc, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, deriv_zpow, InnerProductSpace.rankOne_comp, inner_eq_neg_one_iff_of_norm_eq_one, Submodule.mem_orthogonal, StrongDual.mem_polarSubmodule, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, FormalMultilinearSeries.apply_eq_prod_smul_coeff, EuclideanSpace.basisFun_inner, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, hasFPowerSeriesWithinAt_pi_iff, UnitAddTorus.hasSum_mFourier_series_of_summable, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, hasDerivAt_iff_isLittleO_nhds_zero, inner_smul_right, SchwartzMap.tsupport_smulLeftCLM_subset, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, cfcβHom_real_eq_restrict, CFC.abs_algebraMap_nnreal, EuclideanSpace.ofLp_single, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, UnitAddTorus.mFourierSubalgebra_separatesPoints, RCLike.nonneg_iff_exists_ofReal, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, Commute.cfcHom, Real.hasDerivAt_cosh, HasFDerivAt.sin, continuousMultilinearCurryLeftEquiv_apply, LeftInvariantDerivation.coe_smul, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, cfc_apply_mem_elemental, HasFDerivAt.csin, Complex.hasDerivAt_sin, RCLike.ofReal_nonpos, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, hfdifferential_apply, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, ContinuousLinearMap.intervalIntegral_apply, hasDerivAt_intCast, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcβHom, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, MeasureTheory.integral_fin_nat_prod_eq_prod, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, CFC.nnnorm_rpow, spectrum.differentiableOn_inverse_one_sub_smul, Continuous.cfcβ_nnreal_of_mem_nhdsSet, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, ContinuousMultilinearMap.changeOriginSeries_support, ContDiffMapSupportedIn.seminorm_apply, LinearMap.tripolar_eq_polar, RCLike.toIsOrderedAddMonoid, OrthogonalFamily.eq_ite, Complex.hasStrictDerivAt_exp, logDeriv_inv, DoubleCentralizer.algebraMap_fst, differentiableOn_euclidean, RCLike.reLm_coe, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, Complex.hasStrictDerivAt_cosh, tsum_prod_pow_eq_tsum_sigma, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, toSpanSingleton_derivWithin, fderiv_norm_smul, PadicComplex.coe_zero, HasFDerivAt.hasFDerivAt_norm_smul, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, HasFiniteFPowerSeriesOnBall.eq_partialSum', cfc_comp_norm, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, CFC.abs_intCast, apply_le_nnnorm_cfc_nnreal, MeromorphicOn.eventually_analyticAt_or_mem_compl, IsBoundedBilinearMap.toContinuousLinearMap_apply, HasFPowerSeriesOnBall.pi, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, HasFPowerSeriesWithinOnBall.fderivWithin_eq, ContinuousMultilinearMap.piβα΅’_symm_apply, integral_coe_re_add_coe_im, RCLike.wInner_one_const_right, Commute.cfc, Matrix.posSemidef_iff_eq_sum_vecMulVec, HasFDerivWithinAt.sqrt, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, range_cfc_nnreal_eq_image_cfc_real, SchwartzMap.integralCLM_apply, MeasureTheory.lpNorm_one, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, hasDerivAt_one, HasStrictFDerivAt.hasStrictDerivAt, Polynomial.fourierCoeff_toAddCircle_natCast, PadicInt.limNthHom_add, fderivWithin_sqrt, RCLike.norm_sq_re_conj_add, ContinuousMap.spectrum_eq_range, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, EuclideanSpace.inner_basisFun_real, innerSLFlip_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, fderivWithin_derivWithin, hasDerivAt_const_mul, RCLike.sqrt_neg_I, hasLineDerivAt_iff_tendsto_slope_zero, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, InnerProductSpace.Core.inner_sub_left, IsSelfAdjoint.commute_cfcβHom, fderiv_sinh, inner_eq_ofReal_norm_sq_left_iff, contDiff_nat_iff_continuous_differentiable, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, HasFDerivWithinAt.const_cpow, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, iteratedDeriv_comp_const_sub, Function.RCLike.hasTemperateGrowth_ofReal, PadicInt.instIsAdicCompleteMaximalIdeal, Polynomial.hasDerivAt, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, ContinuousLinearMap.opNorm_lsmul_le, RCLike.conj_I, ProbabilityTheory.covarianceBilin_of_not_memLp, MultilinearMap.mkContinuousMultilinear_norm_le, WeakDual.CharacterSpace.norm_le_norm_one, contDiff_inner, Matrix.linfty_opNorm_toMatrix, hasDerivAt_natCast, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, Real.fourier_bilin_convolution_eq_integral, Real.hasStrictDerivAt_cos, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_symm_apply, iter_deriv_inv, Matrix.frobenius_norm_mul, Matrix.star_dotProduct_gram_mulVec, ContinuousLinearMap.norm_compL_le, RCLike.hasSum_iff, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, RCLike.inv_def, RCLike.sqrt_I, HasFPowerSeriesAt.sub, Matrix.PosDef.kronecker, StarAlgHom.realContinuousMapOfNNReal_injective, hasDerivWithinAt_zpow, HasFDerivWithinAt.arctan, OrthogonalFamily.range_linearIsometry, Monotone.deriv_nonneg, locallyIntegrableOn_mul_sum_Icc, innerSL_real_flip, ProbabilityTheory.covarianceBilinDual_comm, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, ContinuousLinearMap.opNNNorm_mul_flip_apply, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, TensorProduct.norm_lid, HasFDerivWithinAt.rpow, HasFPowerSeriesOnBall.hasFDerivAt, Matrix.instIsOrderedAddMonoid, Submodule.IsOrtho.inner_eq, fderivWithin_csin, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, norm_cfc_le, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, NNReal.orderIsoRpow_symm_eq, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Matrix.PosSemidef.re_dotProduct_nonneg, ContMDiff.clm_postcomp, MeasureTheory.lpNorm_div_natCast, Polynomial.isBoundedUnder_abs_atTop_iff, instSMulCommClass_sphere_ball_ball, CFC.exists_measure_nnrpow_eq_integral_cfcβ_rpowIntegrandββ, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, CFC.spectrum_abs, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, MDifferentiableWithinAt.clm_postcomp, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, lp.hasSum_inner, RCLike.ofReal_pos, DoubleCentralizer.coe_eq_algebraMap, ContinuousLinearMap.opNorm_mul_apply_le, HasFPowerSeriesAt.tendsto_partialSum, circleAverage_log_norm_factorizedRational, RCLike.wInner_zero_left, deriv_pow_field, ContinuousLinearMap.orthogonal_range, HasFiniteFPowerSeriesAt.add, hasDerivWithinAt_congr_set', Real.instContinuousMapUniqueHom, MeromorphicOn.min_divisor_le_divisor_add, deriv_comp_neg, ProbabilityTheory.covarianceBilin_apply, instSymmEqInnerOfNat, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, HasFDerivAt.cos, HasFDerivAt.linear_multilinear_comp, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, ContinuousMap.comp_attachBound_mem_closure, MeasureTheory.convolutionExistsAt_iff_integrable_swap, PadicInt.norm_sub_modPart, hasDerivAt_norm_rpow, inner_sub_right, HasFDerivAt.hasDerivAt, LeftInvariantDerivation.map_sub, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, PadicInt.valuation_p_pow_mul, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, ContinuousLinearMap.isPositive_iff, Unitization.isUniformEmbedding_addEquiv, ContinuousMultilinearMap.compContinuousLinearMapL_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, InnerProductSpace.Core.inner_add_right, MeromorphicOn.extract_zeros_poles, ContinuousOn.cfc', ContinuousLinearMap.norm_bilinearRestrictScalars, RCLike.inv_pos, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, RCLike.real_smul_ofReal, BoundedContinuousFunction.integral_add_const, cfcβ_norm_sq_nonneg, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, HasFPowerSeriesWithinOnBall.neg, norm_deriv_eq_norm_fderiv, PadicInt.fwdDiff_mahlerSeries, HasFDerivAt.const_rpow, ContinuousLinearMap.bilinearComp_zero_left, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, SchwartzMap.fderivCLM_fourier_eq, MeasureTheory.L2.mem_L1_inner, Bundle.ContinuousRiemannianMetric.pos, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, hasSum_fourier_series_of_summable, MeromorphicOn.negPart_divisor_add_le_max, IsCoercive.continuousLinearEquivOfBilin_apply, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, hasDerivWithinAt_inter', Complex.hasStrictDerivAt_cpow_const, MDifferentiableOn.clm_precomp, RCLike.I_mul_re, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', PadicInt.pow_p_dvd_int_iff, differentiable_neg, RCLike.wInner_neg_left, deriv_comp_mul_left, hasDerivAt_neg, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, hasFTaylorSeriesUpToOn_succ_iff_left, PadicInt.continuous_multichoose, Polynomial.hasStrictDerivAt, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, Commute.cfcβ, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, Bundle.RiemannianMetric.pos, HilbertBasis.repr_self, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', CFC.sqrt_eq_cfc, continuousMultilinearCurryRightEquiv_symm_apply', InnerProductSpace.Core.inner_self_of_eq_zero, HasFDerivAt.arsinh, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, UpperHalfPlane.det_J, ContDiffMapSupportedIn.continuousSMul, Real.hasStrictDerivAt_sin, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, BoundedContinuousFunction.add_norm_nonneg, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, LinearMap.isStarProjection_toContinuousLinearMap_iff, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, PadicInt.instNormMulClass, iteratedFDerivWithin_two_apply, extDerivWithin_smul, fderiv_ccosh, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, inner_mul_symm_re_eq_norm, DoubleCentralizer.coe_fst, Filter.Tendsto.cfc_nnreal, HasStrictFDerivAt.cpow, IsSelfAdjoint.instContinuousFunctionalCalculus, CompactlySupportedContinuousMap.toReal_smul, ContDiffWithinAt.inner, Submodule.adjoint_orthogonalProjection, CFC.abs_eq_cfcβ_norm, continuousOn_cfcβ_nnreal, ContinuousMapZero.instCStarRing, iteratedDeriv_comp_add_const, hasFDerivWithinAt_iff_hasGradientWithinAt, CurveIntegrable.smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, Polynomial.abs_tendsto_atBot, FormalMultilinearSeries.min_radius_le_radius_add, CFC.abs_sq, hasStrictDerivAt_one, ContinuousLinearMap.closed_range_of_antilipschitz, ProbabilityTheory.uncenteredCovarianceBilin_zero, HasStrictFDerivAt.multiset_prod, LinearMap.IsPositive.inner_nonneg_right, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, InnerProductSpace.inner_gramSchmidtOrthonormalBasis_eq_zero, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, HasFPowerSeriesAt.pi, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', RCLike.mul_im, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, VectorFourier.fourierPowSMulRight_apply, Matrix.linfty_opNorm_eq_opNorm, nnnorm_cfc_lt_iff, ContinuousAlternatingMap.prodLIE_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, RCLike.ofReal_tsum, hasDerivAt_pow, contDiff_succ_iff_deriv, Submodule.mem_adjoint_iff, PadicInt.norm_sub_zmodRepr_lt_one, inner_eq_zero_symm, Function.FactorizedRational.extractFactor, integrableOn_mul_sum_Icc, PadicInt.mahlerEquiv_apply, Polynomial.div_tendsto_atTop_zero_of_degree_lt, Orthonormal.orthogonalFamily, continuousSMul_closedBall_closedBall, ContinuousLinearMap.opNorm_flip, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, limit_zero_of_norm_tendsto_zero, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, logDeriv_const_mul, IsConformalMap.smul, isCoveringMap_npow, Irreducible.maximalIdeal_eq_closedBall, Complex.instContinuousMapUniqueHom, Real.hasStrictDerivAt_sqrt, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular, PadicInt.norm_add_eq_max_of_ne, Complex.hasDerivAt_Gamma_one, intervalIntegral.integral_smul_const, BumpCovering.exists_finset_toPOUFun_eventuallyEq, Polynomial.deriv, FormalMultilinearSeries.derivSeries_eq_zero, HilbertBasis.summable_inner_mul_inner, Polynomial.div_tendsto_zero_of_degree_lt, ContinuousLinearMap.isPositive_iff', ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, EisensteinSeries.vecMulSL_gcd, Real.hasDerivAt_tan_of_mem_Ioo, ContinuousLinearMap.star_eq_adjoint, AffineMap.differentiableOn, ContinuousMultilinearMap.curryLeft_apply, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, CStarAlgebra.isStrictlyPositive_TFAE, continuousOn_cfcβ_setProd, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, fderiv_sqrt, derivWithin_comp_add_const, hasStrictDerivAt_inv, Polynomial.contDiff_aeval, RCLike.wInner_one_const_left, AlternatingMap.mkContinuousLinear_norm_le, ProperCone.hyperplane_separation_of_notMem, RCLike.ofReal_mul_neg_iff, LinearMap.continuous_of_isClosed_ker, ContinuousAlternatingMap.curryLeftLI_apply, LDL.diag_eq_lowerInv_conj, deriv_comp_const_add, RCLike.norm_sq_re_add_conj, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, differentiableAt_iff_comp_add_const, ContinuousLinearMap.norm_compSL_le, ContDiffMapSupportedIn.withSeminorms, MeasureTheory.withDensityα΅₯_smul, CStarAlgebra.norm_negPart_le, LinearMap.polar_isClosed, innerββ_apply, cfcβ_nnreal_eq_real, deriv_inner_apply, CFC.sqrt_algebraMap, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, CFC.posPart_algebraMap, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, CFC.sqrt_one, Summable.hasProdLocallyUniformlyOn_nat_one_add, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, Polynomial.abs_isBoundedUnder_iff, hasDerivAtFilter_pi, StrongDual.toLp_apply, ContinuousLinearMap.coe_flipβα΅’, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, CFC.nnrpow_eq_cfcβ_real, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, InnerProductSpaceable.innerProp, instSMulCommClass_closedBall_closedBall_ball, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, ProbabilityTheory.measure_condCDF_Iic, polynomialFunctions.topologicalClosure, FormalMultilinearSeries.changeOrigin_eval, Unitization.nndist_inr, LinearMap.toSeminorm_ball_zero, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, iter_deriv_inv_linear_sub, RCLike.imCLM_coe, IsSelfAdjoint.adjoint_conj, UnitAddTorus.mFourierBasis_repr, HasDerivAt.inner, HasFPowerSeriesAt.prod, LinearMap.toSeminorm_apply, hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable, ProbabilityTheory.measurable_measure_condCDF, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, LeftInvariantDerivation.toDerivation_injective, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, MeasureTheory.lpNorm_natCast_mul, AlternatingMap.mkContinuousAlternating_norm_le_max, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, norm_apply_le_norm_cfc, hasDerivAt_finCons', fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, isScalarTower_sphere_ball_ball, iteratedDeriv_id, HasFPowerSeriesWithinAt.add, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, CFC.negPart_def, Profinite.NobelingProof.CC_comp_zero, MeasureTheory.integral_fintype_prod_volume_eq_prod, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, RCLike.mul_re, LinearMap.isPositive_iff, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, integrable_cfc, MeasureTheory.convolution_mul_swap, ContDiffMapSupportedIn.postcompLM_apply, UnitAddTorus.span_mFourier_closure_eq_top, ContinuousLinearMap.norm_smulRightL_le, MeasureTheory.withDensityα΅₯_smul', hasDerivAtFilter_const, analyticOrderAt_eq_zero, SchwartzMap.tsupport_derivCLM_subset, CFC.sqrt_rpow_nnreal, RCLike.normSq_zero, hasDerivAt_single, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, nnnorm_cfc_nnreal_lt_iff, orthonormal_iff_ite, RCLike.wInner_add_left, SchwartzMap.integral_smul_laplacian_right_eq_left, FormalMultilinearSeries.radius_prod_eq_min, RCLike.re_le_neg_norm_iff_eq_neg_norm, OrthonormalBasis.coe_equiv_euclideanSpace, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, CompactlySupportedContinuousMap.nnrealPart_smul_pos, ContinuousMap.polynomial_comp_attachBound, VectorFourier.norm_fourierSMulRight_le, RCLike.neg_iff_exists_ofReal, RCLike.wInner_one_eq_sum, InnerProductSpace.Core.inner_add_add_self, norm_cfcHom, RCLike.to_complex_nonneg_iff, integral_ofReal, RCLike.sqrt_zero, ContinuousMultilinearMap.currySum_apply, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, signedDist_apply, Unitization.norm_splitMul_snd_sq, WeakDual.CharacterSpace.equivAlgHom_coe, Valued.toNormedField.setOf_mem_integer_eq_closedBall, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipβα΅’'_symm, EuclideanSpace.inner_toLp_toLp, cfc_real_eq_complex, CFC.norm_rpow, RCLike.im_ofReal_mul, ContinuousMap.toNNReal_neg_one, Matrix.l2_opNNNorm_diagonal, MeromorphicOn.negPart_divisor_add_le_add, HasFiniteFPowerSeriesOnBall.hasFDerivAt, ordinaryHypergeometric_radius_top_of_neg_natβ, hasStrictDerivAt_zero, HasStrictFDerivAt.sin, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, Complex.hasDerivAt_tan, Matrix.instCStarRing, RCLike.normSq_eq_zero, FormalMultilinearSeries.coeff_iterate_fslope, HasFDerivWithinAt.const_rpow, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, PadicInt.continuousAddCharEquiv_symm_apply, hasStrictDerivAt_exp_smul_const_of_mem_ball', Unitization.antilipschitzWith_addEquiv, ContinuousLinearMap.extendToπ'_apply, derivWithin_comp_sub_const, fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, ContinuousLinearMap.isAdjointPair_inner, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, VectorFourier.norm_fourierPowSMulRight_le, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, RCLike.instPosMulReflectLE, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, Padic.norm_rat_le_one_iff_padicValuation_le_one, Unitization.splitMul_injective, ProbabilityTheory.measure_condCDF_univ, Antitone.deriv_nonpos, ContDiffMapSupportedIn.continuous_iff_comp, MonotoneOn.nnnorm_cfc, VectorFourier.norm_fourierSMulRight, Polynomial.differentiable, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, ContinuousLinearEquiv.coord_norm', ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, hasStrictFDerivAt_inv', LinearMap.mem_span_iff_bound, ContinuousOn.cfcβ_nnreal, hasFDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_mul_const, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, cfcβ_apply_mem_elemental, CFC.posPart_def, iteratedDeriv_fun_pow_zero, CFC.nnrpow_eq_rpow, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, hasStrictFDerivAt_exp_smul_const, Complex.hasStrictFDerivAt_log_real, iteratedFDeriv_two_apply, Real.hasStrictDerivAt_tan, RCLike.instNormSMulClassInt, ContDiffAt.inner, CFC.cfcβ_rpowIntegrandββ_eq_cfcβ_rpowIntegrandββ_one, RCLike.wInner_cWeight_const_right, HasStrictFDerivAt.mul, iter_deriv_inv_linear, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, Summable.hasProdUniformlyOn_one_add, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, MDifferentiable.clm_precomp, Real.differentiable_fourierChar_neg_bilinear_left, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, IsSelfAdjoint.commute_cfcβ, FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, continuousMultilinearCurryLeftEquiv_symm_apply, WithLp.unitization_mul, hasDerivAt_exp_smul_const', dist_right_lineMap, DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, polynomialFunctions_closure_eq_top', innerββ_apply_coe, fderiv_csinh, PiLp.inner_apply, Complex.im_eq_zero_iff_isSelfAdjoint, meromorphicOrderAt_of_not_meromorphicAt, iteratedFDeriv_succ_eq_comp_left, ContinuousMapZero.toNNReal_neg_smul, AddChar.wInner_cWeight_eq_boole, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, continuousOn_cfc_nnreal_setProd, differentiableAt_of_deriv_ne_zero, PadicInt.limNthHom_mul, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousMap.polynomial_comp_attachBound_mem, range_cfcHom, ContinuousLinearMap.opNorm_mulLeftRight_le, RCLike.re_ofReal_mul, HasFDerivAt.sqrt, ClosedSubmodule.orthogonal_closure, EisensteinSeries.eisSummand_SL2_apply, meromorphicOrderAt_const_intCast, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, CFC.abs_one, hasGradientWithinAt_iff_tendsto, InnerProductSpace.add_left, ContDiffMapSupportedIn.structureMapCLM_zero_injective, EuclideanSpace.inner_single_right, ContinuousMultilinearMap.piβα΅’_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, integrableOn_cfc, Matrix.PosSemidef.sqrt_mul_self, ContMDiffWithinAt.clm_precomp, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonβα΅’_apply, continuousOn_cfc, HasFDerivWithinAt.finset_prod, continuousMultilinearCurryFin1_symm_apply, FormalMultilinearSeries.radius_pi_le, Submodule.orthogonal_eq_inter, BoundedContinuousFunction.charMonoidHom_apply, RCLike.normSq_add, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, Asymptotics.IsEquivalent.listProd, hasDerivAt_iff_tendsto, ProbabilityTheory.iIndepFun.integral_prod_comp, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, sub_smul_dslope, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, setIntegral_re_add_im, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_apply, ContDiffAt.differentiableAt_iteratedFDeriv, MeromorphicNFAt.meromorphicOrderAt_eq_zero_iff, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, MeasureTheory.lpNorm_one', ContinuousLinearMap.norm_map_iff_adjoint_comp_self, HasStrictFDerivAt.cosh, Matrix.toEuclideanLin_eq_toLin_orthonormal, Polynomial.toAddCircle_X_eq_fourier_one, Real.hasStrictDerivAt_const_rpow, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, hasDerivWithinAt_intCast, differentiableWithinAt_zpow, ContMDiff.clm_precomp, RCLike.intervalIntegral_ofReal, contDiffOn_infty_iff_deriv_of_isOpen, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, instSMulCommClass_sphere_closedBall_ball, LeftInvariantDerivation.commutator_apply, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, OrthonormalBasis.coe_singleton, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, hasStrictFDerivAt_pow, FormalMultilinearSeries.derivSeries_apply_diag, derivWithin_comp_const_add, AnalyticOn.eval_polynomial, prod_vanishing_of_summable_norm, Matrix.l2_opNNNorm_conjTranspose_mul_self, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, ContinuousLinearMap.opNorm_lsmul, coe_innerββ_apply, isCoveringMapOn_zpow, ProbabilityTheory.covarianceBilinDual_of_not_memLp, FormalMultilinearSeries.norm_changeOriginSeriesTerm, fderivWithin_arctan, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Unitization.uniformity_eq_aux, isScalarTower_closedBall_closedBall_ball, hasDerivAt_exp_zero, HasFTaylorSeriesUpTo.zero_eq', MeasureTheory.charFun_map_eq_charFunDual_smul, ProbabilityTheory.gaussianPDFReal_mul, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, instFieldContMDiffRing, hasGradientWithinAt_iff_isLittleO, Matrix.cstar_norm_def, CStarAlgebra.toStarModule, PointwiseConvergenceCLM.withSeminorms, MeasureTheory.convolution_eq_swap, CFC.isUnit_nnrpow_iff, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, Real.zero_at_infty_vector_fourierIntegral, hasDerivAt_const_add_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, RCLike.conj_eq_re_sub_im, ContDiffMapSupportedIn.withSeminorms', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, DFinsupp.inner_sum, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, fderiv_csin, MeromorphicOn.divisor_def, PadicInt.limNthHom_zero, WeakDual.isSeqCompact_polar, inner_matrix_row_row, HasFTaylorSeriesUpTo.fderiv, CFC.monotoneOn_cfcβ_rpowIntegrandββ, UpperHalfPlane.neg_smul, Int.padicValuation_le_one, ContinuousMap.idealOf_compl_singleton_isMaximal, fderiv_cosh, HasStrictFDerivAt.fun_mul, ContinuousLinearMap.norm_holderL_le, hasFDerivWithinAt_pow, logDeriv_mul_const, LinearMap.polar_mem_iff, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Unitization.lipschitzWith_addEquiv, hasStrictDerivAt_id, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, deriv_neg, integral_re, HasStrictFDerivAt.sinh, LeftInvariantDerivation.ext_iff, HasFDerivAt.cpow, MeromorphicOn.countable_compl_analyticAt, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Real.hasStrictDerivAt_rpow_const, Matrix.instStarOrderedRing, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, HasFiniteFPowerSeriesOnBall.fderiv_eq, PreInnerProductSpace.Core.add_left, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, PadicInt.unitCoeff_spec, Complex.hasDerivAt_log_sub_logTaylor, hasStrictDerivAt_iff_hasStrictFDerivAt, hasDerivAt_iff_tendsto_slope, ContinuousLinearMap.analyticAt_bilinear, PadicInt.norm_natCast_zmodRepr_eq_iff, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', HasFPowerSeriesAt.hasStrictFDerivAt, MeasureTheory.integral_prod_smul, inner_sub_sub_self, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, isBoundedLinearMap_continuousMultilinearMap_comp_linear, ContinuousAt.cfc_nnreal, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, hasStrictDerivAt_exp_smul_const_of_mem_ball, Real.hasDerivAt_Gamma_nat, ordinaryHypergeometricSeries_norm_div_succ_norm, HasStrictFDerivAt.inner, hasDerivAt_pi, ContinuousWithinAt.cfc, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, hasDerivWithinAt_finCons, WeakDual.CharacterSpace.exists_apply_eq_zero, HasFDerivAt.cosh, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, exists_continuousLinearEquiv_fderiv_symm_eq, FormalMultilinearSeries.rightInv_coeff, differentiableAt_dslope_of_ne, Complex.hasDerivAt_log, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, hasDerivAt_zpow, MeasureTheory.AEStronglyMeasurable.convolution_integrand', WeakDual.CharacterSpace.compContinuousMap_id, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, instSMulCommClass_sphere_sphere_closedBall, ContDiffOn.differentiableOn_iteratedFDerivWithin, EuclideanSpace.single_eq_zero_iff, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, ValueDistribution.log_counting_zero_sub_logCounting_top, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, Asymptotics.IsTheta.mul, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, nnnorm_cfcβ_le, Asymptotics.isTheta_const_mul_left, integral_re_add_im, ContinuousLinearMap.holderL_apply_apply, FormalMultilinearSeries.comp_rightInv_aux2, ZSpan.coe_fract_self, LeftInvariantDerivation.toFun_eq_coe, Real.hasDerivAt_sinh, Polynomial.toAddCircle_C_eq_smul_fourier_zero, isConformalMap_const_smul, Matrix.l2_opNorm_mul, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, norm_innerSL_le, polynomialFunctions_closure_eq_top, VectorFourier.hasFDerivAt_fourierChar_smul, BoundedContinuousFunction.separatesPoints_charPoly, HasStrictFDerivAt.csinh, ContMDiffWithinAt.cle_arrowCongr, HasFDerivWithinAt.cos, ContinuousWithinAt.cfc_nnreal, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, continuousMultilinearCurryRightEquiv_apply, RCLike.norm_le_im_iff_eq_I_mul_norm, RCLike.real_smul_eq_coe_mul, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, nnnorm_cfcβ_nnreal_le, CFC.sqrt_eq_real_sqrt, orthonormal_vecCons_iff, AffineMap.deriv, ContinuousAlternatingMap.prodLIE_symm_apply, Summable.multipliableUniformlyOn_nat_one_add, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcβ_nnreal, ProbabilityTheory.covarianceBilinDual_of_not_memLp', SchwartzMap.fourier_convolution, AnalyticOnNhd.eval_continuousLinearMap', PadicInt.instIsAddTorsionFree, fderivWithin_comp_smul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, instSMulCommClass_closedBall_closedBall_closedBall, ContinuousLinearMap.flipβα΅’_symm, HasFPowerSeriesAt.compContinuousLinearMap, continuousOn_cfcβ_nnreal_setProd, exists_continuousLinearEquiv_fderivWithin_symm_eq, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, HasGradientWithinAt.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, hasFDerivAt_exp, EuclideanSpace.single_apply, RCLike.hasSum_conj', MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, Matrix.PosDef.det_pos, ZSpan.mem_fundamentalDomain, differentiableAt_iff_comp_sub_const, LinearMap.polar_mem, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, LinearMap.isAdjointPair_inner, CFC.continuousOn_rpow, ContinuousLinearMap.norm_holder_apply_apply_le, WithLp.unitization_norm_inr, AnalyticOnNhd.eval_mvPolynomial, range_cfc, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, hasDerivWithinAt_iff_tendsto_slope, constFormalMultilinearSeries_apply_succ, Polynomial.fourierCoeff_toAddCircle, FormalMultilinearSeries.continuousOn, RCLike.wInner_add_right, hasFDerivAt_inv, DifferentiableWithinAt.inner, MonotoneOn.nnnorm_cfcβ, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.fpowerSeries_apply_one, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, BoundedContinuousFunction.char_add_eq_mul, constFormalMultilinearSeries_zero, ValueDistribution.logCounting_inv, HasStrictFDerivAt.mul_const, HilbertBasis.hasSum_inner_mul_inner, Real.hasDerivWithinAt_arccos_Iic, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, ContinuousMultilinearMap.curryFinFinset_apply, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, nndist_self_homothety, FormalMultilinearSeries.changeOriginSeriesTerm_bound, spectrum.subset_circle_of_unitary, spectrum.subset_closedBall_norm, RCLike.I_mul_I_of_nonzero, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, summable_mul_of_bigO_atTop', VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, CFC.nnnorm_nnrpow, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, Function.locallyFinsuppWithin.logCounting_even, HasFTaylorSeriesUpToOn.restrictScalars, ContinuousLinearMap.apply_apply, RCLike.span_one_I, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, instSMulCommClass_sphere_sphere_ball, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, PiTensorProduct.mapLMultilinear_opNorm, hasDerivWithinAt_inter, hasFPowerSeriesAt_iff', MeasureTheory.eLpNorm_conj, hasDerivAt_exp_smul_const_of_mem_ball, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, DFinsupp.sum_inner, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, differentiableAt_comp_sub_const, smooth_functions_tower, RCLike.ofReal_sum, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, Real.hasStrictDerivAt_exp, CFC.norm_nnrpow, WithLp.unitization_isometry_inr, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, HasCompactSupport.convolution_integrand_bound_right, isBigO_norm_restrict_cocompact, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, Commute.cfcβ_real, ContMDiffAt.cle_arrowCongr, AnalyticOnNhd.eval_continuousLinearMap, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, ContinuousLinearMap.adjoint_innerSL_apply, HasFDerivAt.rpow, LSeries.hasDerivAt_term, ContDiffMapSupportedIn.structureMapLM_apply, RCLike.normSq_sub, isBoundedLinearMap_prod_multilinear, nndist_homothety_self, Orthonormal.inner_sum, HasCompactSupport.convolution_integrand_bound_right_of_subset, intervalIntegral.integral_mul_const, HasStrictDerivAt_ofNat, Filter.IsBoundedUnder.isLittleO_sub_self_inv, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, ContinuousMap.idealOfSet_isMaximal_iff, LeftInvariantDerivation.coeFnAddMonoidHom_apply, hasDerivWithinAt_iff_tendsto, MeasureTheory.condExpL2_const_inner, Unitary.path_apply, InnerProductSpace.Core.inner_zero_left, Unitary.spectrum_subset_circle, PadicInt.existsUnique_mem_range, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, inner_eq_ofReal_norm_sq_right_iff, HasFDerivWithinAt.sin, cfcβ_complex_eq_real, PadicInt.toZMod_spec, differentiableAt_iff_comp_neg, DoubleCentralizer.coe_snd, hasFPowerSeriesAt_iff, HasStrictFDerivAt.exp, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, Matrix.IsHermitian.instContinuousFunctionalCalculus, MeasureTheory.integral_convolution, contDiff_euclidean, fderiv_norm_sq_apply, IsSelfAdjoint.commute_cfc, RCLike.imCLM_apply, fderiv_sin, cfcHom_apply_mem_elemental, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, RCLike.conj_neg_I, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, cfc_setIntegral, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, RCLike.inv_I, Submodule.starProjection_tendsto_closure_iSup, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, HasFDerivAtFilter.hasDerivAtFilter, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, MeasureTheory.integral_mul_const, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, ContinuousMap.idealOpensGI_choice, HasMFDerivAt.const_smul, Int.Matrix.exists_ne_zero_int_vec_norm_le, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulβα΅’, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', Unitization.norm_inr, PadicInt.zmodRepr_eq_zero_iff_dvd, norm_cfc_lt, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, inner_vsub_left_eq_zero_symm, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, HilbertBasis.hasSum_repr_symm, inner_neg_left, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_derivβ, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, differentiableWithinAt_Ioi_iff_Ici, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj, inner_smul_left, Unitization.continuous_inr, integral_im, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, CFC.rpow_eq_cfc_real, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Function.FactorizedRational.meromorphicNFOn, fderiv_inner_apply, contDiff_one_iff_deriv, inner_matrix_col_col, Real.hasStrictDerivAt_log_of_pos, derivWithin_comp_neg, HasFDerivWithinAt.fun_mul, RCLike.div_I, OrthonormalBasis.inner_eq_ite, BoundedContinuousFunction.char_mem_charPoly, MeasureTheory.SignedMeasure.im_toComplexMeasure, ContinuousLinearMap.orthogonal_ker, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, BoxIntegral.unitPartition.tag_mem_smul_span, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, Rat.padicValuation_le_one_iff, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, HasStrictFDerivAt.finset_prod, Continuous.cfcβ_nnreal', Filter.EventuallyEq.hasDerivWithinAt_iff, ProbabilityTheory.instIsProbabilityMeasurecdf, InnerProductSpace.norm_rankOne, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, Asymptotics.IsTheta.const_mul_right, Complex.hasDerivAt_Gamma_nat, HasFDerivAt.const_cpow, hasFDerivAt_integral_of_dominated_loc_of_lip, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, PadicInt.valuation_mul, PiTensorProduct.mapLMultilinear_toFun_apply, HasFDerivWithinAt.cosh, CFC.isUnit_sqrt_iff, Matrix.PosDef.re_dotProduct_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, Unitization.nnnorm_inr, MeasureTheory.SignedMeasure.rnDeriv_add, fderiv_eq_smul_deriv, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Int.Matrix.exists_ne_zero_int_vec_norm_le', HasStrictFDerivAt.rpow_const, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Matrix.gram_single, Function.locallyFinsuppWithin.toClosedBall_eval_within, InnerProductSpace.Core.inner_sub_right, NormedSpace.exp_add, PadicInt.addChar_of_value_at_one_def, deriv_comp_sub_const, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, Orthonormal.inner_eq_zero, hasDerivWithinAt_sub_const_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, RCLike.zero_im, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, fderiv_inv', ContinuousLinearMapWOT.ext_inner_iff, Matrix.permMatrix_l2_opNorm_eq, norm_inner_div_norm_mul_norm_eq_one_iff, tendsto_zero_geometric_tsum_pnat, CFC.rpow_sqrt, FormalMultilinearSeries.comp_assoc, HasFPowerSeriesWithinAt.comp, Real.hasDerivAt_negMulLog, continuousMultilinearCurryFin1_apply, LeftInvariantDerivation.evalAt_apply, InnerProductSpace.gramSchmidt_inv_triangular, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, HilbertBasis.finite_spans_dense, nnnorm_cfcβ_lt, RCLike.ofReal_lt_zero
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toNormedRing π | CompOp | 1476 mathmath: Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, MeasureTheory.L1.setToL1_eq_setToL1', instSeparatingDual, hasFDerivAt_iff_hasDerivAt, TensorProduct.mapInclIsometry_apply, HasSum.exp, closure_diff_intrinsicFrontier, Submodule.starProjection_apply_eq_isComplProjection, MeasureTheory.Lp.toTemperedDistributionCLM_apply, fderiv_iteratedFDeriv, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, SchwartzMap.lineDerivOpCLM_eq, MeasureTheory.condExpInd_of_measurable, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, RCLike.one_re, HasMFDerivAt.mul, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, MeasureTheory.condExpL1_smul, AffineIsometry.image_intrinsicClosure, Submodule.IsCompl.projection_isSymmetricProjection_iff, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, MDifferentiableOn.clm_postcomp, OrthonormalBasis.orthogonalProjection_eq_sum, MeasureTheory.aestronglyMeasurable_condExpInd, ContinuousLinearMap.compSL_apply, LinearMap.IsSymmetric.inner_map_polarization, Affine.Simplex.orthogonalProjectionSpan_map, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, PadicInt.lift_sub_val_mem_span, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, hasFDerivAt_iff_hasGradientAt, norm_zsmul, PadicInt.norm_int_lt_one_iff_dvd, smooth_barycentric_coord, IsHilbertSum.surjective_isometry, MeasureTheory.L1.setToL1_indicatorConstLp, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, dist_midpoint_right, PadicInt.norm_intCast_eq_padic_norm, Submodule.orthogonalDecomposition_symm_apply, OrthogonalFamily.linearIsometry_apply_single, InnerProductSpace.rankOne_one_left_eq_innerSL, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, AffineIsometryEquiv.coe_symm_toAffineEquiv, ContinuousAffineMap.fderiv, HasFiniteFPowerSeriesAt.neg, PadicInt.valuation_p, HasFDerivWithinAt.pow, WeakDual.isCompact_polar, EuclideanSpace.orthonormal_single, meromorphicOrderAt_const_ofNat, ContinuousAffineMap.differentiableWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, Matrix.IsHermitian.det_abs, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, hasFDerivAt_multiset_prod, PadicInt.isCauSeq_nthHom, MDifferentiableAt.cle_arrowCongr, Submodule.toLinearEquiv_orthogonalDecomposition_symm, derivWithin_id', hasFTaylorSeriesUpToOn_top_iff_right, Matrix.spectrum_toEuclideanLin, MeasureTheory.lpNorm_fun_div_natCast, MeasureTheory.norm_condExpL2_le, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, Padic.withValUniformEquiv_norm_le_one_iff, Matrix.IsHermitian.cfc_eq, Rat.padicValuation_cast, StrongDual.polarSubmodule_eq_setOf, HasStrictDerivAt.pow, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, ContinuousLinearMap.hasDerivAtFilter, DoubleCentralizer.intCast_snd, MeasureTheory.L1.norm_setToL1_le, HasDerivAtFilter.comp_hasFDerivAtFilter, Submodule.re_inner_starProjection_eq_normSq, ordinaryHypergeometric_radius_top_of_neg_natβ, inner_self_eq_one_of_norm_eq_one, MeasureTheory.inner_condExpL2_left_eq_right, AffineIsometryEquiv.linear_eq_linear_isometry, WeakDual.isClosed_image_polar_of_mem_nhds, PadicComplex.valuation_extends, ContinuousLinearMap.integral_apply, LinearMap.polar_eq_iInter, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_toLinearEquiv, LinearMap.IsSymmetric.diagonalization_apply_self_apply, EuclideanGeometry.orthogonalProjection_congr, ContinuousAlternatingMap.instIsUniformAddGroup, PadicInt.appr_spec, Matrix.le_iff, Submodule.starProjection_orthogonal', Submodule.toLinearEquiv_orthogonalDecomposition, PadicComplex.coe_eq, RCLike.sub_conj, HasFPowerSeriesWithinAt.const_smul, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, SchwartzMap.lineDerivOp_fourier_eq, isClosedEmbedding_cfcβAux, PadicInt.norm_intCast_lt_one_iff, AddChar.wInner_cWeight_self, innerSL_apply_apply, fderiv_multiset_prod, EisensteinSeries.summand_bound_of_mem_verticalStrip, Orthonormal.codRestrict, EuclideanSpace.basisFun_toBasis, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, hasDerivAt_neg', ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, HasFDerivAtFilter.sub, ContMDiffOn.clm_postcomp, ContinuousLinearMap.toBilinForm_apply, HasFDerivAt.fun_mul, dist_left_midpoint, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, MeasureTheory.condExpIndL1Fin_smul, PadicSeq.ne_zero_iff_nequiv_zero, NumberField.mixedEmbedding.norm_le_convexBodySumFun, FormalMultilinearSeries.derivSeries_coeff_one, Matrix.spectrum_toLpLin, PadicInt.sub_zmodRepr_mem, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, SchwartzMap.bilinLeftCLM_apply, HasDerivAt.comp_hasFDerivAt_of_eq, InnerProductSpace.toDual_symm_apply, OrthogonalFamily.of_pairwise, MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, IsHilbertSum.linearIsometryEquiv_symm_apply, iteratedDeriv_pow, AffineMap.hasDerivWithinAt, RCLike.conj_nat_cast, LeftInvariantDerivation.left_invariant, EuclideanSpace.basisFun_apply, HasFPowerSeriesAt.neg, EuclideanGeometry.orthogonalProjection_contLinear, EisensteinSeries.abs_le_right_of_norm, ContinuousAffineMap.differentiable, MeasureTheory.charFun_toDual_symm_eq_charFunDual, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, PadicInt.norm_p_pow, Differentiable.fderiv_norm_rpow, curveIntegrable_fun_neg_iff, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces, NormedSpace.exp_series_hasSum_exp', PadicComplex.norm_def, EuclideanGeometry.reflection_map, fderiv_fun_pow, AffineEquiv.continuous_of_finiteDimensional, HasFDerivAtFilter.const_sub, iteratedFDerivWithin_succ_eq_comp_left, contDiffOn_iff_continuousOn_differentiableOn, SchwartzMap.laplacianCLM_eq, MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM, nndist_midpoint_right, HasStrictFDerivAt.pow, iter_deriv_zpow', Matrix.exp_conj', ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, InnerProductSpace.inner_left_rankOne_apply, MeasureTheory.Lp.instFourierInvSMul, HasFDerivAt.finset_prod, Matrix.exp_neg, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, OrthonormalBasis.repr_self, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, PadicComplex.coe_natCast, ContinuousLinearMap.topologicalAddGroup, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, SchwartzMap.toLpCLM_apply, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, PadicInt.irreducible_p, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, LinearMap.polar_singleton, NormedSpace.Dual.toWeakDual_continuous, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, ContinuousMap.toLp_norm_le, ContinuousMultilinearMap.norm_smulRightL_le, ContinuousLinearMap.precompL_apply, curveIntegral_neg, HasFDerivAt.sub, FormalMultilinearSeries.radius_le_smul, MDifferentiable.clm_postcomp, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, fderivWithin_const_sub, Affine.Simplex.orthogonalProjectionSpan_eq_point, HasFDerivAtFilter.neg, nndist_right_lineMap, CommCStarAlgebra.toCStarRing, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, FormalMultilinearSeries.radius_compNeg, Padic.exi_rat_seq_conv_cauchy, Matrix.toEuclideanLin_apply, iteratedDerivWithin_eq_iteratedFDerivWithin, HasFDerivWithinAt.mul, VectorFourier.fourierPowSMulRight_eq_comp, RCLike.intCast_re, EuclideanGeometry.orthogonalProjection_map, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, HasFDerivWithinAt.multiset_prod, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Rat.padicValuation_self, MDifferentiable.cle_arrowCongr, PadicInt.maximalIdeal_eq_span_p, MeasureTheory.dominatedFinMeasAdditive_condExpInd, nndist_left_lineMap, fderivWithin_fun_neg, ContinuousLinearMap.flipMultilinear_apply_apply, PadicInt.norm_lt_one_iff_dvd, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, MeromorphicOn.divisor_natCast, Submodule.coe_orthogonalDecomposition_symm, PadicInt.mul_inv, MeasureTheory.aestronglyMeasurable_condExpL2, RCLike.I_mul_I, MeasureTheory.L1.setToL1_smul_left, RingHomIsometric.starRingEnd, fderiv_neg, MeasureTheory.L1.setToL1_zero_left, EuclideanGeometry.angle_orthogonalProjection_self, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, Pi.counit_eq_adjoint, HasDerivAt.comp_hasFDerivWithinAt, MeasureTheory.condExpInd_nonneg, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, VectorFourier.fourierIntegral_continuousLinearMap_apply, ContinuousAffineMap.norm_def, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, AffineSubspace.coe_subtypeβα΅’, SchwartzMap.fourier_lineDerivOp_eq, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, MeasureTheory.condExpL2_indicator_ae_eq_smul, fderiv_fun_sub, Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, PadicInt.exists_mem_range, LinearIsometry.toAffineIsometry_toAffineMap, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, EulerProduct.eulerProduct_completely_multiplicative, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', PadicInt.exists_mem_range_of_norm_rat_le_one, HasMFDerivAt.neg, derivWithin_zpow, UnitAddTorus.mFourierCoeff_toLp, WeakDual.toStrongDual_inj, ContinuousLinearMap.mulLeftRight_apply, ContinuousLinearMap.holderβ_apply_apply, hasDerivAt_id', Matrix.IsHermitian.eigenvectorUnitary_mulVec, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', AffineIsometryEquiv.pointReflection_toAffineEquiv, Padic.zero_def, FDerivMeasurableAux.norm_sub_le_of_mem_A, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, MDifferentiableAt.clm_postcomp, coe_innerSL_apply, fderivWithin_finset_prod, HasFDerivWithinAt.const_sub, HasDerivAt.pow, PadicInt.inv_mul, MeasureTheory.integral_condExpL2_eq, range_cfcβHom, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow, ContinuousLinearMap.hasDerivAt, PadicInt.fwdDiff_tendsto_zero, Valued.integer.exists_norm_lt_one, Module.Basis.coe_toOrthonormalBasis_repr, hasFDerivAt_ringInverse, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, HasMFDerivWithinAt.neg, dist_left_midpoint_eq_dist_right_midpoint, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, BoundedContinuousFunction.mem_charPoly, spectrum.gelfandTransform_eq, OrthonormalBasis.orthogonalProjection_apply_eq_sum, BoundedContinuousFunction.charAlgHom_apply, HasDerivAt.fun_pow, AffineMap.differentiableWithinAt, AffineIsometryEquiv.toContinuousAffineEquiv_symm, logDeriv_fun_pow, Submodule.IsCompl.closedComplemented_of_isClosed, InnerProductSpace.isSymmetricProjection_rankOne_self, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, MeasureTheory.L1.setToL1_mono_left', hasMFDerivAt_neg, Matrix.IsHermitian.charpoly_cfc_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, LinearMap.hasStrictDerivAt, AffineMap.hasDerivAt_lineMap, iteratedFDerivWithin_neg_apply, NormedSpace.smul_mem_polar, WeakDual.CharacterSpace.continuousMapEval_bijective, EuclideanGeometry.orthogonalProjection_apply', MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, AffineMap.hasDerivWithinAt_lineMap, ContinuousLinearMap.fderiv_of_bilinear, RCLike.ofReal_natCast, Matrix.PosSemidef.posSemidef_sqrt, MeasureTheory.setIntegral_condExpInd, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, deriv_id'', OrthonormalBasis.coe_ofRepr, ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, Submodule.adjoint_subtypeL, hasStrictFDerivAt_exp, ContinuousLinearMap.norm_smulRightL, Function.FactorizedRational.mulSupport, MeasureTheory.L1.setToL1_eq_setToL1SCLM, PadicInt.mahlerSeries_apply_nat, Matrix.LE.le.posSemidef, Affine.Triangle.dist_circumcenter_reflection_orthocenter, MeasureTheory.norm_condExpL2_coe_le, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, InnerProductSpace.trace_rankOne, MDifferentiableWithinAt.cle_arrowCongr, MeasureTheory.L1.setToL1_nonneg, MDifferentiableWithinAt.clm_precomp, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, HasFDerivWithinAt.neg, AffineIsometry.toContinuousAffineMap_id, hasFDerivAt_norm_rpow, ContinuousLinearMap.compL_apply, ZSpan.repr_ceil_apply, Asymptotics.isEquivalent_nat_ceil, iteratedDeriv_fun_id_zero, DoubleCentralizer.neg_snd, ContinuousAlternatingMap.instIsTopologicalAddGroup, IsIntegral.ratCast_iff, dist_lineMap_left, MeasureTheory.L1.integral_def, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, Submodule.IsCompl.projection_isSymmetricProjection_of_isOrtho, hasSum_fourier_series_L2, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, contDiffOn_stereoToFun, ContinuousLinearMap.isUniformAddGroup, LeftInvariantDerivation.evalAt_coe, fderiv_inverse, SchwartzMap.smulLeftCLM_fun_neg, deriv_pow, Matrix.posDef_gram_of_linearIndependent, ContMDiffOn.clm_precomp, contDiffOn_nat_iff_continuousOn_differentiableOn, HilbertBasis.hasSum_orthogonalProjection, padicNormE.defn, MeasureTheory.mem_lpMeas_indicatorConstLp, InnerProductSpace.adjoint_rankOne, fderiv_pow, InnerProductSpace.rankOne_eq_zero, Convex.toWeakSpace_closure, hasDerivAtFilter_neg, tsum_pow_div_one_sub_eq_tsum_sigma, AffineIsometry.linear_eq_linearIsometry, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, HasFDerivAt.pow, meromorphicOrderAt_const_natCast, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, MeasureTheory.condExpIndSMul_smul, fderivWithin_inv', AffineIsometryEquiv.vaddConst_toAffineEquiv, hasDerivWithinAt_pow, MeasureTheory.lintegral_nnnorm_condExpL2_le, PadicInt.norm_ascPochhammer_le, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, AffineSubspace.isometryEquivMap.toAffineMap_eq, AffineSubspace.signedInfDist_eq_signedDist_of_mem, MeasureTheory.L1.setToFun_eq_setToL1, LinearMap.IsSymmetric.coe_toSelfAdjoint, MeromorphicOn.divisor_intCast, NormedSpace.norm_expSeries_summable_of_mem_ball', Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, LinearMap.IsSymmetric.diagonalization_symm_apply, NormedSpace.inclusionInDoubleDual_norm_le, mfderiv_sub, WeakDual.isCompact_closedBall, MeasureTheory.L1.integral_eq_setToL1, Affine.Simplex.signedInfDist_apply_self, LinearMap.norm_mkContinuousβ_aux, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, ContinuousLinearMap.derivWithin, ContinuousLinearMap.holder_smul_left, ContinuousLinearMap.precompR_apply, AffineIsometry.image_intrinsicInterior, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, dist_right_midpoint, NormedSpace.exp_continuousMap_eq, HasFDerivWithinAt.mul_const, MeasureTheory.hasFDerivAt_convolution_right_with_param, fderiv_mul, FormalMultilinearSeries.coeff_ofScalars, MeasureTheory.condExpL1CLM_indicatorConstLp, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, Matrix.l2_opNNNorm_mulVec, AffineIsometryEquiv.toContinuousAffineEquiv_refl, HasCompactSupport.hasFDerivAt_convolution_right, MeasureTheory.L1.setToL1_add_left', Submodule.norm_orthogonalProjection_apply_le, instPolynormableSpaceSubtypeMemSubmodule, LinearMap.deriv, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, InnerProductSpace.toDualMap_apply, MeasureTheory.L1.setToL1_mono_left, MeasureTheory.condExpInd_disjoint_union, TensorProduct.inner_mapIncl_mapIncl, ContinuousMultilinearMap.instIsUniformAddGroup, Matrix.l2_opNorm_diagonal, hasDerivAtFilter_id, hasDerivAt_update, iteratedDeriv_fun_id, OrthonormalBasis.singleton_apply, RCLike.sqrt_one, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, fderiv_pow_ring, LinearMap.IsSymmetric.restrict_invariant, hasFTaylorSeriesUpToOn_top_iff', Padic.comap_mulValuation_eq_padicValuation, FormalMultilinearSeries.radius_smul_eq, AffineIsometryEquiv.ofEq_symm, LinearIsometry.extend_apply, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, Module.Basis.coe_toOrthonormalBasis_repr_symm, HasFDerivWithinAt.fun_sub, InnerProductSpace.toDual_apply_apply, ContinuousLinearMap.adjointAux_apply, fderivWithin_fun_sub, coe_lpBCFβα΅’, ContinuousAffineMap.norm_contLinear_le, ProperCone.innerDual_singleton, RCLike.add_conj, EuclideanGeometry.reflection_eq_self_iff, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, RCLike.im_eq_conj_sub, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure, hasFDerivAt_list_prod', hasFDerivAt_integral_of_dominated_loc_of_lip', Submodule.toLinearMap_starProjection_eq_isComplProjection, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, InnerProductSpace.rankOne_def, EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, Finset.norm_prod_one_add_sub_one_le, stereoToFun_apply, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.lpNorm_fun_mul_natCast, fderivWithin_fderivWithin_eq_of_mem_nhds, contDiff_iff_continuous_differentiable, PadicSeq.norm_neg, iteratedDerivWithin_comp_three, AffineIsometry.coe_toAffineMap, iter_deriv_zpow, Summable.hasProdUniformlyOn_nat_one_add, ClosedSubmodule.orthogonal_eq_inter, hasFDerivWithinAt_iff_hasDerivWithinAt, nndist_left_midpoint, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, AffineIsometryEquiv.dist_pointReflection_self, ContinuousAffineMap.hasStrictFDerivAt, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', Valued.coe_valuation_eq_rankOne_hom_comp_valuation, MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.L1.setToL1_smul_left', LinearMap.IsSymmetric.toSelfAdjoint_apply, Submodule.coe_continuous_linearProjOfClosedCompl, EuclideanGeometry.orthogonalProjection_subtype, iteratedFDeriv_neg_apply, Submodule.coe_orthogonalDecomposition, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, fderivWithin_fderivWithin_eq_of_eventuallyEq, EulerProduct.eulerProduct_completely_multiplicative_tprod, StrongDual.polarSubmodule_eq_polar, summable_prod_mul_pow, dist_right_pointReflection, Matrix.nonneg_iff_posSemidef, EisensteinSeries.norm_eq_max_natAbs, Matrix.exp_zsmul, Submodule.norm_subtypeL, AffineSubspace.closed_of_finiteDimensional, Matrix.posDef_gram_iff_linearIndependent, MeasureTheory.Lp.instFourierSMul, SchwartzMap.smulLeftCLM_const, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, AffineSubspace.toContinuousAffineMap_subtypeβα΅’, Matrix.permMatrix_l2_opNorm_le, PointwiseConvergenceCLM.equivWeakDual_symm_apply, PadicAlgCl.instUniformContinuousConstSMulPadic, PadicSeq.norm_nonarchimedean, AffineMap.hasDerivAt, Submodule.norm_sq_eq_add_norm_sq_projection, ContinuousAffineMap.contDiff, iteratedDerivWithin_zpow, HasFDerivWithinAt.fun_neg, ContinuousLinearMap.norm_precompR_le, dist_lineMap_right, MeasureTheory.lpNorm_fun_natCast_mul, AffineMap.differentiableAt, RCLike.sqrt_eq_real_add_ite, PadicInt.norm_int_le_pow_iff_dvd, WeakDual.isSeqCompact_closedBall, PiTensorProduct.liftEquiv_apply, MeasureTheory.norm_condExpInd_apply_le, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, PadicInt.denseRange_natCast, WeakDual.exists_countable_separating, PadicAlgCl.valuation_p, hasFDerivAtFilter_iff_hasDerivAtFilter, PadicComplex.valuation_p, innerSLFlip_apply_apply, AffineMap.lipschitzWith_of_finiteDimensional, Affine.Triangle.dist_orthocenter_reflection_circumcenter, OrthogonalFamily.hasSum_linearIsometry, isOpen_setOf_affineIndependent, finrank_euclideanSpace, EuclideanGeometry.oangle_orthogonalProjection_self, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, PadicSeq.not_equiv_zero_const_of_nonzero, Submodule.fst_orthogonalDecomposition_apply, Matrix.IsHermitian.posSemidef_of_eigenvalues_nonneg, RCLike.one_im, nndist_midpoint_left, RCLike.toZeroLEOneClass, RCLike.natCast_re, Valued.integer.norm_le_one, contMDiffOn_continuousLinearMapCoordChange, InnerProductSpace.enorm_rankOne, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousLinearMap.toLinearMap_innerSL_apply, HasFPowerSeriesAt.hasStrictDerivAt, Submodule.orthogonalFamily_self, Polynomial.cyclotomic.isCoprime_rat, HasStrictFDerivAt.neg, HasGradientAt.hasFDerivAt, PadicComplex.isNonarchimedean, LinearMap.hasDerivWithinAt, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, Real.fourier_fderiv, Submodule.inner_orthogonalProjection_eq_of_mem_right, ContinuousMap.adjoin_id_eq_span_one_union, hasFTaylorSeriesUpTo_succ_nat_iff_right, HasFDerivWithinAt.norm_sq, ordinaryHypergeometric_radius_top_of_neg_natβ, LipschitzWith.coordinate, HasFPowerSeriesOnBall.neg, Matrix.isStrictlyPositive_iff_posDef, ZSpan.coe_floor_self, Orthonormal.linearIsometryEquiv_symm_apply_single_one, nndist_midpoint_midpoint_le', AddChar.tendsto_eval_one_sub_pow, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, dist_homothety_self, MeasureTheory.condExpIndL1_smul, Affine.Simplex.orthogonalProjection_circumcenter, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Matrix.ofLp_toEuclideanCLM, hasFTaylorSeriesUpToOn_succ_nat_iff_right, summable_pow_div_add, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, mahler_natCast_eq, PadicInt.coe_adicCompletionIntegersEquiv_apply, HasFPowerSeriesWithinAt.sub, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', NormedSpace.algebraMap_exp_comm, fourierCoeff_toLp, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, AddChar.wInner_cWeight_eq_one_iff_eq, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, iteratedDerivWithin_one_div, fderivWithin_fun_pow, iteratedFDerivWithin_two_apply', PadicInt.mahlerTerm_one, curveIntegral_fun_neg, Matrix.instFiniteElemRealSpectrum, HasStrictFDerivAt.to_implicitFunction, HasFDerivAt.multiset_prod, dist_self_homothety, HasFDerivAt.mul_const, differentiableWithinAt_euclidean, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, iteratedDerivWithin_fun_id, DoubleCentralizer.neg_toProd, LinearPMap.adjointDomainMkCLM_apply, Matrix.isPositive_toEuclideanLin_iff, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, RCLike.re_eq_add_conj, PiTensorProduct.dualSeminorms_bounded, NormedSpace.exp_sum, CommCStarAlgebra.toStarModule, FormalMultilinearSeries.radius_neg, HasDerivAt.comp_hasFDerivWithinAt_of_eq, GromovHausdorff.ghDist_eq_hausdorffDist, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, Summable.multipliableLocallyUniformlyOn_one_add, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, PadicInt.zmodRepr_spec, WeakDual.polar_def, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, iteratedFDerivWithin_succ_apply_left, hasStrictFDerivAt_norm_sq, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, derivWithin_pow_field, Summable.multipliableLocallyUniformlyOn_nat_one_add, iteratedDeriv_comp_neg, logDeriv_id, EisensteinSeries.summable_one_div_norm_rpow, HasFDerivAtFilter.fun_sub, Int.toNat_add_toNat_neg_eq_norm, PadicInt.norm_natCast_zmodRepr_eq_one_iff, Matrix.posDef_iff_eq_conjTranspose_mul_self, MeasureTheory.condExpIndL1_smul', Int.instNormMulClass, WeakDual.CharacterSpace.compContinuousMap_apply, hasDerivAt_id, HasFTaylorSeriesUpToOn.fderivWithin, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, deriv_update, orthonormal_subtype_iff_ite, Summable.hasProdLocallyUniformlyOn_one_add, nndist_lineMap_right, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, Summable.multipliableUniformlyOn_one_add, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, PadicInt.nthHomSeq_mul, norm_fderiv_iteratedFDeriv, curveIntegralFun_neg, binomialSeries_radius_eq_top_of_nat, MeasureTheory.Lp.norm_constL_le, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, HasStrictFDerivAt.const_sub, Submodule.coe_inner, fderiv_sub, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, KuratowskiEmbedding.embeddingOfSubset_isometry, ContMDiffAt.clm_precomp, MeasureTheory.condExpL2_indicator_of_measurable, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, iter_deriv_pow', MeasureTheory.condExp_ae_eq_condExpL1CLM, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, AffineIsometry.norm_map, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, AffineSubspace.isometryEquivMap.coe_apply, Padic.mk_eq, deriv_neg'', Submodule.sndL_comp_coe_orthogonalDecomposition, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, PadicInt.limNthHom_spec, GromovHausdorff.eq_toGHSpace, MeasureTheory.L1.tendsto_setToL1, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', MeasureTheory.condExpL1CLM_indicatorConst, MeasureTheory.L1.nnnorm_Integral_le_one, RCLike.ofReal_alg, SchwartzMap.smulLeftCLM_add, UnitAddTorus.hasSum_mFourier_series_L2, norm_fderivWithin_iteratedFDerivWithin, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, HasFDerivWithinAt.hasDerivWithinAt, ContinuousMultilinearMap.integral_apply, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, HasFiniteFPowerSeriesOnBall.neg, ContinuousLinearMap.le_def, WeakDual.isClosed_closedBall, AffineMap.derivWithin, coe_lpPiLpβα΅’, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, RCLike.sqrt_neg_one, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, InnerProductSpace.rankOne_def', EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, ContinuousLinearMap.holder_smul_right, HasFPowerSeriesWithinOnBall.const_smul, fderiv_apply_one_eq_deriv, HasFPowerSeriesOnBall.sub, Submodule.norm_orthogonalProjection_apply, EisensteinSeries.isBigO_linear_add_const_vec, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', meromorphicTrailingCoeffAt_id_sub_const, PadicComplex.instIsScalarTowerPadicPadicAlgCl, MeasureTheory.condExpL1CLM_lpMeas, HasStrictFDerivAt.fun_sub, Matrix.IsHermitian.spectrum_eq_image_range, logDeriv_id', RCLike.isCauSeq_im, StrongDual.toLpβ_apply, MeasureTheory.L1.setToL1_apply_coeToLp, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, PadicInt.fwdDiff_iter_le_of_forall_le, DoubleCentralizer.sub_toProd, Valued.integer.coe_span_singleton_eq_closedBall, PadicInt.mem_span_pow_iff_le_valuation, HasFTaylorSeriesUpToOn.add, NormedSpace.norm_expSeries_summable', formalMultilinearSeries_geometric_eq_ofScalars, Matrix.posSemidef_gram, fderivWithin_multiset_prod, HasFDerivAt.mul, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, toWeakSpace_closedConvexHull_eq, MeasureTheory.L1.setToL1_congr_left', Submodule.det_reflection, Finset.norm_prod_le', deriv_neg', fderivWithin_neg, Submodule.inner_orthogonalProjection_eq_of_mem_left, CurveIntegrable.fun_neg, AffineSubspace.subtypeβα΅’_linear, CauSeq.cauchySeq, EisensteinSeries.r_mul_max_le, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, MDifferentiableAt.clm_precomp, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, LinearPMap.isSelfAdjoint_def, PadicInt.norm_intCast_eq_one_iff, EisensteinSeries.norm_symm, summable_norm_pow_mul_geometric_div_one_sub, hasGradientAt_iff_hasFDerivAt, Asymptotics.isEquivalent_nat_floor, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, curveIntegrable_neg_iff, MeasureTheory.L1.setToL1_congr_left, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, Matrix.exp_conj, mdifferentiableOn_continuousLinearMapCoordChange, fderiv_deriv, MeasureTheory.L1.setToL1_smul, PadicInt.isUnit_den, continuous_barycentric_coord, PadicSeq.not_limZero_const_of_nonzero, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, InnerProductSpace.isStarProjection_rankOne_self, RCLike.norm_natCast, Rat.padicValuation_eq_zero_iff, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, PadicInt.norm_le_pow_iff_mem_span_pow, WeakDual.isClosed_polar, spec_cfcβAux, iteratedDerivWithin_pow, FormalMultilinearSeries.zero_radius, PadicInt.zmodRepr_natCast, RCLike.ofReal_intCast, fderiv_finset_prod, ContinuousLinearMap.coeFn_compLpL, PadicInt.valuation_one, deriv_single, PadicInt.norm_natCast_zmodRepr_eq, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, DoubleCentralizer.sub_fst, isCauSeq_iff_cauchySeq, Submodule.starProjection_orthogonal, LinearMap.mem_polar_singleton, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', Submodule.ClosedComplemented.of_finiteDimensional, ContinuousAffineMap.hasFDerivAtFilter, hasStrictFDerivAt_ringInverse, PadicInt.ker_toZModPow, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, InnerProductSpace.rankOne_comp_rankOne, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, LipschitzOnWith.coordinate, parallelogram_law, AnalyticAt.hasFPowerSeriesAt, Asymptotics.IsTheta.listProd, Matrix.toEuclideanLin_eq_toLin, LinearMap.mkContinuous_norm_le', StrongDual.toLpβ_of_not_memLp, Matrix.isHermitian_iff_isSymmetric, ContinuousAffineMap.hasFDerivAt, Asymptotics.Filter.Tendsto.isBigOTVS_one, Polynomial.cyclotomic_eq_minpoly_rat, hasStrictFDerivAt_finset_prod, fderiv_fun_neg, Valued.integer.norm_unit, Matrix.finite_real_spectrum, deriv_zpow, InnerProductSpace.rankOne_comp, HasDerivWithinAt.comp_hasFDerivAt, inner_eq_neg_one_iff_of_norm_eq_one, ContinuousAffineMap.norm_image_zero_le, StrongDual.mem_polarSubmodule, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, SchwartzMap.tsupport_smulLeftCLM_subset, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, HasMFDerivAt.sub, InnerProductSpace.toMatrix_rankOne, differentiableAt_euclidean, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, dist_pointReflection_right, EuclideanGeometry.orthogonalProjection_mem, InnerProductSpace.isSymmetric_rankOne_self, inner_eq_one_iff_of_norm_eq_one, fderiv_const_sub, HasFPowerSeriesAt.deriv, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, PadicAlgCl.valuation_def, AnalyticAt.exists_eq_sum_add_pow_mul, ContinuousLinearMap.intervalIntegral_apply, span_fourierLp_closure_eq_top, HasFDerivWithinAt.sub, HasFDerivAtFilter.fun_neg, SchwartzMap.smulLeftCLM_neg, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, MeasureTheory.aestronglyMeasurable_condExpL1CLM, HasFPowerSeriesAt.const_smul, curveIntegralFun_sub, RCLike.ofReal_one, logDeriv_inv, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, differentiableOn_euclidean, fderiv_continuousLinearEquiv_comp, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, PadicInt.instNormOneClass, RCLike.natCast_im, tsum_prod_pow_eq_tsum_sigma, PadicAlgCl.valuation_coe, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, MeasureTheory.integrable_condExpL2_indicator, PadicComplex.coe_zero, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, coe_lpBCFβα΅’_symm, coe_lpPiLpβα΅’_symm, Matrix.posSemidef_iff_eq_sum_vecMulVec, SchwartzMap.pairing_continuous_left, Matrix.ofLp_toEuclideanLin_apply, ContinuousAffineMap.fderivWithin, SchwartzMap.integralCLM_apply, MeasureTheory.lpNorm_one, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, RCLike.norm_two, HasStrictFDerivAt.hasStrictDerivAt, ContinuousMap.spectrum_eq_range, innerSLFlip_apply, LinearMap.mkContinuous_norm_le, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, fderivWithin_derivWithin, RCLike.sqrt_neg_I, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, HasFDerivAt.fun_neg, contDiff_nat_iff_continuous_differentiable, SchwartzMap.lineDerivOp_fourierInv_eq, EulerProduct.norm_tsum_factoredNumbers_sub_tsum_lt, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, iteratedDeriv_comp_const_sub, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, OrthonormalBasis.repr_symm_single, NumberField.canonicalEmbedding.norm_le_iff, WeakDual.CharacterSpace.norm_le_norm_one, MeasureTheory.L1.norm_setToL1_le_mul_norm', innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, AffineIsometryEquiv.toAffineEquiv_injective, iter_deriv_inv, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, RCLike.sqrt_I, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, HasFPowerSeriesAt.sub, HasStrictFDerivAt.fun_neg, hasDerivWithinAt_zpow, OrthogonalFamily.range_linearIsometry, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, NormedField.v_eq_valuation, RCLike.nnnorm_two, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, HasDerivWithinAt.fun_pow, MeasureTheory.lpTrimToLpMeas_ae_eq, MeasureTheory.charFun_eq_charFunDual_toDualMap, AffineIsometry.toContinuousAffineMap_injective, HasMFDerivAt.prod, iteratedDeriv_eq_iteratedFDeriv, EuclideanGeometry.orthogonalProjection_orthogonalProjection, iter_deriv_inv', MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ContMDiff.clm_postcomp, MeasureTheory.lpNorm_div_natCast, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, dist_left_lineMap, MDifferentiableWithinAt.clm_postcomp, cosetToCuspOrbit_apply_mk, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, deriv_pow_field, ZSpan.repr_fract_apply, HasFPowerSeriesAt.hasDerivAt, ordinaryHypergeometricSeries_eq_zero_iff, MeasureTheory.L1.norm_setToL1_le', MeasureTheory.withDensitySMulLI_apply, ContinuousMap.comp_attachBound_mem_closure, PadicInt.norm_sub_modPart, Polynomial.X_pow_sub_X_sub_one_irreducible_rat, PadicInt.norm_p, OrthonormalBasis.span_apply, Padic.withValUniformEquiv_cast_apply, HasFDerivAt.hasDerivAt, PadicInt.valuation_p_pow_mul, spectrum.exp_mem_exp, Matrix.IsHermitian.cfcAux_id, cfcβAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, Padic.coe_withValRingEquiv, HasFPowerSeriesWithinOnBall.neg, PadicInt.fwdDiff_mahlerSeries, deriv_id, SchwartzMap.fderivCLM_fourier_eq, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, EuclideanGeometry.Sphere.orthRadius_map, AffineSubspace.subtypeβα΅’_linearIsometry, PadicInt.zmodRepr_natCast_zmodRepr, MDifferentiableOn.clm_precomp, PadicInt.pow_p_dvd_int_iff, Asymptotics.isEquivalent_iff_tendsto_one, hasDerivAt_neg, LinearMap.derivWithin, hasFTaylorSeriesUpToOn_succ_iff_left, Padic.isUniformInducing_cast_withVal, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, derivWithin_fun_pow, EuclideanGeometry.Sphere.IsTangent.isTangentAt, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, Polynomial.cyclotomic.irreducible_rat, HasMFDerivWithinAt.mul, HilbertBasis.repr_self, fderivWithin_sub, MeasureTheory.condExpInd_smul', MeasureTheory.L1.setToL1_add_left, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, HasFDerivAt.const_sub, PadicInt.p_nonunit, PadicInt.limNthHom_one, BoundedContinuousFunction.toLp_norm_le, iteratedFDerivWithin_two_apply, Pretrivialization.continuousOn_continuousLinearMapCoordChange, fderiv_fun_mul, curveIntegral_fun_sub, PadicComplex.norm_extends, Submodule.adjoint_orthogonalProjection, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime, EuclideanGeometry.reflection_apply', hasFDerivWithinAt_iff_hasGradientWithinAt, AffineIsometryEquiv.ofEq_rfl, ContinuousAffineMap.differentiableOn, ContinuousLinearMap.hasFDerivAt_of_bilinear, Unitization.instNormOneClass, EuclideanGeometry.oangle_self_orthogonalProjection, ContinuousAffineMap.norm_comp_le, HasStrictFDerivAt.multiset_prod, Matrix.toEuclideanLin_apply_piLp_toLp, PadicSeq.add_eq_max_of_ne, hasFDerivAt_integral_of_dominated_of_fderiv_le, LinearIsometry.strictConvexSpace_range_iff, Affine.Simplex.altitude_map, hasDerivAt_pow, PadicInt.norm_sub_zmodRepr_lt_one, PadicInt.mahlerEquiv_apply, MeasureTheory.L1.norm_setToL1_le_mul_norm, AffineIsometry.toAffineMap_injective, AffineIsometryEquiv.toAffineEquiv_refl, EisensteinSeries.abs_le_left_of_norm, hasStrictDerivAt_exp, nndist_lineMap_lineMap, isCoveringMap_npow, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left', HasDerivWithinAt.pow, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, AffineMap.differentiableOn, iteratedDeriv_comp_three, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, HasFPowerSeriesWithinAt.neg, PadicInt.isCauSeq_padicNorm_of_pow_dvd_sub, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, logDeriv_fun_zpow, OrthonormalBasis.inner_eq_one, orthogonalFamily_iff_pairwise, EisensteinSeries.abs_norm_eq_max_natAbs, iteratedDerivWithin_id, Padic.coe_withValRingEquiv_symm, HasFiniteFPowerSeriesAt.sub, ContinuousLinearMap.norm_compSL_le, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, MeasureTheory.norm_condExpInd_le, Affine.Simplex.orthogonalProjectionSpan_reindex, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, Valued.integer.isUnit_iff_norm_eq_one, hasStrictFDerivAt_list_prod, Summable.hasProdLocallyUniformlyOn_nat_one_add, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.IsPositive.spectrumRestricts, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, LinearIsometry.strictConvexSpace_range, ContinuousLinearMap.opNorm_neg, MeasureTheory.condExpInd_disjoint_union_apply, Submodule.fstL_comp_coe_orthogonalDecomposition, iter_deriv_inv_linear_sub, ContinuousLinearMap.add_compLpL, MeasureTheory.L1.setToL1_simpleFunc_indicatorConst, IsHilbertSum.linearIsometryEquiv_symm_apply_single, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, UnitAddTorus.mFourierBasis_repr, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, EuclideanGeometry.orthogonalProjection_linear, MeasureTheory.lpNorm_natCast_mul, DoubleCentralizer.natCast_toProd, OrthonormalBasis.sum_rankOne_eq_id, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, AffineSubspace.signedInfDist_def, iteratedDeriv_id, PadicInt.nthHomSeq_add, MeasureTheory.L1.setToL1_zero_left', MeasureTheory.BoundedContinuousFunction.inner_toLp, PadicComplex.rankOne_hom_eq, exists_extension_norm_eq, MeasureTheory.L1.norm_Integral_le_one, ContinuousLinearMap.norm_smulRightL_le, derivWithin_neg, SchwartzMap.tsupport_derivCLM_subset, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, hasDerivAt_single, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, orthonormal_iff_ite, Int.norm_coe_units, fderivWithin_mul_const, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, ContinuousMap.polynomial_comp_attachBound, EisensteinSeries.abs_norm_eq_max_natAbs_neg, ContinuousAffineMap.hasFDerivWithinAt, inner_self_eq_one_of_norm_one, Complex.isOpenQuotientMap_pow_compl_zero, isOpenMap_barycentric_coord, Affine.Simplex.signedInfDist_affineCombination, signedDist_apply, WeakDual.CharacterSpace.equivAlgHom_coe, EuclideanGeometry.angle_self_orthogonalProjection, Valued.toNormedField.setOf_mem_integer_eq_closedBall, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, HasFDerivAt.hasGradientAt, ordinaryHypergeometric_radius_top_of_neg_natβ, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, MeasureTheory.L1.setToL1_mono, continuous_descPochhammer_eval, EuclideanGeometry.orthogonalProjection_eq_self_iff, Padic.norm_rat_le_one_iff_padicValuation_le_one, PadicInt.norm_natCast_eq_one_iff, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, EuclideanGeometry.reflection_subtype, DoubleCentralizer.sub_snd, ContinuousLinearEquiv.coord_norm', deriv_fun_pow, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, HasFPowerSeriesAt.eq_zero_of_eventually, Rat.surjective_padicValuation, hasStrictFDerivAt_inv', AffineIsometryEquiv.coe_vaddConst', SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, SchwartzMap.smulLeftCLM_apply_apply, deriv_descPochhammer_eval_eq_sum_prod_range_erase, Module.Basis.ofZLatticeBasis_repr_apply, derivWithin_id, dist_midpoint_midpoint_le', iteratedDeriv_fun_pow_zero, SchwartzMap.fourier_fderivCLM_eq, NumberField.InfinitePlace.map_intCast, iteratedFDeriv_two_apply, AffineSubspace.isometryEquivMap.apply_symm_apply, RCLike.instNormSMulClassInt, HasStrictFDerivAt.mul, iter_deriv_inv_linear, AffineMap.differentiable, Summable.hasProdUniformlyOn_one_add, WeakDual.toStrongDual_apply, AffineEquiv.coe_toHomeomorphOfFiniteDimensional, PadicInt.nthHomSeq_one, MDifferentiable.clm_precomp, PadicInt.ideal_eq_span_pow_p, dist_right_lineMap, WeakDual.CharacterSpace.compContinuousMap_comp, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, RCLike.nnnorm_natCast, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, ContinuousLinearMap.smul_compLpL, AddChar.wInner_cWeight_eq_boole, PadicSeq.norm_const, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousMap.polynomial_comp_attachBound_mem, mul_comm, ContinuousLinearMap.opNorm_mulLeftRight_le, DoubleCentralizer.intCast_fst, ContinuousLinearMap.norm_compLpL_le, meromorphicOrderAt_const_intCast, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left, PadicSeq.norm_one, MeasureTheory.setIntegral_condExpL1CLM, ContMDiffWithinAt.clm_precomp, WeakDual.CharacterSpace.equivAlgHom_symm_coe, AffineIsometryEquiv.norm_map, HasFDerivWithinAt.finset_prod, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, MeasureTheory.eLpNorm_condExpL2_le, Asymptotics.IsEquivalent.listProd, closure_diff_intrinsicInterior, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, ContinuousLinearEquiv.coord_self, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, SchwartzMap.smulLeftCLM_ofReal, ContDiffAt.differentiableAt_iteratedFDeriv, ContinuousLinearEquiv.coord_norm, fderiv_norm_rpow, MeasureTheory.lpNorm_one', MeasureTheory.lpMeasToLpTrim_smul, PadicInt.continuousAddCharEquiv_apply, LinearPMap.mem_adjoint_domain_iff, ContMDiff.clm_precomp, PadicInt.complete, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, NormedSpace.expSeries_hasSum_exp_of_mem_ball', fderivWithin_pow, KuratowskiEmbedding.exists_isometric_embedding, EuclideanGeometry.orthogonalProjection_apply, PadicInt.denseRange_intCast, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, OrthonormalBasis.coe_singleton, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono, ContinuousLinearMap.hasDerivWithinAt, hasStrictFDerivAt_pow, Submodule.norm_orthogonalProjection, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, EuclideanGeometry.orthogonalProjection_mem_orthogonal, PadicSeq.norm_zero_iff, hasDerivAt_exp_zero, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, AffineIsometryEquiv.toAffineEquiv_symm, SchwartzMap.smulLeftCLM_apply, ZSpan.repr_floor_apply, WeakDual.isSeqCompact_polar, MeasureTheory.condExpIndSMul_ae_eq_smul, HasFTaylorSeriesUpTo.fderiv, lipschitzWith_lineMap, HasStrictFDerivAt.fun_mul, ContinuousLinearMap.norm_holderL_le, hasFDerivWithinAt_pow, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, NormedField.valuation_apply, LinearMap.polar_mem_iff, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, MeasureTheory.lpMeas.ae_fin_strongly_measurable', hasStrictDerivAt_id, curveIntegral_sub, Matrix.IsHermitian.charpoly_eq, TemperedDistribution.derivCLM_apply_apply, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, MeasureTheory.L1.setToL1'_eq_setToL1SCLM, deriv_neg, AffineIsometryEquiv.toContinuousAffineEquiv_injective, dist_midpoint_left, MeasureTheory.condExpIndSMul_smul', LinearMap.hasDerivAt, LinearMap.hasDerivAtFilter, CurveIntegrable.sub, PadicInt.unitCoeff_spec, Valued.integer.norm_coe_unit, HasFPowerSeriesAt.locally_zero_iff, PadicInt.norm_natCast_zmodRepr_eq_iff, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, ordinaryHypergeometricSeries_norm_div_succ_norm, MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, hasFDerivAt_inv', Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Matrix.IsStrictlyPositive.posDef, inner_eq_one_iff_of_norm_one, exists_continuousLinearEquiv_fderiv_symm_eq, FormalMultilinearSeries.rightInv_coeff, hasDerivAt_zpow, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, WeakDual.CharacterSpace.compContinuousMap_id, mfderiv_neg, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContDiffOn.differentiableOn_iteratedFDerivWithin, NormedSpace.expSeries_summable_of_mem_ball', Finset.norm_prod_le, Matrix.l2_opNorm_def, OrthogonalFamily.linearIsometry_apply, HasFiniteFPowerSeriesOnBall.sub, Matrix.toEuclideanLin_toLp, ContinuousLinearMap.holderL_apply_apply, ZSpan.coe_fract_self, CauchySeq.isCauSeq, MeasureTheory.condExpInd_empty, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, MeasureTheory.condExpL1CLM_smul, norm_innerSL_le, AffineSubspace.subtypeβα΅’_toAffineMap, BoundedContinuousFunction.separatesPoints_charPoly, HasStrictFDerivAt.sub, ContMDiffWithinAt.cle_arrowCongr, antilipschitzWith_lineMap, Submodule.starProjection_coe_eq_isCompl_projection, HasFDerivAt.neg, RCLike.normSq_one, AffineMap.deriv, Submodule.ClosedComplemented.of_quotient_finiteDimensional, Summable.multipliableUniformlyOn_nat_one_add, ContinuousLinearMap.apply_apply', PadicComplex.nnnorm_extends, LinearMap.posSemidef_toMatrix_iff, Int.instNormOneClass, SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, UnitAddTorus.span_mFourierLp_closure_eq_top, PadicInt.coe_dpow_eq, RCLike.charZero_rclike, CommCStarAlgebra.toCompleteSpace, exists_continuousLinearEquiv_fderivWithin_symm_eq, HasGradientWithinAt.hasFDerivWithinAt, hasFDerivAt_exp, RCLike.isCauSeq_re, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, PadicInt.norm_natCast_p_sub_one, LinearMap.polar_mem, Submodule.IsCompl.projection_isSymmetric_iff, PadicInt.prime_p, MeasureTheory.condExpIndL1Fin_smul', Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Submodule.norm_subtypeL_le, ContinuousLinearMap.hasStrictDerivAt, AffineIsometry.coe_toContinuousAffineMap, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, fderivWithin_pow_ring, MeasureTheory.L1.integral_eq, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, logDeriv_pow, derivWithin_pow, constFormalMultilinearSeries_zero, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, ContinuousMultilinearMap.instIsTopologicalAddGroup, HasStrictFDerivAt.mul_const, AffineIsometry.image_intrinsicFrontier, EuclideanGeometry.orthogonalProjection_eq_iff_mem, nndist_self_homothety, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, PadicSeq.norm_mul, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, MeasureTheory.L1.setToL1'_apply_coeToLp, RCLike.I_mul_I_of_nonzero, SchwartzMap.denseRange_toLpCLM, EisensteinSeries.vec_add_const_isTheta, ContinuousLinearMap.norm_precompL_le, Padic.const_equiv, ContinuousLinearMap.apply_apply, MeasureTheory.L1.setToL1_const, intrinsicClosure_eq_closure, RCLike.span_one_I, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, iteratedFDeriv_neg, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, IsSymmSndFDerivWithinAt.eq, EisensteinSeries.summand_bound, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Submodule.orthogonalProjection_norm_le, DoubleCentralizer.intCast_toProd, ContinuousAffineMap.differentiableAt, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, RCLike.intCast_im, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, MeasureTheory.L1.setToL1_lipschitz, MeasureTheory.norm_condExpL2_le_one, Padic.isDenseInducing_cast_withVal, logDeriv_zpow, GromovHausdorff.eq_toGHSpace_iff, MeasureTheory.setToFun_eq, MeasureTheory.condExpL2_comp_continuousLinearMap, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, AffineIsometry.id_toAffineMap, ContMDiffAt.cle_arrowCongr, HasDerivWithinAt.comp_hasFDerivAt_of_eq, PadicInt.zmodRepr_natCast_of_lt, ContinuousLinearMap.adjoint_innerSL_apply, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, nndist_homothety_self, fderivWithin_fun_mul, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, EuclideanGeometry.reflection_apply, MeasureTheory.condExpL2_const_inner, PadicInt.existsUnique_mem_range, Submodule.coe_prodEquivOfClosedCompl, ContinuousLinearMap.norm_smulRightL_apply, isOpen_setOf_nat_le_rank, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, PadicInt.toZMod_spec, Matrix.IsHermitian.instContinuousFunctionalCalculus, fderiv_norm_sq_apply, hasStrictDerivAt_pow, PadicComplexInt.integers, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, LinearMap.exists_map_addHaar_eq_smul_addHaar', MeasureTheory.Lp.toTemperedDistribution_smul_eq, NormedSpace.dual_def, EulerProduct.norm_tsum_smoothNumbers_sub_tsum_lt, HasFDerivAtFilter.hasDerivAtFilter, fderiv_norm_sq, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, ContinuousMap.idealOpensGI_choice, Submodule.ClosedComplemented.of_isCompl_isClosed, TensorProduct.toLinearMap_mapInclIsometry, Int.Matrix.exists_ne_zero_int_vec_norm_le, MeasureTheory.condExpL1_eq, PadicInt.zmodRepr_eq_zero_iff_dvd, orthonormal_span, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.toSesqForm_apply_norm_le, PiTensorProduct.injectiveSeminorm_def, HilbertBasis.hasSum_repr_symm, ContMDiff.cle_arrowCongr, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, dist_lineMap_lineMap, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, MeasureTheory.condExpL2_indicator_nonneg, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, HasCompactSupport.hasFDerivAt_convolution_left, PadicSeq.eq_zero_iff_equiv_zero, Submodule.coe_prodEquivOfClosedCompl_symm, fderivWithin_mul, TemperedDistribution.smulLeftCLM_apply_apply, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, nndist_lineMap_left, HasFDerivWithinAt.fun_mul, OrthonormalBasis.inner_eq_ite, BoundedContinuousFunction.char_mem_charPoly, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', EisensteinSeries.div_max_sq_ge_one, iter_deriv_pow, Rat.padicValuation_le_one_iff, HasStrictFDerivAt.finset_prod, InnerProductSpace.norm_rankOne, HasFDerivAt.fun_sub, hasFDerivAt_integral_of_dominated_loc_of_lip, Submodule.isHilbertSumOrthogonal, DoubleCentralizer.neg_fst, kuratowskiEmbedding.isometry, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, ContinuousLinearMap.flipAlternating_apply_apply, Int.Matrix.exists_ne_zero_int_vec_norm_le', NormedSpace.exp_add, EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, PadicInt.addChar_of_value_at_one_def, AffineMap.continuous_of_finiteDimensional, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, niven_fract_angle_div_pi_eq, fderiv_inv', Matrix.permMatrix_l2_opNorm_eq, MeasureTheory.lpMeas.aestronglyMeasurable, AffineIsometryEquiv.coe_toAffineEquiv, AffineIsometryEquiv.coe_toContinuousAffineEquiv, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, PadicInt.norm_natCast_lt_one_iff, HasStrictDerivAt.fun_pow
|
toSeminormedCommRing π | CompOp | 4580 mathmath: ArithmeticFunction.vonMangoldt.residueClass_eq, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, LinearMap.det_toContinuousLinearMap, ValueDistribution.logCounting_zero, instSeparatingDual, hasFDerivAt_iff_hasDerivAt, ContMDiffAt.coordChangeL, HurwitzZeta.hasSum_int_hurwitzZetaOdd, iteratedDeriv_scomp_two, LinearMap.IsSymmetric.clm_adjoint_eq, Real.differentiableOn_arcosh, isEquivalent_descFactorial, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, WeakFEPair.differentiableAt_Ξ, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, TemperedDistribution.lineDerivOpCLM_eq, continuousSMul_sphere_ball, BoundedContinuousFunction.tietze_extension_step, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, MeasureTheory.Lp.toTemperedDistributionCLM_apply, InformationTheory.integrable_klFun_rnDeriv_iff, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Polynomial.differentiableWithinAt, MeasureTheory.convolution_flip, FormalMultilinearSeries.comp_rightInv_aux1, tendsto_zero_iff_meromorphicOrderAt_pos, MDifferentiable.coordChangeL, UpperHalfPlane.mdifferentiable_num, MeasureTheory.Integrable.integral_norm_prod_right, Complex.cos_eq_tsum, Seminorm.isBounded_const, ContinuousAt.inner, isConformalMap_conj, LinearMap.mkContinuousβ_norm_le', MeasureTheory.eLpNorm'_norm, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, HasStrictFDerivAt.isLittleOTVS, Bundle.ContMDiffRiemannianMetric.isVonNBounded, NormedSpace.isBounded_polar_of_mem_nhds_zero, SchwartzMap.lineDerivOpCLM_eq, HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_div, Valued.instIsUltrametricDist, TensorProduct.enorm_lid, differentiableAt_comp_neg, continuousAt_const_cpow, hasDerivWithinAt_Iio_iff_Iic, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, Real.integrableOn_rpowIntegrandββ_Ioi, LinearMap.mkContinuousβ_apply, Matrix.frobenius_nnnorm_mul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, Complex.differentiableAt_sin, Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero, Bundle.ContMDiffRiemannianMetric.contMDiff, Complex.norm_circleTransformBoundingFunction_le, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, Seminorm.absorbent_closedBall_zero, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, MonotoneOn.intervalIntegral_slope_le, LeftInvariantDerivation.lift_zero, ProbabilityTheory.isGaussian_iff_gaussian_charFun, Complex.isOpen_re_lt_EReal, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, Real.differentiable_arctan, norm_cfcβHom, RCLike.map_apply, IsUltrametricDist.isNonarchimedean_invariantExtension, differentiable_const_cpow_of_neZero, Real.differentiableAt_mulExpNegMulSq, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, completedZeta_eq_tsum_of_one_lt_re, Complex.continuousOn_exp, ContinuousLinearMap.continuousβ, RCLike.geometric_hahn_banach_point_open, hasDerivWithinAt_add_const_iff, IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, CuspFormClass.holo, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, IsUltrametricDist.algNormOfAlgEquiv_extends, RCLike.ofRealCLM_apply, SchwartzMap.integral_sesq_fourier_fourier, HurwitzZeta.differentiableAt_hurwitzZeta_sub_one_div, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, ModularFormClass.differentiableAt_comp_ofComplex, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, Real.hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, hasStrictDerivAt_intCast, Complex.linearEquiv_det_conjLIE, LeftInvariantDerivation.leibniz, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.convolution_eq_right', EisensteinSeries.hasSum_e2Summand_symmetricIcc, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, RCLike.reCLM_apply, NumberField.Units.finrank_eq_rank, HurwitzZeta.differentiableAt_hurwitzZetaEven, curveIntegral_smul, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, RCLike.separate_convex_open_set, NumberField.canonicalEmbedding.mem_span_latticeBasis, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, ConvexOn.rightDeriv_le_slope_of_mem_interior, PeriodPair.hasSumLocallyUniformly_weierstrassP, ContinuousMap.abs_mem_subalgebra_closure, Subalgebra.spectrum_sUnion_connectedComponentIn, Function.FactorizedRational.divisor, hasDerivAt_sqrt_mul_log, LinearMap.IsSymmetric.restrictScalars, LSeries.term_sum, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, ContinuousLinearMap.continuous_det, HurwitzZeta.hasSum_int_cosKernelβ, HasFiniteFPowerSeriesAt.neg, Complex.isOpenMap_im, Polynomial.isEquivalent_atBot_div, SchwartzMap.norm_le_seminorm, ZSpan.volume_real_fundamentalDomain, HurwitzZeta.hasSum_int_hurwitzZetaEven, Complex.ofRealCLM_coe, Complex.kahler, Complex.norm_polarCoord_symm, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, ContinuousLinearMap.map_add_add, ContinuousAlternatingMap.isEmbedding_restrictScalars, RightDerivMeasurableAux.D_subset_differentiable_set, Complex.areaForm, WeakDual.isCompact_polar, MeromorphicOn.divisor_fun_smul, finrank_real_complex_fact', PeriodPair.deriv_weierstrassP, EuclideanSpace.orthonormal_single, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, Real.deriv_negMulLog, Real.hasDerivAt_sigmoid, PeriodPair.coeff_weierstrassPExceptSeries, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, Matrix.IsHermitian.det_abs, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, RCLike.ofRealLI_apply, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Complex.comap_exp_cobounded, ModularForm.mul_slash, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, deriv_abs, differentiableAt_zpow, hasFDerivAt_multiset_prod, Stirling.factorial_isEquivalent_stirling, ProbabilityTheory.covarianceBilinDual_apply', Circle.exp_arg, Real.nnnorm_deriv_mulExpNegMulSq_le_one, spectrum.subset_closedBall_norm_mul, Circle.injective_arg, OrthonormalBasis.repr_injective, continuousSMul_sphere_sphere, spectrum.instCompactSpace, Real.deriv_binEntropy, ContinuousLinearMap.continuousSMul, hasFTaylorSeriesUpToOn_top_iff_right, DirichletCharacter.LSeries_eulerProduct_tprod, smoothSheafCommRing.nonunits_stalk, LSeries.term_convolution', MeasureTheory.convolution_mul, Complex.ofRealLI_apply, CuspFormClass.zero_at_infty_comp_ofComplex, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, PeriodPair.derivWeierstrassPExcept_sub, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, deriv_mem_iff, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, Bornology.isVonNBounded_add_of_nonempty, NumberField.canonicalEmbedding.latticeBasis_apply, Complex.integral_comp_pi_polarCoord_symm, FormalMultilinearSeries.radius_pi_eq_iInf, integrableOn_exp_mul_Iic, ProbabilityTheory.IsGaussian.integrable_dual, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, Padic.withValUniformEquiv_norm_le_one_iff, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, ApproximatesLinearOn.lipschitz, summableLocallyUniformlyOn_iteratedDerivWithin_cexp, tendsto_cobounded_iff_meromorphicOrderAt_neg, Real.hasStrictDerivAt_rpow_const_of_ne, Matrix.IsHermitian.cfc_eq, lp.inner_eq_tsum, UpperHalfPlane.image_coe_sphere, Complex.isCoveringMap_exp, StrongDual.polarSubmodule_eq_setOf, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, ContinuousLinearMap.isUniformEmbedding_restrictScalars, PeriodPair.Οβ_div_two_notMem_lattice, ContinuousMap.attachBound_apply_coe, OrthonormalBasis.sum_inner_mul_inner, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, range_circleMap, Asymptotics.isLittleOTVS_one, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, ContinuousLinearMap.hasDerivAtFilter, HasFPowerSeriesAt.locally_ne_zero, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, span_fourier_closure_eq_top, Complex.GammaSeq_tendsto_Gamma, PeriodPair.basis_one, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, RCLike.conjCLE_norm, HasFPowerSeriesOnBall.add, Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, ContDiffBump.integrable, SchwartzMap.seminorm_le_bound, Bornology.isVonNBounded_add_self, WeakDual.isClosed_image_polar_of_mem_nhds, ZLattice.covolume_eq_det_inv, one_add_cpow_hasFPowerSeriesAt_zero, RCLike.algebraMap_eq_ofReal, circleIntegrable_iff, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', MeasureTheory.MemLp.const_inner, DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontriv, Complex.tsum_exp_neg_mul_int_sq, not_integrableOn_Ioi_cpow, MeasureTheory.AEStronglyMeasurable.memLp_truncation, Real.fderiv_fourierChar_neg_bilinear_right_apply, WithSeminorms.mem_nhds_iff, UpperHalfPlane.isOpenEmbedding_coe, Unitization.real_cfcβ_eq_cfc_inr, intervalIntegral.fderiv_integral_of_tendsto_ae, ContDiffAt.fderiv_right_succ, flip_innerSL_real, LipschitzWith.memLp_lineDeriv, hasFPowerSeriesOnBall_pi_iff, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, differentiableWithinAt_abs_pos, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, Complex.uniformlyContinuous_im, eventually_enorm_mfderivWithin_symm_extChartAt_lt, HasFPowerSeriesWithinAt.const_smul, ProbabilityTheory.integrable_preCDF, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, isClosedEmbedding_cfcβAux, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, AddChar.wInner_cWeight_self, AddCircle.coe_real_preimage_closedBall_eq_iUnion, LeftInvariantDerivation.coe_derivation, innerSL_apply_apply, RCLike.norm_expect_le, HasGradientAt.continuousOn, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, SeminormFamily.filter_eq_iInf, MeasureTheory.Integrable.norm_integral_condExpKernel, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerββ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, inner_sum, Real.differentiable_sinh, HasFTaylorSeriesUpTo.hasFDerivAt, Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_ne, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, UpperHalfPlane.comp_ofComplex_of_im_pos, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContinuousLinearMap.toBilinForm_apply, Seminorm.restrictScalars_closedBall, RCLike.map_same_eq_id, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, DoubleCentralizer.nnnorm_def', NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, Seminorm.bddAbove_range_iff, Complex.continuousOn_arg, dist_iteratedFDerivWithin_one, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, NormedSpace.image_isVonNBounded_iff, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, UpperHalfPlane.dist_le_iff_dist_coe_center_le, LeftInvariantDerivation.left_invariant', Int.enorm_natCast, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, hasSum_one_div_nat_pow_mul_fourier, derivWithin_fderivWithin, two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even, MultilinearMap.mkContinuousMultilinear_apply, ContDiffBump.integrable_normed, SchwartzMap.instContinuousSMul, ProbabilityTheory.uncenteredCovarianceBilin_apply, Complex.UnitDisc.instSMulCommClass_closedBall_circle, TemperedDistribution.lineDerivOp_fourier_eq, Complex.frontier_setOf_re_le, Real.deriv_log, PadicInt.norm_mahlerTerm, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, ContDiff.differentiable_deriv_two, Seminorm.smul_inf, FormalMultilinearSeries.derivSeries_coeff_one, Polynomial.isCoveringMapOn_eval, Complex.ofRealCLM_norm, Complex.UnitDisc.instSMulCommClass_closedBall_left, Matrix.spectrum_toLpLin, contMDiff_neg_sphere, not_differentiableAt_norm_zero, mdifferentiableOn_symm_coordChangeL, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, StarAlgebra.elemental.characterSpaceToSpectrum_coe, rotation_injective, Bornology.IsBounded.reProdIm, Circle.ofConjDivSelf_coe, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, NumberField.mixedEmbedding.mem_idealLattice, MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE, BoxIntegral.unitPartition.mem_smul_span_iff, SchwartzMap.bilinLeftCLM_apply, Complex.borelSpace, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', SmoothBumpCovering.exists_immersion_euclidean, AffineMap.hasDerivWithinAt, MeromorphicOn.divisor_const, LeftInvariantDerivation.left_invariant, MeasureTheory.pdf.IsUniform.mul_pdf_integrable, ProbabilityTheory.integrable_toReal_condExpKernel, instSMulCommClass_sphere_sphere_sphere, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, Complex.convexHull_reProdIm, NormedSpace.toIsBoundedSMul, Complex.conjLIE_apply, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, Complex.hasStrictDerivAt_tan, Circle.starRingEnd_addChar, ContDiff.continuous_deriv_one, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, curveIntegralFun_smul, Complex.closure_preimage_im, egauge_ball_le_of_one_lt_norm, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasDerivWithinAt_iff_isLittleO, hasStrictFDerivAt_iff_isLittleOTVS, not_IntegrableOn_Ioi_inv, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, RCLike.re_add_im_ax, ContinuousMap.continuousMap_mem_subalgebra_closure_of_separatesPoints, ContinuousAlternatingMap.piLIE_apply_apply, Matrix.PosSemidef.sqrt_eq_zero_iff, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, lintegral_fderiv_lineMap_eq_edist, NumberField.InfiniteAdeleRing.algebraMap_apply, UnitAddTorus.mFourierSubalgebra_coe, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, hasDerivWithinAt_zero, iteratedDerivWithin_tsum_cexp_eq, ContDiffAt.hasStrictDerivAt, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, MeasureTheory.integral_const_mul, Complex.continuous_sin, FormalMultilinearSeries.hasSum_of_finite, signedDist_right_congr, hasDerivAtFilter_ofNat, Complex.exp_eq_exp_β, FormalMultilinearSeries.changeOriginSeries_summable_auxβ, curveIntegrable_smul_iff, TensorProduct.toLinearEquiv_lidIsometry, HasFPowerSeriesOnBall.restrictScalars, Real.differentiableOn_arcsin, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, ContinuousLinearMap.isometry_mul_flip, PeriodPair.weierstrassP_coe, AnalyticOnNhd.eval_linearMap', HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, MeasureTheory.MemLp.integrable_norm_rpow', ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, ClosedSubmodule.inf_orthogonal, LinearMap.coe_toContinuousLinearMap', balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, ModularForm.prod_slash, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, contDiffOn_iff_continuousOn_differentiableOn, Complex.isQuotientCoveringMap_npow, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.parallelepiped_basisFun, sum_cauchyPowerSeries_eq_integral, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, SchwartzMap.laplacianCLM_eq, CStarModule.innerSL_apply, monomial_has_deriv_aux, continuous_equivFun_basis, DirichletCharacter.LSeries_twist_vonMangoldt_eq, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.hasFiniteIntegral_prod_iff', Real.vector_fourierIntegral_eq_integral_exp_smul, PadicInt.mahlerTerm_apply, LinearMap.toMatrixOrthonormal_reindex, MeasureTheory.integral_div, MeasureTheory.ConvolutionExistsAt.integrable, Matrix.IsHermitian.eigenvalues_eq, MeasureTheory.MemLp.norm_rpow, nndist_midpoint_right, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, Asymptotics.isLittleOTVS_prodMk_left, NNReal.enorm_eq, Filter.tendsto_ofReal_iff', iter_deriv_zpow', differentiableWithinAt_abs, PadicInt.coe_sum, Complex.deriv_cos, WithSeminorms.continuousSMul, Matrix.exp_conj', hasLineDerivAt_iff_isLittleO_nhds_zero, Complex.not_differentiableAt_Gamma_neg_nat, Real.deriv_arccos, RCLike.borelSpace, Real.hasStrictDerivAt_sinh, AddCircle.homeomorphCircle'_symm_apply, TestFunction.continuous_iff_continuous_comp, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, HasFiniteFPowerSeriesOnBall.sum, LocallyBoundedVariationOn.ae_differentiableWithinAt, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, ConvexOn.univ_sSup_of_countable_affine_eq, integrableOn_exp_Iic, IsUltrametricDist.of_normedAlgebra', RCLike.hasSum_ofReal, InnerProductSpace.inner_left_rankOne_apply, Matrix.PosSemidef.commute_iff, cfcβHom_nnreal_eq_restrict, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, TestFunction.toBoundedContinuousFunctionCLM_apply, RCLike.continuous_normSq, IsLocalFrameOn.coeff_apply_of_mem, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, IsLocalMax.fderiv_eq_zero, Matrix.exp_neg, Manifold.IsImmersionAtOfComplement.ofOpen, HasFPowerSeriesAt.add, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, ContinuousAlternatingMap.curryLeft_smul, continuous_const_cpow, ContinuousLinearMap.hasBasis_nhds_zero, polynomialFunctions.starClosure_topologicalClosure, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerββ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, hasSum_nat_jacobiTheta, differentiableAt_sigmoid, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, iteratedDeriv_scomp_three, hasDerivWithinAt_pi, differentiableOn_iteratedDerivWithin_cotTerm, smoothSheafCommRing.instLocalRing_stalk, Real.integrable_prod_sub, NormedSpace.isVonNBounded_ball, MeasureTheory.eLpNorm_mono_real, MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt, ContinuousLinearMap.eq_adjoint_iff, PeriodPair.hasSum_derivWeierstrassPExcept, ContDiffAt.fderiv_succ, Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, convexHull_union_neg_eq_absConvexHull, RCLike.smul_re, Icc_isBoundaryPoint_bot, mellin_convergent_zero_of_isBigO, Polynomial.div_tendsto_zero_iff_degree_lt, deriv_abs_neg, ProbabilityTheory.evariance_lt_top_iff_memLp, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Real.differentiableWithinAt_arccos_Ici, HasFPowerSeriesAt.comp, Complex.differentiableAt_GammaAux, ContinuousLinearMap.IsPositive.smul_of_nonneg, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, EuclideanSpace.nndist_eq, LinearMap.polar_singleton, FormalMultilinearSeries.sum_of_finite, MeromorphicOn.divisor_pow, ModularForm.prod_slash_sum_weights, MeasureTheory.convolution_tendsto_right, gelfandStarTransform_apply_apply, HasFTaylorSeriesUpToOn.zero_eq', HarmonicAt.analyticAt_complex_partial, Complex.instPathConnectedSpaceUnits, integrableOn_Ioi_rpow_of_lt, ContDiff.continuous_deriv, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, NormedSpace.Dual.toWeakDual_continuous, WithSeminorms.withSeminorms_eq, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, signedDist_left_congr, NormedField.exists_lt_nnnorm_lt, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, exists_deriv_eq_zero, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, ContinuousMultilinearMap.norm_smulRightL_le, NormedField.exists_nnnorm_lt_one, ContinuousLinearMap.precompL_apply, DoubleCentralizer.nnnorm_snd, differentiableAt_comp_add_const, IsSelfAdjoint.adjoint_eq, spectralAlgNorm_def, integrableOn_Ioi_norm_cpow_of_lt, Complex.continuousOn_cos, QuadraticForm.equivalent_signType_weighted_sum_squared, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ZMod.completedLFunction_def_even, SchwartzMap.integral_fourierInv_smul_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, RCLike.geometric_hahn_banach_closed_point, signedDist_triangle, MeasureTheory.AEStronglyMeasurable.inner_const, IsUltrametricDist.invariantExtension_apply, Real.hasDerivAt_arcosh, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, Complex.isOpen_slitPlane, HasGradientAt.continuousAt, VectorBundleCore.contMDiffOn_coordChange, FormalMultilinearSeries.radius_le_smul, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, MeasureTheory.SignedMeasure.toComplexMeasure_apply, ModularForm.tsum_logDeriv_eta_q, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, ConvexOn.monotoneOn_rightDeriv, CStarMatrix.toCLM_injective, enorm_fderiv_norm_rpow_le, ContinuousLinearMap.isPositive_self_comp_adjoint, dslope_eventuallyEq_slope_nhdsNE, LinearMap.adjoint_toContinuousLinearMap, StrongFEPair.differentiable_Ξ, hasDerivAt_iff_isLittleO, spectrum.isOpen_resolventSet, LocallyBoundedVariationOn.ae_differentiableAt, Polynomial.toAddCircle_X_pow_eq_fourier, HasDerivWithinAt.hasFDerivWithinAt, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, hasFPowerSeriesAt_const, fderiv_eq_deriv_mul, nndist_right_lineMap, HasFPowerSeriesOnBall.const_smul, Orientation.abs_volumeForm_apply_of_orthonormal, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, HasFPowerSeriesWithinOnBall.fderivWithin, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, FormalMultilinearSeries.radius_compNeg, SeminormFamily.comp_apply, gelfandTransform_bijective, Polynomial.differentiableOn_aeval, SchwartzMap.integral_bilin_fourierIntegral_eq, NumberField.mixedEmbedding.polarSpaceCoord_target, OnePoint.isZeroAt_iff_exists_SL2Z, LinearIsometryEquiv.adjoint_eq_symm, NumberField.mixedEmbedding.negAt_apply_snd, extDeriv_fun_smul, Real.GammaIntegral_convergent, ContinuousAlternatingMap.toAlternatingMap_curryLeft, MeromorphicAt.inv_iff, Matrix.toEuclideanLin_apply, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, NormedField.discreteTopology_or_nontriviallyNormedField, WithSeminorms.tendsto_nhds', Complex.tendsto_exp_nhds_zero_iff, fourier_norm, ContinuousLinearMap.opNorm_mul, Complex.uniformContinuous_im, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, Complex.frontier_preimage_re, CuspForm.coe_trace, EisensteinSeries.e2Summand_summable, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, image_circleMap_Ioc, TemperedDistribution.smulLeftCLM_neg, analyticOrderAt_eq_top, Real.hasStrictDerivAt_arccos, AnalyticAt.frequently_zero_iff_eventually_zero, RCLike.conjCLE_apply, MeasureTheory.integrable_norm_rpow_iff, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Complex.reCLM_nnnorm, Unitization.nnnorm_def, UpperHalfPlane.coe_pos_real_smul, isScalarTower_closedBall_closedBall_closedBall, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, nndist_left_lineMap, IsUltrametricDist.invariantExtension_extends, Complex.instContinuousStar, Euclidean.closedBall_eq_image, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, HasLineDerivAt.tendsto_slope_zero_right, isScalarTower_sphere_closedBall_closedBall, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, Complex.hasDerivAt_GammaIntegral, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, Complex.deriv_ofReal_cpow_const, UpperHalfPlane.comp_ofComplex, Complex.starConvex_ofReal_slitPlane, PiTensorProduct.mapL_smul, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, ApproximatesLinearOn.norm_fderiv_sub_le, ContinuousLinearMap.adjointAux_norm, RCLike.toIsStrictOrderedModule, CStarMatrix.norm_def', NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, MeasureTheory.eLpNorm_norm, HurwitzZeta.hasSum_nat_sinZeta, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, Real.norm_deriv_mulExpNegMulSq_le_one, ValueDistribution.logCounting_top, Quaternion.linearIsometryEquivTuple_symm_apply, LeftInvariantDerivation.lift_add, hasDerivAtFilter_natCast, Polynomial.isEquivalent_atTop_lead, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, ContinuousAlternatingMap.instContinuousSMul, LinearMap.toMatrixOrthonormal_apply_apply, MeasureTheory.charFun_apply_real, HasFDerivAt.restrictScalars, balancedHull_subset_convexHull_union_neg, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, Orientation.areaForm_to_volumeForm, Complex.UnitDisc.coe_smul_circle, Icc_isInteriorPoint_interior, PiTensorProduct.projectiveSeminorm_apply, Complex.summable_conj, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, HasGradientWithinAt.continuousWithinAt, Real.not_continuousAt_deriv_mul_log_zero, integrable_one_add_norm, ProbabilityTheory.integrable_condCDF, HasFDerivAtFilter.isThetaTVS_sub, Complex.continuousAt_arg, PeriodPair.latticeBasis_zero, integrableOn_add_rpow_Ioi_of_lt, ZMod.LFunction_def_odd, InformationTheory.klDiv_eq_top_iff, SchwartzMap.fourier_lineDerivOp_eq, Complex.starConvex_one_slitPlane, LinearMap.isBigOTVS_rev_comp, AddChar.wInner_cWeight_eq_zero_iff_ne, NormedField.exists_one_lt_enorm, ContinuousLinearMapWOT.inducingFn_apply, TemperedDistribution.instLineDerivLeftSMulReal, meromorphicOrderAt_eq_top_iff, CStarMatrix.inner_toCLM_conjTranspose_left, Orientation.areaForm_neg_orientation, hasStrictDerivAt_exp_smul_const, ContinuousMap.setOfIdeal_ofSet_of_isOpen, isBoundedBilinearMap_comp, Complex.interior_setOf_le_re, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, Filter.tendsto_ofReal_iff, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, Monotone.ae_differentiableAt, hasStrictDerivAt_add_const_iff, Finsupp.sum_inner, TemperedDistribution.fourierInv_lineDerivOp_eq, mfderivWithin_comp_projIcc_one, UpperHalfPlane.mdifferentiable_inv_denom, multipliable_one_add_of_summable, LeftInvariantDerivation.lift_smul, FormalMultilinearSeries.rightInv_removeZero, WithAbs.uniformSpace_comap_eq_of_comp, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', contDiffWithinAt_euclidean, hasStrictDerivAt_exp_smul_const', SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, AddCircle.norm_div_natCast, InnerProductSpace.toDualMap_apply_apply, Orientation.kahler_eq_zero_iff, AddChar.sum_apply_eq_ite, EulerProduct.eulerProduct_completely_multiplicative, PositiveLinearMap.preGNS_norm_def, contDiff_succ_iff_fderiv, ContinuousLinearMap.opNNNorm_prod, BoundedContinuousFunction.integral_const_sub, UpperHalfPlane.dist_eq_iff_eq_sinh, hasDerivAtFilter_zero, Complex.integral_comp_polarCoord_symm, Complex.uniformContinuous_re, signedDist_apply_apply, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, PeriodPair.Οβ_div_two_notMem_lattice, Real.differentiableAt_rpow_const_of_ne, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, WeakDual.toStrongDual_inj, ContinuousLinearMap.uniformContinuous_restrictScalars, IccLeftChart_extend_interior_pos, HurwitzZeta.differentiable_expZeta_of_ne_zero, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, isModuleTopologyOfFiniteDimensional, PeriodPair.hasSum_derivWeierstrassP, Orientation.areaForm_swap, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, PeriodPair.compl_lattice_diff_singleton_mem_nhds, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, hasDerivAt_id', integrableOn_Ioi_cpow_iff, Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, HurwitzZeta.differentiable_hurwitzZetaOdd, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, MeasureTheory.MemLp.inner_const, LSeries_deriv_eqOn, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, MeasureTheory.convolution_lsmul, HurwitzZeta.differentiable_hurwitzZeta_sub_hurwitzZeta, PeriodPair.hasSumLocallyUniformly_derivWeierstrassP, Complex.sameRay_of_arg_eq, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, SeminormFamily.finset_sup_comp, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, UpperHalfPlane.ofComplex_apply_of_im_nonpos, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, Real.deriv_sqrt_aux, deriv_fderiv, IsOpen.reProdIm, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, RegularNormedAlgebra.isometry_mul', Complex.frontier_setOf_im_lt, cauchyPowerSeries_apply, summable_eisSummand, ContDiffWithinAt.hasFDerivWithinAt_nhds, ModularFormClass.continuous, Matrix.PosSemidef.det_sqrt, Real.deriv_rpow_const, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, DifferentiableWithinAt.dist, MeasureTheory.integrable_thickenedIndicator, NormedField.exists_nnnorm_lt, Complex.isConnected_of_lowerHalfPlane, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, tendsto_cobounded_of_meromorphicOrderAt_neg, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, MeasureTheory.integrable_of_tendsto, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, TensorProduct.lidIsometry_apply, ContDiffMapSupportedIn.seminorm_le_iff, MeasureTheory.StronglyMeasurable.inner, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Complex.tendsto_exp_comap_re_atTop, convex_halfSpace_re_le, Complex.reCLM_coe, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, PadicInt.fwdDiff_tendsto_zero, Complex.deriv_Gamma_add_one, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux', MeasureTheory.eLpNorm_ofReal, Seminorm.ball_norm_mul_subset, EuclideanSpace.dist_single_same, EulerProduct.eulerProduct_hasProd, Complex.continuous_re, Real.deriv_sinh, NormedField.exists_lt_enorm, Module.Basis.coe_toOrthonormalBasis_repr, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, Filter.HasBasis.isLittleOTVS_iff, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, Matrix.linfty_opNNNorm_eq_opNNNorm, VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, UpperHalfPlane.contMDiff_coe, PadicInt.compactSpace, InformationTheory.hasDerivAt_klFun, CuspForm.holo', integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, InnerProductSpace.nnnorm_rankOne, PeriodPair.mem_lattice, spectrum.gelfandTransform_eq, Orientation.kahler_comp_rightAngleRotation, Seminorm.ball_smul, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, LeftInvariantDerivation.comp_L, ae_differentiableAt_norm, ArithmeticFunction.vonMangoldt.residueClass_apply, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, FormalMultilinearSeries.continuousOn_of_finite, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, LinearMap.trace_eq_sum_inner, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, MeasureTheory.memLp_haarAddCircle_iff, ContinuousLinearMap.flip_smul, NumberField.Units.instZLattice_unitLattice, MeromorphicOn.divisor_inv, PadicInt.mahlerSeries_apply, Circle.arg_eq_arg, HasFDerivAt.isBigOTVS_sub, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, NumberField.mixedEmbedding.convexBodySum_compact, Orientation.volumeForm_zero_pos, MeromorphicOn.divisor_fun_pow, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, ProbabilityTheory.complexMGF_mul_I, Matrix.IsHermitian.charpoly_cfc_eq, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow, MeasureTheory.ConvolutionExistsAt.integrable_swap, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, spectrum.isCompact, HasFiniteFPowerSeriesOnBall.eq_partialSum, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, IsLocalFrameOn.coeff_congr, ProbabilityTheory.Kernel.integrable_densityProcess, NumberField.Units.span_basisOfIsMaxRank, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, AffineMap.hasDerivAt_lineMap, FiniteDimensional.rclike_to_real, Complex.comap_exp_nhds_zero, EisensteinSeries.G2_eq_tsum_symmetricIco, Complex.equivRealProdCLM_symm_apply, Seminorm.convexOn, Complex.cos_eq_tsum', ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasDerivWithinAt.norm_sq, HasGradientAtFilter.hasDerivAtFilter', WeakDual.CharacterSpace.continuousMapEval_bijective, cot_series_rep', DirichletCharacter.differentiableAt_LFunction, CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, LowerSemicontinuousOn.isClosed_re_epigraph, NumberField.canonicalEmbedding.integralBasis_repr_apply, Complex.interior_preimage_re, Complex.continuous_cosh, IsLocalExtr.fderiv_eq_zero, fourier_one, Polynomial.ofReal_eval, HasFPowerSeriesOnBall.fderiv_eq, Seminorm.coe_restrictScalars, NumberField.Units.basisOfIsMaxRank_apply, Real.differentiableOn_rpow_const, MeasureTheory.MemLp.integrable_norm_pow, ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd, NormedField.denseRange_nnnorm, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, Asymptotics.IsLittleOTVS.zero, ContinuousLinearMap.flip_mul, NormedSpace.inclusionInDoubleDual_norm_eq, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, PiTensorProduct.projectiveSeminorm_tprod_le, PadicInt.continuous_choose, AffineMap.hasDerivWithinAt_lineMap, PeriodPair.basis_zero, UpperHalfPlane.image_coe_ball, MeasureTheory.Integrable.norm_integral_condDistrib, ContinuousLinearMap.fderiv_of_bilinear, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Complex.closure_setOf_lt_im, Real.Angle.coe_toCircle, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, Seminorm.gaugeSeminorm_ball, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ContinuousLinearMap.nnnorm_toSpanSingleton, iteratedFDerivWithin_succ_apply_right, ContinuousAlternatingMap.alternatizeUncurryFin_smul, InformationTheory.leftDeriv_klFun, contDiffAt_map_inverse, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, EulerProduct.eulerProduct, Complex.hasDerivAt_Gammaβ_one, SchwartzMap.toBoundedContinuousFunctionCLM_apply, hasSum_jacobiThetaβ_term, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, deriv_id'', hasFDerivAt_jacobiThetaβ_term, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, Complex.continuousAt_cpow_const_of_re_pos, AddCircle.exists_norm_nsmul_le, isEquivalent_choose, Asymptotics.isBigOTVS_iff_smallSets, ContinuousAlternatingMap.norm_restrictScalars, OrthonormalBasis.coe_ofRepr, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, LSeries_deriv, Submodule.adjoint_subtypeL, MeasureTheory.convolutionExistsAt_flip, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, AbsoluteValue.Completion.locallyCompactSpace, MeasureTheory.Integrable.integral_norm_comp, AnalyticOn.fderivWithin, EuclideanSpace.nnnorm_single, ProbabilityTheory.differentiableAt_mgf, UpperHalfPlane.contMDiff_inv_denom, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, RCLike.conjLIE_apply, Complex.uniformlyContinuous_re, WithAbs.tendsto_one_div_one_add_pow_nhds_one, PadicInt.coe_addChar_of_value_at_one, Complex.map_exp_comap_re_atTop, RCLike.summable_ofReal, Complex.orthonormalBasisOneI_repr_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, PadicInt.mahlerSeries_apply_nat, ContDiffAt.fderiv_right, Complex.differentiable_exp, MeasureTheory.convolution_def, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, Complex.UnitDisc.isEmbedding_coe, HurwitzZeta.hasSum_nat_completedCosZeta, HasDerivAt.hasFDerivAt, tendsto_sub_mul_tsum_nat_cpow, Polynomial.toAddCircle.integrable, fourier_zero, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, RCLike.imLm_coe, fourier_neg', HasFPowerSeriesWithinOnBall.prod, Real.differentiable_cos, NormedSpace.eq_iff_forall_dual_eq, Function.Periodic.boundedAtFilter_cuspFunction, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, isAddFundamentalDomain_Ioc, ContinuousLinearMap.continuous_restrictScalars, hasStrictDerivAt_const_add_iff, Summable_cotTerm, isBoundedBilinearMap_compMultilinear, norm_cauchyPowerSeries_le, hasFDerivAt_norm_rpow, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, intervalIntegral.integrableOn_Ioo_rpow_iff, Asymptotics.isEquivalent_nat_ceil, HasFPowerSeriesOnBall.uniform_geometric_approx, summable_jacobiThetaβ_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, MeromorphicOn.divisor_sub_const_self, Unitization.cobounded_eq_aux, AddCircle.norm_coe_mul, Asymptotics.isBigOTVS_fun_neg_left, sum_inner, Polynomial.div_tendsto_atBot_zero_of_degree_lt, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, HurwitzZeta.hasSum_nat_hurwitzZetaEven, HasFPowerSeriesWithinAt.fderivWithin_eq, ContDiffBump.convolution_tendsto_right, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, continuousWithinAt_dslope_of_ne, HurwitzZeta.hasSum_int_cosKernel, Asymptotics.isBigOTVS_fun_neg_right, ZMod.completedLFunction_def_odd, AnalyticOnNhd.fderiv_of_isOpen, FormalMultilinearSeries.id_comp', Seminorm.rescale_to_shell_zpow, OnePoint.isZeroAt_infty_iff, Circle.smul_def, contDiffOn_infty_iff_fderivWithin, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, Matrix.toEuclideanCLM_toLp, Seminorm.smul_closedBall_zero, WeakDual.CharacterSpace.homeoEval_naturality, signedDist_eq_zero_of_orthogonal, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, PeriodPair.isClosed_lattice, ProbabilityTheory.memLp_of_mem_interior_integrableExpSet, BoundedContinuousFunction.innerProbChar_zero, ZSpan.volume_fundamentalDomain, FormalMultilinearSeries.coeff_eq_zero, Complex.tendsto_normSq_cocompact_atTop, ProbabilityTheory.covarianceBilin_zero, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, RCLike.conjCLE_coe, HasFPowerSeriesOnBall.sum, contDiffOn_stereoToFun, LeftInvariantDerivation.evalAt_coe, Matrix.IsHermitian.trace_eq_sum_eigenvalues, fderiv_inverse, AddCircle.norm_half_period_eq, hasStrictFDerivAt_exp_smul_const', HasFPowerSeriesOnBall.fderiv, convex_halfSpace_im_gt, contDiffOn_nat_iff_continuousOn_differentiableOn, Matrix.PosSemidef.sqrt_eq_one_iff, EisensteinSeries.tendsto_zero_inv_linear_sub, Real.deriv_Gamma_nat, GaussianFourier.integrable_cexp_neg_mul_sum_add, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Complex.continuousOn_sin, Complex.hasStrictFDerivAt_cpow, MeasureTheory.integrable_add_iff_of_nonneg, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, tendsto_riemannZeta_sub_one_div, ZetaAsymptotics.tendsto_Gamma_term_aux, NumberField.InfinitePlace.Completion.locallyCompactSpace, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, Seminorm.restrictScalars_ball, InnerProductSpace.rankOne_eq_zero, Polynomial.differentiable_aeval, Complex.polarCoord_apply, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Convex.toWeakSpace_closure, Complex.differentiable_iteratedDeriv_sin, AddChar.expect_apply_eq_zero_iff_ne_zero, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, Complex.hasStrictDerivAt_sinh, tsum_pow_div_one_sub_eq_tsum_sigma, integrable_rpow_neg_one_add_norm_sq, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, Bundle.ContMDiffRiemannianMetric.symm, ContMDiffOn.coordChangeL, EisensteinSeries.linear_right_summable, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, spectrum.eventually_isUnit_resolvent, Asymptotics.isBigOTVS_iff_isBigO, UnitAddTorus.mFourier_add, Bornology.isVonNBounded_sub_of_nonempty, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, PositiveLinearMap.preGNS_inner_def, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, fderivWithin_inv', spectralAlgNorm_mul, hasDerivAt_add_const_iff, spectralNorm_eq_invariantExtension, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, UpperHalfPlane.cosh_dist, LSeries_eq_mul_integral_of_nonneg, UpperHalfPlane.image_coe_closedBall, MeasureTheory.lintegral_nnnorm_condExpL2_le, PeriodPair.periodic_derivWeierstrassP, EisensteinSeries.summable_linear_left_mul_linear_left, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, HasFPowerSeriesOnBall.compContinuousLinearMap, AffineSubspace.signedInfDist_eq_signedDist_of_mem, Finset.nnnorm_prod_le', differentiableWithinAt_of_derivWithin_ne_zero, LinearMap.IsSymmetric.coe_toSelfAdjoint, one_mem_posTangentConeAt_iff_mem_closure, MeromorphicOn.divisor_intCast, Complex.tendsto_one_add_div_pow_exp, quasispectrum.isCompact, Real.integrable_sinc, RealRMK.rieszMeasure_le_of_eq_one, TensorProduct.inner_lid_lid, ContDiffMapSupportedIn.uniformSpace_eq_iInf, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, riemannZeta_eulerProduct_exp_log, PiTensorProduct.liftIsometry_tprodL, NormedSpace.inclusionInDoubleDual_norm_le, not_IntegrableOn_Ici_inv, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, hasDerivWithinAt_one, IsSelfAdjoint.isConnected_spectrum_compl, MeasureTheory.memLp_two_iff_integrable_sq, WeakDual.isCompact_closedBall, Affine.Simplex.signedInfDist_apply_self, PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm, ConvexOn.sSup_of_countable_affine_eq, TestFunction.coe_ofSupportedInCLM, Real.differentiableAt_rpow_of_ne, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, RCLike.reCLM_coe, ContDiffBump.normed_convolution_eq_right, continuousSMul_closedBall_ball, UpperHalfPlane.dist_coe_center, ProbabilityTheory.gaussianReal_map_linearMap, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, HasDerivWithinAt.inner, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, DifferentiableAt.inner, MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, tendsto_logDeriv_euler_sin_div, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, NormedSpace.exp_continuousMap_eq, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, EisensteinSeries.div_linear_zpow_differentiableOn, Seminorm.comp_smul, UnitAddTorus.mFourier_zero, absorbent_nhds_zero, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, isScalarTower_sphere_sphere_sphere, MeromorphicOn.analyticAt_mem_codiscreteWithin, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', Real.deriv_inv_log, ProbabilityTheory.covarianceBilinDual_eq_covariance, ContMDiffAt.mfderiv_const, smoothSheafCommRing.isUnit_stalk_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, FormalMultilinearSeries.coeff_ofScalars, UpperHalfPlane.ofComplex_apply_of_im_pos, signedDist_zero, Asymptotics.IsLittleO.isLittleOTVS, hasDerivAt_ofNat, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, iteratedFDerivWithin_eq_equiv_comp, spectralMulAlgNorm_def, RCLike.isUniformEmbedding_ofReal, CompactlySupportedContinuousMap.toRealLinearMap_apply, DifferentiableAt.isBigOTVS_sub, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, Orthonormal.inner_left_right_finset, MeasureTheory.Integrable.integral_norm_prod_left, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, ContDiffMapSupportedIn.structureMapCLM_zero_apply, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, differentiableAt_inv_iff, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, AddCircle.instIsUnifLocDoublingMeasureRealVolume, SchwartzMap.norm_iteratedFDeriv_le_seminorm, ProbabilityTheory.covarianceBilinDual_zero, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, RealRMK.integral_rieszMeasure, Finsupp.inner_sum, LinearMap.deriv, SchwartzMap.seminorm_le_bound', RCLike.nnnorm_nnratCast, contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, EuclideanSpace.instIsManifoldSphere, zeta_eq_tsum_one_div_nat_cpow, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, Bornology.IsVonNBounded.restrict_scalars_of_nontrivial, Real.isEquivalent_sin, continuousAt_cpow, InnerProductSpace.toDualMap_apply, gelfandTransform_map_star, TotallyBounded.isVonNBounded, NumberField.mixedEmbedding.convexBodySumFun_smul, Complex.interior_preimage_im, Real.differentiable_exp, NumberField.mixedEmbedding.logMap_real_smul, ContinuousLinearMap.adjoint_inner_left, Complex.isBigO_re_sub_re, AddChar.sum_apply_eq_zero_iff_ne_zero, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, isQuotientCoveringMap_npow, EulerProduct.eulerProduct_tprod, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, ProbabilityTheory.differentiableOn_mgf, Real.abs_mulExpNegMulSq_comp_le_norm, Complex.comap_exp_nhdsNE, ContinuousLinearMap.isBoundedBilinearMap, nnnorm_algebraMap, fdifferential_apply, ContinuousMultilinearMap.hasBasis_nhds_zero, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, Asymptotics.isEquivalent_iff_exists_eq_mul, UnitAddTorus.coeFn_mFourierLp, MeasureTheory.Integrable.integral_norm_condExpKernel, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, MeromorphicOn.divisor_sub_const_of_ne, ContinuousMultilinearMap.ofSubsingletonβα΅’_symm_apply, Real.differentiableAt_cos, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, innerβ_apply, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, totallyBounded_absConvexHull, ProperSpace.of_nontriviallyNormedField_of_weaklyLocallyCompactSpace, Asymptotics.isBigOTVS_congr, NumberField.mixedEmbedding.polarCoord_symm_apply, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, ProbabilityTheory.complexMGF_id_mul_I, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, Complex.deriv_Gamma_nat, ModularGroup.lcRow0Extend_apply, Asymptotics.isBigOTVS_neg_right, MDifferentiableOn.coordChangeL, Real.deriv_log', hasDerivAt_update, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, Real.one_div_sub_hasFPowerSeriesOnBall_zero, FormalMultilinearSeries.compAlongComposition_bound, ProbabilityTheory.integrable_condVar, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, fderiv_pow_ring, Complex.continuous_sinh, constFormalMultilinearSeries_apply_zero, Padic.instCompleteSpace, DifferentiableAt.fderiv_restrictScalars, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, Complex.UnitDisc.coe_closedBall_smul, FormalMultilinearSeries.radius_smul_eq, Bundle.ContMDiffRiemannianMetric.pos, signedDist_triangle_left, ContinuousLinearMap.bilinearComp_zero_right, Circle.ext_iff, IsContMDiffRiemannianBundle.exists_contMDiff, ContDiffWithinAt.fderivWithin'', ContinuousMap.ideal_isMaximal_iff, Complex.isOpen_compl_range_intCast, BaireSpace.instBarrelledSpace, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, integral_conj, Complex.hasSum_ofReal, CuspFormClass.zero_at_infty, hasDerivAtFilter_add_const_iff, HurwitzZeta.completedHurwitzZetaEven_residue_one, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, hasDerivAt_jacobiThetaβ_fst, Real.deriv2_binEntropy, InnerProductSpace.rank_rankOne, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, UnitAddTorus.mFourier_neg, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, contMDiffAt_coordChangeL, InnerProductSpace.toDual_apply_apply, Complex.continuousOn_norm_circleTransformBoundingFunction, Complex.continuousAt_Gamma_one, intervalIntegral.intervalIntegrable_cpow, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, contMDiff_subtype_coe_Icc, Real.hasDerivAt_arcsin, coe_lpBCFβα΅’, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, PeriodPair.differentiableOn_derivWeierstrassP, ProperCone.innerDual_singleton, Complex.hasDerivAt_sinh, PeriodPair.weierstrassPExcept_def, RCLike.nnnorm_ofNat, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, RCLike.ofReal_re_ax, differentiable_inner, LeftInvariantDerivation.coe_sub, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, HasLineDerivAt.tendsto_slope_zero_left, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, tendsto_nhds_iff_meromorphicOrderAt_nonneg, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, LDL.lower_conj_diag, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionβ_apply_apply, hasFDerivAt_list_prod', HurwitzZeta.hasSum_int_cosZeta, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, ArithmeticFunction.IsMultiplicative.eulerProduct_tprod, InnerProductSpace.rankOne_def, MDifferentiableWithinAt.coordChangeL, Real.deriv_tan_sub_id, AddCircle.volume_closedBall, ContinuousLinearMap.coe_flipβα΅’', Real.leftDeriv_mul_log, PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, deriv_inv, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, Real.differentiableAt_Gamma, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, orthogonalBilin_innerβ, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, ConvexOn.real_univ_sSup_of_countable_affine_eq, contDiff_iff_continuous_differentiable, NumberField.mixedEmbedding.mem_span_latticeBasis, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaβ, ProbabilityTheory.evariance_eq_top_iff, hasDerivAt_const, Complex.tendsto_norm_tan_atTop, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, BoundedContinuousFunction.innerProbChar_apply, OrthonormalBasis.repr_apply_apply, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, UniformSpace.Completion.norm_toComplL, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, instSMulCommClass_sphere_closedBall_closedBall, Circle.coe_inv_eq_conj, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, Complex.hasDerivAt_Gammaβ_one, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, AnalyticAt.eventually_constant_or_nhds_le_map_nhds, MeasureTheory.lintegral_ofReal_ne_top_iff_integrable, Complex.hasSum_sin, Complex.tendsto_self_mul_Gamma_nhds_zero, BoundedContinuousFunction.neg_norm_le_apply, SchwartzMap.integral_bilin_fourier_eq, gradient_eq_deriv', Complex.hasStrictDerivAt_const_cpow, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ClosedSubmodule.orthogonal_eq_inter, Chebyshev.integrableOn_theta_div_id_mul_log_sq, ContinuousMultilinearMap.prodL_apply, Orientation.kahler_neg_orientation, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, MonotoneOn.intervalIntegrable_slope, nndist_left_midpoint, hasFTaylorSeriesUpToOn_succ_iff_right, EisensteinSeries.hasSum_e2Summand_symmetricIco, ContinuousLinearMap.coe_flipMultilinearEquiv, Seminorm.bddAbove_iff, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', intervalIntegral.integrableOn_Ioo_cpow_iff, Circle.coe_mul, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, Real.differentiableOn_mul_log, LinearIsometryEquiv.conjStarAlgEquiv_refl, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, InformationTheory.klDiv_def, hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.Integrable.norm_integral_condKernel, RCLike.abs_wInner_le, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, contDiff_nat_iff_iteratedDeriv, eventually_singleton_add_smul_subset, LinearMap.IsSymmetric.toSelfAdjoint_apply, hasSum_jacobiThetaβ'_term, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, ProbabilityTheory.memLp_id_gaussianReal', Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, circleMap_notMem_ball, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, ContinuousLinearMap.coe_restrict_scalarsL', ContinuousLinearMapWOT.isInducing_inducingFn, SlashInvariantFormClass.periodic_comp_ofComplex, fderivWithin_fderivWithin_eq_of_eventuallyEq, integrableOn_Ioi_deriv_ofReal_cpow, NormedField.nhdsNE_neBot, EulerProduct.eulerProduct_completely_multiplicative_tprod, Complex.map_exp_comap_re_atBot, Real.deriv_mulExpNegMulSq, StrongDual.polarSubmodule_eq_polar, fourier_coe_apply, summable_prod_mul_pow, PiTensorProduct.liftEquiv_symm_apply, Complex.interior_setOf_le_im, RCLike.summable_conj, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, RCLike.geometric_hahn_banach_point_point, TestFunction.coe_ofSupportedInLM, extDerivWithin_fun_smul, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, inner_smul_real_right, fourierSubalgebra_separatesPoints, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Asymptotics.isLittleOTVS_fun_neg_right, Complex.isEquivalent_sinh, AnalyticOnNhd.is_constant_or_isOpenMap, hasFDerivAt_exp_smul_const', dense_differentiableAt_norm, Real.Angle.arg_toCircle, MeasureTheory.SignedMeasure.re_toComplexMeasure, TemperedDistribution.smulLeftCLM_sub, Complex.one_add_cpow_hasFPowerSeriesAt_zero, Matrix.exp_zsmul, HurwitzZeta.hasSum_nat_cosZeta, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContinuousLinearMapWOT.hasBasis_seminorms, MonotoneOn.intervalIntegral_deriv_mem_uIcc, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, OnePoint.isZeroAt_iff_forall_SL2Z, ContDiff.continuous_iteratedDeriv, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, LinearMap.toMatrixOrthonormal_symm_apply, Real.deriv_qaryEntropy, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, WithSeminorms.topology_eq_withSeminorms, Real.deriv_arctan, hasSum_cauchyPowerSeries_integral, ContinuousLinearMap.aestronglyMeasurable_compβ, continuousSMul_sphere_closedBall, Circle.coe_pow, monotoneOn_deriv_descPochhammer_eval, SchwartzMap.smulLeftCLM_const, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, mellin_convergent_top_of_isBigO, UpperHalfPlane.contMDiff_num, UpperHalfPlane.mdifferentiable_denom, LinearMap.toMatrix_innerββ_apply, UpperHalfPlane.dist_self_center, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Complex.continuous_conj, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Function.locallyFinsuppWithin.toClosedBall_divisor, LSeries.term_convolution, PointwiseConvergenceCLM.equivWeakDual_symm_apply, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, MeasureTheory.ComplexMeasure.integrable_rnDeriv, RCLike.wInner_one_eq_inner, NumberField.mixedEmbedding.negAt_apply_isComplex, isBigO_riemannZeta_sub_one_div, ProbabilityTheory.hasFiniteIntegral_compProd_iff', AffineMap.hasDerivAt, Complex.hasFDerivAt_cpow, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, Complex.differentiableAt_exp, LinearMap.range_toContinuousLinearMap, Complex.not_continuousAt_Gamma_zero, Complex.differentiable_Gammaβ_inv, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, continuous_circleMap, differentiableAt_jacobiThetaβ_fst, not_integrableOn_Ioi_rpow, AffineMap.differentiableAt, hasStrictDerivAt_finCons', isScalarTower_closedBall_ball_ball, Complex.iter_deriv_exp, MeromorphicOn.meromorphicNFAt_mem_codiscreteWithin, HasProdLocallyUniformlyOn_euler_sin_prod, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, NormedSpace.ofReal_exp_β_β, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMapβ'_zero_iff, convex_halfSpace_im_lt, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, NormedSpace.isVonNBounded_iff', Polynomial.rootSet_derivative_subset_convexHull_rootSet, VonNeumannAlgebra.mem_carrier, WeakDual.isSeqCompact_closedBall, hasStrictDerivAt_finCons, Complex.differentiableAt_tan, PiTensorProduct.liftEquiv_apply, ModularForm.differentiableAt_eta_tprod, MeasureTheory.Measure.integrable_measure_prodMk_left, has_antideriv_at_fourier_neg, Real.differentiableAt_log_iff, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, PadicInt.denseRange_natCast, UnitAddTorus.mFourier_norm, toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhds, Matrix.instNonnegSpectrumClass, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, LSeriesSummable.sum, DifferentiableAt.norm_sq, Function.Periodic.continuous_qParam, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, HurwitzZeta.hasSum_expZeta_of_one_lt_re, innerSLFlip_apply_apply, UniformContinuousOn.cexp, ContinuousLinearMap.nnnorm_holder_apply_apply_le, Polynomial.hasFDerivAt, RCLike.ofReal_finsupp_sum, tendsto_zero_of_meromorphicOrderAt_pos, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, finrank_euclideanSpace, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Complex.continuous_exp, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, NormedField.exists_enorm_lt, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, Complex.frontier_preimage_im, MeasureTheory.MemLp.integrable_norm_rpow, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, Submodule.orthogonal_orthogonal_eq_closure, continuousAt_clog, EisensteinSeries.linear_left_summable, AnalyticOnNhd.preimage_zero_mem_codiscrete, PeriodPair.hasSumLocallyUniformly_weierstrassPExcept, Circle.invOn_arg_exp, contMDiff_smul, MeasureTheory.dist_convolution_le, MeromorphicOn.divisor_ofNat, nndist_midpoint_left, DoubleCentralizer.nnnorm_fst, intervalIntegral.integral_hasStrictFDerivAt, with_gaugeSeminormFamily, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Complex.hasDerivAt_cos, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, MeasureTheory.IntegrableAtFilter.norm, contMDiffOn_continuousLinearMapCoordChange, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, UpperHalfPlane.ofComplex_apply_eq_of_im_nonpos, Complex.log_sub_self_isBigO, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Module.Basis.exists_opNNNorm_le, aestronglyMeasurable_smul_const_iff, absConvexHull_add_subset, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, NumberField.Units.regOfFamily_of_isMaxRank, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Module.Basis.equivFunL_apply, WithSeminorms.tendsto_nhds, inner_map_complex, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, BoundedContinuousFunction.probCharDual_zero, ContinuousMultilinearMap.flipLinear_apply_apply, tendsto_integral_mul_one_add_inv_smul_sq_pow, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, Complex.arg_eq_nhds_of_im_neg, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, LinearMap.hasDerivWithinAt, WithSeminorms.isOpen_iff_mem_balls, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, CStarMatrix.toCLM_apply_single, MeromorphicOn.inv_iff, MeasureTheory.AEStronglyMeasurable.inner, FormalMultilinearSeries.comp_id, Complex.tendsto_exp_comap_re_atBot, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, ContinuousMap.adjoin_id_eq_span_one_union, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, Seminorm.const_isBounded, hasFTaylorSeriesUpTo_succ_nat_iff_right, MeasureTheory.integrable_prod_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, HasFDerivWithinAt.norm_sq, tsum_riemannZetaSummand, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, differentiableAt_abs_neg, ClosedSubmodule.iInf_orthogonal, Asymptotics.isLittleOTVS_iff_smallSets, Complex.summable_ofReal, BoundedContinuousFunction.apply_le_norm, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, ProbabilityTheory.isGaussian_gaussianReal, norm_fderiv_norm_rpow_le, HasFPowerSeriesOnBall.neg, deriv_abs_zero, ContinuousLinearMap.uncurryBilinear_apply, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, Seminorm.sSup_empty, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, nndist_midpoint_midpoint_le', fourier_eval_zero, Matrix.PosDef.commute_iff, Matrix.IsHermitian.cfcAux_apply, Polynomial.Chebyshev.integrable_measureT, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, RCLike.finrank_le_two, Complex.tendsto_euler_sin_prod, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Bundle.RiemannianMetric.symm, MeasureTheory.integral_charFun_Icc, ZMod.completedLFunction_eq, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, iteratedFDeriv_eq_equiv_comp, Complex.hasStrictDerivAt_log, linear_isometry_complex, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Unitization.norm_eq_sup, Real.hasDerivAt_cos, Matrix.ofLp_toEuclideanCLM, NumberField.mixedEmbedding.convexBodySumFun_continuous, hasFTaylorSeriesUpToOn_succ_nat_iff_right, AffineSubspace.signedInfDist_eq_const_of_mem, hasDerivAtFilter_iff_isLittleO, ProbabilityTheory.HasSubgaussianMGF.integrable, CStarMatrix.toCLM_apply_eq_sum, HasStrictFDerivAt.restrictScalars, mahler_natCast_eq, PadicInt.coe_adicCompletionIntegersEquiv_apply, MeromorphicAt.eventually_continuousAt, UpperHalfPlane.dist_eq, Circle.star_addChar, HurwitzZeta.hurwitzZeta_residue_one, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ContinuousMap.sup_mem_subalgebra_closure, hasDerivAt_exp_smul_const, RCLike.continuous_re, AddCircle.exists_norm_eq_of_isOfFinAddOrder, NormedSpace.algebraMap_exp_comm, Asymptotics.isBigOTVS_neg_left, exists_dual_vector, nndist_center_homothety, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, hasFDerivWithinAt_comp_smul_smul_iff, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, RCLike.instContinuousStar, ProbabilityTheory.hasDerivAt_complexMGF, Differentiable.norm_rpow, MeromorphicOn.divisor_fun_zpow, DifferentiableWithinAt.isBigOTVS_sub, LinearMap.isPositive_toContinuousLinearMap_iff, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, Complex.tsum_exp_neg_quadratic, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', Real.differentiableWithinAt_arcsin_Ici, AddChar.wInner_cWeight_eq_one_iff_eq, logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, FormalMultilinearSeries.changeOrigin_eval_of_finite, InformationTheory.klDiv_ne_top_iff, RCLike.sqrt_map, MeasureTheory.integrable_conv_iff, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, iteratedFDerivWithin_two_apply', PadicInt.mahlerTerm_one, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, HasStrictDerivAt.hasStrictFDerivAt, PeriodPair.derivWeierstrassP_sub_coe, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, Matrix.instFiniteElemRealSpectrum, AnalyticAt.analyticOrderAt_eq_natCast, rotationOf_rotation, IsMIntegralCurveAt.hasMFDerivAt, RCLike.smul_im, SpectrumRestricts.real_iff, Matrix.l2_opNNNorm_mul, contDiffWithinAt_succ_iff_hasFDerivWithinAt', HurwitzZeta.differentiableAt_completedHurwitzZetaEven, Complex.cosh_eq_tsum, IsLocalFrameOn.eventually_eq_sum_coeff_smul, contDiffOn_succ_iff_hasFDerivWithinAt, RCLike.tendsto_ofReal_cobounded_cobounded, differentiableWithinAt_euclidean, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, unitary.spectrum_subset_circle, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, FormalMultilinearSeries.radius_unshift, Complex.frontier_setOf_lt_im, HasFPowerSeriesAt.fderiv_eq, LinearPMap.adjointDomainMkCLM_apply, deriv_abs_pos, MeromorphicOn.divisor_apply, Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.coe_restrictScalarsIsometry, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, Polynomial.aeval_conj, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, exists_polynomial_near_continuousMap, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, continuousMultilinearCurryFin0_apply, Complex.interior_reProdIm, HurwitzZeta.differentiableAt_one_completedHurwitzZetaEven_sub_completedHurwitzZetaEven, HasGradientAt.differentiableAt, ContinuousMap.inf_mem_subalgebra_closure, PiTensorProduct.dualSeminorms_bounded, LinearMap.hasBasis_weakBilin, NormedSpace.exp_sum, FormalMultilinearSeries.radius_neg, Real.differentiableAt_cosh, extDeriv_smul, Complex.contDiff_exp, spectrum.isClosed, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, WeakBilin.locallyConvexSpace, GromovHausdorff.ghDist_eq_hausdorffDist, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, ProbabilityTheory.integral_linearMap_gaussianReal, IsSelfAdjoint.conj_adjoint, AddCircle.coe_real_preimage_closedBall_inter_eq, ContinuousMultilinearMap.curryMidEquiv_apply, Real.nnnorm_mul_toNNReal, Complex.closure_preimage_re, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, Polynomial.hermite_eq_deriv_gaussian', tendsto_ne_zero_of_meromorphicOrderAt_eq_zero, DoubleCentralizer.algebraMap_snd, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, MeasureTheory.integrable_of_integral_eq_one, MeasureTheory.integrable_norm_iff, WeakDual.polar_def, MeasureTheory.integrable_toReal_of_lintegral_ne_top, RCLike.wInner_const_left, AnalyticAt.analyticOrderNatAt_eq_iff, Complex.isOpenQuotientMap_pow, ProbabilityTheory.covarianceBilinDual_self_eq_variance, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, HurwitzZeta.hasSum_int_sinKernel, MeasureTheory.integrable_smul_const, hasFiniteFPowerSeriesOnBall_const, contDiffAt_inv, iteratedFDerivWithin_succ_apply_left, Orientation.areaForm_comp_linearIsometryEquiv, NormedField.exists_one_lt_nnnorm, hasStrictFDerivAt_norm_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', SchwartzMap.fourier_evalCLM_eq, support_deriv_subset, Bornology.IsVonNBounded.restrict_scalars, LinearMap.adjoint_toSpanSingleton, ContDiff.differentiable_iteratedDeriv, Complex.interior_setOf_im_le, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, ContinuousMultilinearMap.norm_mkPiAlgebra, NontriviallyNormedField.cobounded_neBot, contDiffOn_infty_iff_fderiv_of_isOpen, hasDerivWithinAt_natCast, MeromorphicOn.divisor_fun_mul, Asymptotics.superpolynomialDecay_iff_isLittleO, Real.deriv_exp, NumberField.canonicalEmbedding.nnnorm_eq, MeromorphicOn.divisor_zpow, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, QuasispectrumRestricts.real_iff, ContinuousLinearMap.bilinearComp_apply, TemperedDistribution.instLineDerivSMulReal, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, RCLike.inner_apply, cot_series_rep, SchwartzMap.evalCLM_apply_apply, NormedField.exists_enorm_lt_one, upperHemicontinuous_quasispectrum, spectrum.isBounded, UpperHalfPlane.ofComplex_apply_eq_ite, Matrix.posDef_iff_eq_conjTranspose_mul_self, Polynomial.differentiableAt_aeval, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, HurwitzZeta.completedCosZeta_residue_zero, hasDerivAt_id, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, CStarMatrix.toCLM_apply, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, Real.toNNReal_mul_nnnorm, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, MeasureTheory.Integrable.re_im_iff, RCLike.hasSum_conj, Polynomial.isEquivalent_atBot_lead, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, differentiableAt_norm_smul, FormalMultilinearSeries.id_comp, ContinuousLinearMap.norm_map_tail_le, deriv_update, UpperHalfPlane.qParam_tendsto_atImInfty, MeasureTheory.HasFiniteIntegral.norm, HasFPowerSeriesAt.restrictScalars, Real.iter_deriv_exp, contMDiffOn_symm_coordChangeL, ContinuousLinearMap.instStarModuleId, Real.differentiable_iteratedDeriv_cos, nndist_lineMap_right, Polynomial.hasFDerivAt_aeval, Seminorm.convex_ball, Differentiable.norm_sq, NormedField.continuousAt_inv, ContDiffAt.restrictScalars_iteratedFDeriv, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, RCLike.norm_wInner_le, ContinuousLinearMap.isBoundedLinearMap_comp_left, LeftInvariantDerivation.map_add, ProbabilityTheory.IsGaussian.memLp_dual, Complex.isConnected_of_upperHalfPlane, AnalyticOnNhd.codiscreteWithin_setOf_analyticOrderAt_eq_zero_or_top, norm_fderiv_iteratedFDeriv, Complex.differentiable_sin, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, Complex.continuous_normSq, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, PeriodPair.weierstrassP_add_coe, Asymptotics.isLittleOTVS_map, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, TemperedDistribution.fourier_lineDerivOp_eq, Matrix.l2_opNNNorm_def, hasDerivAtFilter_sub_const_iff, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.adjointAux_adjointAux, PeriodPair.instProperSpaceSubtypeComplexMemSubmoduleIntLattice, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, LinearMap.polar_gc, hasDerivAt_exp, circleMap_mem_sphere, UniformSpace.Completion.Continuous.inner, LeftInvariantDerivation.coe_add, signedDist_lineMap_left, Complex.hasDerivAt_logTaylor, DirichletCharacter.differentiable_LFunction, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow, Real.tendsto_rightDeriv_mul_log_atTop, NumberField.mixedEmbedding.norm_smul, Real.hasStrictDerivAt_arsinh, circleMap_preimage_codiscrete, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', MeasureTheory.AEStronglyMeasurable.const_inner, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, MeasureTheory.Integrable.integral_norm_compProd, Complex.lintegral_comp_polarCoord_symm, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, Asymptotics.isLittleOTVS_iff_isLittleO, integrable_rpow_mul_exp_neg_mul_sq, EuclideanSpace.basisFun_repr, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, zero_cpow_eq_nhds, HasFTaylorSeriesUpToOn.hasFDerivAt, RCLike.realLinearIsometryEquiv_symm_apply, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, ContinuousLinearMap.flip_add, hasFiniteFPowerSeriesAt_const, Circle.leftInverse_exp_arg, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, Complex.continuousAt_ofReal_cpow, Subalgebra.spectrum_isBounded_connectedComponentIn, MeromorphicOn.eventually_codiscreteWithin_analyticAt, InformationTheory.klDiv_eq_integral_klFun, ArithmeticFunction.IsMultiplicative.eulerProduct, ContinuousAlternatingMap.hasBasis_nhds_zero, LinearIsometry.coe_toSpanSingleton, AnalyticAt.eventually_constant_or_nhds_le_map_nhds_aux, Bornology.isBounded_iff_isVonNBounded, circleMap_mem_closedBall, MeasureTheory.hasFiniteIntegral_iff_ofReal, integrable_mul_exp_neg_mul_sq, VectorFourier.fourierSMulRight_apply, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', HasFDerivWithinAt.restrictScalars, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, RCLike.continuous_ofReal, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, IsLocalFrameOn.coeff_apply_of_notMem, ProbabilityTheory.evariance_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, GromovHausdorff.eq_toGHSpace, ContinuousMultilinearMap.uncurryRight_apply, Seminorm.closedBall_smul, NumberField.mixedEmbedding.polarCoord_source, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, fderiv_inv, differentiableWithinAt_iff_restrictScalars, Complex.orthonormalBasisOneI_repr_symm_apply, MeasureTheory.L1.nnnorm_Integral_le_one, Manifold.riemannianEDist_def, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, RCLike.ofReal_alg, ContinuousLinearMap.bilinearComp_zero, isScalarTower_sphere_sphere_closedBall, signedDist_anticomm, Complex.UnitDisc.instSMulCommClass_closedBall_right, iteratedDeriv_eq_equiv_comp, UnitAddTorus.hasSum_mFourier_series_L2, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Orientation.areaForm_comp_rightAngleRotation, NumberField.mixedEmbedding.continuous_norm, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, modelWithCornersEuclideanHalfSpace_zero, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, UnitAddCircle.mem_approxAddOrderOf_iff, Complex.continuousOn_tan, ContinuousLinearMap.norm_extendToπ'_bound, MeasureTheory.hausdorffMeasure_homothety_image, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, Real.differentiableAt_arctan, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, spectralNorm_smul, hasDerivAt_iff_hasFDerivAt, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, HasFiniteFPowerSeriesOnBall.neg, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, differentiableWithinAt_abs_neg, LinearMap.weakBilin_withSeminorms, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, PadicInt.continuous_addChar_of_value_at_one, norm_derivWithin_eq_norm_fderivWithin, ModularForm.differentiableAt_eta_of_mem_upperHalfPlaneSet, differentiableWithinAt_dslope_of_ne, LinearMap.polar_weak_closed, ProbabilityTheory.integrable_exp_mul_gaussianReal, WeakDual.isClosed_closedBall, MeasureTheory.integrable_add_iff_of_nonpos, hasDerivAt_fourier, Filter.Tendsto.ofReal, Complex.continuousAt_cpow_zero_of_re_pos, Circle.norm_coe, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Complex.UnitDisc.instIsScalarTower_closedBall, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Complex.instCompleteSpace, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.rightDeriv_mul_log, ProbabilityTheory.Kernel.integrable_density, ZMod.LFunction_def_even, Real.fourier_bilin_convolution_eq, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, ProbabilityTheory.hasFiniteIntegral_prodMk_left, UpperHalfPlane.le_dist_coe, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, CStarMatrix.mul_entry_mul_eq_inner_toCLM, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, continuous_inner, ModularFormClass.differentiableAt_cuspFunction, fourier_apply, ContinuousLinearMap.le_opNormβ, nnnorm_inner_le_nnnorm, ContinuousLinearMap.lpPairing_eq_integral, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, Seminorm.continuous_iff, ProbabilityTheory.hasFiniteIntegral_comp_iff', ContinuousLinearMap.norm_uncurryMid, IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, QuadraticForm.equivalent_sum_squares, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, LeftInvariantDerivation.coe_injective, ContinuousLinearMap.uncurryLeft_norm, MeromorphicOn.divisor_restrict, ContDiffWithinAt.fderivWithin', hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, WithSeminorms.continuous_seminorm, HasFPowerSeriesOnBall.tendstoUniformlyOn', Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, fderiv_apply_one_eq_deriv, HurwitzZeta.hasSum_nat_completedSinZeta, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, EulerProduct.eulerProduct_hasProd_mulIndicator, isScalarTower_sphere_sphere_ball, IsUltrametricDist.algNormOfAlgEquiv_apply, integrableOn_exp_mul_complex_Iic, ContinuousAlternatingMap.continuous_restrictScalars, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, AddCircle.norm_coe_eq_abs_iff, HasFDerivAt.inner, MeasureTheory.L2.eLpNorm_inner_lt_top, Complex.frontier_setOf_le_re, MeasureTheory.Integrable.convolution_integrand, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, LinearMap.toMatrixOrthonormal_apply, ProbabilityTheory.integrable_pow_of_mem_interior_integrableExpSet, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, UpperHalfPlane.contMDiff_denom_zpow, contDiffOn_tsum_cexp, convex_halfSpace_re_ge, OrthogonalFamily.inner_sum, deriv_circleMap, NormedSpace.vonNBornology_eq, PeriodPair.latticeBasis_one, ProbabilityTheory.exp_neg_integrableOn_Ioc, ProbabilityTheory.deriv_mgf, EuclideanSpace.inner_eq_star_dotProduct, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, MeasureTheory.hasFiniteIntegral_norm_iff, isCoveringMapOn_npow, MeasureTheory.Integrable.norm_integral_condDistrib_map, OrthonormalBasis.sum_repr_symm, LeftInvariantDerivation.coe_neg, Complex.hasStrictDerivAt_cos, StrongDual.toLpβ_apply, Orientation.kahler_apply_self, Complex.frontier_setOf_re_lt, DifferentiableWithinAt.restrictScalars_fderivWithin, IsPrimitiveRoot.nnnorm_eq_one, PeriodPair.weierstrassP_sub_coe, Real.differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, isCompact_closedAbsConvexHull_of_totallyBounded, ProbabilityTheory.hasFiniteIntegral_comp_iff, Complex.analyticOn_univ_iff_differentiable, Valued.integer.coe_span_singleton_eq_closedBall, Complex.conjCLE_nnorm, Polynomial.differentiableOn, IsLocalFrameOn.coeff_apply_zero_at, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, hasFDerivAt_polarCoord_symm, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', isQuotientCoveringMap_zpow, AnalyticOnNhd.eval_polynomial, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, differentiableOn_neg, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, LinearMap.continuous_of_nonzero_on_open, MeasureTheory.HasFiniteIntegral.of_mem_Icc, ConvexOn.real_univ_sSup_affine_eq, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, Complex.isBigO_im_sub_im, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, ArithmeticFunction.LSeries_vonMangoldt_eq, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', SchwartzMap.le_seminorm, DoubleCentralizer.nnnorm_fst_eq_snd, AddCircle.closedBall_eq_univ_of_half_period_le, toWeakSpace_closedConvexHull_eq, ConvexOn.monotoneOn_leftDeriv, Unitization.norm_def, EisensteinSeries.qExpansion_identity_pnat, SchwartzMap.eLpNorm_le_seminorm, Complex.isCoveringMapOn_exp, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, deriv_neg', Orientation.kahler_rotation_left', Real.differentiable_sin, hasFDerivAtFilter_iff_isLittleOTVS, zeta_eq_tsum_one_div_nat_add_one_cpow, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, Complex.continuous_cos, DirichletCharacter.differentiableAt_completedLFunction, ContinuousAlternatingMap.curryLeft_same, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ContinuousMultilinearMap.curryRight_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, ContMDiffWithinAt.mfderivWithin, convex_halfSpace_im_ge, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, contDiffOn_inv, ContinuousLinearMap.extendToπ_apply, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, rotation_trans, integrableOn_Ioi_rpow_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, Real.eulerMascheroniConstant_eq_neg_deriv, Real.not_differentiableAt_inv_log_zero, UpperHalfPlane.le_dist_iff_le_dist_coe_center, Orientation.abs_areaForm_le, PadicInt.hasSum_mahlerSeries, Real.deriv_mul_log, NumberField.mixedEmbedding.polarCoord_target, Complex.continuousAt_arg_coe_angle, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, CauSeq.cauchySeq, Asymptotics.superpolynomialDecay_iff_isBigO, ContinuousLinearMap.norm_extendToπ', integrableOn_rpow_mul_exp_neg_rpow, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, StrongDual.polar_univ, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, PeriodPair.hasSum_weierstrassP, convex_halfSpace_re_lt, differentiableAt_iff_comp_const_sub, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, UpperHalfPlane.ofComplex_apply, MeasureTheory.Integrable.integral_norm_condDistrib, ContDiffMapSupportedIn.postcompCLM_apply, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, signedDist_neg, PeriodPair.coeff_weierstrassPSeries, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, Complex.ball_one_subset_slitPlane, dslope_eventuallyEq_slope_of_ne, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, PeriodPair.isOpen_compl_lattice_diff, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, integrableOn_exp_mul_Ioi, Orientation.normSq_kahler, Complex.volume_closedBall, ProbabilityTheory.IsCondKernelCDF.integrable, Complex.UnitDisc.mk_neg, Complex.tendsto_one_add_div_cpow_exp, hasGradientAt_iff_hasFDerivAt, Complex.hasSum_cos', Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, Complex.closure_setOf_re_lt, ProbabilityTheory.integrable_of_mem_integrableExpSet, Complex.deriv_cosh, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, PeriodPair.derivWeierstrassP_coe, HasFPowerSeriesOnBall.tendsto_partialSum, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, Manifold.IsImmersionOfComplement.ofOpen, hasFDerivAt_exp_smul_const_of_mem_ball, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, Real.differentiableAt_tan, Real.differentiable_cosh, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, HasFPowerSeriesWithinAt.prod, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, iteratedFDeriv_succ_apply_right, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, FormalMultilinearSeries.leftInv_coeff_one, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ProbabilityTheory.integrable_compProd_iff, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, Complex.inner, RCLike.instStarModuleReal, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, continuousAt_const_cpow', fderiv_deriv, Complex.hasStrictDerivAt_sin, Complex.polarCoord_source, hasFPowerSeriesAt_pi_iff, Module.Basis.continuous_toMatrix, NormedField.continuousAt_zpow, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, Seminorm.ball_zero_absorbs_ball_zero, RCLike.continuous_conj, MeasureTheory.MemLp.norm_rpow_div, NumberField.mixedEmbedding.polarCoord_symm_eq, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, continuous_barycentric_coord, signedDist_vsub_self_rev, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, Complex.exp_sub_sum_range_succ_isLittleO_pow, ContinuousLinearMapWOT.ext_dual_iff, Int.Matrix.one_le_norm_A_of_ne_zero, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, contDiff_clm_apply_iff, Complex.continuousOn_prod_circle_transform_function, HasFPowerSeriesAt.hasFDerivAt, OrthonormalBasis.measurePreserving_repr_symm, lp.summable_inner, spectrum.exists_nnnorm_eq_spectralRadius_of_nonempty, WeakDual.isClosed_polar, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, spec_cfcβAux, MeasureTheory.measureReal_abs_gt_le_integral_charFun, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, eventually_enorm_mfderiv_extChartAt_lt, EuclideanSpace.piLpCongrLeft_single, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, hasFDerivAt_exp_smul_const, Differentiable.inner, UpperHalfPlane.dist_center_dist, LinearMap.mkContinuousβ_norm_le, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, LeftInvariantDerivation.map_smul, hasFDerivAt_jacobiThetaβ, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, oneTangentSpaceIcc_def, Complex.isHomeomorphicTrivialFiberBundle_re, WithSeminorms.congr_equiv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, NumberField.mixedEmbedding.polarSpaceCoord_target', hasStrictDerivAt_const, IccRightChart_extend_top_mem_frontier, rotationOf_coe, NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, HasFPowerSeriesWithinAt.restrictScalars, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, Complex.deriv_tan, contDiffOn_clm_apply, isCauSeq_iff_cauchySeq, MeromorphicAt.frequently_eq_iff_eventuallyEq, UpperHalfPlane.dist_le_dist_coe_div_sqrt, MeasureTheory.tendsto_eLpNorm_condExp, Seminorm.inf_apply, PiTensorProduct.mapLMultilinear_apply_apply, iteratedDeriv_comp_two, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, LinearMap.mem_polar_singleton, ContinuousMap.setOfIdeal_eq_compl_singleton, signedDist_self, MeasureTheory.MemLp.norm, Complex.hasDerivAt_cosh, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, EisensteinSeries.tendsto_zero_inv_linear, Unitization.nnreal_cfcβ_eq_cfc_inr, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, integrable_inv_one_add_sq, ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, Complex.UnitDisc.coe_smul_closedBall, signedDist_vsub_self, ContinuousLinearMap.mul_apply', spectralAlgNorm_one, HurwitzZeta.differentiableAt_hurwitzZeta, MeasureTheory.SignedMeasure.rnDeriv_smul, MeromorphicNFOn.zero_set_eq_divisor_support, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, signedDist_smul, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, MeasureTheory.eLpNorm_mono_ae_real, InnerProductSpace.rankOne_comp_rankOne, TemperedDistribution.fourierTransform_apply, MeasureTheory.convolution_lsmul_swap, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem, Real.hasStrictDerivAt_arctan, Complex.interior_setOf_re_le, DirichletCharacter.deriv_LFunctionTrivCharβ_apply_of_ne_one, AnalyticAt.hasFPowerSeriesAt, ZLattice.volume_image_eq_volume_div_covolume, hasDerivAtFilter_finCons', Complex.isOpen_im_gt_EReal, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Real.map_linearMap_volume_pi_eq_smul_volume_pi, MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero, Matrix.toEuclideanLin_eq_toLin, tendsto_logDeriv_euler_cot_sub, SlashInvariantForm.coe_trace, StrongDual.toLpβ_of_not_memLp, isConformalMap_complex_linear_conj, hasDerivWithinAt_finCons', Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, BoundedContinuousFunction.instIsBoundedSMul_1, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, LSeries_differentiableOn, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, differentiableAt_riemannZeta, spectralAlgNorm_extends, ProbabilityTheory.memLp_id_gaussianReal, Complex.tendsto_partialGamma, intervalIntegral.differentiable_integral_of_continuous, Complex.exp_sub_sum_range_isBigO_pow, Matrix.finite_real_spectrum, deriv_zpow, Complex.tendsto_norm_tan_of_cos_eq_zero, riemannZeta_eulerProduct, Complex.isOpenQuotientMap_zpow_compl_zero, LipschitzWith.locallyIntegrable_lineDeriv, UpperHalfPlane.eventuallyEq_coe_comp_ofComplex, InnerProductSpace.rankOne_comp, AddCircle.norm_neg_period, SmoothBumpCovering.embeddingPiTangent_injOn, EisensteinSeries.summable_linear_sub_mul_linear_add, MeasureTheory.memLp_norm_rpow_iff, StrongDual.mem_polarSubmodule, exists_dual_vector', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Orientation.kahler_rightAngleRotation_left, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, hasFPowerSeriesWithinAt_pi_iff, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, hasDerivAt_iff_isLittleO_nhds_zero, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, PadicInt.hasSum_mahler, Function.Periodic.invQParam_tendsto, InnerProductSpace.toMatrix_rankOne, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, cfcβHom_real_eq_restrict, PeriodPair.latticeEquiv_symm_apply, LinearMap.polar_AbsConvex, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, Complex.closure_setOf_lt_re, UnitAddTorus.mFourierSubalgebra_separatesPoints, Complex.betaIntegral_convergent, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, RCLike.geometric_hahn_banach_open, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, Real.differentiableOn_arccos, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, IsLocalMin.deriv_eq_zero, Real.hasDerivAt_cosh, PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept, Real.tendsto_deriv_mul_log_atTop, continuousMultilinearCurryLeftEquiv_apply, Orientation.abs_areaForm_of_orthogonal, LipschitzOnWith.ae_differentiableWithinAt_real, LeftInvariantDerivation.coe_smul, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, UnitAddCircle.norm_eq, HasFPowerSeriesAt.deriv, ModularForm.summable_logDeriv_one_sub_eta_q, innerβ_apply_apply, LSeries_sum, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, MeasureTheory.eLpNorm_norm_rpow, UpperHalfPlane.comp_ofComplex_of_im_le_zero, Asymptotics.IsBigOTVS.rfl, Complex.hasDerivAt_sin, fourierCoeff_eq_intervalIntegral, Seminorm.bddBelow_range_add, ContinuousAlternatingMap.restrictScalarsCLM_apply, NumberField.mixedEmbedding.continuous_normAtPlace, Asymptotics.IsLittleOTVS.bot, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, ContinuousLinearMap.isBigOTVS_comp, PadicAlgCl.valuation_def, Manifold.IsImmersionAtOfComplement.of_opens, hfdifferential_apply, MeasureTheory.Integrable.inner_const, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, Complex.closure_reProdIm, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, Real.hasDerivAt_fourierChar, bilinFormOfRealInner_orthogonal, AnalyticOnNhd.fderiv, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, hasDerivAt_intCast, Orientation.kahler_rotation_left, multipliable_sineTerm, Seminorm.absorbent_ball_zero, LindemannWeierstrass.integral_exp_mul_eval, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcβHom, ModularFormClass.hasSum_qExpansion_of_abs_lt, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, Complex.isUniformEmbedding_ofReal, Complex.conjCLE_enorm, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, Real.differentiableWithinAt_arccos_Iic, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, DirichletCharacter.LSeries_eulerProduct_hasProd, spectrum.differentiableOn_inverse_one_sub_smul, Continuous.inner_, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, Complex.hasSum_conj, ContinuousMultilinearMap.changeOriginSeries_support, PeriodPair.deriv_derivWeierstrassPExcept_self, Asymptotics.isBigOTVS_fun_comm, mdifferentiableWithinAt_comp_projIcc_iff, ContDiffMapSupportedIn.seminorm_apply, LinearMap.tripolar_eq_polar, RCLike.toIsOrderedAddMonoid, Complex.hasStrictDerivAt_exp, WithSeminorms.tendsto_nhds_atTop, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Orientation.inner_sq_add_areaForm_sq, Continuous.inner, Real.enorm_exp_I_mul_ofReal_sub_one_le, signedDist_smul_of_neg, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, MeasureTheory.lpNorm_const_smul, Seminorm.smul_closedBall_subset, Padic.denseRange_ratCast, DoubleCentralizer.algebraMap_fst, AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top, differentiableOn_euclidean, RCLike.reLm_coe, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, nnnorm_fderiv_norm_rpow_le, differentiableAt_abs_pos, EisensteinSeries.q_expansion_bernoulli, HasStrictFDerivAt.approximates_deriv_on_open_nhds, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, ContinuousLinearMap.toBilinForm_injective, integrableOn_exp_neg_Ioi, Complex.hasStrictDerivAt_cosh, ContinuousMultilinearMap.nnnorm_ofSubsingleton, inner_smul_real_left, eigenvalue_mem_ball, ContDiffOn.fderivWithin, tsum_prod_pow_eq_tsum_sigma, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, toSpanSingleton_derivWithin, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, ContinuousLinearMap.isEmbedding_restrictScalars, RCLike.nnnorm_conj, SchwartzMap.integral_fourier_mul_eq, HasFiniteFPowerSeriesOnBall.eq_partialSum', AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, continuousAt_cpow_const, GaussianFourier.tendsto_verticalIntegral, coe_lpBCFβα΅’_symm, MeromorphicOn.AnalyticOnNhd.divisor_nonneg, range_mfderiv_coe_sphere, MeromorphicOn.eventually_analyticAt_or_mem_compl, IsBoundedBilinearMap.toContinuousLinearMap_apply, Bornology.isVonNBounded_sub, HasFPowerSeriesOnBall.pi, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, HasFPowerSeriesWithinOnBall.fderivWithin_eq, Complex.UnitDisc.continuous_coe, MeasureTheory.integrable_prod_iff', ContinuousMultilinearMap.piβα΅’_symm_apply, RCLike.wInner_one_const_right, AlgHom.coe_toContinuousLinearMap, hahnEmbedding_isOrderedModule_rat, Matrix.posSemidef_iff_eq_sum_vecMulVec, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Affine.Simplex.sign_signedInfDist_touchpoint_empty, AnalyticAt.analyticOrderAt_ne_top, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, signedDist_vadd_right_swap, differentiableAt_const_cpow_of_neZero, tsum_dirichletSummand, Filter.Tendsto.isVonNBounded_range, AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, PolynormableSpace.withSeminorms', Real.differentiable_mulExpNegMulSq, ContinuousMap.neg_norm_le_apply, hasDerivAt_one, AddCircle.coe_real_preimage_closedBall_period_zero, Complex.dist_conj_conj, circleIntegrable_sub_zpow_iff, integrable_of_isBigO_exp_neg, FormalMultilinearSeries.radius_shift, Polynomial.fourierCoeff_toAddCircle_natCast, nnnorm_algebraMap', Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, Complex.conjCLE_apply, ContinuousMap.spectrum_eq_range, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, Valued.integer.exists_nnnorm_lt_one, Real.not_DifferentiableAt_log_mul_zero, innerSLFlip_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, iccLeftChart_extend_zero, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, hasDerivAt_const_mul, hasLineDerivAt_iff_tendsto_slope_zero, Circle.coe_eq_one, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, Complex.differentiable_one_div_Gamma, Valued.integer.properSpace_iff_compactSpace_integer, completeSpace_of_cauSeq_isComplete, Euclidean.ball_eq_preimage, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, contDiff_nat_iff_continuous_differentiable, ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, absorbent_ball, UpperHalfPlane.cosh_half_dist, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, DirichletCharacter.LSeries_eulerProduct_exp_log, mdifferentiableOn_coordChangeL, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, Polynomial.hasDerivAt, Complex.not_differentiableAt_Gamma_zero, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, ContinuousLinearMap.opNorm_lsmul_le, MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds, OrthonormalBasis.repr_symm_single, MeasureTheory.hasFiniteIntegral_toReal_iff, Real.fourierChar_apply, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, MultilinearMap.mkContinuousMultilinear_norm_le, interior_range_modelWithCornersEuclideanHalfSpace, WeakDual.CharacterSpace.norm_le_norm_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, hasDerivAt_natCast, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, Seminorm.rescale_to_shell, AddCircle.addWellApproximable_ae_empty_or_univ, ProbabilityTheory.differentiableOn_complexMGF, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, closedBall_normSeminorm, Real.hasStrictDerivAt_cos, PeriodPair.deriv_weierstrassPExcept_same, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_symm_apply, IntervalIntegrable.intervalIntegrable_slope, ContinuousLinearMap.coe_restrictScalarsL, Function.Periodic.qParam_tendsto, continuousAt_jacobiTheta, iter_deriv_inv, PeriodPair.analyticOnNhd_derivWeierstrassP, Matrix.frobenius_norm_mul, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, Complex.Gammaβ_residue_zero, Matrix.star_dotProduct_gram_mulVec, ContinuousLinearMap.norm_compL_le, integrableOn_Ioi_cpow_of_lt, RCLike.hasSum_iff, Differentiable.dist, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, ContMDiffVectorBundle.contMDiffOn_coordChangeL, EulerSine.antideriv_cos_comp_const_mul, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, ProbabilityTheory.condVar_of_sigmaFinite, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Complex.instTietzeExtension, Bornology.isVonNBounded_add, HasFPowerSeriesAt.sub, ProperSpace.of_locallyCompact_module, RightDerivMeasurableAux.differentiable_set_eq_D, hasDerivWithinAt_zpow, OrthogonalFamily.range_linearIsometry, NumberField.mixedEmbedding.convexBodyLT_convex, Complex.instT2Space, mellin_convergent_iff_norm, Monotone.deriv_nonneg, UpperHalfPlane.exp_half_dist, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, Orientation.kahler_mul, innerSL_real_flip, GaussianFourier.integral_cexp_neg_mul_sum_add, Complex.continuous_ofReal_cpow_const, ProbabilityTheory.covarianceBilinDual_comm, RCLike.nnnorm_two, ProbabilityTheory.iteratedDeriv_two_cgf, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, measurableSet_of_differentiableWithinAt_Ioi, TensorProduct.norm_lid, Real.differentiable_iteratedDeriv_sin, ProbabilityTheory.deriv_mgf_zero, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, Matrix.instIsOrderedAddMonoid, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NormedAlgebra.Real.nonempty_algEquiv_or, HurwitzZeta.differentiableAt_completedCosZeta, fourier_neg, spectralAlgNorm_of_finiteDimensional_normal_def, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sigmoid, LSeries.tendsto_cpow_mul_atTop, ContinuousMultilinearMap.curryMid_apply, ProperCone.dual_dual_flip, ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, flip_innerβ, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, EisensteinSeries.tendsto_double_sum_S_act, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, MeasureTheory.LocallyIntegrableOn.norm, HasStrictFDerivAt.isBigOTVS_sub, Matrix.PosSemidef.re_dotProduct_nonneg, Orientation.volumeForm_robust', Complex.sinh_eq_tsum, balanced_closedBall_zero, continuousAt_jacobiThetaβ, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, instSMulCommClass_sphere_ball_ball, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MDifferentiableAt.coordChangeL, Polynomial.isOpenQuotientMap_eval, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, EulerSine.antideriv_sin_comp_const_mul, ContinuousLinearMap.norm_restrictScalars, Complex.differentiableAt_cosh, coe_normSeminorm, signedDist_vadd_left, Diffeology.IsPlot.contDiff, ModularGroup.tendsto_lcRow0, ProbabilityTheory.integrable_kernel_prodMk_left, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NormedSpace.sInter_polar_eq_closedBall, Complex.differentiableAt_Gamma_nat_add_one, ContDiffBump.convolution_eq_right, TemperedDistribution.instFourierInvSMul, PadicInt.totallyBounded_univ, ProbabilityTheory.deriv_cgf, Complex.deriv_cos', Complex.imCLM_coe, lp.hasSum_inner, iteratedDeriv_comp_eq_sum_orderedFinpartition, isBoundedBilinearMap_inner, Complex.isQuotientMap_im, ContinuousLinearMap.opNorm_mul_apply_le, intervalIntegral.integral_hasFDerivWithinAt, HasFPowerSeriesAt.tendsto_partialSum, circleAverage_log_norm_factorizedRational, Polynomial.aeval_ofReal, deriv_pow_field, SmoothBumpCovering.embeddingPiTangent_injective, ContinuousLinearMap.orthogonal_range, ProbabilityTheory.memLp_tilted_mul, HasFiniteFPowerSeriesAt.add, HasFPowerSeriesAt.hasDerivAt, Int.nnnorm_coe_units, MeromorphicOn.min_divisor_le_divisor_add, ProbabilityTheory.covarianceBilin_apply, ContinuousLinearMap.isThetaTVS_comp, AnalyticAt.eventually_eq_or_eventually_ne, Polynomial.hasDerivAt_aeval, MeasureTheory.stronglyMeasurable_charFun, PeriodPair.instDiscreteTopologySubtypeComplexMemSubmoduleIntLattice, HasFDerivAt.linear_multilinear_comp, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, Complex.continuous_ofReal, ContinuousMap.comp_attachBound_mem_closure, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, MeasureTheory.convolutionExistsAt_iff_integrable_swap, Complex.not_continuousAt_Gamma_neg_nat, Polynomial.C_eq_or_isOpenQuotientMap_eval, hasDerivAt_ofReal_cpow_const, EisensteinSeries.summable_e2Summand_symmetricIcc, hasDerivAt_norm_rpow, UnitAddTorus.hasSum_prod_mFourierCoeff, Padic.withValUniformEquiv_cast_apply, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, NumberField.mixedEmbedding.latticeBasis_apply, LeftInvariantDerivation.map_sub, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, spectrum.exp_mem_exp, Unitization.isUniformEmbedding_addEquiv, ContinuousMultilinearMap.compContinuousLinearMapL_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, Seminorm.smul_closedBall_preimage, TemperedDistribution.fourierInv_apply, AnalyticAt.eventually_eq_zero_or_eventually_ne_zero, MeromorphicOn.extract_zeros_poles, Matrix.IsHermitian.cfcAux_id, cfcβAux_mem_range_inr, ContinuousLinearMap.norm_bilinearRestrictScalars, eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top, ContinuousLinearMap.nhds_zero_eq, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, Complex.sin_eq_tsum, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, RCLike.real_smul_ofReal, differentiableAt_jacobiThetaβ_snd, Padic.coe_withValRingEquiv, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, AffineSubspace.signedInfDist_singleton, HasFPowerSeriesWithinOnBall.neg, NumberField.mixedEmbedding.measurable_polarCoord_symm, norm_deriv_eq_norm_fderiv, IsUltrametricDist.normedAlgebra_iff, ContinuousMap.apply_le_norm, PadicInt.fwdDiff_mahlerSeries, LSeries.tendsto_atTop, MeasureTheory.AEStronglyMeasurable.integrable_truncation, AkraBazziRecurrence.differentiableAt_smoothingFn, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ContinuousLinearMap.bilinearComp_zero_left, one_add_cpow_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, Complex.hasSum_conj', MeasureTheory.L2.mem_L1_inner, withSeminorms_pi, Bundle.ContinuousRiemannianMetric.pos, Complex.isOpen_im_lt_EReal, SchwartzMap.derivCLM_apply, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, Seminorm.gauge_ball, Circle.coe_inv, RCLike.map_nonneg_iff, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, MeromorphicOn.negPart_divisor_add_le_max, Real.deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, integrableOn_Ioi_exp_neg_mul_sq_iff, Orientation.volumeForm_zero_neg, BoundedContinuousFunction.nnnorm_coeFn_eq, Real.differentiableAt_binEntropy, Complex.hasStrictDerivAt_cpow_const, ContDiffBump.dist_normed_convolution_le, WithAbs.isUniformInducing_of_comp, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, mellin_differentiableAt_of_isBigO_rpow_exp, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', Orientation.areaForm_map, Real.enorm_rpow_of_nonneg, Asymptotics.isEquivalent_iff_tendsto_one, differentiable_neg, hasDerivAt_neg, ProbabilityTheory.integrable_of_mem_interior_integrableExpSet, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, deriv_bernoulliFun, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, NNReal.nnnorm_eq, det_fderivPiPolarCoordSymm, hasFTaylorSeriesUpToOn_succ_iff_left, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Padic.isUniformInducing_cast_withVal, PadicInt.continuous_multichoose, Complex.hasSum_taylorSeries_neg_log, Polynomial.hasStrictDerivAt, Real.deriv2_qaryEntropy, VectorFourier.integral_bilin_fourierIntegral_eq_flip, Real.differentiableAt_exp, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, NumberField.mixedEmbedding.logMap_real, contDiffOn_succ_iff_fderivWithin, NumberField.mixedEmbedding.commMap_apply_of_isReal, ZSpan.fundamentalDomain_pi_basisFun, AffineMap.hasStrictDerivAt, LipschitzWith.ae_differentiableAt_of_real, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, NormedSpace.of_real_exp_β_β, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, Seminorm.finset_sup_smul, MeasureTheory.Measure.integrable_comp_iff, Bundle.RiemannianMetric.pos, NumberField.mixedEmbedding.polarCoord_apply, TemperedDistribution.instLineDerivSMulComplex, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, euler_sineTerm_tprod, HilbertBasis.repr_self, NormedField.discreteTopology_of_bddAbove_range_norm, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, spectralNorm.spectralMulAlgNorm_eq_of_mem_roots, ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, continuousMultilinearCurryRightEquiv_symm_apply', ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, ContDiffWithinAt.fderivWithin, ContDiffMapSupportedIn.continuousSMul, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, Subalgebra.frontier_spectrum, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, Complex.log_eq_integral, BoundedContinuousFunction.add_norm_nonneg, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, Complex.equivRealProdCLM_symm_apply_re, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, LinearMap.isStarProjection_toContinuousLinearMap_iff, MeromorphicOn.divisor_smul, UpperHalfPlane.sinh_half_dist_add_dist, HasFDerivAtFilter.isLittleOTVS, NumberField.mixedEmbedding.continuous_normAtAllPlaces, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, MeasureTheory.L2.integrable_inner, MeasureTheory.hasFiniteIntegral_prod_iff, IsCompact.reProdIm, LinearPMap.adjointDomainMkCLMExtend_apply, WithAbs.pseudoMetricSpace_induced_of_comp, MeasureTheory.charFun_map_mul, iteratedFDerivWithin_two_apply, extDerivWithin_smul, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, DoubleCentralizer.coe_fst, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, HurwitzZeta.differentiable_cosZeta_of_ne_zero, ContDiffPointwiseHolderAt.fderiv, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, BoundedContinuousFunction.norm_sub_nonneg, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, Filter.HasBasis.isBigOTVS_iff, Complex.deriv_cpow_const, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, DifferentiableWithinAt.norm_sq, ContinuousMapZero.instCStarRing, NormedField.instCompletableTopField, SchwartzMap.integral_fourierInv_mul_eq, hasFDerivWithinAt_iff_hasGradientWithinAt, CurveIntegrable.smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, FormalMultilinearSeries.min_radius_le_radius_add, hasStrictDerivAt_one, Complex.summable_one_div_nat_cpow, signedDist_right_lineMap, Complex.nndist_conj_comm, ContinuousLinearMap.closed_range_of_antilipschitz, ProbabilityTheory.uncenteredCovarianceBilin_zero, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, logDeriv_prod_sineTerm_eq_sum_cotTerm, Complex.differentiableAt_Gamma_one, Real.differentiable_fourierChar, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, HasFPowerSeriesAt.pi, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, VectorFourier.fourierPowSMulRight_apply, summable_prod_eisSummand, mdifferentiable_jacobiTheta, Matrix.linfty_opNorm_eq_opNorm, ContinuousAlternatingMap.prodLIE_apply, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, RCLike.ofReal_tsum, Real.deriv_cos', isBigO_deriv_rpow_const_atTop, hasDerivAt_pow, contDiff_succ_iff_deriv, DifferentiableOn.dist, Complex.instProperSpace, Real.deriv_rpow_const', CPolynomialOn.fderiv, EuclideanSpace.dist_eq, NumberField.mixedEmbedding.normAtPlace_negAt, PadicInt.mahlerEquiv_apply, Complex.nndist_conj_conj, Polynomial.div_tendsto_atTop_zero_of_degree_lt, SchwartzMap.convolution_flip, Orthonormal.orthogonalFamily, Real.differentiableAt_arcosh, continuousSMul_closedBall_closedBall, ContinuousLinearMap.opNorm_flip, IsLocalMaxOn.fderivWithin_eq_zero, AlternatingMap.measure_def, MeasureTheory.Integrable.of_mem_Icc, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, EisensteinSeries.G2_eq_tsum_cexp, Complex.isometryOfOrthonormal_apply, IsConformalMap.smul, nndist_lineMap_lineMap, isCoveringMap_npow, Irreducible.maximalIdeal_eq_closedBall, Complex.frontier_setOf_le_re_and_le_im, Complex.sameRay_iff, AddCircle.norm_le_half_period, Circle.normSq_coe, Real.hasStrictDerivAt_sqrt, Complex.hasDerivAt_Gamma_one, NumberField.mixedEmbedding.normAtPlace_smul, PeriodPair.hasSum_weierstrassPExcept, Polynomial.deriv, FormalMultilinearSeries.derivSeries_eq_zero, HilbertBasis.summable_inner_mul_inner, Polynomial.div_tendsto_zero_of_degree_lt, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, Int.nnnorm_natCast, Real.hasDerivAt_tan_of_mem_Ioo, contMDiffOn_comp_projIcc_iff, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, SchwartzMap.integral_fourier_smul_eq, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, ContinuousMultilinearMap.curryLeft_apply, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, EisensteinSeries.qExpansion_identity, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, Orientation.inner_rightAngleRotation_right, UpperHalfPlane.contMDiffAt_ofComplex, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, ModularForm.prod_fintype_slash, GaussianFourier.integral_cexp_neg_sum_mul_add, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, circleIntegrable_sub_inv_iff, AlternatingMap.mkContinuousLinear_norm_le, ModularFormClass.bounded_at_infty_comp_ofComplex, ProperCone.hyperplane_separation_of_notMem, ProbabilityTheory.HasSubgaussianMGF.memLp, NumberField.mixedEmbedding.convexBodySum_isBounded, LinearMap.continuous_of_isClosed_ker, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Complex.arg_eq_nhds_of_im_pos, ModularForm.holo', FormalMultilinearSeries.radius_le_radius_derivSeries, Orientation.volumeForm_apply_le, ContinuousAlternatingMap.curryLeftLI_apply, LDL.diag_eq_lowerInv_conj, eventuallyConst_iff_analyticOrderAt_sub_eq_top, NumberField.mixedEmbedding.polarSpaceCoord_apply, Real.nonempty_algEquiv_or, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, Padic.coe_withValRingEquiv_symm, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, differentiableAt_iff_comp_add_const, Complex.starConvex_slitPlane, ContinuousLinearMap.norm_compSL_le, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, RCLike.nnnorm_nnqsmul, ContDiffMapSupportedIn.withSeminorms, ProbabilityTheory.Kernel.eLpNorm_density_le, MeasureTheory.withDensityα΅₯_smul, LinearMap.polar_isClosed, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Bornology.isVonNBounded_vadd, innerββ_apply, HasFDerivWithinAt.isBigOTVS_sub, Complex.log_sub_logTaylor_isBigO, differentiable_completedZetaβ, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, fourier_zero', HurwitzZeta.hasSum_int_sinZeta, spectrum.resolvent_tendsto_cobounded, Complex.differentiable_sinh, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, ContinuousMultilinearMap.toUniformOnFun_toFun, UnitAddCircle.mem_addWellApproximable_iff, ZMod.toCircle_intCast, iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum, div_le_egauge_ball, hasDerivAtFilter_pi, StrongDual.toLp_apply, StrongDual.polar_empty, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, ContinuousLinearMap.coe_flipβα΅’, HasGradientAtFilter.tendsto_nhds, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, ZMod.toCircle_natCast, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, ModularFormClass.hasSum_qExpansion_of_norm_lt, ContMDiffAt.mfderiv, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, Complex.volume_ball, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, cpow_eq_nhds', Bornology.isVonNBounded_insert, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, instSMulCommClass_closedBall_closedBall_ball, jacobiTheta_eq_tsum_nat, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Complex.UnitDisc.instSMulCommClass_circle_closedBall, Complex.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.changeOrigin_eval, LSeries.term_sum_apply, LinearMap.toSeminorm_ball_zero, Complex.nnnorm_intCast, Real.differentiableAt_negMulLog, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, UpperHalfPlane.contMDiffAt_iff, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Orientation.inner_rightAngleRotationAuxβ_left, Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet, IsSelfAdjoint.adjoint_conj, closedAbsConvexHull_eq_closure_absConvexHull, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, Complex.differentiableAt_sinh, HasDerivAt.inner, HasFPowerSeriesAt.prod, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, Function.Periodic.differentiable_qParam, VectorPrebundle.contMDiffOn_contMDiffCoordChange, Orientation.areaForm_apply_self, Complex.continuous_tan, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, LeftInvariantDerivation.toDerivation_injective, PeriodPair.differentiableOn_weierstrassPExcept, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, AlternatingMap.mkContinuousAlternating_norm_le_max, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, Complex.conjCLE_norm, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, SchwartzMap.seminorm_apply, mdifferentiableAt_coordChangeL, hasDerivAt_finCons', ProbabilityTheory.variance_linearMap_gaussianReal, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Complex.differentiableAt_log, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, MeasureTheory.SignedMeasure.integrable_rnDeriv, differentiableAt_completedZeta, AffineSubspace.signedInfDist_def, isScalarTower_sphere_ball_ball, PeriodPair.derivWeierstrassPExcept_add_coe, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, HasFPowerSeriesWithinAt.add, MeasureTheory.BoundedContinuousFunction.inner_toLp, Complex.isQuotientMap_re, ContinuousLinearMap.adjoint_inner_right, Circle.coeHom_apply, exists_extension_norm_eq, Complex.dist_conj_comm, ProbabilityTheory.integrable_exp_mul_of_le, hasFDerivAt_integral_of_dominated_of_fderiv_le'', rootsOfUnityCircleEquiv_apply, CuspFormClass.zero_at_infty_slash, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, NormedSpace.closedBall_inv_subset_polar_closedBall, MeasureTheory.convolution_mul_swap, ContDiffMapSupportedIn.postcompLM_apply, PeriodPair.differentiableOn_weierstrassP, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, ContinuousLinearMap.norm_smulRightL_le, MeasureTheory.withDensityα΅₯_smul', AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, differentiableAt_iff_restrictScalars, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, SchwartzMap.tsupport_derivCLM_subset, hasDerivAt_single, OrthonormalBasis.coe_toBasis_repr_apply, det_rotation, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, RCLike.enorm_conj, PadicInt.norm_mahler_eq, UpperHalfPlane.mdifferentiable_coe, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, Circle.coe_inj, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, SchwartzMap.le_seminorm', Complex.arg_eq_nhds_of_re_pos, FormalMultilinearSeries.radius_prod_eq_min, ContinuousOn.inner, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, summable_cotTerm, RCLike.conjAe_coe, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, continuousAt_jacobiThetaβ', Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, AlternatingMap.measure_parallelepiped, Manifold.IsImmersionOfComplement.id, RCLike.wInner_one_eq_sum, ContinuousAlternatingMap.nnnorm_ofSubsingleton, norm_cfcHom, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, KuratowskiEmbedding.embeddingOfSubset_dist_le, EisensteinSeries.eisSummand_extension_differentiableOn, EuclideanSpace.dist_sq_eq, integral_ofReal, HasFiniteFPowerSeriesOnBall.fderiv', Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Complex.isOpenQuotientMap_pow_compl_zero, ContinuousMultilinearMap.currySum_apply, isOpenMap_barycentric_coord, Affine.Simplex.signedInfDist_affineCombination, Complex.deriv_sinh, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, intervalIntegral.intervalIntegrable_cpow', Complex.deriv_sin, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, UniformSpace.Completion.inner_coe, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, WeakDual.CharacterSpace.equivAlgHom_coe, Valued.toNormedField.setOf_mem_integer_eq_closedBall, AddCircle.norm_eq, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipβα΅’'_symm, fourier_coe_apply', le_egauge_ball_one, EuclideanSpace.inner_toLp_toLp, NumberField.mixedEmbedding.polarSpaceCoord_source, TemperedDistribution.lineDerivOp_fourierInv_eq, not_integrableOn_Ici_inv, Complex.hasSum_taylorSeries_log, fourierCoeffOn_eq_integral, Matrix.l2_opNNNorm_diagonal, Int.toNat_add_toNat_neg_eq_nnnorm, MeromorphicOn.negPart_divisor_add_le_add, UpperHalfPlane.dist_coe_le, CompactConvergenceCLM.continuousSMul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, spectrum.exists_nnnorm_eq_spectralRadius, hasStrictDerivAt_zero, PeriodPair.hasSum_sumInvPow, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Real.differentiableAt_sinh, ContinuousAlternatingMap.alternatizeUncurryFin_add, DirichletCharacter.LFunctionTrivChar_residue_one, Complex.hasDerivAt_tan, ContinuousLinearMap.isBigOTVS_fun_comp, NormedField.denselyOrdered_range_nnnorm, signedDist_eq_dist_iff_vsub_mem_span, Real.differentiable_iteratedDeriv_sinh, Complex.lintegral_comp_pi_polarCoord_symm, RCLike.instOrderClosedTopology, FormalMultilinearSeries.coeff_iterate_fslope, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, Filter.Tendsto.inner, exp_neg_integrableOn_Ioi, PadicInt.continuousAddCharEquiv_symm_apply, MeasureTheory.Integrable.const_inner, hasStrictDerivAt_exp_smul_const_of_mem_ball', rotation_symm, LSeriesHasSum.sum, ContinuousLinearMap.extendToπ'_apply, continuous_descPochhammer_eval, IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, VectorFourier.norm_fourierPowSMulRight_le, Complex.equivRealProdCLM_symm_apply_im, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, integrable_exp_neg_mul_sq_iff, Complex.polarCoord_symm_apply, nndist_homothety_center, AnalyticOnNhd.is_constant_or_isOpen, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, summable_bernoulli_fourier, ModularFormClass.differentiableOn_cuspFunction_ball, Unitization.splitMul_injective, Antitone.deriv_nonpos, ZMod.differentiable_completedLFunctionβ, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, ContDiffMapSupportedIn.continuous_iff_comp, PeriodPair.periodic_weierstrassP, ModularFormClass.holo, VectorFourier.norm_fourierSMulRight, RCLike.ofReal_im_ax, ZMod.toCircle_apply, Polynomial.differentiable, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, PadicInt.isOpenEmbedding_coe, ContinuousLinearEquiv.coord_norm', completedRiemannZeta_residue_one, EisensteinSeries.summable_e2Summand_symmetricIco, ContinuousLinearMap.nnnorm_id, GaussianFourier.integrable_cexp_neg_sum_mul_add, ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, differentiableOn_abs, absConvexHull_eq_convexHull_balancedHull, ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, Complex.hasSum_sinh, div_le_egauge_closedBall, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, hasStrictFDerivAt_inv', LinearMap.mem_span_iff_bound, ProbabilityTheory.integrable_toReal_condDistrib, Circle.arg_exp, hasFDerivAt_exp_smul_const_of_mem_ball', WithSeminorms.partial_sups, hasDerivAt_mul_const, TemperedDistribution.smulLeftCLM_const, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, Probability.integrable_cauchyPDFReal, MeasureTheory.integrable_toReal_iff, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, hasStrictFDerivAt_exp_smul_const, integrableOn_rpow_mul_exp_neg_mul_sq, dist_algebraMap, SchwartzMap.fourier_convolution_apply, UpperHalfPlane.sinh_half_dist, Seminorm.smul_ball_zero, Complex.hasStrictFDerivAt_log_real, Complex.differentiableAt_Gamma, Asymptotics.isBigOTVS_map, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, Real.hasStrictDerivAt_tan, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, UpperHalfPlane.dist_le_iff_le_sinh, RCLike.wInner_cWeight_const_right, TemperedDistribution.smulLeftCLM_sum, mahler_apply, SimpleGraph.isEquivalent_extremalNumber, Real.nnnorm_rpow_of_nonneg, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, iter_deriv_inv_linear, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, HurwitzZeta.differentiableAt_cosZeta, ProbabilityTheory.deriv_cgf_zero, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, Complex.hasSum_sin', jacobiThetaβ_fderiv_undef, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, DifferentiableAt.norm, instPerfectSpace, Complex.arg_eq_nhds_of_re_neg_of_im_pos, Real.differentiable_fourierChar_neg_bilinear_left, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, EisensteinSeries.summable_linear_right_add_one_mul_linear_right, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, PadicAlgCl.instIsUltrametricDist, fderiv_norm_smul_pos, gelfandTransform_isometry, MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore, FormalMultilinearSeries.le_radius_pi, Quaternion.coe_ofComplex, Real.hasDerivAt_arctan, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, continuousMultilinearCurryLeftEquiv_symm_apply, Finset.nnnorm_prod_le, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, Complex.betaIntegral_convergent_left, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, Complex.continuousAt_cpow_of_re_pos, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, EuclideanSpace.nnnorm_eq, innerββ_apply_coe, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, RCLike.nnnorm_natCast, Complex.sin_eq_tsum', PiLp.inner_apply, mellin_differentiableAt_of_isBigO_rpow, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Complex.reCLM_norm, iteratedFDeriv_succ_eq_comp_left, range_modelWithCornersEuclideanHalfSpace, ContinuousMapZero.toNNReal_neg_smul, UpperHalfPlane.dist_coe_center_sq, AddChar.wInner_cWeight_eq_boole, differentiableAt_of_deriv_ne_zero, ZMod.LFunction_residue_one, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NumberField.mixedEmbedding.convexBodySum_convex, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, PeriodPair.mul_Οβ_add_mul_Οβ_mem_lattice, ContinuousLinearMap.opNorm_mulLeftRight_le, Circle.coe_exp, convex_halfSpace_im_le, ClosedSubmodule.orthogonal_closure, riemannZeta_eulerProduct_tprod, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, cpow_eq_nhds, ContDiffMapSupportedIn.structureMapCLM_zero_injective, TemperedDistribution.fourier_apply, RCLike.iInter_halfSpaces_eq, StrongDual.polar_zero, ContinuousMultilinearMap.piβα΅’_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, Real.deriv_arcsin_aux, Complex.differentiable_cosh, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonβα΅’_apply, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, fourier_add', RCLike.continuous_im, IsLocalMin.fderiv_eq_zero, norm_iteratedFDerivWithin_fderivWithin, MeasureTheory.Integrable.fourier_smul, LinearMap.coe_toContinuousLinearMap_symm, Complex.frontier_setOf_le_re_and_im_le, Real.differentiableAt_qaryEntropy, continuousMultilinearCurryFin1_symm_apply, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, Complex.continuousAt_Gamma, StrongDual.mem_polar_iff, FormalMultilinearSeries.radius_pi_le, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, Submodule.orthogonal_eq_inter, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, Complex.differentiable_iteratedDeriv_cos, ContinuousLinearEquiv.coord_self, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, riemannZeta_residue_one, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, Complex.ofReal_tsum, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_apply, ContDiffAt.differentiableAt_iteratedFDeriv, Manifold.IsImmersionOfComplement.of_opens, integrable_exp_neg_mul_sq, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, AddChar.coe_complexBasis, Polynomial.toAddCircle_X_eq_fourier_one, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, Complex.differentiable_cos, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, RCLike.geometric_hahn_banach_point_closed, hasDerivWithinAt_intCast, differentiableWithinAt_zpow, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, CircleIntegrable.out, AddCircle.closedBall_ae_eq_ball, UniformSpace.Completion.continuous_inner, SchwartzMap.integrable_pow_mul, HasFPowerSeriesWithinAt.compContinuousLinearMap, MeasureTheory.memLp_of_bounded, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, PadicInt.denseRange_intCast, instSMulCommClass_sphere_closedBall_ball, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, LeftInvariantDerivation.commutator_apply, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, UpperHalfPlane.mdifferentiableAt_iff, fourier_add_half_inv_index, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, NormedField.noncompactSpace, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, PeriodPair.analyticOnNhd_weierstrassPExcept, hasStrictFDerivAt_pow, FormalMultilinearSeries.derivSeries_apply_diag, NormedSpace.polar_closedBall, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, AnalyticAt.fderiv, AnalyticOn.eval_polynomial, Matrix.l2_opNNNorm_conjTranspose_mul_self, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, integrable_mulExpNegMulSq_comp, integrable_cexp_quadratic, AffineSubspace.signedInfDist_apply_self, Complex.image_exp_Ioc_eq_sphere, ContinuousLinearMap.opNorm_lsmul, coe_innerββ_apply, isCoveringMapOn_zpow, ProbabilityTheory.covarianceBilinDual_of_not_memLp, FormalMultilinearSeries.norm_changeOriginSeriesTerm, HurwitzZeta.completedHurwitzZetaEven_residue_zero, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, ContinuousWithinAt.inner, Module.Basis.continuous_coe_repr, Unitization.uniformity_eq_aux, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, ModularGroup.lcRow0_apply, hasDerivAt_exp_zero, HasFTaylorSeriesUpTo.zero_eq', deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, HurwitzZeta.tendsto_hurwitzZeta_sub_one_div_nhds_one, MeasureTheory.integrable_withDensity_iff, InnerProductSpace.continuousLinearMapOfBilin_apply, Circle.toUnits_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, instFieldContMDiffRing, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, spectralAlgNorm_isPowMul, PointwiseConvergenceCLM.withSeminorms, PeriodPair.indep, UpperHalfPlane.tanh_half_dist, MeasureTheory.convolution_eq_swap, Module.Basis.opNorm_le, ContMDiff.codRestrict_sphere, Real.differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, ContDiff.fderiv_right, hasDerivAt_const_add_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, MeasureTheory.Integrable.norm, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, ContDiffMapSupportedIn.withSeminorms', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, DFinsupp.inner_sum, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, AddCircle.norm_eq', MeromorphicOn.divisor_def, WeakDual.isSeqCompact_polar, inner_matrix_row_row, ContinuousAlternatingMap.uniformContinuous_restrictScalars, HasFTaylorSeriesUpTo.fderiv, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.intervalIntegrable_charFun, ContinuousMap.idealOf_compl_singleton_isMaximal, Complex.arg_eq_nhds_of_re_neg_of_im_neg, PiTensorProduct.injectiveSeminorm_tprod_le, ProbabilityTheory.integrable_rpow_of_mem_interior_integrableExpSet, Complex.hasSum_arctan, ContinuousLinearMap.norm_holderL_le, fourier_add, hasFDerivWithinAt_pow, PolynormableSpace.withSeminorms, contDiff_infty_iff_fderiv, MeasureTheory.charFun_eq_integral_innerProbChar, NormedField.valuation_apply, LinearMap.polar_mem_iff, hasDerivWithinAt_inv, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, gaugeSeminormFamily_ball, hasStrictDerivAt_id, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem_of_analyticOn, instNonemptySeedRatReal, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, HurwitzZeta.hasSum_int_completedCosZeta, deriv_neg, Complex.hasSum_cosh, RCLike.tendsto_ofReal_atBot_cobounded, LeftInvariantDerivation.ext_iff, abs_signedDist_le_dist, Complex.frontier_setOf_lt_re, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, Complex.conj_tsum, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, HasFDerivAtFilter.restrictScalars, LinearMap.hasDerivAtFilter, intervalIntegral.integral_hasFDerivAt, MeasureTheory.memLp_norm_iff, HasFiniteFPowerSeriesOnBall.fderiv_eq, ModularForm.coe_trace, integrable_mul_cexp_neg_mul_sq, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.frontier_setOf_le_im, Complex.hasDerivAt_log_sub_logTaylor, Complex.GammaIntegral_convergent, hasStrictDerivAt_iff_hasStrictFDerivAt, MeasureTheory.hausdorffMeasure_homothety_preimage, WithSeminorms.isVonNBounded_iff_seminorm_bounded, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, intervalIntegral.fderiv_integral, ContinuousLinearMap.analyticAt_bilinear, Complex.isOpenMap_exp, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', HasFPowerSeriesAt.hasStrictFDerivAt, convex_halfSpace_re_gt, WithSeminorms.hasBasis, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AddChar.complexBasis_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, AffineSubspace.signedInfDist_apply_of_mem, hasStrictDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, tendsto_algebraMap_cobounded, Real.probChar_apply, StrongDual.polar_singleton, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, hasDerivAt_pi, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, differentiableAt_abs, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, ConvexOn.real_sSup_of_nat_affine_eq, dist_algebraMap', hasFDerivAt_inv', MeasureTheory.dominatedFinMeasAdditive_weightedSMul, ProbabilityTheory.IsRatCondKernelCDF.integrable, tendsto_euler_sin_prod', hasDerivWithinAt_finCons, ProbabilityTheory.charFun_gaussianReal, WeakDual.CharacterSpace.exists_apply_eq_zero, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, exists_continuousLinearEquiv_fderiv_symm_eq, Complex.polarCoord_target, RCLike.conj_smul, FormalMultilinearSeries.rightInv_coeff, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, DifferentiableOn.norm, Complex.map_isometryOfOrthonormal, Complex.hasDerivAt_log, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, hasDerivAt_zpow, TemperedDistribution.fourierTransformInv_apply, AnalyticAt.frequently_eq_iff_eventually_eq, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Circle.coe_injective, Complex.hasSum_cos, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, isClosedMap_smul_left, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, instSMulCommClass_sphere_sphere_closedBall, Complex.isHomeomorphicTrivialFiberBundle_im, ContDiffOn.differentiableOn_iteratedFDerivWithin, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, HurwitzZeta.hasSum_int_completedSinZeta, RCLike.instTietzeExtension, Matrix.IsHermitian.mulVec_eigenvectorBasis, MeasureTheory.MemLp.integrable_norm_pow', HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', zeta_nat_eq_tsum_of_gt_one, Matrix.l2_opNorm_def, UpperHalfPlane.tendsto_comap_im_ofComplex, Circle.coe_zpow, signedDist_apply_linear, Real.differentiableAt_sin, HasFiniteFPowerSeriesOnBall.sub, RCLike.wInner_nonneg, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, ContinuousLinearMapWOT.continuous_dual_apply, parallelepiped_orthonormalBasis_one_dim, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, ContinuousLinearMap.holderL_apply_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, AddChar.expect_apply_eq_ite, LeftInvariantDerivation.toFun_eq_coe, Complex.reCLM_enorm, MeasureTheory.integrable_mconv_iff, UpperHalfPlane.contMDiff_denom, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, isClosedEmbedding_smul_left, Polynomial.toAddCircle_C_eq_smul_fourier_zero, isConformalMap_const_smul, Matrix.l2_opNorm_mul, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, riemannZeta_eulerProduct_hasProd, norm_innerSL_le, MeasureTheory.eLpNorm'_norm_rpow, VectorFourier.hasFDerivAt_fourierChar_smul, Padic.instProperSpace, DirichletCharacter.LSeries_eulerProduct, integrable_cexp_quadratic', Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, InformationTheory.not_differentiableAt_klFun_zero, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, Real.exists_extension_norm_eq, continuousMultilinearCurryRightEquiv_apply, Seminorm.convex_closedBall, RCLike.real_smul_eq_coe_mul, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, Bornology.isVonNBounded_of_smul_tendsto_zero, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, Complex.frontier_reProdIm, RCLike.ofRealAm_coe, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sin, AffineMap.deriv, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, Bornology.sUnion_isVonNBounded_eq_univ, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, ProbabilityTheory.covarianceBilinDual_of_not_memLp', PadicComplex.nnnorm_extends, PeriodPair.Οβ_mem_lattice, ContDiff.fderiv, SchwartzMap.fourier_convolution, Complex.log_inv_eq_integral, OnePoint.isZeroAt_iff, AnalyticOnNhd.eval_continuousLinearMap', UnitAddTorus.span_mFourierLp_closure_eq_top, fderivWithin_comp_smul, ZMod.LFunction_dft, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, MeasureTheory.Integrable.integral_norm_condKernel, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, instSMulCommClass_closedBall_closedBall_closedBall, Complex.nnnorm_eq_one_of_pow_eq_one, PeriodPair.analyticOnNhd_weierstrassP, ContinuousLinearMap.flipβα΅’_symm, HasFPowerSeriesAt.compContinuousLinearMap, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, ProbabilityTheory.integrable_gaussianPDFReal, Asymptotics.IsBigOTVS.refl, EuclideanSpace.nndist_single_same, expNegInvGlue.differentiable_polynomial_eval_inv_mul, Complex.differentiableAt_cos, cfcHom_eq_of_isStarNormal, exists_continuousLinearEquiv_fderivWithin_symm_eq, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, UpperHalfPlane.mdifferentiable_denom_zpow, HasGradientWithinAt.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, hasFDerivAt_exp, Orientation.volumeForm_comp_linearIsometryEquiv, Pi.orthonormalBasis_repr, RCLike.hasSum_conj', MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, Complex.frontier_setOf_im_le, differentiableAt_iff_comp_sub_const, Complex.range_exp_mul_I, LinearMap.polar_mem, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, NumberField.Units.basisOfIsMaxRank_fundSystem, MeromorphicOn.divisor_mul, LinearMap.isAdjointPair_inner, Circle.coe_div, ContinuousLinearMap.norm_holder_apply_apply_le, upperHemicontinuous_spectrum, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, Complex.isUniformEmbedding_equivRealProd, AnalyticOnNhd.eval_mvPolynomial, WithLp.unitization_nnnorm_def, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, Affine.Simplex.signedInfDist_apply_of_ne, tendsto_nhds_of_meromorphicOrderAt_nonneg, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, IsUltrametricDist.isPowMul_invariantExtension, Circle.coe_one, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, hasDerivWithinAt_iff_tendsto_slope, constFormalMultilinearSeries_apply_succ, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, FormalMultilinearSeries.continuousOn, hasFDerivAt_inv, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, Complex.hasSum_iff, Real.deriv_mul_log_zero, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, DoubleCentralizer.toProdHom_apply, HurwitzZeta.differentiable_completedHurwitzZetaEvenβ, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, ContinuousLinearMap.fpowerSeries_apply_one, HurwitzZeta.differentiable_completedHurwitzZetaOdd, summable_pow_mul_cexp, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, WeakFEPair.Ξ_residue_zero, IccRightChart_extend_top, ModularFormClass.hasSum_qExpansion, SchwartzMap.one_add_le_sup_seminorm_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Seminorm.continuous_iff_continuous_comp, constFormalMultilinearSeries_zero, Complex.isOpenMap_re, Asymptotics.IsBigO.isBigOTVS, HilbertBasis.hasSum_inner_mul_inner, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, ContDiffBump.convolution_tendsto_right_of_continuous, measurableSet_of_differentiableWithinAt_Ici, Complex.approx_Gamma_integral_tendsto_Gamma_integral, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, ContinuousMultilinearMap.curryFinFinset_apply, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, nndist_self_homothety, boundary_Icc, FormalMultilinearSeries.changeOriginSeriesTerm_bound, deriv_sqrt_mul_log', spectrum.subset_circle_of_unitary, summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, spectrum.subset_closedBall_norm, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, Real.differentiableAt_binEntropy_iff_ne_zero_one, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, UpperHalfPlane.continuous_coe, MeromorphicAt.frequently_zero_iff_eventuallyEq_zero, SchwartzMap.integrable_pow_mul_iteratedFDeriv, Complex.deriv_exp, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, Real.deriv_tan, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, ContinuousLinearMap.apply_apply, RCLike.span_one_I, PeriodPair.Οβ_mem_lattice, Asymptotics.isThetaTVS_iff_isTheta, DirichletCharacter.differentiable_LFunctionTrivCharβ, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, algebraMap_cobounded_le_cobounded, Real.exists_measure_rpow_eq_integral, summable_jacobiThetaβ'_term_iff, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, instSMulCommClass_sphere_sphere_ball, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, PiTensorProduct.mapLMultilinear_opNorm, AddCircle.norm_eq_of_zero, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, Convex.instPathConnectedSpace, hasFPowerSeriesAt_iff', RCLike.geometric_hahn_banach_closed_compact, ContDiff.continuous_iteratedDeriv', MeasureTheory.eLpNorm_conj, ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, hasDerivAt_exp_smul_const_of_mem_ball, ProbabilityTheory.integrable_comp_iff, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, DFinsupp.sum_inner, UpperHalfPlane.mdifferentiable_iff, meromorphicOrderAt_ne_top_iff_eventually_ne_zero, Real.fourierIntegral_iteratedFDeriv, Complex.isOpen_re_gt_EReal, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, WeakFEPair.Ξ_residue_k, integrable_cexp_neg_mul_sq, WithSeminorms.hasBasis_ball, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, Complex.analyticAt_iff_eventually_differentiableAt, differentiableAt_comp_sub_const, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, smooth_functions_tower, RCLike.ofReal_sum, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, UpperHalfPlane.isOpen_upperHalfPlaneSet, Set.Finite.isVonNBounded, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, UpperHalfPlane.isEmbedding_coe, HurwitzZeta.differentiable_completedSinZeta, HurwitzZeta.differentiable_hurwitzZetaEven_sub_hurwitzZetaEven, le_egauge_closedBall_one, InformationTheory.deriv_klFun, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, boundary_product, HasCompactSupport.convolution_integrand_bound_right, differentiable_sigmoid, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, Padic.isDenseInducing_cast_withVal, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, NormedField.exists_lt_nnnorm, Asymptotics.isBigOTVS_comm, GromovHausdorff.eq_toGHSpace_iff, OrthonormalBasis.repr_reindex, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, MeasureTheory.condExpL2_comp_continuousLinearMap, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, PeriodPair.derivWeierstrassPExcept_def, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.continuousAt_ofReal_cpow_const, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, AnalyticOnNhd.eval_continuousLinearMap, circleMap_mem_sphere', ProbabilityTheory.uncenteredCovarianceBilinDual_zero, Circle.argEquiv_apply_coe, MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, LSeries.hasDerivAt_term, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, UpperHalfPlane.mdifferentiableAt_ofComplex, ProbabilityTheory.integral_tilted_mul_self, LSeries_eq_mul_integral', integrableOn_Ioi_deriv_norm_ofReal_cpow, ContDiffMapSupportedIn.structureMapLM_apply, isBoundedLinearMap_prod_multilinear, integrable_of_le_of_pow_mul_le, nndist_homothety_self, Orthonormal.inner_sum, Summable.hasSumUniformlyOn_log_one_add, HasCompactSupport.convolution_integrand_bound_right_of_subset, HasStrictDerivAt_ofNat, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, ContinuousMap.idealOfSet_isMaximal_iff, LeftInvariantDerivation.coeFnAddMonoidHom_apply, Complex.det_conjLIE, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, hasDerivWithinAt_iff_tendsto, balancedHull_convexHull_subseteq_absConvexHull, WeakFEPair.differentiable_Ξβ, cyclotomicCharacter.continuous, RCLike.realLinearIsometryEquiv_apply, TemperedDistribution.laplacianCLM_apply, Unitary.spectrum_subset_circle, continuousAt_gaussian_integral, ProbabilityTheory.mgf_pos_iff, mem_contMDiffFiberwiseLinear_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, Orientation.areaForm_rightAngleRotation_left, coeFn_fourierLp, Differentiable.norm, RCLike.tendsto_ofReal_atTop_cobounded, differentiableAt_iff_comp_neg, DoubleCentralizer.coe_snd, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NumberField.mixedEmbedding.disjoint_negAt_plusPart, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, Matrix.IsHermitian.instContinuousFunctionalCalculus, MeasureTheory.integral_convolution, DifferentiableAt.dist, Complex.UnitDisc.coe_circle_smul, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, ZMod.stdAddChar_apply, DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivCharβ, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, DirichletCharacter.differentiable_completedLFunction, Complex.continuousAt_tan, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, PositiveLinearMap.preGNS_norm_sq, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, Icc_isBoundaryPoint_top, ConvexOn.slope_le_leftDeriv_of_mem_interior, HurwitzZeta.differentiableAt_expZeta, Submodule.starProjection_tendsto_closure_iSup, NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le, norm_iteratedFDeriv_fderiv, StrongDual.polar_nonempty, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, NumberField.house_eq_sup', RCLike.geometric_hahn_banach_open_open, MeasureTheory.integral_mul_const, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, Seminorm.smul_le_smul, HasMFDerivAt.const_smul, Complex.continuous_im, WeakDual.CharacterSpace.instStarHomClass, Int.Matrix.exists_ne_zero_int_vec_norm_le, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Circle.argPartialEquiv_apply, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulβα΅’, MeasureTheory.charFun_eq_integral_probChar, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', EulerProduct.exp_tsum_primes_log_eq_tsum, Real.integrableOn_rpowIntegrandββ_Ici, ModularGroup.smul_eq_lcRow0_add, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, PeriodPair.finrank_lattice, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, PeriodPair.derivWeierstrassP_add_coe, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Complex.orderClosedTopology, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', CStarMatrix.norm_def, ContinuousLinearMap.coe_derivβ, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, differentiableWithinAt_Ioi_iff_Ici, HurwitzZeta.differentiableAt_sinZeta, ModularForm.multipliableLocallyUniformlyOn_eta, contDiff_succ_iff_hasFDerivAt, dist_lineMap_lineMap, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, balanced_iff_neg_mem, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, Complex.isEquivalent_sin, NumberField.mixedEmbedding.convexBodyLT'_convex, differentiableOn_zpow, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, MeasureTheory.integrable_rnDeriv_mul_log_iff, TemperedDistribution.smulLeftCLM_apply_apply, integrableAtFilter_rpow_atTop_iff, summable_jacobiThetaβ_term_iff, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, nndist_lineMap_left, Complex.continuousOn_one_add_mul_inv, WithSeminorms.hasBasis_zero_ball, Orientation.inner_mul_areaForm_sub, fderiv_inner_apply, contDiff_one_iff_deriv, inner_matrix_col_col, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, ContMDiff.coordChangeL, deriv2_sqrt_mul_log, Real.hasStrictDerivAt_log_of_pos, contMDiffOn_projIcc, MeasureTheory.SignedMeasure.im_toComplexMeasure, differentiableAt_jacobiTheta, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, ContinuousLinearMap.orthogonal_ker, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ContDiffWithinAt.fderivWithin_right, Complex.rotation, MeasureTheory.pdf.hasFiniteIntegral_mul, AnalyticAt.hasStrictDerivAt, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, parallelepiped_single, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, SchwartzMap.norm_pow_mul_le_seminorm, contMDiff_circleExp, pi_mul_cot_pi_q_exp, contDiffWithinAt_succ_iff_hasFDerivWithinAt, Quaternion.nnnorm_coe, BoundedContinuousFunction.probCharDual_apply, PeriodPair.weierstrassPExcept_add, Real.deriv2_negMulLog, InnerProductSpace.norm_rankOne, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Urysohns.CU.lim_eq_midpoint, Complex.hasDerivAt_Gamma_nat, MeasureTheory.Measure.integrable_pow_neg_integrablePower, IsClosed.reProdIm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, PiTensorProduct.mapLMultilinear_toFun_apply, CStarMatrix.inner_toCLM_conjTranspose_right, norm_jacobiThetaβ_term_fderiv_le, HasFiniteFPowerSeriesOnBall.fderiv, Matrix.PosDef.re_dotProduct_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Summable.tendstoUniformlyOn_tsum_nat_log_one_add, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, quasispectrum.instCompactSpace, fderiv_eq_smul_deriv, integrableOn_rpow_mul_exp_neg_mul_rpow, CStarMatrix.toCLM_apply_single_apply, MeasureTheory.Measure.integrable_toReal_rnDeriv, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Real.isEquivalent_sinh, LinearMap.ker_toContinuousLinearMap, Int.Matrix.exists_ne_zero_int_vec_norm_le', intervalIntegral.differentiableOn_integral_of_continuous, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Complex.tendsto_exp_comap_re_atBot_nhdsNE, differentiable_circleMap, HurwitzZeta.tendsto_hurwitzZetaEven_sub_one_div_nhds_one, integrableOn_exp_mul_complex_Ioi, NormedSpace.exp_add, Complex.isClosed_range_intCast, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, WithSeminorms.finset_sups, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, hasDerivWithinAt_sub_const_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, HurwitzZeta.differentiable_completedCosZetaβ, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Complex.restrictScalars_toSpanSingleton', Real.differentiableAt_negMulLog_iff, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, fderiv_inv', ContinuousLinearMapWOT.ext_inner_iff, BoundedContinuousFunction.integrable_of_nnreal, Complex.differentiable_iteratedDeriv_cosh, Complex.closedEmbedding_intCast, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, HurwitzZeta.hurwitzZetaEven_residue_one, IsLocalMinOn.fderivWithin_eq_zero, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, Real.deriv2_mul_log, FormalMultilinearSeries.comp_assoc, HasFPowerSeriesWithinAt.comp, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, continuousAt_dslope_of_ne, Complex.closure_setOf_im_lt, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, Orientation.abs_volumeForm_apply_le, PeriodPair.differentiableOn_derivWeierstrassPExcept, continuousMultilinearCurryFin1_apply, Complex.conjLIE_symm, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding', deriv_id', hasStrictFDerivAt_euclidean, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, hasFDerivAt_finset_prod, fourierCoeff_fourier, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, Affine.Simplex.signedInfDist_incenter, HilbertBasis.finite_spans_dense, toMeromorphicNFOn_eqOn_codiscrete, ProbabilityTheory.integrable_rpow_mul_exp_of_mem_interior_integrableExpSet
|
| Name | Category | Theorems |
|---|
induced π | CompOp | β |
toMetricSpace π | CompOp | 70 mathmath: Filter.Tendsto.cfc, nnnorm_cfc_lt, norm_cfc_lt_iff, ContinuousAt.cfc, ContinuousLinearMap.isometry_mul_flip, norm_cfc_le_iff, Continuous.cfc', Continuous.cfc_nnreal', CFC.continuousOn_log, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, ContinuousOn.cfc, continuousOn_cfc_setProd, IsGreatest.norm_cfc, CStarAlgebra.toCompleteSpace, IsGreatest.nnnorm_cfc, continuousOn_cfc_nnreal, IsometricContinuousFunctionalCalculus.toNonUnital, Matrix.exp_sum_of_commute, Continuous.cfc_nnreal_of_mem_nhdsSet, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, LipschitzWith.coordinate, nnnorm_cfc_le_iff, GromovHausdorff.ghDist_eq_hausdorffDist, continuous_cfcHomSuperset_left, Continuous.cfc_of_mem_nhdsSet, KuratowskiEmbedding.embeddingOfSubset_isometry, ContinuousOn.cfc_nnreal, GromovHausdorff.eq_toGHSpace, nnnorm_cfc_nnreal_lt, nnnorm_cfc_nnreal_le, Continuous.cfc_nnreal, ContinuousOn.cfc_of_mem_nhdsSet, nnnorm_cfc_nnreal_le_iff, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, nnnorm_cfc_le, LipschitzOnWith.coordinate, nnnorm_apply_le_nnnorm_cfc, Continuous.cfc, CFC.nnnorm_rpow, apply_le_nnnorm_cfc_nnreal, norm_cfc_le, ContinuousOn.cfc', Filter.Tendsto.cfc_nnreal, nnnorm_cfc_lt_iff, NormedSpace.continuousOn_exp, norm_apply_le_norm_cfc, nnnorm_cfc_nnreal_lt_iff, norm_cfcHom, CFC.norm_rpow, Unitization.antilipschitzWith_addEquiv, MonotoneOn.nnnorm_cfc, dist_eq, gelfandTransform_isometry, continuousOn_cfc_nnreal_setProd, nnnorm_cfcHom, continuousOn_cfc, KuratowskiEmbedding.exists_isometric_embedding, Unitization.lipschitzWith_addEquiv, IsStarNormal.instIsometricContinuousFunctionalCalculus, NormedSpace.exp_sum_of_commute, ContinuousAt.cfc_nnreal, ContinuousWithinAt.cfc, ContinuousWithinAt.cfc_nnreal, CommCStarAlgebra.toCompleteSpace, CFC.continuousOn_rpow, GromovHausdorff.eq_toGHSpace_iff, norm_cfc_lt, Nonneg.instIsometricContinuousFunctionalCalculus, kuratowskiEmbedding.isometry
|
toNonUnitalNormedRing π | CompOp | 360 mathmath: nnnorm_inv, MeasureTheory.eLpNormEssSup_const_smul_le, NormedSpace.exp_continuous, hasSum_geometric_of_norm_lt_one, CStarRing.norm_unitary_smul, PowerSeries.IsRestricted.smul, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, inverse_one_sub_norm, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, MeasureTheory.eLpNormEssSup_const_smul, NormedSpace.exp_zsmul, hasStrictFDerivAt_list_prod_finRange', ContMDiffMap.coeFnAlgHom_apply, iteratedDerivWithin_const_mul_field, nnnorm_cfc_lt, Filter.Tendsto.exp, BoundedContinuousFunction.algebraMap_apply, geom_series_mul_shift, Matrix.cstar_nnnorm_def, egauge_prod_mk, hasSum_choose_mul_geometric_of_norm_lt_one, tsum_coe_mul_geometric_of_norm_lt_one', ordinaryHypergeometric_radius_top_of_neg_natβ, integrableOn_cfc', Unitary.mem_pathComponentOne_iff, analyticOnNhd_inverse, DoubleCentralizer.nnnorm_def', tendsto_smul_comp_nat_floor_of_tendsto_mul, deriv_mul_const_field, inverse_add_norm_diff_nth_order, tsum_choose_mul_geometric_of_norm_lt_one', hasSum_coe_mul_geometric_of_norm_lt_one', tsum_coe_mul_geometric_of_norm_lt_one, iteratedDeriv_div_const, differentiableWithinAt_inv, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, CFC.exp_log, NormedSpace.exp_series_hasSum_exp', egauge_add_add_le, MeasureTheory.integrable_const_mul_iff, gelfandStarTransform_naturality, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, tsum_geometric_of_norm_lt_one, DoubleCentralizer.nnnorm_snd, egauge_univ, Function.update_exp, formalMultilinearSeries_geometric_apply_norm_le, NormedSpace.map_exp, CommCStarAlgebra.toCStarRing, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, inverse_one_sub_nth_order, ordinaryHypergeometricSeries_radius_eq_one, Quaternion.instCStarRingReal, egauge_zero_zero, Unitization.nnnorm_def, NormedSpace.exp_hasFPowerSeriesOnBall, NormedSpace.expSeries_summable, BoundedContinuousFunction.coe_toContinuousMapStarβ, cfcL_integrable, IsGreatest.nnnorm_cfc_nnreal, Quaternion.linearIsometryEquivTuple_symm_apply, binomialSeries_radius_eq_one, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, hasStrictDerivAt_exp_smul_const, geom_series_succ, hasStrictDerivAt_exp_smul_const', egauge_univ_pi, nnnorm_div, uniqueDiffWithinAt_iff_accPt, tsum_geometric_le_of_norm_lt_one, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, summable_mul_of_summable_norm, hasFDerivAt_ringInverse, ContinuousLinearMap.instCStarRingId, differentiableWithinAt_pow, NormedSpace.norm_expSeries_summable, DoubleCentralizer.nnnorm_def, tsum_mul_tsum_of_summable_norm, nndist_inv_invβ, mul_neg_geom_series, deriv_const_mul_field', PadicInt.coe_addChar_of_value_at_one, infEDist_smulβ, NormedSpace.expSeries_hasSum_exp, WeakDual.CharacterSpace.homeoEval_naturality, norm_commutator_sub_one_le, Units.instIsManifoldModelWithCornersSelf, selfAdjoint.expUnitary_zero, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', analyticAt_smul, IsGreatest.nnnorm_cfc, egauge_le_one, ContinuousMap.isUnit_iff_forall_isUnit, selfAdjoint.nnnorm_pow_two_pow, MeasureTheory.Measure.hausdorffMeasure_smulβ, derivWithin_div_const, spectrum.gelfand_formula, le_egauge_smul_left, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, MeasureTheory.Integrable.toL1_smul, MeasureTheory.condExp_ofNat, NormedSpace.exp_continuousMap_eq, summable_norm_sum_mul_range_of_summable_norm, selfAdjoint.continuous_expUnitary, cfcHom_integral, egauge_pi, deriv_const_mul_field, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', Matrix.exp_nsmul, IsometricContinuousFunctionalCalculus.toNonUnital, AlgHom.instContinuousLinearMapClassOfAlgHomClass, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, SchwartzMap.integral_mul_laplacian_right_eq_left, Units.instLieGroupModelWithCornersSelf, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, NormedSpace.expSeries_summable', hasFDerivAt_exp_smul_const', Matrix.exp_sum_of_commute, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, hasFDerivWithinAt_pow', MeasureTheory.Lp.smul_zero, infEdist_smulβ, DoubleCentralizer.nnnorm_fst, MeasureTheory.Lp.norm_smul_le, hasFDerivAt_list_prod_finRange', summable_choose_mul_geometric_of_norm_lt_one, one_memβp_infty, ordinaryHypergeometric_radius_top_of_neg_natβ, Asymptotics.continuousAt_iff_isLittleO, AddChar.tendsto_eval_one_sub_pow, NormedSpace.expSeries_div_summable, summable_descFactorial_mul_geometric_of_norm_lt_one, differentiableOn_pow, tsum_choose_mul_geometric_of_norm_lt_one, hasDerivAt_exp_smul_const, NormedSpace.algebraMap_exp_comm, LinearIsometryEquiv.toSpanUnitSingleton_apply, derivWithin_mul_const_field, lp.infty_coeFn_pow, NormedSpace.expSeries_radius_eq_top, MeasureTheory.integrable_mul_const_iff, nnnorm_cfc_le_iff, MeasureTheory.eLpNorm_const_smul_le', NormedSpace.invOf_exp, algebraMap_memβp_infty, fderiv_pow_ring', inverse_one_sub, PowerSeries.IsRestricted.neg, WeakDual.CharacterSpace.compContinuousMap_apply, contDiff_smul_const, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, NormedSpace.exp_units_conj', binomialSeries_radius_eq_top_of_nat, spectrum.hasDerivAt_resolvent, MeasureTheory.Lp.add_smul, cfc_integral, MeasureTheory.Integrable.toL1_smul', inverse_add_norm_diff_second_order, nnnorm_cfc_nnreal_lt, Units.nnnorm_pos, le_egauge_smul_right, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, nnnorm_cfc_nnreal_le, IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, NormedSpace.exp_hasFPowerSeriesAt_zero, nnnorm_cfc_nnreal_le_iff, DoubleCentralizer.instCStarRing, NormedSpace.exp_nsmul, formalMultilinearSeries_geometric_apply_norm, hasSum_geom_series_inverse, formalMultilinearSeries_geometric_eq_ofScalars, hasSum_coe_mul_geometric_of_norm_lt_one, hasFDerivAt_exp_zero, MeasureTheory.eLpNorm_const_smul_le, hasSum_choose_mul_geometric_of_norm_lt_one', egauge_le_of_smul_mem, hasStrictFDerivAt_pow', CFC.log_pow', MeasureTheory.eLpNorm'_const_smul, MeasureTheory.Lp.coeFn_lpSMul, hasSum_sum_range_mul_of_summable_norm, hasFDerivAt_exp_smul_const, lp.infty_coeFn_one, hasStrictFDerivAt_list_prod_attach', nnnorm_cfc_le, hasFPowerSeriesOnBall_inv_one_sub, ContinuousLinearMap.instNonnegSpectrumClassRealId, hasFPowerSeriesOnBall_inverse_one_sub, hasStrictFDerivAt_ringInverse, integrable_cfc', Prod.fst_exp, nnnorm_apply_le_nnnorm_cfc, IsometricContinuousFunctionalCalculus.spectrum_le, MeasureTheory.eLpNorm_const_smul, geom_series_mul_one_add, differentiable_pow, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, differentiableOn_inverse, CFC.nnnorm_rpow, spectrum.differentiableOn_inverse_one_sub_smul, Matrix.exp_units_conj', lp.infty_coeFn_intCast, CStarAlgebra.toCStarRing, MeasureTheory.Lp.zero_smul, apply_le_nnnorm_cfc_nnreal, Unitization.instCStarRing, AlgHom.coe_toContinuousLinearMap, intCast_memβp_infty, hasFDerivAt_pow', MeasureTheory.Lp.smul_def, MeasureTheory.Lp.smul_neg, WeakDual.CharacterSpace.norm_le_norm_one, cfcL_integral, MemHolder.nnHolderNorm_smul, hasStrictFDerivAt_exp_zero, formalMultilinearSeries_geometric_radius, AccPt.uniqueDiffWithinAt, egauge_eq_zero_iff, Summable.mul_tendsto_const, analyticOn_inv, StarSubalgebra.to_cstarRing, BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, MeasureTheory.Lp.smul_comm, lp.infty_coeFn_natCast, ediam_smulβ, MeasureTheory.Lp.smul_add, contDiff_mul, spectrum.exp_mem_exp, differentiableWithinAt_inverse, NormedSpace.exp_neg, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, Unitization.nnnorm_eq_sup, NormedSpace.exp_smul, DilationEquiv.smulTorsor_ratio, contDiff_smul, nnnorm_commutator_sub_one_le, summable_geometric_iff_norm_lt_one, summable_pow_mul_geometric_of_norm_lt_one, BoundedContinuousFunction.coe_toContinuousMapβ, NormedSpace.expSeries_div_hasSum_exp, iteratedDeriv_mul_const_field, Units.val_oneSub, tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm, nnnorm_cfc_lt_iff, spectrum.spectralRadius_le_nnnorm, inverse_add_norm_diff_first_order, MeasureTheory.eLpNorm'_const_smul_le, CFC.log_pow, MeasureTheory.Lp.neg_smul, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, BoundedContinuousFunction.toContinuousMapβ_apply, NormedSpace.continuousOn_exp, Matrix.isUnit_exp, lp.instNormOneClassSubtypePreLpMemAddSubgroupTopENNRealOfNonempty, integrable_cfc, NormedSpace.expSeries_radius_pos, nnnorm_cfc_nnreal_lt_iff, analyticAt_mul, NormedSpace.algebraMap_exp_comm_of_mem_ball, analyticAt_inv, contDiffAt_ringInverse, geom_series_mul_neg, WeakDual.CharacterSpace.equivAlgHom_coe, spectrum.le_nnnorm_of_mem, ordinaryHypergeometric_radius_top_of_neg_natβ, Units.contMDiff_val, Matrix.instCStarRing, MeasureTheory.eLpNorm'_const_smul_le', Polynomial.cauchyBound_X_add_C, MeasureTheory.Lp.smul_assoc, MonotoneOn.nnnorm_cfc, analyticAt_inverse_one_sub, cfc_setIntegral', hasStrictFDerivAt_inv', analyticAt_inv_one_sub, iteratedDeriv_const_mul_field, hasStrictFDerivAt_exp_smul_const, hasDerivAt_exp_smul_const', WeakDual.CharacterSpace.compContinuousMap_comp, MeasureTheory.Lp.neg_smul_neg, summable_geometric_of_norm_lt_one, Polynomial.cauchyBound_X_sub_C, nnnorm_cfcHom, integrableOn_cfc, inverse_one_sub_nth_order', NormedSpace.exp_add_of_commute, WeakDual.CharacterSpace.equivAlgHom_symm_coe, hasStrictFDerivAt_list_prod', Prod.snd_exp, NormedSpace.isUnit_exp, PadicInt.continuousAddCharEquiv_apply, summable_norm_sum_mul_antidiagonal_of_summable_norm, CFC.log_exp, ContinuousLinearMap.opNorm_lsmul, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, inverse_add_nth_order, analyticOnNhd_inv, Quaternion.linearIsometryEquivTuple_apply, coe_algEquiv_lpBCF_symm, egauge_smul_right, NormedSpace.exp_analytic, differentiableAt_inv, NormedSpace.exp_sum_of_commute, hasFDerivAt_inv', Matrix.exp_units_conj, NormedSpace.exp_units_conj, tangentConeAt_eq_univ, WeakDual.CharacterSpace.compContinuousMap_id, differentiableAt_inverse, BoundedContinuousFunction.separatesPoints_charPoly, enorm_inv, nnnorm_zpow, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, eHolderNorm_smul, deriv_mul_const_field', WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, Ring.inverse_exp, one_le_nnnorm_one, unitary.mem_pathComponentOne_iff, derivWithin_const_mul_field, egauge_zero_right, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, analyticAt_inverse, toRingNorm_apply, coe_algEquiv_lpBCF, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, hasFDerivAt_list_prod_attach', iteratedDerivWithin_mul_const_field, geom_series_eq_inverse, binomialSeries_radius_ge_one, CFC.complex_exp_eq_normedSpace_exp, deriv_div_const, isUnit_one_sub_of_norm_lt_one, one_le_formalMultilinearSeries_geometric_radius, cfc_setIntegral, differentiableOn_inv, MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, Ideal.IsMaximal.closure_eq, egauge_le_of_smul_mem_of_ne, tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm, SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left, egauge_pi', Pi.exp_def, cfc_integral', Polynomial.IsRoot.norm_lt_cauchyBound, selfAdjoint.expUnitary_coe, intervalIntegral.integral_const_mul, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, MeasureTheory.eLpNormEssSup_const_smul_le', IsSelfAdjoint.nnnorm_pow_two_pow, Unitization.nnnorm_inr, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, fderiv_inv', natCast_memβp_infty, egauge_smul_left, Pi.coe_exp
|
toNorm π | CompOp | 157 mathmath: CStarRing.norm_mul_coe_unitary, CStarRing.norm_unitary_smul, inverse_one_sub_norm, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, spectrum.norm_le_norm_of_mem, PositiveLinearMap.apply_le_of_isSelfAdjoint, spectrum.subset_closedBall_norm_mul, LinearMap.polar_eq_iInter, norm_cfc_lt_iff, EisensteinSeries.summand_bound_of_mem_verticalStrip, inverse_add_norm_diff_nth_order, NumberField.mixedEmbedding.norm_le_convexBodySumFun, selfAdjoint.norm_sq_expUnitary_sub_one, CStarAlgebra.norm_or_neg_norm_mem_spectrum, EisensteinSeries.abs_le_right_of_norm, CStarAlgebra.mem_Icc_iff_norm_le_one, norm_cfc_le_iff, CStarAlgebra.norm_le_natCast_iff_of_nonneg, CStarRing.norm_of_mem_unitary, LinearMap.polar_singleton, formalMultilinearSeries_geometric_apply_norm_le, Asymptotics.isLittleO_const_mul_right_iff, DoubleCentralizer.norm_def', CStarMatrix.norm_def', RingHomIsometric.starRingEnd, spectrum.norm_le_norm_mul_of_mem, DoubleCentralizer.norm_def, Valued.integer.exists_norm_lt_one, Unitary.norm_sub_one_lt_two_iff, toRingNorm_toFun, NormedSpace.norm_expSeries_summable, IsGreatest.norm_cfc, IsSelfAdjoint.neg_algebraMap_norm_le_self, Valued.integer.norm_irreducible_lt_one, unitary.norm_sub_eq, NormedSpace.norm_expSeries_summable_of_mem_ball', AlgHom.norm_apply_le_self, Matrix.l2_opNorm_diagonal, NormMulClass.isAbsoluteValue_norm, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, Finset.norm_prod_one_add_sub_one_le, CStarRing.instNormOneClassOfNontrivial, NormedSpace.norm_expSeries_summable_of_mem_ball, Unitary.norm_sub_one_sq_eq, EisensteinSeries.norm_eq_max_natAbs, Matrix.permMatrix_l2_opNorm_le, PowerSeries.IsRestricted.isRestricted_iff, DoubleCentralizer.norm_snd, Asymptotics.isBigOWith_self_const_mul, Valued.integer.norm_le_one, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Asymptotics.continuousAt_iff_isLittleO, Unitization.norm_eq_sup, IsSelfAdjoint.norm_pow_two_pow, IsSelfAdjoint.toReal_spectralRadius_complex_eq_norm, Polynomial.exists_forall_norm_le, Asymptotics.isBigO_const_mul_right_iff, CStarRing.norm_mul_mem_unitary, unitary.two_mul_one_sub_le_norm_sub_one_sq, EisensteinSeries.summable_one_div_norm_rpow, Int.toNat_add_toNat_neg_eq_norm, inverse_add_norm, Int.instNormMulClass, inverse_add_norm_diff_second_order, Asymptotics.isBigO_const_mul_left_iff, EisensteinSeries.isBigO_linear_add_const_vec, WithAbs.norm_eq_abv, CauSeq.tendsto_limit, Valued.integer.coe_span_singleton_eq_closedBall, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, NormedSpace.norm_expSeries_summable', Unitization.norm_def, Finset.norm_prod_le', EisensteinSeries.r_mul_max_le, AddChar.norm_apply, EisensteinSeries.norm_symm, CStarAlgebra.mul_star_le_algebraMap_norm_sq, LinearMap.mem_polar_singleton, Asymptotics.isLittleO_const_mul_left_iff, spectrum.coe_le_norm_of_mem, CStarAlgebra.norm_le_iff_le_algebraMap, one_le_norm_one, Valued.integer.norm_unit, CStarAlgebra.star_mul_le_algebraMap_norm_sq, IsometricContinuousFunctionalCalculus.norm_spectrum_le, EulerProduct.norm_tsum_factoredNumbers_sub_tsum_lt, NumberField.canonicalEmbedding.norm_le_iff, Unitary.two_mul_one_sub_le_norm_sub_one_sq, WeakDual.CharacterSpace.norm_le_norm_one, norm_cfc_le, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, ContinuousMap.comp_attachBound_mem_closure, isLittleO_coe_const_pow_of_one_lt, IsOfFinOrder.norm_eq_one, Unitary.norm_sub_eq, DoubleCentralizer.norm_fst, Unitization.instNormOneClass, inverse_add_norm_diff_first_order, Asymptotics.isBigO_self_const_mul, Matrix.l2_opNorm_le_one_of_mem_doublyStochastic, EisensteinSeries.abs_le_left_of_norm, Irreducible.maximalIdeal_eq_closedBall, EisensteinSeries.abs_norm_eq_max_natAbs, Valued.integer.isUnit_iff_norm_eq_one, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, PositiveLinearMap.norm_apply_le_of_nonneg, norm_apply_le_norm_cfc, IsSelfAdjoint.toReal_spectralRadius_eq_norm, Int.norm_coe_units, ContinuousMap.polynomial_comp_attachBound, EisensteinSeries.abs_norm_eq_max_natAbs_neg, norm_cfcHom, CFC.norm_rpow, CStarRing.norm_coe_unitary_mul, CStarAlgebra.norm_le_one_iff_of_nonneg, unitary.norm_sub_one_lt_two_iff, CStarRing.norm_mem_unitary_mul, dist_eq, NumberField.InfinitePlace.map_intCast, Units.norm_pos, RCLike.instNormSMulClassInt, Irreducible.maximalIdeal_pow_eq_closedBall_pow, lp.norm_const_smul_le, ContinuousMap.polynomial_comp_attachBound_mem, unitary.norm_sub_one_sq_eq, CStarAlgebra.norm_mem_spectrum_of_nonneg, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, Matrix.cstar_norm_def, isLittleO_pow_const_const_pow_of_one_lt, LinearMap.polar_mem_iff, spectrum.resolvent_isBigO_inv, Finset.norm_prod_le, CStarAlgebra.exists_sum_four_unitary, IsSelfAdjoint.le_algebraMap_norm_self, Int.instNormOneClass, LinearMap.polar_mem, CStarRing.norm_one, spectrum.subset_closedBall_norm, EisensteinSeries.vec_add_const_isTheta, EisensteinSeries.summand_bound, toRingNorm_apply, CStarRing.norm_coe_unitary, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, le_iff_norm_sqrt_mul_rpow, EulerProduct.norm_tsum_smoothNumbers_sub_tsum_lt, Int.Matrix.exists_ne_zero_int_vec_norm_le, Unitization.norm_inr, norm_cfc_lt, EisensteinSeries.div_max_sq_ge_one, Valued.integer.norm_irreducible_pos, Int.Matrix.exists_ne_zero_int_vec_norm_le', norm_mul_le, le_iff_norm_sqrt_mul_sqrt_inv, Matrix.permMatrix_l2_opNorm_eq, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, AlgHom.norm_apply_le_self_mul_norm_one
|
toRing π | CompOp | 1977 mathmath: AnalyticWithinAt.const_smul, Unitary.openPartialHomeomorph_source, Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, instSeparatingDual, hasFDerivAt_iff_hasDerivAt, absorbent_iff_eventually_nhdsNE_zero, TensorProduct.mapInclIsometry_apply, ContinuousMap.toLp_inj, CStarRing.norm_mul_coe_unitary, HasSum.exp, closure_diff_intrinsicFrontier, Submodule.starProjection_apply_eq_isComplProjection, fderiv_iteratedFDeriv, MeasureTheory.LpToLpRestrictCLM_coeFn, MeasureTheory.eLpNormEssSup_const_smul_le, NormedSpace.exp_continuous, SchwartzMap.lineDerivOpCLM_eq, HasStrictFDerivAt.fun_mul', AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, RCLike.one_re, HasMFDerivAt.mul, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, AffineIsometry.image_intrinsicClosure, Submodule.IsCompl.projection_isSymmetricProjection_iff, MeasureTheory.Lp.instIsScalarTower, hasSum_geometric_of_norm_lt_one, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, MDifferentiableOn.clm_postcomp, OrthonormalBasis.orthogonalProjection_eq_sum, ContinuousLinearMap.compSL_apply, LinearMap.IsSymmetric.inner_map_polarization, IsStarNormal.spectralRadius_eq_nnnorm, MeasureTheory.Integrable.bdd_mul', CStarRing.norm_unitary_smul, AnalyticOnNhd.smul, Affine.Simplex.orthogonalProjectionSpan_map, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, PowerSeries.IsRestricted.smul, PadicInt.lift_sub_val_mem_span, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, inverse_one_sub_norm, hasFDerivAt_iff_hasGradientAt, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, norm_zsmul, PadicInt.norm_int_lt_one_iff_dvd, smooth_barycentric_coord, AnalyticOn.aeval_polynomial, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, NormedSpace.exp_zsmul, dist_midpoint_right, IntervalIntegrable.smul_continuousOn, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1, PadicInt.norm_intCast_eq_padic_norm, derivWithin_smul, MeasureTheory.MemLp.const_mul, Submodule.orthogonalDecomposition_symm_apply, hasStrictFDerivAt_list_prod_finRange', InnerProductSpace.rankOne_one_left_eq_innerSL, Subalgebra.spectrum_sUnion_connectedComponentIn, ContMDiffMap.coeFnAlgHom_apply, AffineIsometryEquiv.coe_symm_toAffineEquiv, AlgHomClass.instStarHomClass, ContinuousAffineMap.fderiv, iteratedDerivWithin_const_mul_field, HasFiniteFPowerSeriesAt.neg, PadicInt.valuation_p, HasFDerivWithinAt.pow, WeakDual.isCompact_polar, nnnorm_cfc_lt, EuclideanSpace.orthonormal_single, MeasureTheory.IntegrableOn.continuousOn_smul, meromorphicOrderAt_const_ofNat, fderivWithin_fun_smul, ContinuousAffineMap.differentiableWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, Matrix.IsHermitian.det_abs, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, hasFDerivAt_multiset_prod, ContDiffOn.smul_const, Filter.Tendsto.exp, PadicInt.isCauSeq_nthHom, MDifferentiableAt.cle_arrowCongr, Absorbs.eventually_nhds_zero, BoundedContinuousFunction.algebraMap_apply, Submodule.toLinearEquiv_orthogonalDecomposition_symm, spectrum.subset_closedBall_norm_mul, derivWithin_id', spectrum.instCompactSpace, geom_series_mul_shift, hasFTaylorSeriesUpToOn_top_iff_right, DifferentiableAt.mul, MeasureTheory.Lp.const_smul_mem_Lp, MeasureTheory.MemLp.smul, Matrix.spectrum_toEuclideanLin, MeasureTheory.lpNorm_fun_div_natCast, MeasureTheory.norm_condExpL2_le, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, Padic.withValUniformEquiv_norm_le_one_iff, hasSum_choose_mul_geometric_of_norm_lt_one, derivWithin_mul_const, MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport, Matrix.IsHermitian.cfc_eq, tsum_coe_mul_geometric_of_norm_lt_one', Rat.padicValuation_cast, StrongDual.polarSubmodule_eq_setOf, HasStrictDerivAt.pow, Function.HasTemperateGrowth.fun_pow, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, Filter.inv_nhdsWithin_ne_zero, ContinuousLinearMap.hasDerivAtFilter, DoubleCentralizer.intCast_snd, HasDerivAtFilter.comp_hasFDerivAtFilter, Submodule.re_inner_starProjection_eq_normSq, ordinaryHypergeometric_radius_top_of_neg_natβ, inner_self_eq_one_of_norm_eq_one, tendsto_zpow_nhdsNE_zero_cobounded, ContinuousMap.toLp_denseRange, AffineIsometryEquiv.linear_eq_linear_isometry, WeakDual.isClosed_image_polar_of_mem_nhds, PadicComplex.valuation_extends, ContinuousLinearMap.integral_apply, Unitary.mem_pathComponentOne_iff, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_toLinearEquiv, LinearMap.IsSymmetric.diagonalization_apply_self_apply, EuclideanGeometry.orthogonalProjection_congr, ContinuousAlternatingMap.instIsUniformAddGroup, PadicInt.appr_spec, norm_iteratedFDeriv_mul_le, fderivWithin_fun_pow', Matrix.le_iff, Submodule.starProjection_orthogonal', analyticOnNhd_inverse, Units.nhds, Submodule.toLinearEquiv_orthogonalDecomposition, Asymptotics.IsBigOWith.pow, PadicComplex.coe_eq, RCLike.sub_conj, HasFPowerSeriesWithinAt.const_smul, SchwartzMap.lineDerivOp_fourier_eq, isClosedEmbedding_cfcβAux, PadicInt.norm_intCast_lt_one_iff, AddChar.wInner_cWeight_self, innerSL_apply_apply, fderiv_multiset_prod, Orthonormal.codRestrict, EuclideanSpace.basisFun_toBasis, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, hasDerivAt_neg', ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, HasFDerivAtFilter.sub, ContMDiffOn.clm_postcomp, ContinuousLinearMap.toBilinForm_apply, MeasureTheory.MemLp.integrable_mul, HasFDerivAt.fun_mul, dist_left_midpoint, ContinuousMap.range_toLp, deriv_mul_const_field, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Differentiable.fun_smul, selfAdjoint.expUnitaryPathToOne_apply, inverse_add_norm_diff_nth_order, Unitary.continuousOn_argSelfAdjoint, deriv_fun_pow', MDifferentiableWithinAt.mul, PadicSeq.ne_zero_iff_nequiv_zero, FormalMultilinearSeries.derivSeries_coeff_one, Matrix.spectrum_toLpLin, StarAlgebra.elemental.characterSpaceToSpectrum_coe, PadicInt.sub_zmodRepr_mem, AnalyticAt.fun_const_smul, tsum_choose_mul_geometric_of_norm_lt_one', OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, ContDiff.pow, SchwartzMap.bilinLeftCLM_apply, HasDerivAt.comp_hasFDerivAt_of_eq, InnerProductSpace.toDual_symm_apply, OrthogonalFamily.of_pairwise, deriv_mul_const, iteratedDeriv_pow, hasSum_coe_mul_geometric_of_norm_lt_one', AffineMap.hasDerivWithinAt, RCLike.conj_nat_cast, LeftInvariantDerivation.left_invariant, isUltrametricDist_iff_forall_norm_natCast_le_one, EuclideanSpace.basisFun_apply, tsum_coe_mul_geometric_of_norm_lt_one, HasFPowerSeriesAt.neg, EuclideanGeometry.orthogonalProjection_contLinear, ContinuousAffineMap.differentiable, MeasureTheory.charFun_toDual_symm_eq_charFunDual, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, MeasureTheory.IntegrableOn.smul_continuousOn, PadicInt.norm_p_pow, Filter.map_mul_left_cobounded, Differentiable.fderiv_norm_rpow, curveIntegrable_fun_neg_iff, CStarAlgebra.mem_Icc_iff_norm_le_one, MeasureTheory.Integrable.mul_prod, Asymptotics.IsLittleO.mul, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, analyticAt_iff_analytic_mul, NormedSpace.exp_series_hasSum_exp', PadicComplex.norm_def, DifferentiableOn.fun_mul, HasStrictFDerivAt.mul', EuclideanGeometry.reflection_map, fderiv_fun_pow, AffineEquiv.continuous_of_finiteDimensional, HasFDerivAtFilter.const_sub, ContDiffWithinAt.fun_smul, iteratedFDerivWithin_succ_eq_comp_left, summable_norm_mul_geometric_of_norm_lt_one, contDiffOn_iff_continuousOn_differentiableOn, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, nndist_midpoint_right, HasStrictFDerivAt.pow, iter_deriv_zpow', derivWithin_fun_mul, Matrix.exp_conj', HasStrictFDerivAt.const_mul, MeasureTheory.L1.integral_smul, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, DifferentiableOn.smul_const, InnerProductSpace.inner_left_rankOne_apply, HasFDerivAt.finset_prod, ContinuousLinearMap.smul_compLp, Matrix.exp_neg, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, CircleIntegrable.const_smul, OrthonormalBasis.repr_self, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, fderiv_fun_pow', PadicComplex.coe_natCast, ContinuousLinearMap.topologicalAddGroup, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, PadicInt.irreducible_p, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, summable_sum_mul_range_of_summable_norm', Filter.map_mul_right_cobounded, Filter.inv_nhdsNE_zero, NormedSpace.Dual.toWeakDual_continuous, MeasureTheory.Lp.compMeasurePreservingβ_apply, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, HasFDerivWithinAt.const_mul, ContinuousMap.toLp_norm_le, ContinuousMultilinearMap.norm_smulRightL_le, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, tsum_geometric_of_norm_lt_one, ContinuousLinearMap.precompL_apply, PowerSeries.IsRestricted.add, CStarAlgebra.mem_Icc_iff_nnnorm_le_one, curveIntegral_neg, HasFDerivAt.sub, FormalMultilinearSeries.radius_le_smul, MDifferentiable.clm_postcomp, Function.update_exp, tendsto_norm_inv_nhdsNE_zero_atTop, formalMultilinearSeries_geometric_apply_norm_le, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, fderivWithin_const_sub, Absorbs.eventually_nhdsNE_zero, spectrum.isOpen_resolventSet, Affine.Simplex.orthogonalProjectionSpan_eq_point, NormedSpace.map_exp, HasFDerivAtFilter.neg, nndist_right_lineMap, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, FormalMultilinearSeries.radius_compNeg, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, Padic.exi_rat_seq_conv_cauchy, IntervalIntegrable.mul_continuousOn, inverse_one_sub_nth_order, ordinaryHypergeometricSeries_radius_eq_one, Matrix.toEuclideanLin_apply, iteratedDerivWithin_eq_iteratedFDerivWithin, HasFDerivWithinAt.mul, VectorFourier.fourierPowSMulRight_eq_comp, RCLike.intCast_re, EuclideanGeometry.orthogonalProjection_map, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, DifferentiableOn.mul, Asymptotics.IsLittleO.pow, Rat.padicValuation_self, AnalyticOn.pow, Asymptotics.isLittleO_const_mul_right_iff, MDifferentiable.cle_arrowCongr, PadicInt.maximalIdeal_eq_span_p, CFC.continuousOn_log, nndist_left_lineMap, HasFDerivAt.fun_smul, NormedSpace.exp_hasFPowerSeriesOnBall, fderivWithin_fun_neg, ContinuousLinearMap.flipMultilinear_apply_apply, NormedSpace.expSeries_summable, PadicInt.norm_lt_one_iff_dvd, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, MeromorphicOn.divisor_natCast, Submodule.coe_orthogonalDecomposition_symm, PadicInt.mul_inv, BoundedContinuousFunction.coe_toContinuousMapStarβ, RCLike.I_mul_I, iteratedDerivWithin_mul_const, MeasureTheory.Integrable.smul_bdd, fderiv_neg, Asymptotics.IsBigO.listProd, EuclideanGeometry.angle_orthogonalProjection_self, binomialSeries_radius_eq_one, MeasureTheory.LocallyIntegrableOn.continuousOn_mul, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, Pi.counit_eq_adjoint, HasDerivAt.comp_hasFDerivWithinAt, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, deriv_fun_mul, VectorFourier.fourierIntegral_continuousLinearMap_apply, ContinuousAffineMap.norm_def, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, ContDiffOn.pow, AffineSubspace.coe_subtypeβα΅’, MeasureTheory.Integrable.const_mul, MeasureTheory.HasFiniteIntegral.mul_const, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, iteratedDeriv_smul_const, Asymptotics.IsLittleO.tendsto_div_nhds_zero, HasStrictFDerivAt.list_prod', SchwartzMap.fourier_lineDerivOp_eq, DifferentiableAt.smul, hasStrictDerivAt_exp_smul_const, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, MeasureTheory.Integrable.essSup_smul, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, fderiv_fun_sub, multipliable_one_add_of_summable, Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, geom_series_succ, Asymptotics.isLittleO_pow_pow, PadicInt.exists_mem_range, hasStrictDerivAt_exp_smul_const', iteratedDeriv_const_mul, MDifferentiableAt.mul, LinearIsometry.toAffineIsometry_toAffineMap, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, EulerProduct.eulerProduct_completely_multiplicative, tsum_geometric_le_of_norm_lt_one, PadicInt.exists_mem_range_of_norm_rat_le_one, HasMFDerivAt.neg, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, derivWithin_zpow, UnitAddTorus.mFourierCoeff_toLp, WeakDual.toStrongDual_inj, ContinuousLinearMap.mulLeftRight_apply, MDifferentiableAt.pow, Differentiable.pow, hasDerivAt_id', Matrix.IsHermitian.eigenvectorUnitary_mulVec, deriv_fun_smul, AffineIsometryEquiv.pointReflection_toAffineEquiv, Padic.zero_def, FDerivMeasurableAux.norm_sub_le_of_mem_A, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, MDifferentiableAt.clm_postcomp, coe_innerSL_apply, fderivWithin_finset_prod, HasFDerivWithinAt.const_sub, HasDerivAt.pow, summable_mul_of_summable_norm, LinearEquiv.toSpanNonzeroSingleton_homothety, PadicInt.inv_mul, multipliable_norm_one_add_of_summable_norm, range_cfcβHom, Unitary.openPartialHomeomorph_symm_apply, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow, NormedDivisionRing.toNormMulClass, ContinuousLinearMap.hasDerivAt, PadicInt.fwdDiff_tendsto_zero, Module.Basis.coe_toOrthonormalBasis_repr, hasFDerivAt_ringInverse, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, Filter.inv_coboundedβ, MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc, HasMFDerivWithinAt.neg, DifferentiableWithinAt.mul, dist_left_midpoint_eq_dist_right_midpoint, InnerProductSpace.nnnorm_rankOne, fderiv_smul, spectrum.gelfandTransform_eq, OrthonormalBasis.orthogonalProjection_apply_eq_sum, HasDerivAt.fun_pow, AffineMap.differentiableWithinAt, AffineIsometryEquiv.toContinuousAffineEquiv_symm, MeasureTheory.Integrable.mul_of_top_right, logDeriv_fun_pow, ContinuousMap.spectrum_eq_preimage_range, Submodule.IsCompl.closedComplemented_of_isClosed, InnerProductSpace.isSymmetricProjection_rankOne_self, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, DifferentiableWithinAt.const_mul, differentiableWithinAt_pow, hasMFDerivAt_neg, toRingNorm_toFun, Matrix.IsHermitian.charpoly_cfc_eq, NormedSpace.norm_expSeries_summable, DifferentiableWithinAt.fun_pow, hasGradientWithinAt_iff_hasFDerivWithinAt, spectrum.isCompact, tsum_mul_tsum_of_summable_norm, LinearMap.hasStrictDerivAt, AffineMap.hasDerivAt_lineMap, iteratedFDerivWithin_neg_apply, ContDiffAt.pow, NormedSpace.smul_mem_polar, Polynomial.cauchyBound_smul, EuclideanGeometry.orthogonalProjection_apply', Polynomial.isClosedMap_eval, PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, AffineMap.hasDerivWithinAt_lineMap, ContinuousLinearMap.fderiv_of_bilinear, RCLike.ofReal_natCast, Matrix.PosSemidef.posSemidef_sqrt, continuousOn_cfc_setProd, fderiv_mul_const', spectrum.spectralRadius_lt_of_forall_lt, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, deriv_id'', OrthonormalBasis.coe_ofRepr, ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, Submodule.adjoint_subtypeL, hasStrictFDerivAt_exp, NormedSpace.exp_conj, ContinuousLinearMap.norm_smulRightL, mul_neg_geom_series, deriv_const_mul_field', unitSphereToUnits_apply_coe, Function.FactorizedRational.mulSupport, HasFDerivWithinAt.fun_smul, PadicInt.mahlerSeries_apply_nat, Matrix.LE.le.posSemidef, Affine.Triangle.dist_circumcenter_reflection_orthocenter, InnerProductSpace.trace_rankOne, MDifferentiableWithinAt.cle_arrowCongr, MDifferentiableWithinAt.clm_precomp, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, HasFDerivWithinAt.neg, AffineIsometry.toContinuousAffineMap_id, AnalyticAt.smul, Filter.tendsto_invβ_cobounded, hasFDerivAt_norm_rpow, ContinuousLinearMap.compL_apply, PowerSeries.IsRestricted.mul, tendsto_intCast_atBot_sup_atTop_cobounded, ZSpan.repr_ceil_apply, Asymptotics.isEquivalent_nat_ceil, iteratedDeriv_fun_id_zero, unitary.norm_sub_eq, DoubleCentralizer.neg_snd, ContinuousAlternatingMap.instIsTopologicalAddGroup, IsIntegral.ratCast_iff, dist_lineMap_left, NormedSpace.expSeries_hasSum_exp, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, Submodule.IsCompl.projection_isSymmetricProjection_of_isOrtho, norm_commutator_sub_one_le, contDiffOn_stereoToFun, Asymptotics.IsBigO.eventually_mul_div_cancel, absorbs_iff_eventually_nhdsNE_zero, Units.instIsManifoldModelWithCornersSelf, ContinuousLinearMap.isUniformAddGroup, LeftInvariantDerivation.evalAt_coe, selfAdjoint.expUnitary_zero, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, deriv_pow, Matrix.posDef_gram_of_linearIndependent, ContMDiffOn.clm_precomp, BoundedContinuousFunction.toLp_inj, contDiffOn_nat_iff_continuousOn_differentiableOn, HilbertBasis.hasSum_orthogonalProjection, padicNormE.defn, InnerProductSpace.adjoint_rankOne, analyticAt_smul, fderiv_pow, InnerProductSpace.rankOne_eq_zero, BoundedContinuousFunction.toLp_injective, Convex.toWeakSpace_closure, Unitary.instLocPathConnectedSpace, hasDerivAtFilter_neg, ContinuousMap.isUnit_iff_forall_isUnit, tsum_pow_div_one_sub_eq_tsum_sigma, AffineIsometry.linear_eq_linearIsometry, InnerProductSpace.inner_right_rankOne_apply, ContDiff.differentiable_iteratedFDeriv, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, HasFDerivAt.pow, spectrum.eventually_isUnit_resolvent, meromorphicOrderAt_const_natCast, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, fderivWithin_inv', AffineIsometryEquiv.vaddConst_toAffineEquiv, hasDerivWithinAt_pow, Asymptotics.isLittleO_pow_id, Ideal.IsMaximal.isClosed, PadicInt.norm_ascPochhammer_le, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, AffineSubspace.isometryEquivMap.toAffineMap_eq, MeasureTheory.Lp.compMeasurePreservingβα΅’_apply_coe, AffineSubspace.signedInfDist_eq_signedDist_of_mem, LinearMap.IsSymmetric.coe_toSelfAdjoint, MeromorphicOn.divisor_intCast, unitSphereToUnits_injective, spectrum.gelfand_formula, Matrix.piLp_ofLp_toEuclideanLin, iteratedFDerivWithin_smul_const_apply, cfcβAux_id, LinearMap.IsSymmetric.diagonalization_symm_apply, MeasureTheory.Integrable.bdd_mul, NormedSpace.inclusionInDoubleDual_norm_le, mfderiv_sub, WeakDual.isCompact_closedBall, Affine.Simplex.signedInfDist_apply_self, Real.fourier_mul_convolution_eq, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, MeasureTheory.Integrable.toL1_smul, isClosedMap_pow, LinearMap.norm_mkContinuousβ_aux, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, ContinuousLinearMap.derivWithin, MeasureTheory.condExp_ofNat, ContinuousLinearMap.precompR_apply, AffineIsometry.image_intrinsicInterior, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, dist_right_midpoint, NormedSpace.exp_continuousMap_eq, HasFDerivWithinAt.mul_const, iteratedDerivWithin_smul_const, MeasureTheory.hasFDerivAt_convolution_right_with_param, fderiv_pow', MeasureTheory.Lp.coeFn_smul, fderiv_mul, FormalMultilinearSeries.coeff_ofScalars, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, summable_norm_sum_mul_range_of_summable_norm, Matrix.l2_opNNNorm_mulVec, AffineIsometryEquiv.toContinuousAffineEquiv_refl, HasCompactSupport.hasFDerivAt_convolution_right, Submodule.norm_orthogonalProjection_apply_le, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, instPolynormableSpaceSubtypeMemSubmodule, LinearMap.deriv, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, InnerProductSpace.toDualMap_apply, continuousOn_cfc_nnreal, selfAdjoint.continuous_expUnitary, TensorProduct.inner_mapIncl_mapIncl, ContinuousMultilinearMap.instIsUniformAddGroup, Asymptotics.IsBigOWith.pow', nonunits.isClosed, hasDerivAtFilter_id, Differentiable.fun_pow, hasDerivAt_update, iteratedDeriv_fun_id, OrthonormalBasis.singleton_apply, spectrum.map_pow, RCLike.sqrt_one, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, fderiv_pow_ring, LinearMap.IsSymmetric.restrict_invariant, AnalyticAt.fun_smul, hasFTaylorSeriesUpToOn_top_iff', Padic.comap_mulValuation_eq_padicValuation, FormalMultilinearSeries.radius_smul_eq, AffineIsometryEquiv.ofEq_symm, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, deriv_const_mul_field, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', LinearIsometry.extend_apply, Matrix.exp_nsmul, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, Module.Basis.coe_toOrthonormalBasis_repr_symm, NormMulClass.isAbsoluteValue_norm, HasFDerivWithinAt.fun_sub, InnerProductSpace.toDual_apply_apply, IsSelfAdjoint.log, ContinuousLinearMap.adjointAux_apply, fderivWithin_fun_sub, hasSum_sum_range_mul_of_summable_norm', ContinuousAffineMap.norm_contLinear_le, fderivWithin_fun_mul', ProperCone.innerDual_singleton, RCLike.add_conj, EuclideanGeometry.reflection_eq_self_iff, HasFPowerSeriesWithinOnBall.sub, analyticAt_iff_analytic_fun_mul, CFC.exp_eq_normedSpace_exp, RCLike.im_eq_conj_sub, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure, hasFDerivAt_list_prod', hasFDerivAt_integral_of_dominated_loc_of_lip', Submodule.toLinearMap_starProjection_eq_isComplProjection, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, InnerProductSpace.rankOne_def, EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, SchwartzMap.integral_mul_laplacian_right_eq_left, Finset.norm_prod_one_add_sub_one_le, ContDiffWithinAt.mul, stereoToFun_apply, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.lpNorm_fun_mul_natCast, fderivWithin_fderivWithin_eq_of_mem_nhds, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, contDiff_iff_continuous_differentiable, PadicSeq.norm_neg, iteratedDerivWithin_comp_three, AffineIsometry.coe_toAffineMap, fderiv_mul', Bornology.IsVonNBounded.tendsto_smallSets_nhds, iter_deriv_zpow, ContinuousMap.toLp_def, Units.instLieGroupModelWithCornersSelf, Summable.hasProdUniformlyOn_nat_one_add, ClosedSubmodule.orthogonal_eq_inter, hasFDerivWithinAt_iff_hasDerivWithinAt, IsSelfAdjoint.cfc_arg, nndist_left_midpoint, hasFTaylorSeriesUpToOn_succ_iff_right, CStarRing.instNormOneClassOfNontrivial, ContinuousLinearMap.coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, AffineIsometryEquiv.dist_pointReflection_self, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, ContinuousAffineMap.hasStrictFDerivAt, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', MeasureTheory.MemLp.const_smul, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, LinearMap.IsSymmetric.toSelfAdjoint_apply, MeasureTheory.IntegrableOn.continuousOn_mul_of_subset, MeasureTheory.Lp.constβ_apply, Submodule.coe_continuous_linearProjOfClosedCompl, EuclideanGeometry.orthogonalProjection_subtype, DifferentiableAt.const_mul, iteratedFDeriv_neg_apply, Submodule.coe_orthogonalDecomposition, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, fderivWithin_fderivWithin_eq_of_eventuallyEq, EulerProduct.eulerProduct_completely_multiplicative_tprod, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2, StrongDual.polarSubmodule_eq_polar, summable_prod_mul_pow, dist_right_pointReflection, Matrix.nonneg_iff_posSemidef, iteratedDeriv_mul, DifferentiableWithinAt.fun_mul, ContDiffWithinAt.smul, hasFDerivAt_exp_smul_const', Matrix.exp_zsmul, Submodule.norm_subtypeL, AffineSubspace.closed_of_finiteDimensional, Matrix.posDef_gram_iff_linearIndependent, SchwartzMap.smulLeftCLM_const, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, AffineSubspace.toContinuousAffineMap_subtypeβα΅’, Matrix.permMatrix_l2_opNorm_le, PointwiseConvergenceCLM.equivWeakDual_symm_apply, PadicAlgCl.instUniformContinuousConstSMulPadic, PadicSeq.norm_nonarchimedean, AffineMap.hasDerivAt, Submodule.norm_sq_eq_add_norm_sq_projection, ContinuousAffineMap.contDiff, Asymptotics.IsBigOWith.eventually_mul_div_cancel, iteratedDerivWithin_zpow, HasFDerivWithinAt.fun_neg, Asymptotics.IsBigO.mul, ContinuousLinearMap.norm_precompR_le, dist_lineMap_right, hasFDerivWithinAt_pow', MeasureTheory.lpNorm_fun_natCast_mul, AffineMap.differentiableAt, PowerSeries.IsRestricted.isRestricted_iff, NormedDivisionRing.to_normOneClass, MeasureTheory.Lp.smul_zero, RCLike.sqrt_eq_real_add_ite, PadicInt.norm_int_le_pow_iff_dvd, WeakDual.isSeqCompact_closedBall, PiTensorProduct.liftEquiv_apply, AnalyticWithinAt.aeval_polynomial, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, PadicInt.denseRange_natCast, WeakDual.exists_countable_separating, PadicAlgCl.valuation_p, hasFDerivAtFilter_iff_hasDerivAtFilter, PadicComplex.valuation_p, innerSLFlip_apply_apply, AffineMap.lipschitzWith_of_finiteDimensional, Affine.Triangle.dist_orthocenter_reflection_circumcenter, isOpen_setOf_affineIndependent, finrank_euclideanSpace, StarSubalgebra.spectrum_eq, Summable.summable_log_norm_one_add, EuclideanGeometry.oangle_orthogonalProjection_self, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, PadicSeq.not_equiv_zero_const_of_nonzero, Submodule.fst_orthogonalDecomposition_apply, AnalyticOn.const_smul, Matrix.IsHermitian.posSemidef_of_eigenvalues_nonneg, RCLike.one_im, nndist_midpoint_left, RCLike.toZeroLEOneClass, RCLike.natCast_re, fderivWithin_mul_const', summable_powerSeries_of_norm_lt_one, Asymptotics.isBigOWith_self_const_mul, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, InnerProductSpace.enorm_rankOne, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousLinearMap.toLinearMap_innerSL_apply, HasFPowerSeriesAt.hasStrictDerivAt, Submodule.orthogonalFamily_self, AnalyticOn.smul, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Polynomial.cyclotomic.isCoprime_rat, hasFDerivAt_list_prod_finRange', MeasureTheory.LocallyIntegrableOn.mul_continuousOn, summable_mul_of_summable_norm', Asymptotics.isLittleO_iff_tendsto', HasStrictFDerivAt.neg, HasGradientAt.hasFDerivAt, PadicComplex.isNonarchimedean, LinearMap.hasDerivWithinAt, summable_choose_mul_geometric_of_norm_lt_one, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, Real.fourier_fderiv, Submodule.inner_orthogonalProjection_eq_of_mem_right, ContinuousMap.adjoin_id_eq_span_one_union, MeasureTheory.MemLp.mul, hasFTaylorSeriesUpTo_succ_nat_iff_right, HasFDerivWithinAt.norm_sq, ordinaryHypergeometric_radius_top_of_neg_natβ, HasFPowerSeriesOnBall.neg, Asymptotics.continuousAt_iff_isLittleO, Matrix.isStrictlyPositive_iff_posDef, ZSpan.coe_floor_self, HasFDerivWithinAt.smul_const, Orthonormal.linearIsometryEquiv_symm_apply_single_one, nndist_midpoint_midpoint_le', MeasureTheory.LocallyIntegrableOn.smul_continuousOn, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, dist_homothety_self, CFC.log_monotoneOn, Affine.Simplex.orthogonalProjection_circumcenter, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Matrix.ofLp_toEuclideanCLM, hasFTaylorSeriesUpToOn_succ_nat_iff_right, summable_pow_div_add, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, Absorbent.eventually_nhdsNE_zero, NormedSpace.expSeries_div_summable, mahler_natCast_eq, PadicInt.coe_adicCompletionIntegersEquiv_apply, summable_descFactorial_mul_geometric_of_norm_lt_one, differentiableOn_pow, tsum_choose_mul_geometric_of_norm_lt_one, HasFPowerSeriesWithinAt.sub, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', hasDerivAt_exp_smul_const, NormedSpace.algebraMap_exp_comm, Asymptotics.IsBigOWith.exists_eq_mul, fourierCoeff_toLp, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, DifferentiableAt.fun_pow, IntervalIntegrable.mul_const, LinearIsometryEquiv.toSpanUnitSingleton_apply, CFC.monotone_rpow, derivWithin_mul_const_field, AddChar.wInner_cWeight_eq_one_iff_eq, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, iteratedDerivWithin_one_div, fderivWithin_fun_pow, Polynomial.exists_forall_norm_le, iteratedFDerivWithin_two_apply', PadicInt.mahlerTerm_one, curveIntegral_fun_neg, Matrix.instFiniteElemRealSpectrum, HasStrictFDerivAt.to_implicitFunction, CFC.rpow_neg_one_eq_cfc_inv, HasFDerivAt.multiset_prod, dist_self_homothety, Differentiable.mul_const, HasFDerivAt.mul_const, NormedSpace.expSeries_radius_eq_top, differentiableWithinAt_euclidean, unitary.spectrum_subset_circle, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, iteratedDerivWithin_fun_id, DoubleCentralizer.neg_toProd, LinearPMap.adjointDomainMkCLM_apply, Asymptotics.isBigO_const_mul_right_iff, Matrix.isPositive_toEuclideanLin_iff, MeasureTheory.Integrable.bdd_smul, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, inverse_add, RCLike.re_eq_add_conj, PiTensorProduct.dualSeminorms_bounded, NormedSpace.exp_sum, CommCStarAlgebra.toStarModule, FormalMultilinearSeries.radius_neg, HasFDerivWithinAt.mul_const', HasDerivAt.comp_hasFDerivWithinAt_of_eq, spectrum.isClosed, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, fderiv_const_mul, nonunits.subset_compl_ball, Summable.multipliableLocallyUniformlyOn_one_add, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, PadicInt.zmodRepr_spec, WeakDual.polar_def, NormedSpace.invOf_exp, iteratedFDerivWithin_succ_apply_left, hasStrictFDerivAt_norm_sq, MeasureTheory.IntegrableOn.mul_continuousOn_of_subset, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, fderiv_pow_ring', derivWithin_pow_field, Summable.multipliableLocallyUniformlyOn_nat_one_add, NormedSpace.exp_conj', Function.HasTemperateGrowth.pow, iteratedDeriv_comp_neg, logDeriv_id, inverse_one_sub, HasFDerivAtFilter.fun_sub, spectrum.isBounded, inverse_add_norm, MeasureTheory.MemLp.const_mul', PadicInt.norm_natCast_zmodRepr_eq_one_iff, Matrix.posDef_iff_eq_conjTranspose_mul_self, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, hasDerivAt_id, contDiff_smul_const, HasFTaylorSeriesUpToOn.fderivWithin, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, deriv_update, orthonormal_subtype_iff_ite, Summable.hasProdLocallyUniformlyOn_one_add, ContDiff.smul_const, nndist_lineMap_right, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, Summable.multipliableUniformlyOn_one_add, Asymptotics.IsBigO.const_mul_right, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, Asymptotics.isBigOWith_iff_exists_eq_mul, PadicInt.nthHomSeq_mul, NormedSpace.exp_units_conj', norm_fderiv_iteratedFDeriv, curveIntegralFun_neg, binomialSeries_radius_eq_top_of_nat, MeasureTheory.Lp.norm_constL_le, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, Filter.tendsto_invβ_nhdsWithin_ne_zero, HasStrictFDerivAt.const_sub, Submodule.coe_inner, fderiv_sub, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, ContMDiffAt.clm_precomp, MeasureTheory.Lp.add_smul, deriv_smul, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', MeasureTheory.Integrable.smul_of_top_left, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, AffineIsometry.norm_map, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, MeasureTheory.Integrable.mul_bdd, BoundedContinuousFunction.coeFn_toLp, spectrum.nonempty, AnalyticAt.aeval_polynomial, MeasureTheory.Integrable.toL1_smul', AffineSubspace.isometryEquivMap.coe_apply, Padic.mk_eq, deriv_neg'', Submodule.sndL_comp_coe_orthogonalDecomposition, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, inverse_add_norm_diff_second_order, PadicInt.limNthHom_spec, nnnorm_cfc_nnreal_lt, RCLike.ofReal_alg, derivWithin_fun_smul, HasFDerivAt.fun_pow', Unitary.openPartialHomeomorph_target, SchwartzMap.smulLeftCLM_add, Units.nnnorm_pos, HasMFDerivWithinAt.mul', CFC.rpow_le_rpow, norm_fderivWithin_iteratedFDerivWithin, HasFDerivWithinAt.hasDerivWithinAt, ContinuousMultilinearMap.integral_apply, HasFiniteFPowerSeriesOnBall.neg, DifferentiableWithinAt.smul_const, ContinuousLinearMap.le_def, WeakDual.isClosed_closedBall, AffineMap.derivWithin, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, nnnorm_cfc_nnreal_le, Asymptotics.isBigO_const_mul_left_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, RCLike.sqrt_neg_one, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, HasFDerivAt.smul_const, InnerProductSpace.rankOne_def', EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, NormedSpace.exp_hasFPowerSeriesAt_zero, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, fderiv_apply_one_eq_deriv, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, AnalyticAt.fun_mul, HasFPowerSeriesOnBall.sub, Submodule.norm_orthogonalProjection_apply, meromorphicTrailingCoeffAt_id_sub_const, PadicComplex.instIsScalarTowerPadicPadicAlgCl, Function.HasTemperateGrowth.fun_mul, DifferentiableAt.mul_const, NormedDivisionRing.to_continuousInvβ, HasStrictFDerivAt.fun_sub, CauSeq.tendsto_limit, Matrix.IsHermitian.spectrum_eq_image_range, logDeriv_id', HasFDerivAt.const_mul, RCLike.isCauSeq_im, StrongDual.toLpβ_apply, MeasureTheory.L1.setToL1_apply_coeToLp, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, NormedSpace.exp_nsmul, PadicInt.fwdDiff_iter_le_of_forall_le, DoubleCentralizer.sub_toProd, MeasureTheory.Integrable.mul_of_top_left, Valued.integer.coe_span_singleton_eq_closedBall, hasSum_geom_series_inverse, PadicInt.mem_span_pow_iff_le_valuation, HasFTaylorSeriesUpToOn.add, NormedSpace.norm_expSeries_summable', formalMultilinearSeries_geometric_eq_ofScalars, Matrix.posSemidef_gram, fderivWithin_multiset_prod, HasFDerivAt.mul, MDifferentiable.mul, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, hasSum_coe_mul_geometric_of_norm_lt_one, Metric.unitSphere.coe_inv, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, MeasureTheory.Integrable.const_mul', toWeakSpace_closedConvexHull_eq, Submodule.det_reflection, deriv_neg', fderivWithin_neg, MeasureTheory.eLpNorm_const_smul_le, Submodule.inner_orthogonalProjection_eq_of_mem_left, Units.isOpen, hasSum_choose_mul_geometric_of_norm_lt_one', CurveIntegrable.fun_neg, AffineSubspace.subtypeβα΅’_linear, hasStrictFDerivAt_pow', MeasureTheory.Integrable.mul_const', CauSeq.cauchySeq, Asymptotics.IsBigO.mul_isLittleO, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, DifferentiableWithinAt.pow, AddChar.norm_apply, MDifferentiableAt.clm_precomp, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, LinearPMap.isSelfAdjoint_def, PadicInt.norm_intCast_eq_one_iff, summable_norm_pow_mul_geometric_div_one_sub, CStarAlgebra.mul_star_le_algebraMap_norm_sq, CFC.log_zero, hasGradientAt_iff_hasFDerivAt, Asymptotics.isEquivalent_nat_floor, NormedDivisionRing.unitClosedBall_eq_univ_of_discrete, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, curveIntegrable_neg_iff, fderiv_fun_mul', AnalyticOnNhd.mul, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, HilbertBasis.repr_symm_single, Matrix.exp_conj, mdifferentiableOn_continuousLinearMapCoordChange, fderiv_deriv, MeasureTheory.Lp.coeFn_lpSMul, AnalyticWithinAt.pow, PadicInt.isUnit_den, upperHemicontinuous_spectrum_nnreal, continuous_barycentric_coord, PadicSeq.not_limZero_const_of_nonzero, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, InnerProductSpace.isStarProjection_rankOne_self, RCLike.norm_natCast, Rat.padicValuation_eq_zero_iff, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, PadicInt.norm_le_pow_iff_mem_span_pow, MeasureTheory.IntegrableOn.continuousOn_mul, WeakDual.isClosed_polar, spec_cfcβAux, iteratedDerivWithin_pow, hasSum_sum_range_mul_of_summable_norm, hasFDerivAt_exp_smul_const, FormalMultilinearSeries.zero_radius, PadicInt.zmodRepr_natCast, RCLike.ofReal_intCast, fderiv_finset_prod, Metric.unitSphere.coe_zpow, hasStrictFDerivAt_list_prod_attach', PadicInt.valuation_one, deriv_single, PadicInt.norm_natCast_zmodRepr_eq, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, DoubleCentralizer.sub_fst, nnnorm_cfc_le, MeasureTheory.Lp.instIsCentralScalar, isCauSeq_iff_cauchySeq, Submodule.starProjection_orthogonal, hasFPowerSeriesOnBall_inv_one_sub, Asymptotics.isLittleO_const_mul_left_iff, hasFPowerSeriesOnBall_inverse_one_sub, Submodule.ClosedComplemented.of_finiteDimensional, ContinuousAffineMap.hasFDerivAtFilter, hasStrictFDerivAt_ringInverse, PadicInt.ker_toZModPow, ContDiff.smul, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, DifferentiableOn.fun_pow, InnerProductSpace.rankOne_comp_rankOne, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, one_le_norm_one, parallelogram_law, AnalyticAt.hasFPowerSeriesAt, Prod.fst_exp, ContinuousMap.toLp_injective, Asymptotics.IsTheta.listProd, Matrix.toEuclideanLin_eq_toLin, LinearMap.mkContinuous_norm_le', StrongDual.toLpβ_of_not_memLp, fderiv_smul_const, Matrix.isHermitian_iff_isSymmetric, ContinuousAffineMap.hasFDerivAt, Asymptotics.Filter.Tendsto.isBigOTVS_one, Polynomial.cyclotomic_eq_minpoly_rat, hasStrictFDerivAt_finset_prod, fderiv_fun_neg, Valued.integer.norm_unit, Matrix.finite_real_spectrum, deriv_zpow, InnerProductSpace.rankOne_comp, HasDerivWithinAt.comp_hasFDerivAt, inner_eq_neg_one_iff_of_norm_eq_one, ContinuousAffineMap.norm_image_zero_le, StrongDual.mem_polarSubmodule, DifferentiableWithinAt.fun_smul, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, CircleIntegrable.const_fun_smul, SchwartzMap.tsupport_smulLeftCLM_subset, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, HasMFDerivAt.sub, InnerProductSpace.toMatrix_rankOne, differentiableAt_euclidean, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, geom_series_mul_one_add, iteratedFDeriv_smul_const_apply, dist_pointReflection_right, Asymptotics.isLittleO_iff_exists_eq_mul, EuclideanGeometry.orthogonalProjection_mem, AnalyticAt.fun_pow, MeasureTheory.Lp.instIsBoundedSMul, InnerProductSpace.isSymmetric_rankOne_self, ContinuousMap.coe_toLp, inner_eq_one_iff_of_norm_eq_one, fderiv_const_sub, HasFPowerSeriesAt.deriv, differentiable_pow, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, ContDiffAt.smul_const, PadicAlgCl.valuation_def, AnalyticAt.exists_eq_sum_add_pow_mul, ContinuousMap.canLift, ContinuousLinearMap.intervalIntegral_apply, Differentiable.const_mul, iteratedDerivWithin_mul, HasFDerivWithinAt.sub, HasFDerivAtFilter.fun_neg, SchwartzMap.smulLeftCLM_neg, differentiableOn_inverse, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, HasFPowerSeriesAt.const_smul, MeasureTheory.MemLp.mul_const, curveIntegralFun_sub, RCLike.ofReal_one, logDeriv_inv, Matrix.exp_units_conj', ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, MeasureTheory.Lp.simpleFunc.isBoundedSMul, differentiableOn_euclidean, fderiv_continuousLinearEquiv_comp, ContinuousLinearMap.adjoint_toSpanSingleton, IsStarNormal.instContinuousFunctionalCalculus, ContinuousLinearMap.toBilinForm_injective, DifferentiableAt.fun_smul, PadicInt.instNormOneClass, RCLike.natCast_im, tsum_prod_pow_eq_tsum_sigma, PadicAlgCl.valuation_coe, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, CStarAlgebra.star_mul_le_algebraMap_norm_sq, MeasureTheory.Lp.zero_smul, PadicComplex.coe_zero, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, MeasureTheory.Integrable.smul_essSup, tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm', AlgHom.coe_toContinuousLinearMap, Matrix.posSemidef_iff_eq_sum_vecMulVec, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, Matrix.ofLp_toEuclideanLin_apply, ContinuousAffineMap.fderivWithin, SchwartzMap.integralCLM_apply, MeasureTheory.lpNorm_one, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, RCLike.norm_two, HasStrictFDerivAt.hasStrictDerivAt, ContinuousMap.spectrum_eq_range, AnalyticAt.const_smul, innerSLFlip_apply, LinearMap.mkContinuous_norm_le, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, fderivWithin_derivWithin, RCLike.sqrt_neg_I, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', AnalyticWithinAt.fun_pow, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, HasFDerivAt.fun_neg, DifferentiableOn.smul, contDiff_nat_iff_continuous_differentiable, hasFDerivAt_pow', MeasureTheory.Lp.simpleFunc.coe_smul, SchwartzMap.lineDerivOp_fourierInv_eq, Asymptotics.IsBigO.exists_eq_mul, MeasureTheory.Lp.smul_def, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, iteratedDeriv_comp_const_sub, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, MeasureTheory.Lp.smul_neg, OrthonormalBasis.repr_symm_single, WeakDual.CharacterSpace.norm_le_norm_one, StarSubalgebra.mem_spectrum_iff, ContinuousMap.coeFn_toLp, innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, AffineIsometryEquiv.toAffineEquiv_injective, MemHolder.nnHolderNorm_smul, Unitary.isPathConnected_ball, iter_deriv_inv, MeasureTheory.Integrable.integral_smul, hasStrictFDerivAt_exp_zero, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, RCLike.sqrt_I, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, HasFPowerSeriesAt.sub, IntervalIntegrable.continuousOn_mul, MeasureTheory.Lp.instSMulCommClass, HasStrictFDerivAt.fun_neg, hasDerivWithinAt_zpow, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, NormedField.v_eq_valuation, RCLike.nnnorm_two, MeasureTheory.L1.SimpleFunc.integral_smul, DifferentiableOn.pow, iteratedDerivWithin_smul, ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, HasDerivWithinAt.fun_pow, MeasureTheory.charFun_eq_charFunDual_toDualMap, AffineIsometry.toContinuousAffineMap_injective, egauge_eq_zero_iff, Summable.mul_tendsto_const, HasMFDerivAt.prod, iteratedDeriv_eq_iteratedFDeriv, norm_cfc_le, EuclideanGeometry.orthogonalProjection_orthogonalProjection, iter_deriv_inv', WeakDual.CharacterSpace.mem_spectrum_iff_exists, analyticOn_inv, ContinuousMap.toLp_comp_toContinuousMap, StarSubalgebra.to_cstarRing, AnalyticOnNhd.fun_pow, ContMDiff.clm_postcomp, MeasureTheory.lpNorm_div_natCast, BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MeasureTheory.Lp.smul_comm, dist_left_lineMap, MDifferentiableWithinAt.clm_postcomp, cosetToCuspOrbit_apply_mk, MeasureTheory.AEEqFun.Integrable.smul, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, ContDiffOn.smul, deriv_smul_const, deriv_pow_field, ZSpan.repr_fract_apply, HasFPowerSeriesAt.hasDerivAt, MeasureTheory.MemLp.mul', ordinaryHypergeometricSeries_eq_zero_iff, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, MeasureTheory.Lp.smul_add, contDiff_mul, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, PadicInt.norm_sub_modPart, Polynomial.X_pow_sub_X_sub_one_irreducible_rat, PadicInt.norm_p, OrthonormalBasis.span_apply, isLittleO_coe_const_pow_of_one_lt, Padic.withValUniformEquiv_cast_apply, HasFDerivAt.hasDerivAt, PadicInt.valuation_p_pow_mul, NormedSpace.exp_neg, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, Matrix.IsHermitian.cfcAux_id, cfcβAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, Padic.coe_withValRingEquiv, HasFPowerSeriesWithinOnBall.neg, Asymptotics.isBigO_iff_exists_eq_mul, PadicInt.fwdDiff_mahlerSeries, deriv_id, MeasureTheory.Lp.constL_apply, SchwartzMap.fderivCLM_fourier_eq, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, EuclideanGeometry.Sphere.orthRadius_map, NormedSpace.exp_smul, AffineSubspace.subtypeβα΅’_linearIsometry, PadicInt.zmodRepr_natCast_zmodRepr, MDifferentiableOn.clm_precomp, PadicInt.pow_p_dvd_int_iff, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, Asymptotics.isEquivalent_iff_tendsto_one, hasDerivAt_neg, LinearMap.derivWithin, hasFTaylorSeriesUpToOn_succ_iff_left, Padic.isUniformInducing_cast_withVal, deriv_const_mul, Unitary.norm_sub_eq, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, contDiff_smul, derivWithin_fun_pow, EuclideanGeometry.Sphere.IsTangent.isTangentAt, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, Polynomial.cyclotomic.irreducible_rat, HasMFDerivWithinAt.mul, HilbertBasis.repr_self, nnnorm_commutator_sub_one_le, PowerSeries.IsRestricted.one, fderivWithin_sub, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, Asymptotics.IsLittleO.listProd, summable_pow_mul_geometric_of_norm_lt_one, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapβ, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, HasFDerivAt.const_sub, PadicInt.p_nonunit, PadicInt.limNthHom_one, BoundedContinuousFunction.toLp_norm_le, iteratedFDerivWithin_two_apply, NormedSpace.expSeries_div_hasSum_exp, Pretrivialization.continuousOn_continuousLinearMapCoordChange, HasStrictFDerivAt.fun_smul, iteratedDeriv_mul_const_field, fderiv_fun_mul, curveIntegral_fun_sub, PadicComplex.norm_extends, Submodule.adjoint_orthogonalProjection, HasFDerivAt.pow', IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime, Units.val_oneSub, HasStrictFDerivAt.pow', EuclideanGeometry.reflection_apply', ContDiffWithinAt.smul_const, hasFDerivWithinAt_iff_hasGradientWithinAt, AffineIsometryEquiv.ofEq_rfl, ContinuousAffineMap.differentiableOn, ContinuousLinearMap.hasFDerivAt_of_bilinear, Unitization.instNormOneClass, EuclideanGeometry.oangle_self_orthogonalProjection, ContinuousAffineMap.norm_comp_le, tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm, Filter.tendsto_mul_left_cobounded, HasStrictFDerivAt.multiset_prod, Matrix.toEuclideanLin_apply_piLp_toLp, PadicSeq.add_eq_max_of_ne, hasFDerivAt_integral_of_dominated_of_fderiv_le, IntervalIntegrable.continuousOn_smul, LinearIsometry.strictConvexSpace_range_iff, HasFDerivWithinAt.smul, Affine.Simplex.altitude_map, StarSubalgebra.coe_isUnit, spectrum.spectralRadius_le_nnnorm, hasDerivAt_pow, inverse_add_norm_diff_first_order, MeasureTheory.Lp.simpleFunc.toLp_smul, PadicInt.norm_sub_zmodRepr_lt_one, spectrum.isCompact_nnreal, Asymptotics.isBigO_self_const_mul, MeasureTheory.Integrable.mul_const, PadicInt.mahlerEquiv_apply, AffineIsometry.toAffineMap_injective, AffineIsometryEquiv.toAffineEquiv_refl, tsum_mul_tsum_of_summable_norm', hasStrictDerivAt_exp, HasStrictFDerivAt.mul_const', nndist_lineMap_lineMap, HasDerivWithinAt.pow, MeasureTheory.eLpNorm'_const_smul_le, MeasureTheory.Lp.neg_smul, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, AffineMap.differentiableOn, differentiableAt_pow, ContDiffWithinAt.pow, iteratedDeriv_comp_three, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, ContDiffAt.fun_smul, HasFPowerSeriesWithinAt.neg, PadicInt.isCauSeq_padicNorm_of_pow_dvd_sub, selfAdjoint.val_re_map_spectrum, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, fderivWithin_list_prod', logDeriv_fun_zpow, Asymptotics.IsLittleO.const_mul_right, OrthonormalBasis.inner_eq_one, Unitization.complex_cfcβ_eq_cfc_inr, orthogonalFamily_iff_pairwise, iteratedDerivWithin_id, Padic.coe_withValRingEquiv_symm, HasFiniteFPowerSeriesAt.sub, HasFDerivWithinAt.fun_mul', ContinuousLinearMap.norm_compSL_le, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, BoundedContinuousFunction.toContinuousMapβ_apply, fderivWithin_smul_const, AnalyticOn.fun_const_smul, NormMulClass.toNoZeroDivisors, NormedSpace.continuousOn_exp, Affine.Simplex.orthogonalProjectionSpan_reindex, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, Valued.integer.isUnit_iff_norm_eq_one, hasStrictFDerivAt_list_prod, Metric.unitSphere.coe_div, spectrum.resolvent_tendsto_cobounded, Summable.hasProdLocallyUniformlyOn_nat_one_add, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Matrix.isUnit_exp, fderivWithin_continuousLinearEquiv_comp, StrongDual.toLp_apply, ContinuousLinearMap.IsPositive.spectrumRestricts, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, MeasureTheory.Lp.coe_LpSubmodule, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, LinearIsometry.strictConvexSpace_range, ContinuousLinearMap.opNorm_neg, fderivWithin_pow_ring', inverse_continuousAt, Submodule.fstL_comp_coe_orthogonalDecomposition, iter_deriv_inv_linear_sub, DifferentiableOn.const_mul, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, EuclideanGeometry.orthogonalProjection_linear, MeasureTheory.lpNorm_natCast_mul, DoubleCentralizer.natCast_toProd, OrthonormalBasis.sum_rankOne_eq_id, LeftInvariantDerivation.evalAt_mul, absorbs_iff_eventually_nhds_zero, AffineSubspace.signedInfDist_def, MeasureTheory.HasFiniteIntegral.const_mul, iteratedDeriv_id, PadicInt.nthHomSeq_add, MeasureTheory.BoundedContinuousFunction.inner_toLp, PadicComplex.rankOne_hom_eq, exists_extension_norm_eq, spectrum.instCompactSpaceNNReal, HasFDerivWithinAt.fun_pow', IntervalIntegrable.integral_smul, summable_sum_mul_antidiagonal_of_summable_norm', ContinuousLinearMap.norm_smulRightL_le, derivWithin_neg, NormedSpace.expSeries_radius_pos, SchwartzMap.tsupport_derivCLM_subset, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, PowerSeries.IsRestricted.monomial, hasDerivAt_single, Function.HasTemperateGrowth.mul, WeakDual.Complex.instStarHomClass, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, MDifferentiableOn.mul, orthonormal_iff_ite, analyticAt_mul, fderivWithin_mul_const, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, summable_norm_geometric_of_norm_lt_one, ContinuousAffineMap.hasFDerivWithinAt, inner_self_eq_one_of_norm_one, HasFDerivAt.mul_const', norm_cfcHom, DifferentiableOn.mul_const, isOpenMap_barycentric_coord, Affine.Simplex.signedInfDist_affineCombination, contDiffAt_ringInverse, signedDist_apply, geom_series_mul_neg, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', EuclideanGeometry.angle_self_orthogonalProjection, Valued.toNormedField.setOf_mem_integer_eq_closedBall, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, spectrum.exists_nnnorm_eq_spectralRadius, HasFDerivAt.hasGradientAt, ordinaryHypergeometric_radius_top_of_neg_natβ, Units.contMDiff_val, CStarRing.norm_coe_unitary_mul, AnalyticOnNhd.aeval_polynomial, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, Differentiable.fun_mul, continuous_descPochhammer_eval, NormedSpace.norm_expSeries_div_summable, EuclideanGeometry.orthogonalProjection_eq_self_iff, DifferentiableAt.smul_const, Padic.norm_rat_le_one_iff_padicValuation_le_one, PadicInt.norm_natCast_eq_one_iff, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, MeasureTheory.Lp.smul_assoc, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, EuclideanGeometry.reflection_subtype, DoubleCentralizer.sub_snd, analyticAt_inverse_one_sub, norm_iteratedFDerivWithin_mul_le, ContinuousLinearEquiv.coord_norm', deriv_fun_pow, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, HasFPowerSeriesAt.eq_zero_of_eventually, Rat.surjective_padicValuation, Asymptotics.IsLittleO.eventually_mul_div_cancel, hasStrictFDerivAt_inv', MeasureTheory.Integrable.smul_prod, AffineIsometryEquiv.coe_vaddConst', SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, SchwartzMap.smulLeftCLM_apply_apply, deriv_descPochhammer_eval_eq_sum_prod_range_erase, Module.Basis.ofZLatticeBasis_repr_apply, analyticAt_inv_one_sub, derivWithin_id, Differentiable.mul, dist_eq, iteratedDerivWithin_const_mul, iteratedDeriv_const_mul_field, dist_midpoint_midpoint_le', iteratedDeriv_fun_pow_zero, SchwartzMap.fourier_fderivCLM_eq, hasStrictFDerivAt_exp_smul_const, AnalyticAt.mul, Units.norm_pos, derivWithin_mul, iteratedFDeriv_two_apply, AffineSubspace.isometryEquivMap.apply_symm_apply, ContDiffAt.smul, HasStrictFDerivAt.mul, iter_deriv_inv_linear, AffineMap.differentiable, Summable.hasProdUniformlyOn_one_add, WeakDual.toStrongDual_apply, AffineEquiv.coe_toHomeomorphOfFiniteDimensional, PadicInt.nthHomSeq_one, MDifferentiable.clm_precomp, PadicInt.ideal_eq_span_pow_p, hasDerivAt_exp_smul_const', dist_right_lineMap, WeakDual.CharacterSpace.compContinuousMap_comp, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, RCLike.nnnorm_natCast, MeasureTheory.Lp.neg_smul_neg, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, ContinuousLinearMap.smul_compLpL, AddChar.wInner_cWeight_eq_boole, summable_geometric_of_norm_lt_one, unitary.isPathConnected_ball, continuousOn_cfc_nnreal_setProd, NormedAlgebra.Complex.nonempty_algEquiv, PadicSeq.norm_const, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, NormedCommRing.mul_comm, ContinuousLinearMap.opNorm_mulLeftRight_le, Polynomial.cauchyBound_X_sub_C, DoubleCentralizer.intCast_fst, meromorphicOrderAt_const_intCast, PadicSeq.norm_one, Memβp.const_mul, nnnorm_cfcHom, CFC.log_one, ContMDiffWithinAt.clm_precomp, inverse_one_sub_nth_order', WeakDual.CharacterSpace.equivAlgHom_symm_coe, continuousOn_cfc, ProbabilityTheory.IndepFun.integrable_mul, AffineIsometryEquiv.norm_map, Asymptotics.IsLittleO.mul_isBigO, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', spectrum.mem_resolventSet_of_norm_lt, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, Prod.snd_exp, Submodule.orthogonal_eq_inter, Asymptotics.IsEquivalent.listProd, closure_diff_intrinsicInterior, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, HasStrictFDerivAt.smul_const, ContinuousLinearEquiv.coord_self, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, SchwartzMap.smulLeftCLM_ofReal, ContDiffAt.differentiableAt_iteratedFDeriv, Asymptotics.IsBigO.pow, MeasureTheory.Integrable.smul_const, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, MeasureTheory.lpNorm_one', tendsto_intCast_atTop_cobounded, MeasureTheory.L1.integral_eq', NormedSpace.isUnit_exp, summable_norm_sum_mul_antidiagonal_of_summable_norm, LinearPMap.mem_adjoint_domain_iff, unitary.norm_argSelfAdjoint_le_pi, summable_norm_pow_mul_geometric_of_norm_lt_one, ContMDiff.clm_precomp, PadicInt.complete, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, fderivWithin_pow, EuclideanGeometry.orthogonalProjection_apply, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, PadicInt.denseRange_intCast, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, OrthonormalBasis.coe_singleton, ContinuousLinearMap.hasDerivWithinAt, hasStrictFDerivAt_pow, Submodule.norm_orthogonalProjection, prod_vanishing_of_summable_norm, iteratedDeriv_fun_mul, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, CFC.log_algebraMap, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, EuclideanGeometry.orthogonalProjection_mem_orthogonal, PadicSeq.norm_zero_iff, inverse_add_nth_order, Filter.tendsto_mul_right_cobounded, analyticOnNhd_inv, hasDerivAt_exp_zero, Unitary.norm_argSelfAdjoint_le_pi, DifferentiableAt.pow, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, NormedDivisionRing.to_hasContinuousInvβ, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, CStarAlgebra.toStarModule, AffineIsometryEquiv.toAffineEquiv_symm, SchwartzMap.smulLeftCLM_apply, ZSpan.repr_floor_apply, WeakDual.isSeqCompact_polar, HasFTaylorSeriesUpTo.fderiv, Filter.tendsto_invβ_nhdsNE_zero, lipschitzWith_lineMap, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, isLittleO_pow_const_const_pow_of_one_lt, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, coe_algEquiv_lpBCF_symm, NormedField.valuation_apply, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, hasStrictDerivAt_id, curveIntegral_sub, Matrix.IsHermitian.charpoly_eq, HasFDerivWithinAt.mul', AnalyticAt.pow, TemperedDistribution.derivCLM_apply_apply, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, deriv_neg, AffineIsometryEquiv.toContinuousAffineEquiv_injective, DifferentiableAt.fun_mul, dist_midpoint_left, LinearMap.hasDerivAt, deriv_mul, NormedSpace.exp_analytic, LinearMap.hasDerivAtFilter, IsStarNormal.instIsometricContinuousFunctionalCalculus, CurveIntegrable.sub, deriv_pow', AnalyticOnNhd.pow, PadicInt.unitCoeff_spec, Valued.integer.norm_coe_unit, HasFPowerSeriesAt.locally_zero_iff, MeasureTheory.IntegrableOn.continuousOn_smul_of_subset, DifferentiableWithinAt.mul_const, PadicInt.norm_natCast_zmodRepr_eq_iff, AnalyticOnNhd.fun_const_smul, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, fderivWithin_mul', HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, Unitary.openPartialHomeomorph_apply, ordinaryHypergeometricSeries_norm_div_succ_norm, Unitary.argSelfAdjoint_coe, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, hasFDerivAt_inv', Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Matrix.IsStrictlyPositive.posDef, Matrix.exp_units_conj, inner_eq_one_iff_of_norm_one, exists_continuousLinearEquiv_fderiv_symm_eq, Units.isOpenEmbedding_val, FormalMultilinearSeries.rightInv_coeff, NormedSpace.exp_units_conj, hasDerivAt_zpow, tangentConeAt_eq_univ, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, mfderiv_neg, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContDiffOn.differentiableOn_iteratedFDerivWithin, Matrix.l2_opNorm_def, spectrum.map_polynomial_aeval, AnalyticOn.fun_pow, MeasureTheory.IntegrableOn.mul_continuousOn, HasFiniteFPowerSeriesOnBall.sub, Matrix.toEuclideanLin_toLp, ContDiffOn.fun_smul, ContinuousLinearMap.holderL_apply_apply, ContDiffOn.mul, ZSpan.coe_fract_self, CauchySeq.isCauSeq, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, norm_innerSL_le, AnalyticOn.mul, AffineSubspace.subtypeβα΅’_toAffineMap, BoundedContinuousFunction.separatesPoints_charPoly, MeasureTheory.LocallyIntegrableOn.continuousOn_smul, HasStrictFDerivAt.sub, ContMDiffWithinAt.cle_arrowCongr, CStarAlgebra.exists_sum_four_unitary, antilipschitzWith_lineMap, Submodule.starProjection_coe_eq_isCompl_projection, HasFDerivAt.neg, RCLike.normSq_one, Units.chartAt_source, AffineMap.deriv, Submodule.ClosedComplemented.of_quotient_finiteDimensional, isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt, AnalyticOnNhd.const_smul, Summable.multipliableUniformlyOn_nat_one_add, ContinuousLinearMap.apply_apply', PadicComplex.nnnorm_extends, LinearMap.posSemidef_toMatrix_iff, fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, tendsto_intCast_atBot_cobounded, PadicInt.coe_dpow_eq, HasMFDerivAt.mul', RCLike.charZero_rclike, Asymptotics.IsBigOWith.mul, cfcHom_eq_of_isStarNormal, exists_continuousLinearEquiv_fderivWithin_symm_eq, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, eHolderNorm_smul, HasGradientWithinAt.hasFDerivWithinAt, MDifferentiableWithinAt.pow, hasFDerivAt_exp, RCLike.isCauSeq_re, deriv_mul_const_field', Differentiable.smul_const, ZSpan.mem_fundamentalDomain, PadicInt.norm_natCast_p_sub_one, Submodule.IsCompl.projection_isSymmetric_iff, CFC.continuousOn_rpow, PadicInt.prime_p, upperHemicontinuous_spectrum, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Asymptotics.IsLittleO.exists_eq_mul, BoundedContinuousFunction.range_toLp, Submodule.norm_subtypeL_le, ContinuousLinearMap.hasStrictDerivAt, AffineIsometry.coe_toContinuousAffineMap, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, fderivWithin_pow_ring, ContinuousMap.isUnit_iff_forall_ne_zero, CStarRing.norm_one, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, logDeriv_pow, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, derivWithin_pow, HasFDerivAt.fun_mul', constFormalMultilinearSeries_zero, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, ContinuousMultilinearMap.instIsTopologicalAddGroup, Ring.inverse_exp, HasStrictFDerivAt.mul_const, AffineIsometry.image_intrinsicFrontier, one_le_nnnorm_one, EuclideanGeometry.orthogonalProjection_eq_iff_mem, Summable.mul_norm, unitary.mem_pathComponentOne_iff, nndist_self_homothety, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, derivWithin_smul_const, PadicSeq.norm_mul, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, spectrum.subset_closedBall_norm, RCLike.I_mul_I_of_nonzero, derivWithin_const_mul_field, ContinuousLinearMap.norm_precompL_le, Padic.const_equiv, Differentiable.smul, Units.isOpenMap_val, ContinuousLinearMap.apply_apply, intrinsicClosure_eq_closure, RCLike.span_one_I, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, iteratedFDeriv_neg, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, IsSymmSndFDerivWithinAt.eq, tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm', PowerSeries.IsRestricted.C, analyticAt_inverse, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, Real.fourierIntegral_iteratedFDeriv, hasMellin_const_smul, hasStrictDerivAt_exp_zero, Submodule.orthogonalProjection_norm_le, HasFDerivAt.mul', toRingNorm_apply, DoubleCentralizer.intCast_toProd, ContinuousAffineMap.differentiableAt, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, ContDiff.fun_smul, CStarRing.norm_coe_unitary, RCLike.intCast_im, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, MeasureTheory.MemLp.toLp_const_smul, continuousFunctionalCalculus_map_id, coe_algEquiv_lpBCF, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, hasFDerivAt_list_prod_attach', iteratedDerivWithin_mul_const_field, MeasureTheory.IntegrableOn.smul_continuousOn_of_subset, geom_series_eq_inverse, MeasureTheory.norm_condExpL2_le_one, Padic.isDenseInducing_cast_withVal, logDeriv_zpow, Polynomial.supNorm_eq_zero_iff, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, AffineIsometry.id_toAffineMap, ContMDiffAt.cle_arrowCongr, HasDerivWithinAt.comp_hasFDerivAt_of_eq, PadicInt.zmodRepr_natCast_of_lt, ContinuousLinearMap.adjoint_innerSL_apply, DifferentiableWithinAt.smul, MDifferentiableOn.pow, CStarAlgebra.span_unitary, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, binomialSeries_radius_ge_one, nndist_homothety_self, fderivWithin_fun_mul, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, EuclideanGeometry.reflection_apply, CFC.complex_exp_eq_normedSpace_exp, BoundedContinuousFunction.toLp_denseRange, Unitary.spectrum_subset_circle, PadicInt.existsUnique_mem_range, Submodule.coe_prodEquivOfClosedCompl, ContinuousLinearMap.norm_smulRightL_apply, HasFDerivAt.smul, isOpen_setOf_nat_le_rank, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, PadicInt.toZMod_spec, isUnit_one_sub_of_norm_lt_one, Matrix.IsHermitian.instContinuousFunctionalCalculus, fderiv_norm_sq_apply, hasStrictDerivAt_pow, differentiableOn_inv, PadicComplexInt.integers, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, LinearMap.exists_map_addHaar_eq_smul_addHaar', MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, Ideal.IsMaximal.closure_eq, MeasureTheory.Lp.toTemperedDistribution_smul_eq, NormedSpace.dual_def, HasFDerivAtFilter.hasDerivAtFilter, MeasureTheory.Lp_toLp_restrict_smul, fderiv_norm_sq, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, ContinuousMap.idealOpensGI_choice, WeakDual.CharacterSpace.instStarHomClass, Submodule.ClosedComplemented.of_isCompl_isClosed, TensorProduct.toLinearMap_mapInclIsometry, tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm, Filter.tendsto_invβ_cobounded', SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left, PadicInt.zmodRepr_eq_zero_iff_dvd, orthonormal_span, norm_cfc_lt, Pi.exp_def, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.toSesqForm_apply_norm_le, PiTensorProduct.injectiveSeminorm_def, ContMDiff.cle_arrowCongr, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, dist_lineMap_lineMap, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, derivWithin_fun_pow', ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, HasCompactSupport.hasFDerivAt_convolution_left, PadicSeq.eq_zero_iff_equiv_zero, Submodule.coe_prodEquivOfClosedCompl_symm, selfAdjoint.expUnitary_coe, fderivWithin_mul, intervalIntegral.integral_const_mul, MeasureTheory.Integrable.smul_of_top_right, TemperedDistribution.smulLeftCLM_apply_apply, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, nndist_lineMap_left, ContDiff.mul, DifferentiableOn.fun_smul, HasFDerivWithinAt.fun_mul, derivWithin_pow', OrthonormalBasis.inner_eq_ite, HasStrictFDerivAt.smul, IntervalIntegrable.const_mul, iter_deriv_pow, Rat.padicValuation_le_one_iff, HasStrictFDerivAt.finset_prod, PowerSeries.IsRestricted.zero, InnerProductSpace.norm_rankOne, HasFDerivAt.fun_sub, Nonneg.instIsometricContinuousFunctionalCalculus, hasFDerivAt_integral_of_dominated_loc_of_lip, tendsto_smul_comp_nat_floor_of_tendsto_nsmul, Submodule.isHilbertSumOrthogonal, DoubleCentralizer.neg_fst, Units.chartAt_apply, MDifferentiable.pow, AnalyticWithinAt.mul, AnalyticWithinAt.smul, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, ContinuousLinearMap.flipAlternating_apply_apply, Metric.sphere.instIsTopologicalGroup, norm_mul_le, derivWithin_const_mul, selfAdjoint.joined_one_expUnitary, NormedSpace.exp_add, ContDiffAt.mul, EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, AffineMap.continuous_of_finiteDimensional, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, niven_fract_angle_div_pi_eq, HasFDerivWithinAt.list_prod', fderiv_inv', unitary.continuousOn_argSelfAdjoint, Matrix.permMatrix_l2_opNorm_eq, AffineIsometryEquiv.coe_toAffineEquiv, Pi.coe_exp, Asymptotics.IsBigOWith.const_mul_right, AlgHom.norm_apply_le_self_mul_norm_one, fderivWithin_pow', AffineIsometryEquiv.coe_toContinuousAffineEquiv, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, tendsto_natCast_atTop_cobounded, PadicInt.norm_natCast_lt_one_iff, HasStrictDerivAt.fun_pow
|
toSeminormedRing π | CompOp | 500 mathmath: Unitary.openPartialHomeomorph_source, absorbent_iff_eventually_nhdsNE_zero, ContinuousMap.toLp_inj, NormedSpace.exp_continuous, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasSum_geometric_of_norm_lt_one, IsStarNormal.spectralRadius_eq_nnnorm, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, PowerSeries.IsRestricted.smul, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, inverse_one_sub_norm, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, NormedSpace.exp_zsmul, hasStrictFDerivAt_list_prod_finRange', Subalgebra.spectrum_sUnion_connectedComponentIn, ContMDiffMap.coeFnAlgHom_apply, iteratedDerivWithin_const_mul_field, nnnorm_cfc_lt, PositiveLinearMap.apply_le_of_isSelfAdjoint, BoundedContinuousFunction.algebraMap_apply, spectrum.subset_closedBall_norm_mul, spectrum.instCompactSpace, geom_series_mul_shift, MeasureTheory.Lp.const_smul_mem_Lp, CFC.tendsto_cfc_rpow_sub_one_log, hasSum_choose_mul_geometric_of_norm_lt_one, tsum_coe_mul_geometric_of_norm_lt_one', Filter.inv_nhdsWithin_ne_zero, ordinaryHypergeometric_radius_top_of_neg_natβ, tendsto_zpow_nhdsNE_zero_cobounded, ContinuousMap.toLp_denseRange, Unitary.mem_pathComponentOne_iff, Quaternion.continuous_imI, analyticOnNhd_inverse, Units.nhds, HasFPowerSeriesWithinAt.const_smul, ContinuousMap.range_toLp, deriv_mul_const_field, selfAdjoint.expUnitaryPathToOne_apply, inverse_add_norm_diff_nth_order, Unitary.continuousOn_argSelfAdjoint, CStarAlgebra.norm_or_neg_norm_mem_spectrum, StarAlgebra.elemental.characterSpaceToSpectrum_coe, tsum_choose_mul_geometric_of_norm_lt_one', Bornology.isVonNBounded_pi_iff, hasSum_coe_mul_geometric_of_norm_lt_one', isUltrametricDist_iff_forall_norm_natCast_le_one, tsum_coe_mul_geometric_of_norm_lt_one, Filter.map_mul_left_cobounded, iteratedDeriv_div_const, differentiableWithinAt_inv, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, CFC.exp_log, NormedSpace.exp_series_hasSum_exp', MeasureTheory.integrable_const_mul_iff, ContinuousLinearMap.smul_compLp, gelfandStarTransform_naturality, Filter.map_mul_right_cobounded, Filter.inv_nhdsNE_zero, ContinuousMap.toLp_norm_le, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, tsum_geometric_of_norm_lt_one, FormalMultilinearSeries.radius_le_smul, dist_inv_invβ, tendsto_norm_inv_nhdsNE_zero_atTop, formalMultilinearSeries_geometric_apply_norm_le, spectrum.isOpen_resolventSet, HasFPowerSeriesOnBall.const_smul, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, inverse_one_sub_nth_order, ordinaryHypergeometricSeries_radius_eq_one, Unitization.dist_inr, CFC.continuousOn_log, NormedSpace.exp_hasFPowerSeriesOnBall, NormedSpace.expSeries_summable, BoundedContinuousFunction.coe_toContinuousMapStarβ, binomialSeries_radius_eq_one, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, Asymptotics.IsLittleO.tendsto_div_nhds_zero, hasStrictDerivAt_exp_smul_const, geom_series_succ, Asymptotics.isLittleO_pow_pow, hasStrictDerivAt_exp_smul_const', uniqueDiffWithinAt_iff_accPt, tsum_geometric_le_of_norm_lt_one, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, UnitAddTorus.mFourierCoeff_toLp, balancedCore_mem_nhds_zero, Bornology.isVonNBounded_iff_absorbing_le, summable_mul_of_summable_norm, Unitary.openPartialHomeomorph_symm_apply, hasFDerivAt_ringInverse, Filter.inv_coboundedβ, ContinuousMap.spectrum_eq_preimage_range, Unitary.norm_sub_one_lt_two_iff, differentiableWithinAt_pow, NormedSpace.norm_expSeries_summable, spectrum.isCompact, tsum_mul_tsum_of_summable_norm, IsUltrametricDist.isUltrametricDist_of_forall_norm_sub_one_of_norm_le_one, subset_balancedCore, nndist_inv_invβ, CStarAlgebra.nnnorm_le_iff_of_nonneg, Polynomial.isClosedMap_eval, continuousOn_cfc_setProd, spectrum.spectralRadius_lt_of_forall_lt, NormedSpace.exp_conj, IsSelfAdjoint.neg_algebraMap_norm_le_self, mul_neg_geom_series, deriv_const_mul_field', unitSphereToUnits_apply_coe, IsUltrametricDist.isUltrametricDist_of_forall_pow_norm_le_nsmul_pow_max_one_norm, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_le_max_norm_one, Filter.tendsto_invβ_cobounded, tendsto_intCast_atBot_sup_atTop_cobounded, Unitization.cobounded_eq_aux, NormedSpace.expSeries_hasSum_exp, WeakDual.CharacterSpace.homeoEval_naturality, IsSelfAdjoint.val_re_map_spectrum, absorbs_iff_eventually_nhdsNE_zero, Units.instIsManifoldModelWithCornersSelf, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', BoundedContinuousFunction.toLp_inj, analyticAt_smul, BoundedContinuousFunction.toLp_injective, Unitary.instLocPathConnectedSpace, ContinuousMap.isUnit_iff_forall_isUnit, spectrum.eventually_isUnit_resolvent, Asymptotics.isLittleO_pow_id, Ideal.IsMaximal.isClosed, Quaternion.expSeries_odd_of_imaginary, unitSphereToUnits_injective, derivWithin_div_const, spectrum.gelfand_formula, IsSelfAdjoint.isConnected_spectrum_compl, Quaternion.continuous_imJ, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, isClosedMap_pow, NormedSpace.exp_continuousMap_eq, summable_norm_sum_mul_range_of_summable_norm, nhds_basis_balanced, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, Quaternion.instCompleteSpaceReal, continuousOn_cfc_nnreal, selfAdjoint.continuous_expUnitary, nonunits.isClosed, spectrum.map_pow, FormalMultilinearSeries.radius_smul_eq, selfAdjoint.unitarySelfAddISMul_coe, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, deriv_const_mul_field, Matrix.exp_nsmul, IsometricContinuousFunctionalCalculus.toNonUnital, AlgHom.instContinuousLinearMapClassOfAlgHomClass, CFC.exp_eq_normedSpace_exp, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, IsUltrametricDist.of_normedAlgebra, ContinuousMap.toLp_def, Units.instLieGroupModelWithCornersSelf, IsSelfAdjoint.cfc_arg, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, NormedSpace.expSeries_summable', hasFDerivAt_exp_smul_const', Quaternion.exp_of_re_eq_zero, Matrix.exp_sum_of_commute, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, Polynomial.isProperMap_eval, Quaternion.re_exp, hasFDerivWithinAt_pow', StarSubalgebra.spectrum_eq, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, hasFDerivAt_list_prod_finRange', Asymptotics.isLittleO_iff_tendsto', summable_choose_mul_geometric_of_norm_lt_one, ordinaryHypergeometric_radius_top_of_neg_natβ, Asymptotics.continuousAt_iff_isLittleO, CFC.log_monotoneOn, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Quaternion.expSeries_even_of_imaginary, NormedSpace.expSeries_div_summable, summable_descFactorial_mul_geometric_of_norm_lt_one, differentiableOn_pow, tsum_choose_mul_geometric_of_norm_lt_one, hasDerivAt_exp_smul_const, NormedSpace.algebraMap_exp_comm, fourierCoeff_toLp, IsSelfAdjoint.toReal_spectralRadius_complex_eq_norm, CFC.monotone_rpow, derivWithin_mul_const_field, CFC.rpow_neg_one_eq_cfc_inv, NormedSpace.expSeries_radius_eq_top, unitary.spectrum_subset_circle, MeasureTheory.integrable_mul_const_iff, inverse_add, CommCStarAlgebra.toStarModule, spectrum.isClosed, nonunits.subset_compl_ball, NormedSpace.invOf_exp, fderiv_pow_ring', NormedSpace.exp_conj', spectrum.isBounded, inverse_add_norm, IsSelfAdjoint.sq_spectrumRestricts, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, contDiff_smul_const, NormedSpace.exp_units_conj', binomialSeries_radius_eq_top_of_nat, Filter.tendsto_invβ_nhdsWithin_ne_zero, PositiveLinearMap.gnsStarAlgHom_apply, BoundedContinuousFunction.coeFn_toLp, spectrum.nonempty, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, inverse_add_norm_diff_second_order, ContinuousLinearMap.isVonNBounded_iff, nnnorm_cfc_nnreal_lt, Unitary.openPartialHomeomorph_target, CFC.rpow_le_rpow, Quaternion.normSq_exp, unitary.joined, IsSelfAdjoint.exp_nonneg, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, nnnorm_cfc_nnreal_le, NormedSpace.exp_hasFPowerSeriesAt_zero, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, Quaternion.im_exp, NormedDivisionRing.to_continuousInvβ, algEquivComplexOfComplete_symm_apply, CauSeq.tendsto_limit, NormedSpace.exp_nsmul, formalMultilinearSeries_geometric_apply_norm, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, hasSum_geom_series_inverse, NormedSpace.norm_expSeries_summable', formalMultilinearSeries_geometric_eq_ofScalars, hasSum_coe_mul_geometric_of_norm_lt_one, Metric.unitSphere.coe_inv, hasFDerivAt_exp_zero, selfAdjoint.star_coe_unitarySelfAddISMul, Units.isOpen, hasSum_choose_mul_geometric_of_norm_lt_one', CStarAlgebra.rpow_neg_one_le_rpow_neg_one, hasStrictFDerivAt_pow', Quaternion.summable_coe, CStarAlgebra.mul_star_le_algebraMap_norm_sq, NormedDivisionRing.unitClosedBall_eq_univ_of_discrete, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, upperHemicontinuous_spectrum_nnreal, hasSum_sum_range_mul_of_summable_norm, hasFDerivAt_exp_smul_const, Metric.unitSphere.coe_zpow, hasStrictFDerivAt_list_prod_attach', nnnorm_cfc_le, hasFPowerSeriesOnBall_inv_one_sub, hasFPowerSeriesOnBall_inverse_one_sub, hasStrictFDerivAt_ringInverse, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_of_norm_le_one, CStarAlgebra.norm_le_iff_le_algebraMap, Quaternion.tsum_coe, Prod.fst_exp, ContinuousMap.toLp_injective, CFC.log_smul', Quaternion.continuous_im, IsSelfAdjoint.spectralRadius_eq_nnnorm, Unitary.joined, geom_series_mul_one_add, Asymptotics.isLittleO_iff_exists_eq_mul, MeasureTheory.Lp.instIsBoundedSMul, ContinuousMap.coe_toLp, differentiable_pow, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, ContinuousMap.canLift, differentiableOn_inverse, CFC.nnnorm_rpow, IsUltrametricDist.isUltrametricDist_of_forall_norm_natCast_le_one, HasFPowerSeriesAt.const_smul, algEquivComplexOfComplete_apply, Matrix.exp_units_conj', MeasureTheory.Lp.simpleFunc.isBoundedSMul, IsStarNormal.instContinuousFunctionalCalculus, IsClosed.balancedCore, CStarAlgebra.star_mul_le_algebraMap_norm_sq, nhds_basis_closed_balanced, AlgHom.coe_toContinuousLinearMap, balancedCoreAux_subset, hasFDerivAt_pow', WeakDual.CharacterSpace.norm_le_norm_one, StarSubalgebra.mem_spectrum_iff, ContinuousMap.coeFn_toLp, Unitary.isPathConnected_ball, hasStrictFDerivAt_exp_zero, formalMultilinearSeries_geometric_radius, AccPt.uniqueDiffWithinAt, ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, egauge_eq_zero_iff, norm_cfc_le, analyticOn_inv, ContinuousMap.toLp_comp_toContinuousMap, BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, CStarAlgebra.rpow_neg_one_le_one, MeasureTheory.AEEqFun.Integrable.smul, ordinaryHypergeometricSeries_eq_zero_iff, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, Quaternion.norm_exp, contDiff_mul, Quaternion.continuous_coe, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, IsSelfAdjoint.map_spectrum_real, differentiableWithinAt_inverse, NormedSpace.exp_neg, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, IsUltrametricDist.normedAlgebra_iff, NormedSpace.exp_smul, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, contDiff_smul, summable_geometric_iff_norm_lt_one, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, summable_pow_mul_geometric_of_norm_lt_one, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapβ, BoundedContinuousFunction.toLp_norm_le, NormedSpace.expSeries_div_hasSum_exp, iteratedDeriv_mul_const_field, tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm, Filter.tendsto_mul_left_cobounded, StarSubalgebra.coe_isUnit, spectrum.spectralRadius_le_nnnorm, inverse_add_norm_diff_first_order, spectrum.isCompact_nnreal, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, selfAdjoint.val_re_map_spectrum, BoundedContinuousFunction.toContinuousMapβ_apply, NormedSpace.continuousOn_exp, Metric.unitSphere.coe_div, CFC.log_le_log, spectrum.resolvent_tendsto_cobounded, Matrix.isUnit_exp, MeasureTheory.Lp.coe_LpSubmodule, NormedDivisionRing.to_isTopologicalDivisionRing, PositiveLinearMap.norm_apply_le_of_nonneg, Unitization.nndist_inr, inverse_continuousAt, absorbs_iff_eventually_nhds_zero, MeasureTheory.BoundedContinuousFunction.inner_toLp, spectrum.instCompactSpaceNNReal, IsSelfAdjoint.toReal_spectralRadius_eq_norm, spectralValue_le_one_iff, NormedSpace.expSeries_radius_pos, analyticAt_mul, NormedSpace.algebraMap_exp_comm_of_mem_ball, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, Asymptotics.isLittleO_iff_tendsto, norm_cfcHom, analyticAt_inv, contDiffAt_ringInverse, geom_series_mul_neg, WeakDual.CharacterSpace.equivAlgHom_coe, CFC.norm_rpow, spectrum.exists_nnnorm_eq_spectralRadius, ordinaryHypergeometric_radius_top_of_neg_natβ, Units.contMDiff_val, analyticAt_inverse_one_sub, unitary.norm_sub_one_lt_two_iff, hasStrictFDerivAt_inv', analyticAt_inv_one_sub, iteratedDeriv_const_mul_field, hasStrictFDerivAt_exp_smul_const, hasDerivAt_exp_smul_const', WeakDual.CharacterSpace.compContinuousMap_comp, ContinuousLinearMap.smul_compLpL, summable_geometric_of_norm_lt_one, unitary.isPathConnected_ball, continuousOn_cfc_nnreal_setProd, NormedAlgebra.Complex.nonempty_algEquiv, nnnorm_cfcHom, inverse_one_sub_nth_order', NormedSpace.exp_add_of_commute, WeakDual.CharacterSpace.equivAlgHom_symm_coe, continuousOn_cfc, hasStrictFDerivAt_list_prod', spectrum.mem_resolventSet_of_norm_lt, Quaternion.hasSum_expSeries_of_imaginary, Prod.snd_exp, spectralValue_eq_zero_iff, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, tendsto_intCast_atTop_cobounded, NormedSpace.isUnit_exp, CStarAlgebra.norm_mem_spectrum_of_nonneg, summable_norm_sum_mul_antidiagonal_of_summable_norm, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, CFC.log_exp, CFC.log_algebraMap, ContinuousLinearMap.opNorm_lsmul, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, inverse_add_nth_order, Filter.tendsto_mul_right_cobounded, Unitization.uniformity_eq_aux, analyticOnNhd_inv, NormedDivisionRing.to_hasContinuousInvβ, CStarAlgebra.toStarModule, Filter.tendsto_invβ_nhdsNE_zero, coe_algEquiv_lpBCF_symm, NormedSpace.exp_analytic, IsStarNormal.instIsometricContinuousFunctionalCalculus, differentiableAt_inv, NormedSpace.exp_sum_of_commute, Unitary.openPartialHomeomorph_apply, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, Unitary.argSelfAdjoint_coe, MeasureTheory.ContinuousMap.inner_toLp, hasFDerivAt_inv', Matrix.exp_units_conj, Units.isOpenEmbedding_val, NormedSpace.exp_units_conj, tangentConeAt_eq_univ, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, differentiableAt_inverse, spectrum.map_polynomial_aeval, Quaternion.hasSum_coe, BoundedContinuousFunction.separatesPoints_charPoly, Quaternion.continuous_imK, CStarAlgebra.exists_sum_four_unitary, Units.chartAt_source, IsSelfAdjoint.le_algebraMap_norm_self, tendsto_intCast_atBot_cobounded, cfcHom_eq_of_isStarNormal, DoubleCentralizer.instCompleteSpace, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, NormedSpace.exp_mem_unitary_of_mem_skewAdjoint, deriv_mul_const_field', CFC.real_exp_eq_normedSpace_exp, CFC.continuousOn_rpow, upperHemicontinuous_spectrum, UniformConvergenceCLM.isVonNBounded_iff, Asymptotics.IsLittleO.exists_eq_mul, BoundedContinuousFunction.range_toLp, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, ContinuousMap.isUnit_iff_forall_ne_zero, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, Ring.inverse_exp, unitary.mem_pathComponentOne_iff, spectrum.subset_circle_of_unitary, spectrum.subset_closedBall_norm, derivWithin_const_mul_field, Units.isOpenMap_val, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, analyticAt_inverse, continuousFunctionalCalculus_map_id, coe_algEquiv_lpBCF, Quaternion.continuous_normSq, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, hasFDerivAt_list_prod_attach', Quaternion.continuous_re, iteratedDerivWithin_mul_const_field, CFC.conjugate_rpow_neg_one_half, geom_series_eq_inverse, Polynomial.supNorm_eq_zero_iff, CFC.log_smul, CStarAlgebra.span_unitary, binomialSeries_radius_ge_one, CFC.complex_exp_eq_normedSpace_exp, le_iff_norm_sqrt_mul_rpow, deriv_div_const, balancedCore_eq_iInter, BoundedContinuousFunction.toLp_denseRange, Unitary.path_apply, CStarAlgebra.nnnorm_mem_spectrum_of_nonneg, SpectrumRestricts.nnreal_iff_nnnorm, Unitary.spectrum_subset_circle, Quaternion.exp_coe, one_le_formalMultilinearSeries_geometric_radius, differentiableOn_inv, Ideal.IsMaximal.closure_eq, Quaternion.exp_eq, WeakDual.CharacterSpace.instStarHomClass, tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm, spectrum.mem_resolventSet_of_norm_lt_mul, Filter.tendsto_invβ_cobounded', balancedCoreAux_empty, norm_cfc_lt, selfAdjoint.expUnitary_coe, intervalIntegral.integral_const_mul, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Nonneg.instIsometricContinuousFunctionalCalculus, Units.chartAt_apply, balancedCore_subset_balancedCoreAux, Metric.sphere.instIsTopologicalGroup, selfAdjoint.joined_one_expUnitary, le_iff_norm_sqrt_mul_sqrt_inv, fderiv_inv', unitary.continuousOn_argSelfAdjoint, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, tendsto_natCast_atTop_cobounded
|
| Name | Category | Theorems |
|---|
induced π | CompOp | β |
toCommRing π | CompOp | 26 mathmath: Submodule.Quotient.instIsBoundedSMul, MulAlgebraNorm.extends_norm', AlgebraNorm.extends_norm, AlgebraNormClass.map_smul_eq_mul, Seminorm.comp_smul, Asymptotics.IsLittleO.multisetProd, AlgebraNorm.smul', instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, StrongDual.dualPairing_separatingLeft, Asymptotics.IsBigO.multisetProd, Asymptotics.IsBigO.finsetProd, norm_prod, MulAlgebraNormClass.toSeminormClass, TrivSqZeroExt.instL1IsBoundedSMul, MulAlgebraNormClass.map_smul_eq_mul, PiLp.basis_toMatrix_basisFun_mul, Ideal.Quotient.norm_mk_lt, AlgebraNorm.extends_norm', Asymptotics.IsLittleO.finsetProd, nnnorm_prod, Seminorm.comp_smul_apply, Ideal.Quotient.norm_mk_le, AlgebraNormClass.toSeminormClass, Filter.BoundedAtFilter.prod, MulAlgebraNorm.smul', MulAlgebraNorm.extends_norm
|
toNonUnitalSeminormedCommRing π | CompOp | 2140 mathmath: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, hasFDerivAt_iff_hasDerivAt, iteratedDeriv_scomp_two, Real.differentiableOn_arcosh, isEquivalent_descFactorial, Real.hasDerivAt_arccos, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, HasSum.exp, BoundedContinuousFunction.tietze_extension_step, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, InformationTheory.integrable_klFun_rnDeriv_iff, Polynomial.differentiableWithinAt, MeasureTheory.Integrable.integral_norm_prod_right, Seminorm.isBounded_const, isConformalMap_conj, MeasureTheory.eLpNorm'_norm, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, HasStrictFDerivAt.isLittleOTVS, Bundle.ContMDiffRiemannianMetric.isVonNBounded, NormedSpace.isBounded_polar_of_mem_nhds_zero, TensorProduct.enorm_lid, differentiableAt_comp_neg, Real.integrableOn_rpowIntegrandββ_Ioi, Matrix.frobenius_nnnorm_mul, HasMFDerivAt.mul, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, MonotoneOn.intervalIntegral_slope_le, ProbabilityTheory.isGaussian_iff_gaussian_charFun, Real.differentiable_arctan, RCLike.map_apply, Real.differentiableAt_mulExpNegMulSq, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, Complex.restrictScalars_one_smulRight', IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, HasFDerivWithinAt.ccos, InnerProductSpace.toLinearIsometry_toDual, RCLike.ofRealCLM_apply, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, Real.hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, Complex.linearEquiv_det_conjLIE, Ideal.toCharacterSpace_apply_eq_zero_of_mem, hasFDerivAt_iff_hasGradientAt, RCLike.reCLM_apply, NumberField.Units.finrank_eq_rank, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, InnerProductSpace.rankOne_one_left_eq_innerSL, ConvexOn.rightDeriv_le_slope_of_mem_interior, ContinuousMap.abs_mem_subalgebra_closure, hasDerivAt_sqrt_mul_log, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, HasStrictFDerivAt.csin, Polynomial.isEquivalent_atBot_div, ZSpan.volume_real_fundamentalDomain, ContinuousLinearMap.opNorm_bound_of_ball_bound, Complex.ofRealCLM_coe, Complex.kahler, RightDerivMeasurableAux.D_subset_differentiable_set, Complex.areaForm, WeakDual.isCompact_polar, finrank_real_complex_fact', EuclideanSpace.orthonormal_single, Real.deriv_negMulLog, Real.hasDerivAt_sigmoid, AffineMap.hasDerivAtFilter, Matrix.IsHermitian.det_abs, RCLike.ofRealLI_apply, deriv_abs, differentiableAt_zpow, hasFDerivAt_multiset_prod, Stirling.factorial_isEquivalent_stirling, ProbabilityTheory.covarianceBilinDual_apply', Real.nnnorm_deriv_mulExpNegMulSq_le_one, OrthonormalBasis.repr_injective, Real.deriv_binEntropy, MeasureTheory.convolution_mul, Complex.ofRealLI_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, deriv_mem_iff, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, integrableOn_exp_mul_Iic, ProbabilityTheory.IsGaussian.integrable_dual, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, norm_iteratedFDerivWithin_smul_le, Matrix.cstar_nnnorm_def, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Real.hasStrictDerivAt_rpow_const_of_ne, StrongDual.polarSubmodule_eq_setOf, ContinuousMap.attachBound_apply_coe, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, ContinuousLinearMap.hasDerivAtFilter, fderivWithin_csinh, span_fourier_closure_eq_top, PeriodPair.basis_one, RCLike.conjCLE_norm, HasDerivWithinAt.complexToReal_fderiv', Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, ContDiffBump.integrable, WeakDual.isClosed_image_polar_of_mem_nhds, ZLattice.covolume_eq_det_inv, ContinuousLinearMap.integral_apply, circleIntegrable_iff, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', MeasureTheory.MemLp.const_inner, not_integrableOn_Ioi_cpow, MeasureTheory.AEStronglyMeasurable.memLp_truncation, Real.fderiv_fourierChar_neg_bilinear_right_apply, intervalIntegral.fderiv_integral_of_tendsto_ae, flip_innerSL_real, LipschitzWith.memLp_lineDeriv, differentiableWithinAt_abs_pos, continuousOn_dslope, ProbabilityTheory.integrable_preCDF, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, isClosedEmbedding_cfcβAux, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, AddChar.wInner_cWeight_self, AddCircle.coe_real_preimage_closedBall_eq_iUnion, innerSL_apply_apply, MeasureTheory.Integrable.norm_integral_condExpKernel, LinearMap.adjoint_innerββ_apply, Real.differentiable_sinh, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, hasDerivAt_neg', AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, nnnorm_cfcβ_lt_iff, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, LeftInvariantDerivation.left_invariant', Int.enorm_natCast, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, derivWithin_fderivWithin, ContDiffBump.integrable_normed, ProbabilityTheory.uncenteredCovarianceBilin_apply, Real.deriv_log, ContDiff.differentiable_deriv_two, Submodule.Quotient.instIsBoundedSMul, FormalMultilinearSeries.derivSeries_coeff_one, Complex.ofRealCLM_norm, Matrix.spectrum_toLpLin, contMDiff_neg_sphere, HasDerivAt.comp_ofReal, not_differentiableAt_norm_zero, rotation_injective, BoxIntegral.unitPartition.mem_smul_span_iff, SchwartzMap.bilinLeftCLM_apply, InnerProductSpace.toDual_symm_apply, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, HasGradientAt.hasDerivAt', SmoothBumpCovering.exists_immersion_euclidean, AffineMap.hasDerivWithinAt, LeftInvariantDerivation.left_invariant, MeasureTheory.pdf.IsUniform.mul_pdf_integrable, ProbabilityTheory.integrable_toReal_condExpKernel, Bundle.RiemannianMetric.isVonNBounded, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, IsGreatest.nnnorm_cfcβ, Complex.convexHull_reProdIm, Complex.conjLIE_apply, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, hasDerivAt_exp_zero_of_radius_pos, egauge_ball_le_of_one_lt_norm, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasStrictFDerivAt_iff_isLittleOTVS, not_IntegrableOn_Ioi_inv, ContinuousMap.continuousMap_mem_subalgebra_closure_of_separatesPoints, Matrix.PosSemidef.sqrt_eq_zero_iff, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, lintegral_fderiv_lineMap_eq_edist, UnitAddTorus.mFourierSubalgebra_coe, signedDist_right_congr, TensorProduct.toLinearEquiv_lidIsometry, Real.differentiableOn_arcsin, AnalyticOnNhd.eval_linearMap', MeasureTheory.MemLp.integrable_norm_rpow', Complex.hasStrictFDerivAt_exp_real, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.parallelepiped_basisFun, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, monomial_has_deriv_aux, MeasureTheory.hasFiniteIntegral_prod_iff', Real.vector_fourierIntegral_eq_integral_exp_smul, MeasureTheory.MemLp.norm_rpow, nndist_midpoint_right, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, Asymptotics.isLittleOTVS_prodMk_left, NNReal.enorm_eq, iter_deriv_zpow', differentiableWithinAt_abs, Matrix.exp_conj', Real.deriv_arccos, Real.hasStrictDerivAt_sinh, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, LocallyBoundedVariationOn.ae_differentiableWithinAt, ConvexOn.univ_sSup_of_countable_affine_eq, integrableOn_exp_Iic, cfcβHom_nnreal_eq_restrict, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, IsLocalFrameOn.coeff_apply_of_mem, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, IsLocalMax.fderiv_eq_zero, Matrix.exp_neg, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, polynomialFunctions.starClosure_topologicalClosure, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerββ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, differentiableAt_sigmoid, OrthonormalBasis.repr_self, iteratedDeriv_scomp_three, Real.integrable_prod_sub, HasFDerivWithinAt.csin, MeasureTheory.eLpNorm_mono_real, Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, Icc_isBoundaryPoint_bot, mellin_convergent_zero_of_isBigO, deriv_abs_neg, ProbabilityTheory.evariance_lt_top_iff_memLp, Real.differentiableWithinAt_arccos_Ici, gelfandStarTransform_naturality, gelfandStarTransform_apply_apply, HarmonicAt.analyticAt_complex_partial, integrableOn_Ioi_rpow_of_lt, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, NormedSpace.Dual.toWeakDual_continuous, signedDist_left_congr, NormedField.exists_lt_nnnorm_lt, exists_deriv_eq_zero, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, ContinuousMultilinearMap.norm_smulRightL_le, NormedField.exists_nnnorm_lt_one, differentiableAt_comp_add_const, integrableOn_Ioi_norm_cpow_of_lt, QuadraticForm.equivalent_signType_weighted_sum_squared, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, SchwartzMap.integral_fourierInv_smul_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, signedDist_triangle, Real.hasDerivAt_arcosh, ConvexOn.monotoneOn_rightDeriv, enorm_fderiv_norm_rpow_le, LocallyBoundedVariationOn.ae_differentiableAt, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, fderiv_eq_deriv_mul, nndist_right_lineMap, Orientation.abs_volumeForm_apply_of_orthonormal, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, Polynomial.differentiableOn_aeval, NumberField.mixedEmbedding.negAt_apply_snd, fderivWithin_ccosh, Real.GammaIntegral_convergent, Matrix.toEuclideanLin_apply, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, fourier_norm, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, Real.hasStrictDerivAt_arccos, RCLike.conjCLE_apply, MeasureTheory.integrable_norm_rpow_iff, Complex.reCLM_nnnorm, Unitization.nnnorm_def, isScalarTower_closedBall_closedBall_closedBall, nndist_left_lineMap, Euclidean.closedBall_eq_image, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, isScalarTower_sphere_closedBall_closedBall, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, Complex.deriv_ofReal_cpow_const, PiTensorProduct.mapL_smul, MeasureTheory.L1.setToL1_smul_left, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, MeasureTheory.eLpNorm_norm, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, Real.norm_deriv_mulExpNegMulSq_le_one, Quaternion.linearIsometryEquivTuple_symm_apply, Polynomial.isEquivalent_atTop_lead, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, MeasureTheory.charFun_apply_real, Orientation.areaForm_to_volumeForm, Icc_isInteriorPoint_interior, VectorFourier.fourierIntegral_continuousLinearMap_apply, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, Real.not_continuousAt_deriv_mul_log_zero, integrable_one_add_norm, ProbabilityTheory.integrable_condCDF, HasFDerivAtFilter.isThetaTVS_sub, integrableOn_add_rpow_Ioi_of_lt, InformationTheory.klDiv_eq_top_iff, SchwartzMap.fourier_lineDerivOp_eq, LinearMap.isBigOTVS_rev_comp, AddChar.wInner_cWeight_eq_zero_iff_ne, NormedField.exists_one_lt_enorm, ContinuousLinearMapWOT.inducingFn_apply, Orientation.areaForm_neg_orientation, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, Monotone.ae_differentiableAt, mfderivWithin_comp_projIcc_one, contDiffWithinAt_euclidean, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, AddCircle.norm_div_natCast, InnerProductSpace.toDualMap_apply_apply, Orientation.kahler_eq_zero_iff, BoundedContinuousFunction.integral_const_sub, signedDist_apply_apply, Real.differentiableAt_rpow_const_of_ne, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, WeakDual.toStrongDual_inj, IccLeftChart_extend_interior_pos, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, Orientation.areaForm_swap, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, hasDerivAt_id', integrableOn_Ioi_cpow_iff, Bundle.ContinuousRiemannianMetric.symm, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, MeasureTheory.MemLp.inner_const, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, Complex.sameRay_of_arg_eq, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, Real.deriv_sqrt_aux, deriv_fderiv, HasStrictDerivAt.real_of_complex, Matrix.PosSemidef.det_sqrt, Real.deriv_rpow_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, HasDerivAt.differentiableAt, DifferentiableWithinAt.dist, MeasureTheory.integrable_thickenedIndicator, NormedField.exists_nnnorm_lt, hasDerivWithinAt_abs, MeasureTheory.integrable_of_tendsto, TensorProduct.lidIsometry_apply, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ContinuousLinearMap.hasDerivAt, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, Complex.reCLM_coe, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, MeasureTheory.eLpNorm_ofReal, Real.deriv_sinh, NormedField.exists_lt_enorm, Module.Basis.coe_toOrthonormalBasis_repr, Filter.HasBasis.isLittleOTVS_iff, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, Matrix.linfty_opNNNorm_eq_opNNNorm, VectorFourier.fourierIntegral_iteratedFDeriv, ModularGroup.lcRow0Extend_symm_apply, InformationTheory.hasDerivAt_klFun, integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, Orientation.kahler_comp_rightAngleRotation, Seminorm.ball_smul, ae_differentiableAt_norm, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, HasGradientWithinAt.differentiableWithinAt, MeasureTheory.memLp_haarAddCircle_iff, NumberField.Units.instZLattice_unitLattice, HasFDerivAt.isBigOTVS_sub, hasDerivWithinAt_neg, Orientation.volumeForm_zero_pos, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, ProbabilityTheory.complexMGF_mul_I, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, IsLocalFrameOn.coeff_congr, ProbabilityTheory.Kernel.integrable_densityProcess, NumberField.Units.span_basisOfIsMaxRank, LinearMap.hasStrictDerivAt, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, FiniteDimensional.rclike_to_real, Complex.equivRealProdCLM_symm_apply, HasDerivWithinAt.norm_sq, NormedSpace.smul_mem_polar, HasGradientAtFilter.hasDerivAtFilter', CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, IsLocalExtr.fderiv_eq_zero, NumberField.Units.basisOfIsMaxRank_apply, Real.differentiableOn_rpow_const, MeasureTheory.MemLp.integrable_norm_pow, NormedField.denseRange_nnnorm, Asymptotics.IsLittleOTVS.zero, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, PeriodPair.basis_zero, MeasureTheory.Integrable.norm_integral_condDistrib, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, ContinuousLinearMap.nnnorm_toSpanSingleton, InformationTheory.leftDeriv_klFun, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Asymptotics.isLittleOTVS_fun_neg_left, deriv_id'', AddCircle.exists_norm_nsmul_le, isEquivalent_choose, Asymptotics.isBigOTVS_iff_smallSets, OrthonormalBasis.coe_ofRepr, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MeasureTheory.Integrable.integral_norm_comp, EuclideanSpace.nnnorm_single, ProbabilityTheory.differentiableAt_mgf, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, RCLike.conjLIE_apply, Complex.orthonormalBasisOneI_repr_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Complex.differentiable_exp, Polynomial.toAddCircle.integrable, RCLike.imLm_coe, Real.differentiable_cos, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, isAddFundamentalDomain_Ioc, norm_cauchyPowerSeries_le, hasFDerivAt_norm_rpow, intervalIntegral.integrableOn_Ioo_rpow_iff, Asymptotics.isEquivalent_nat_ceil, summable_jacobiThetaβ_term_fderiv_iff, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, AddCircle.norm_coe_mul, Asymptotics.isBigOTVS_fun_neg_left, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Matrix.linfty_opNNNorm_toMatrix, Asymptotics.isBigOTVS_fun_neg_right, hasDerivAt_abs_rpow, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, signedDist_eq_zero_of_orthogonal, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, ProbabilityTheory.memLp_of_mem_interior_integrableExpSet, ZSpan.volume_fundamentalDomain, FormalMultilinearSeries.coeff_eq_zero, ProbabilityTheory.covarianceBilin_zero, RCLike.conjCLE_coe, contDiffOn_stereoToFun, LeftInvariantDerivation.evalAt_coe, AddCircle.norm_half_period_eq, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, Matrix.PosSemidef.sqrt_eq_one_iff, Real.deriv_Gamma_nat, GaussianFourier.integrable_cexp_neg_mul_sum_add, Complex.hasStrictFDerivAt_cpow, MeasureTheory.integrable_add_iff_of_nonneg, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, Polynomial.differentiable_aeval, IsGreatest.nnnorm_cfc, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Convex.toWeakSpace_closure, hasDerivAtFilter_neg, integrable_rpow_neg_one_add_norm_sq, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, Bundle.ContMDiffRiemannianMetric.symm, HilbertBasis.hasSum_repr, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, Asymptotics.isBigOTVS_iff_isBigO, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, hasDerivWithinAt_pow, HasFDerivWithinAt.cpow, MeasureTheory.lintegral_nnnorm_condExpL2_le, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, AffineSubspace.signedInfDist_eq_signedDist_of_mem, HasStrictFDerivAt.const_cpow, Finset.nnnorm_prod_le', differentiableWithinAt_of_derivWithin_ne_zero, one_mem_posTangentConeAt_iff_mem_closure, HasFDerivWithinAt.csinh, Real.integrable_sinc, RealRMK.rieszMeasure_le_of_eq_one, TensorProduct.inner_lid_lid, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, NormedSpace.inclusionInDoubleDual_norm_le, not_IntegrableOn_Ici_inv, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, MeasureTheory.memLp_two_iff_integrable_sq, WeakDual.isCompact_closedBall, Affine.Simplex.signedInfDist_apply_self, ConvexOn.sSup_of_countable_affine_eq, Real.differentiableAt_rpow_of_ne, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, RCLike.reCLM_coe, ProbabilityTheory.gaussianReal_map_linearMap, InnerProductSpace.toDual_apply, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', HasDerivWithinAt.inner, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, DifferentiableAt.inner, HarmonicAt.differentiableAt_complex_partial, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, NormedSpace.exp_continuousMap_eq, Seminorm.comp_smul, isScalarTower_sphere_sphere_sphere, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', Real.deriv_inv_log, ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, Asymptotics.IsLittleO.isLittleOTVS, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, iteratedFDerivWithin_eq_equiv_comp, CompactlySupportedContinuousMap.toRealLinearMap_apply, DifferentiableAt.isBigOTVS_sub, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, MeasureTheory.Integrable.integral_norm_prod_left, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, differentiableAt_inv_iff, AddCircle.instIsUnifLocDoublingMeasureRealVolume, ProbabilityTheory.covarianceBilinDual_zero, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, RealRMK.integral_rieszMeasure, LinearMap.deriv, RCLike.nnnorm_nnratCast, contDiff_iff_iteratedDeriv, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, EuclideanSpace.instIsManifoldSphere, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, Real.isEquivalent_sin, InnerProductSpace.toDualMap_apply, Real.differentiable_exp, ProbabilityTheory.differentiableOn_mgf, Real.abs_mulExpNegMulSq_comp_le_norm, nnnorm_algebraMap, fdifferential_apply, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, Asymptotics.isEquivalent_iff_exists_eq_mul, MeasureTheory.Integrable.integral_norm_condExpKernel, Real.differentiableAt_cos, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, innerβ_apply, Asymptotics.isBigOTVS_congr, ProbabilityTheory.complexMGF_id_mul_I, fderivWithin_ccos, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, ModularGroup.lcRow0Extend_apply, Asymptotics.isBigOTVS_neg_right, Real.deriv_log', hasDerivAt_update, HasStrictFDerivAt.clog, nnnorm_apply_le_nnnorm_cfcβ, Real.one_div_sub_hasFPowerSeriesOnBall_zero, ProbabilityTheory.integrable_condVar, OrthonormalBasis.equiv_apply, Seminorm.bound_of_continuous, fderiv_pow_ring, Bundle.ContMDiffRiemannianMetric.pos, HasDerivWithinAt.complexToReal_fderiv, signedDist_triangle_left, IsContMDiffRiemannianBundle.exists_contMDiff, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, Real.deriv2_binEntropy, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, InnerProductSpace.toDual_apply_apply, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, contMDiff_subtype_coe_Icc, Real.hasDerivAt_arcsin, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, ProperCone.innerDual_singleton, RCLike.nnnorm_ofNat, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, differentiable_inner, Real.hasDerivAt_tan, hasFDerivAt_list_prod', InnerProductSpace.rankOne_def, Real.deriv_tan_sub_id, AddCircle.volume_closedBall, Real.leftDeriv_mul_log, stereoToFun_apply, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, Real.differentiableAt_Gamma, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, orthogonalBilin_innerβ, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, ConvexOn.real_univ_sSup_of_countable_affine_eq, NumberField.mixedEmbedding.mem_span_latticeBasis, ProbabilityTheory.evariance_eq_top_iff, Module.Basis.equivFunL_symm_apply_repr, OrthonormalBasis.repr_apply_apply, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, HasStrictFDerivAt.ccos, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, MeasureTheory.lintegral_ofReal_ne_top_iff_integrable, BoundedContinuousFunction.neg_norm_le_apply, gradient_eq_deriv', QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ClosedSubmodule.orthogonal_eq_inter, Chebyshev.integrableOn_theta_div_id_mul_log_sq, Orientation.kahler_neg_orientation, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, MonotoneOn.intervalIntegrable_slope, nndist_left_midpoint, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', intervalIntegral.integrableOn_Ioo_cpow_iff, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, Real.differentiableOn_mul_log, MeasureTheory.setToFun_smul_left, InformationTheory.klDiv_def, HasDerivAt.complexToReal_fderiv', hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.Integrable.norm_integral_condKernel, RCLike.abs_wInner_le, contDiff_nat_iff_iteratedDeriv, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, ProbabilityTheory.memLp_id_gaussianReal', fderiv_norm_smul_neg, HasDerivAt.complexToReal_fderiv, ContinuousLinearMapWOT.isInducing_inducingFn, integrableOn_Ioi_deriv_ofReal_cpow, Real.deriv_mulExpNegMulSq, StrongDual.polarSubmodule_eq_polar, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, Asymptotics.isLittleOTVS_fun_neg_right, Complex.isEquivalent_sinh, hasFDerivAt_exp_smul_const', dense_differentiableAt_norm, MeasureTheory.SignedMeasure.re_toComplexMeasure, Matrix.exp_zsmul, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, MonotoneOn.intervalIntegral_deriv_mem_uIcc, NumberField.mixedEmbedding.volume_preserving_negAt, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, Real.deriv_qaryEntropy, Real.deriv_arctan, monotoneOn_deriv_descPochhammer_eval, SchwartzMap.smulLeftCLM_const, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, mellin_convergent_top_of_isBigO, LinearMap.toMatrix_innerββ_apply, PointwiseConvergenceCLM.equivWeakDual_symm_apply, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, MeasureTheory.ComplexMeasure.integrable_rnDeriv, RCLike.wInner_one_eq_inner, NumberField.mixedEmbedding.negAt_apply_isComplex, ProbabilityTheory.hasFiniteIntegral_compProd_iff', AffineMap.hasDerivAt, Complex.hasFDerivAt_cpow, Complex.differentiableAt_exp, ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, not_integrableOn_Ioi_rpow, AffineMap.differentiableAt, isScalarTower_closedBall_ball_ball, Matrix.PosSemidef.toLinearMapβ'_zero_iff, Polynomial.rootSet_derivative_subset_convexHull_rootSet, WeakDual.isSeqCompact_closedBall, HasFDerivAt.ccos, MeasureTheory.Measure.integrable_measure_prodMk_left, has_antideriv_at_fourier_neg, Real.differentiableAt_log_iff, hasStrictDerivAt_zpow, norm_iteratedFDerivWithin_prod_le, UnitAddTorus.mFourier_norm, Matrix.instNonnegSpectrumClass, LinearIsometry.toSpanSingleton_apply, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, DifferentiableAt.norm_sq, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, contDiffAt_euclidean, HasFDerivAt.clog, innerSLFlip_apply_apply, Polynomial.hasFDerivAt, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, finrank_euclideanSpace, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, IsContinuousRiemannianBundle.exists_continuous, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, NormedField.exists_enorm_lt, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', MeasureTheory.MemLp.integrable_norm_rpow, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, nndist_midpoint_left, intervalIntegral.integral_hasStrictFDerivAt, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, MeasureTheory.IntegrableAtFilter.norm, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, Module.Basis.equivFunL_apply, inner_map_complex, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, tendsto_integral_mul_one_add_inv_smul_sq_pow, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, LinearMap.hasDerivWithinAt, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, Real.fourier_fderiv, ContinuousMap.adjoin_id_eq_span_one_union, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, Seminorm.const_isBounded, MeasureTheory.integrable_prod_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, HasFDerivWithinAt.norm_sq, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, differentiableAt_abs_neg, Asymptotics.isLittleOTVS_iff_smallSets, BoundedContinuousFunction.apply_le_norm, hasDerivAt_fourier_neg, ProbabilityTheory.isGaussian_gaussianReal, norm_fderiv_norm_rpow_le, StrongDual.dualPairing_separatingLeft, deriv_abs_zero, HasDerivWithinAt.differentiableWithinAt, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, nndist_midpoint_midpoint_le', Polynomial.Chebyshev.integrable_measureT, SchwartzMap.fourierInv_lineDerivOp_eq, RCLike.finrank_le_two, Bundle.RiemannianMetric.symm, MeasureTheory.integral_charFun_Icc, iteratedFDeriv_eq_equiv_comp, linear_isometry_complex, Real.hasDerivAt_cos, Matrix.ofLp_toEuclideanCLM, AffineSubspace.signedInfDist_eq_const_of_mem, ProbabilityTheory.HasSubgaussianMGF.integrable, HasFDerivAt.ccosh, ContinuousMap.sup_mem_subalgebra_closure, AddCircle.exists_norm_eq_of_isOfFinAddOrder, Asymptotics.isBigOTVS_neg_left, exists_dual_vector, nndist_center_homothety, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, Differentiable.norm_rpow, DifferentiableWithinAt.isBigOTVS_sub, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, Real.differentiableWithinAt_arcsin_Ici, AddChar.wInner_cWeight_eq_one_iff_eq, logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, InformationTheory.klDiv_ne_top_iff, RCLike.sqrt_map, MeasureTheory.integrable_conv_iff, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, PadicInt.mahlerTerm_one, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, rotationOf_rotation, IsMIntegralCurveAt.hasMFDerivAt, SpectrumRestricts.real_iff, IsLocalFrameOn.eventually_eq_sum_coeff_smul, differentiableWithinAt_euclidean, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, deriv_abs_pos, Matrix.isPositive_toEuclideanLin_iff, nnnorm_cfc_le_iff, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, exists_polynomial_near_continuousMap, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, HasGradientAt.differentiableAt, ContinuousMap.inf_mem_subalgebra_closure, NormedSpace.exp_sum, Real.differentiableAt_cosh, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, ProbabilityTheory.integral_linearMap_gaussianReal, AddCircle.coe_real_preimage_closedBall_inter_eq, Real.nnnorm_mul_toNNReal, Polynomial.hermite_eq_deriv_gaussian', MeasureTheory.integrable_of_integral_eq_one, MeasureTheory.integrable_norm_iff, WeakDual.polar_def, MeasureTheory.integrable_toReal_of_lintegral_ne_top, RCLike.wInner_const_left, ProbabilityTheory.covarianceBilinDual_self_eq_variance, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, MeasureTheory.integrable_smul_const, Orientation.areaForm_comp_linearIsometryEquiv, NormedField.exists_one_lt_nnnorm, hasStrictFDerivAt_norm_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', LinearMap.adjoint_toSpanSingleton, ContDiff.differentiable_iteratedDeriv, ContinuousMultilinearMap.norm_mkPiAlgebra, Real.deriv_exp, NumberField.canonicalEmbedding.nnnorm_eq, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, QuasispectrumRestricts.real_iff, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, RCLike.inner_apply, NormedField.exists_enorm_lt_one, Polynomial.differentiableAt_aeval, WeakDual.CharacterSpace.compContinuousMap_apply, hasDerivAt_id, Real.hasDerivAt_rpow_const, Real.toNNReal_mul_nnnorm, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, MeasureTheory.Integrable.re_im_iff, Polynomial.isEquivalent_atBot_lead, differentiableAt_norm_smul, deriv_update, MeasureTheory.HasFiniteIntegral.norm, Real.iter_deriv_exp, Real.differentiable_iteratedDeriv_cos, nndist_lineMap_right, Polynomial.hasFDerivAt_aeval, Differentiable.norm_sq, exists_dual_vector'', deriv_zpow', RCLike.norm_wInner_le, ProbabilityTheory.IsGaussian.memLp_dual, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Asymptotics.isLittleOTVS_map, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, hasFDerivAt_pow, Matrix.l2_opNNNorm_def, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, hasDerivAt_exp, contDiffOn_succ_iff_deriv_of_isOpen, signedDist_lineMap_left, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, Real.tendsto_rightDeriv_mul_log_atTop, Real.hasStrictDerivAt_arsinh, iter_deriv_pow', MeasureTheory.Integrable.integral_norm_compProd, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, Asymptotics.isLittleOTVS_iff_isLittleO, integrable_rpow_mul_exp_neg_mul_sq, EuclideanSpace.basisFun_repr, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, RCLike.realLinearIsometryEquiv_symm_apply, hasStrictFDerivAt_inv, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, InformationTheory.klDiv_eq_integral_klFun, LinearIsometry.coe_toSpanSingleton, MeasureTheory.hasFiniteIntegral_iff_ofReal, integrable_mul_exp_neg_mul_sq, VectorFourier.fourierSMulRight_apply, deriv_neg'', UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, IsLocalFrameOn.coeff_apply_of_notMem, ProbabilityTheory.evariance_def', Seminorm.closedBall_smul, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, fderiv_inv, Complex.orthonormalBasisOneI_repr_symm_apply, Manifold.riemannianEDist_def, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, isScalarTower_sphere_sphere_closedBall, signedDist_anticomm, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, UnitAddTorus.hasSum_mFourier_series_L2, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Orientation.areaForm_comp_rightAngleRotation, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, modelWithCornersEuclideanHalfSpace_zero, UnitAddCircle.mem_approxAddOrderOf_iff, ContinuousLinearMap.norm_extendToπ'_bound, MeasureTheory.hausdorffMeasure_homothety_image, Real.differentiableAt_arctan, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, spectralNorm_smul, Asymptotics.isEquivalent_of_tendsto_one, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, HasGradientWithinAt.fderivWithin_apply, differentiableWithinAt_abs_neg, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, ProbabilityTheory.integrable_exp_mul_gaussianReal, WeakDual.isClosed_closedBall, MeasureTheory.integrable_add_iff_of_nonpos, hasDerivAt_fourier, fderiv_ccos, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Real.rightDeriv_mul_log, ProbabilityTheory.Kernel.integrable_density, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, ProbabilityTheory.hasFiniteIntegral_prodMk_left, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, nnnorm_inner_le_nnnorm, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ProbabilityTheory.hasFiniteIntegral_comp_iff', IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, fderiv_apply_one_eq_deriv, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, isScalarTower_sphere_sphere_ball, IsUltrametricDist.algNormOfAlgEquiv_apply, integrableOn_exp_mul_complex_Iic, AddCircle.norm_coe_eq_abs_iff, HasFDerivAt.inner, MeasureTheory.L2.eLpNorm_inner_lt_top, ProbabilityTheory.integrable_pow_of_mem_interior_integrableExpSet, deriv_circleMap, ProbabilityTheory.exp_neg_integrableOn_Ioc, ProbabilityTheory.deriv_mgf, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, MeasureTheory.hasFiniteIntegral_norm_iff, MeasureTheory.Integrable.norm_integral_condDistrib_map, OrthonormalBasis.sum_repr_symm, StrongDual.toLpβ_apply, Orientation.kahler_apply_self, IsPrimitiveRoot.nnnorm_eq_one, Real.differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, ProbabilityTheory.hasFiniteIntegral_comp_iff, Complex.conjCLE_nnorm, Polynomial.differentiableOn, HasStrictDerivAt.complexToReal_fderiv', IsLocalFrameOn.coeff_apply_zero_at, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, egauge_ball_one_le_of_one_lt_norm, differentiableOn_neg, Asymptotics.isBigOTVS_pi, LinearMap.continuous_of_nonzero_on_open, MeasureTheory.HasFiniteIntegral.of_mem_Icc, ConvexOn.real_univ_sSup_affine_eq, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, AddCircle.closedBall_eq_univ_of_half_period_le, toWeakSpace_closedConvexHull_eq, ConvexOn.monotoneOn_leftDeriv, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, deriv_neg', Orientation.kahler_rotation_left', Real.differentiable_sin, hasFDerivAtFilter_iff_isLittleOTVS, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.hasDerivWithinAt_aeval, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, rotation_trans, integrableOn_Ioi_rpow_iff, Real.eulerMascheroniConstant_eq_neg_deriv, Real.not_differentiableAt_inv_log_zero, Orientation.abs_areaForm_le, Real.deriv_mul_log, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, ContinuousLinearMap.norm_extendToπ', integrableOn_rpow_mul_exp_neg_rpow, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, differentiableAt_iff_comp_const_sub, MeasureTheory.Integrable.integral_norm_condDistrib, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, signedDist_neg, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, Complex.restrictScalars_toSpanSingleton, integrableOn_exp_mul_Ioi, Orientation.normSq_kahler, ProbabilityTheory.IsCondKernelCDF.integrable, Complex.UnitDisc.mk_neg, HasFDerivWithinAt.clog, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, ProbabilityTheory.integrable_of_mem_integrableExpSet, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, hasFDerivAt_exp_smul_const_of_mem_ball, Real.differentiableAt_tan, Real.differentiable_cosh, NumberField.mixedEmbedding.negAt_symm, fourierSubalgebra_coe, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ProbabilityTheory.integrable_compProd_iff, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, Complex.inner, cfcHom_nnreal_eq_restrict, fderiv_deriv, Asymptotics.isLittleOTVS_neg_right, MeasureTheory.MemLp.norm_rpow_div, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, signedDist_vsub_self_rev, coord_norm', Int.Matrix.one_le_norm_A_of_ne_zero, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, OrthonormalBasis.measurePreserving_repr_symm, spectrum.exists_nnnorm_eq_spectralRadius_of_nonempty, WeakDual.isClosed_polar, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, spec_cfcβAux, MeasureTheory.measureReal_abs_gt_le_integral_charFun, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, EuclideanSpace.piLpCongrLeft_single, hasFDerivAt_exp_smul_const, Differentiable.inner, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Real.hasDerivAt_log, oneTangentSpaceIcc_def, IccRightChart_extend_top_mem_frontier, rotationOf_coe, NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, Module.Basis.parallelepiped_eq_map, MeasureTheory.tendsto_eLpNorm_condExp, iteratedDeriv_comp_two, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, signedDist_self, MeasureTheory.MemLp.norm, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, integrable_inv_one_add_sq, Complex.sqrt_map, signedDist_vsub_self, MeasureTheory.SignedMeasure.rnDeriv_smul, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, signedDist_smul, MeasureTheory.eLpNorm_mono_ae_real, TemperedDistribution.fourierTransform_apply, Real.hasStrictDerivAt_arctan, ZLattice.volume_image_eq_volume_div_covolume, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Real.map_linearMap_volume_pi_eq_smul_volume_pi, nnnorm_apply_le_nnnorm_cfc, Matrix.toEuclideanLin_eq_toLin, StrongDual.toLpβ_of_not_memLp, isConformalMap_complex_linear_conj, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, TrivSqZeroExt.instL1IsBoundedSMul, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, ProbabilityTheory.memLp_id_gaussianReal, intervalIntegral.differentiable_integral_of_continuous, deriv_zpow, LipschitzWith.locallyIntegrable_lineDeriv, AddCircle.norm_neg_period, SmoothBumpCovering.embeddingPiTangent_injOn, MeasureTheory.memLp_norm_rpow_iff, StrongDual.mem_polarSubmodule, exists_dual_vector', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Orientation.kahler_rightAngleRotation_left, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, UnitAddTorus.hasSum_mFourier_series_of_summable, Real.hasDerivAt_mulExpNegMulSq, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, cfcβHom_real_eq_restrict, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, Real.differentiableOn_arccos, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, IsLocalMin.deriv_eq_zero, Real.hasDerivAt_cosh, Real.tendsto_deriv_mul_log_atTop, Orientation.abs_areaForm_of_orthogonal, LipschitzOnWith.ae_differentiableWithinAt_real, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, UnitAddCircle.norm_eq, HasFPowerSeriesAt.deriv, innerβ_apply_apply, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, HasFDerivAt.csin, MeasureTheory.eLpNorm_norm_rpow, Asymptotics.IsBigOTVS.rfl, Asymptotics.IsLittleOTVS.bot, ContinuousLinearMap.isBigOTVS_comp, PadicAlgCl.valuation_def, hfdifferential_apply, MeasureTheory.Integrable.inner_const, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, CompactlySupportedContinuousMap.toNNRealLinear_apply, Real.hasDerivAt_fourierChar, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, Orientation.kahler_rotation_left, SchwartzMap.smulLeftCLM_neg, Complex.conjCLE_enorm, Real.differentiableWithinAt_arccos_Iic, spectrum.differentiableOn_inverse_one_sub_smul, Asymptotics.isBigOTVS_fun_comm, mdifferentiableWithinAt_comp_projIcc_iff, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Orientation.inner_sq_add_areaForm_sq, Real.enorm_exp_I_mul_ofReal_sub_one_le, signedDist_smul_of_neg, MeasureTheory.lpNorm_const_smul, differentiableOn_euclidean, RCLike.reLm_coe, nnnorm_fderiv_norm_rpow_le, differentiableAt_abs_pos, ContinuousLinearMap.adjoint_toSpanSingleton, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, ContinuousLinearMap.toBilinForm_injective, integrableOn_exp_neg_Ioi, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, toSpanSingleton_derivWithin, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, RCLike.nnnorm_conj, SchwartzMap.integral_fourier_mul_eq, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, range_mfderiv_coe_sphere, MeasureTheory.integrable_prod_iff', RCLike.wInner_one_const_right, hahnEmbedding_isOrderedModule_rat, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Affine.Simplex.sign_signedInfDist_touchpoint_empty, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, signedDist_vadd_right_swap, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, Real.differentiable_mulExpNegMulSq, ContinuousMap.neg_norm_le_apply, AddCircle.coe_real_preimage_closedBall_period_zero, integrable_of_isBigO_exp_neg, nnnorm_algebraMap', Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, Complex.conjCLE_apply, NormedSpace.polar_ball, Valued.integer.exists_nnnorm_lt_one, Real.not_DifferentiableAt_log_mul_zero, innerSLFlip_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, iccLeftChart_extend_zero, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, hasDerivAt_const_mul, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, Euclidean.ball_eq_preimage, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, norm_iteratedFDeriv_prod_le, SchwartzMap.lineDerivOp_fourierInv_eq, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, HasFDerivWithinAt.const_cpow, IsLocalFrameOn.eq_iff_coeff, Polynomial.hasDerivAt, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, OrthonormalBasis.repr_symm_single, MeasureTheory.hasFiniteIntegral_toReal_iff, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, interior_range_modelWithCornersEuclideanHalfSpace, WeakDual.CharacterSpace.norm_le_norm_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, AddCircle.addWellApproximable_ae_empty_or_univ, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.hasStrictDerivAt_cos, IntervalIntegrable.intervalIntegrable_slope, iter_deriv_inv, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, integrableOn_Ioi_cpow_of_lt, Differentiable.dist, EulerSine.antideriv_cos_comp_const_mul, ProbabilityTheory.condVar_of_sigmaFinite, RightDerivMeasurableAux.differentiable_set_eq_D, hasDerivWithinAt_zpow, mellin_convergent_iff_norm, Monotone.deriv_nonneg, Orientation.kahler_mul, innerSL_real_flip, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, RCLike.nnnorm_two, ProbabilityTheory.iteratedDeriv_two_cgf, measurableSet_of_differentiableWithinAt_Ioi, TensorProduct.norm_lid, Real.differentiable_iteratedDeriv_sin, ProbabilityTheory.deriv_mgf_zero, MeasureTheory.charFun_eq_charFunDual_toDualMap, HasMFDerivAt.prod, fderivWithin_csin, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sigmoid, ProperCone.dual_dual_flip, flip_innerβ, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, MeasureTheory.LocallyIntegrableOn.norm, HasStrictFDerivAt.isBigOTVS_sub, Orientation.volumeForm_robust', instSMulCommClass_sphere_ball_ball, PiLp.basis_toMatrix_basisFun_mul, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, EulerSine.antideriv_sin_comp_const_mul, signedDist_vadd_left, Diffeology.IsPlot.contDiff, ModularGroup.tendsto_lcRow0, ProbabilityTheory.integrable_kernel_prodMk_left, NormedSpace.sInter_polar_eq_closedBall, ProbabilityTheory.deriv_cgf, Complex.imCLM_coe, isBoundedBilinearMap_inner, intervalIntegral.integral_hasFDerivWithinAt, deriv_pow_field, SmoothBumpCovering.embeddingPiTangent_injective, ProbabilityTheory.memLp_tilted_mul, HasFPowerSeriesAt.hasDerivAt, Int.nnnorm_coe_units, ProbabilityTheory.covarianceBilin_apply, ContinuousLinearMap.isThetaTVS_comp, Polynomial.hasDerivAt_aeval, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivAt_gronwallBound, ContinuousMap.comp_attachBound_mem_closure, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, hasDerivAt_ofReal_cpow_const, hasDerivAt_norm_rpow, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, NumberField.mixedEmbedding.latticeBasis_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, TemperedDistribution.fourierInv_apply, cfcβAux_mem_range_inr, Ideal.Quotient.norm_mk_lt, ContinuousMap.adjoin_id_eq_span_one_add, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, ProbabilityTheory.covarianceBilin_map, Unitization.nnnorm_eq_sup, AffineSubspace.signedInfDist_singleton, norm_deriv_eq_norm_fderiv, ContinuousMap.apply_le_norm, MeasureTheory.AEStronglyMeasurable.integrable_truncation, AkraBazziRecurrence.differentiableAt_smoothingFn, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, hasSum_fourier_series_of_summable, Real.deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, integrableOn_Ioi_exp_neg_mul_sq_iff, Orientation.volumeForm_zero_neg, BoundedContinuousFunction.nnnorm_coeFn_eq, Real.differentiableAt_binEntropy, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, Real.hasDerivAt_arctan', Orientation.areaForm_map, Real.enorm_rpow_of_nonneg, Asymptotics.isEquivalent_iff_tendsto_one, differentiable_neg, hasDerivAt_neg, ProbabilityTheory.integrable_of_mem_interior_integrableExpSet, deriv_bernoulliFun, NNReal.nnnorm_eq, det_fderivPiPolarCoordSymm, Polynomial.hasStrictDerivAt, Real.deriv2_qaryEntropy, Real.differentiableAt_exp, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.commMap_apply_of_isReal, ZSpan.fundamentalDomain_pi_basisFun, AffineMap.hasStrictDerivAt, LipschitzWith.ae_differentiableAt_of_real, InnerProductSpace.toLinearMap_rankOne, Seminorm.finset_sup_smul, MeasureTheory.Measure.integrable_comp_iff, HasMFDerivWithinAt.mul, Bundle.RiemannianMetric.pos, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, HilbertBasis.repr_self, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, BoundedContinuousFunction.add_norm_nonneg, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, Complex.equivRealProdCLM_symm_apply_re, HasFDerivAtFilter.isLittleOTVS, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, MeasureTheory.L2.integrable_inner, MeasureTheory.hasFiniteIntegral_prod_iff, nnnorm_cfcβ_le_iff, MeasureTheory.charFun_map_mul, fderiv_ccosh, HasStrictFDerivAt.cpow, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, BoundedContinuousFunction.norm_sub_nonneg, NumberField.mixedEmbedding.latticeBasis_repr_apply, Filter.HasBasis.isBigOTVS_iff, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, DifferentiableWithinAt.norm_sq, ContinuousMapZero.instCStarRing, SchwartzMap.integral_fourierInv_mul_eq, hasFDerivWithinAt_iff_hasGradientWithinAt, Real.fourierIntegral_continuousLinearMap_apply', signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, Real.differentiable_fourierChar, VectorFourier.fourierPowSMulRight_apply, Matrix.linfty_opNorm_eq_opNorm, nnnorm_cfc_lt_iff, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, Real.deriv_cos', isBigO_deriv_rpow_const_atTop, hasDerivAt_pow, contDiff_succ_iff_deriv, DifferentiableOn.dist, Real.deriv_rpow_const', NumberField.mixedEmbedding.normAtPlace_negAt, Orthonormal.orthogonalFamily, Real.differentiableAt_arcosh, IsLocalMaxOn.fderivWithin_eq_zero, AlternatingMap.measure_def, MeasureTheory.Integrable.of_mem_Icc, LinearMap.isSymmetric_iff_sesqForm, hasDerivWithinAt_derivWithin_iff, hasStrictDerivAt_exp, Complex.isometryOfOrthonormal_apply, Complex.sameRay_iff, AddCircle.norm_le_half_period, Real.hasStrictDerivAt_sqrt, Polynomial.deriv, Int.nnnorm_natCast, Real.hasDerivAt_tan_of_mem_Ioo, contMDiffOn_comp_projIcc_iff, NumberField.mixedEmbedding.finrank, SchwartzMap.integral_fourier_smul_eq, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, Polynomial.hasFDerivWithinAt_aeval, Orientation.inner_rightAngleRotation_right, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, ProbabilityTheory.HasSubgaussianMGF.memLp, LinearMap.continuous_of_isClosed_ker, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Orientation.volumeForm_apply_le, differentiableAt_iff_comp_add_const, RCLike.nnnorm_nnqsmul, ProbabilityTheory.Kernel.eLpNorm_density_le, NumberField.mixedEmbedding.negAt_apply_norm_isReal, innerββ_apply, HasFDerivWithinAt.isBigOTVS_sub, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, hasStrictFDerivAt_list_prod, UnitAddCircle.mem_addWellApproximable_iff, div_le_egauge_ball, StrongDual.toLp_apply, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, contDiff_infty_iff_deriv, LinearMap.toSeminorm_ball_zero, Complex.nnnorm_intCast, Real.differentiableAt_negMulLog, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Orientation.inner_rightAngleRotationAuxβ_left, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasDerivAt.inner, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', Orientation.areaForm_apply_self, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Real.differentiable_fourierChar_neg_bilinear_right, Complex.conjCLE_norm, ProbabilityTheory.variance_linearMap_gaussianReal, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, MeasureTheory.SignedMeasure.integrable_rnDeriv, AffineSubspace.signedInfDist_def, isScalarTower_sphere_ball_ball, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, MeasureTheory.BoundedContinuousFunction.inner_toLp, exists_extension_norm_eq, ProbabilityTheory.integrable_exp_mul_of_le, hasStrictDerivAt_exp_zero_of_radius_pos, NormedSpace.closedBall_inv_subset_polar_closedBall, MeasureTheory.convolution_mul_swap, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, ContinuousLinearMap.norm_smulRightL_le, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, Complex.imCLM_enorm, SchwartzMap.tsupport_derivCLM_subset, hasDerivAt_single, OrthonormalBasis.coe_toBasis_repr_apply, det_rotation, RCLike.enorm_conj, PadicInt.norm_mahler_eq, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, hasStrictDerivAt_exp_of_mem_ball, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, AlternatingMap.measure_parallelepiped, norm_cfcHom, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Affine.Simplex.signedInfDist_affineCombination, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, WeakDual.CharacterSpace.equivAlgHom_coe, AddCircle.norm_eq, le_egauge_ball_one, not_integrableOn_Ici_inv, Matrix.l2_opNNNorm_diagonal, Int.toNat_add_toNat_neg_eq_nnnorm, spectrum.exists_nnnorm_eq_spectralRadius, HasFDerivAt.hasGradientAt, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Real.differentiableAt_sinh, ContinuousLinearMap.isBigOTVS_fun_comp, NormedField.denselyOrdered_range_nnnorm, signedDist_eq_dist_iff_vsub_mem_span, Real.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, exp_neg_integrableOn_Ioi, MeasureTheory.Integrable.const_inner, rotation_symm, IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, VectorFourier.norm_fourierPowSMulRight_le, Complex.equivRealProdCLM_symm_apply_im, AddChar.linearIndependent, integrable_exp_neg_mul_sq_iff, nndist_homothety_center, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Antitone.deriv_nonpos, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, differentiable_tsum', VectorFourier.norm_fourierSMulRight, Polynomial.differentiable, ContinuousLinearEquiv.coord_norm', GaussianFourier.integrable_cexp_neg_sum_mul_add, ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, differentiableOn_abs, ProbabilityTheory.hasDerivAt_mgf, HasFPowerSeriesAt.eq_zero_of_eventually, div_le_egauge_closedBall, LinearMap.mem_span_iff_bound, ProbabilityTheory.integrable_toReal_condDistrib, hasFDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_mul_const, SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, Probability.integrable_cauchyPDFReal, MeasureTheory.integrable_toReal_iff, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, SchwartzMap.fourier_fderivCLM_eq, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, hasStrictFDerivAt_exp_smul_const, integrableOn_rpow_mul_exp_neg_mul_sq, Complex.hasStrictFDerivAt_log_real, Asymptotics.isBigOTVS_map, Real.hasStrictDerivAt_tan, RCLike.wInner_cWeight_const_right, SimpleGraph.isEquivalent_extremalNumber, Real.nnnorm_rpow_of_nonneg, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, iter_deriv_inv_linear, ProbabilityTheory.deriv_cgf_zero, AffineMap.differentiable, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, DifferentiableAt.norm, Real.differentiable_fourierChar_neg_bilinear_left, fderiv_norm_smul_pos, MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore, Real.hasDerivAt_arctan, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Finset.nnnorm_prod_le, WeakDual.CharacterSpace.compContinuousMap_comp, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, EuclideanSpace.nnnorm_eq, innerββ_apply_coe, RCLike.nnnorm_natCast, fderiv_csinh, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, range_modelWithCornersEuclideanHalfSpace, ContinuousMapZero.toNNReal_neg_smul, AddChar.wInner_cWeight_eq_boole, differentiableAt_of_deriv_ne_zero, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, TemperedDistribution.fourier_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, IsLocalMin.fderiv_eq_zero, Real.differentiableAt_qaryEntropy, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Submodule.orthogonal_eq_inter, ContinuousLinearMap.lsmul_flip_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, norm_iteratedFDeriv_smul_le, integrable_exp_neg_mul_sq, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, LinearPMap.mem_adjoint_domain_iff, differentiableWithinAt_zpow, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, CircleIntegrable.out, nnnorm_prod, AddCircle.closedBall_ae_eq_ball, contDiffOn_infty_iff_deriv_of_isOpen, SchwartzMap.integrable_pow_mul, MeasureTheory.memLp_of_bounded, ContinuousMultilinearMap.norm_smulRight, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearMap.hasDerivWithinAt, hasStrictFDerivAt_pow, NormedSpace.polar_closedBall, ContinuousMapZero.toNNReal_smul, integrable_mulExpNegMulSq_comp, integrable_cexp_quadratic, AffineSubspace.signedInfDist_apply_self, coe_innerββ_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, ModularGroup.lcRow0_apply, hasDerivAt_exp_zero, deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, MeasureTheory.integrable_withDensity_iff, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PeriodPair.indep, Module.Basis.opNorm_le, ContMDiff.codRestrict_sphere, Real.differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, SchwartzMap.smulLeftCLM_apply, MeasureTheory.Integrable.norm, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, fderiv_csin, AddCircle.norm_eq', WeakDual.isSeqCompact_polar, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.intervalIntegrable_charFun, ProbabilityTheory.integrable_rpow_of_mem_interior_integrableExpSet, hasFDerivWithinAt_pow, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, NormedField.valuation_apply, hasDerivWithinAt_inv, Asymptotics.isBigOTVS_prodMk_left, hasStrictDerivAt_id, instNonemptySeedRatReal, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, deriv_neg, abs_signedDist_le_dist, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, HasFDerivAt.cpow, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, LinearMap.hasDerivAtFilter, intervalIntegral.integral_hasFDerivAt, MeasureTheory.memLp_norm_iff, integrable_mul_cexp_neg_mul_sq, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.GammaIntegral_convergent, MeasureTheory.hausdorffMeasure_homothety_preimage, HasFPowerSeriesAt.locally_zero_iff, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, AffineSubspace.signedInfDist_apply_of_mem, hasDerivAt_exp_of_mem_ball, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, differentiableAt_abs, ConvexOn.real_sSup_of_nat_affine_eq, ProbabilityTheory.IsRatCondKernelCDF.integrable, Ideal.Quotient.norm_mk_le, ProbabilityTheory.charFun_gaussianReal, WeakDual.CharacterSpace.exists_apply_eq_zero, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, DifferentiableOn.norm, Complex.map_isometryOfOrthonormal, hasDerivAt_zpow, TemperedDistribution.fourierTransformInv_apply, WeakDual.CharacterSpace.compContinuousMap_id, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, MeasureTheory.MemLp.integrable_norm_pow', Matrix.l2_opNorm_def, signedDist_apply_linear, Real.differentiableAt_sin, RCLike.wInner_nonneg, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, parallelepiped_orthonormalBasis_one_dim, Complex.reCLM_enorm, MeasureTheory.integrable_mconv_iff, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, Polynomial.toAddCircle_C_eq_smul_fourier_zero, norm_innerSL_le, MeasureTheory.eLpNorm'_norm_rpow, VectorFourier.hasFDerivAt_fourierChar_smul, integrable_cexp_quadratic', Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, HasStrictFDerivAt.csinh, InformationTheory.not_differentiableAt_klFun_zero, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, Real.exists_extension_norm_eq, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sin, AffineMap.deriv, SmoothBumpCovering.embeddingPiTangent_coe, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ProbabilityTheory.covarianceBilinDual_of_not_memLp', PadicComplex.nnnorm_extends, SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', UnitAddTorus.span_mFourierLp_closure_eq_top, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, MeasureTheory.Integrable.integral_norm_condKernel, Complex.nnnorm_eq_one_of_pow_eq_one, ProbabilityTheory.integrable_gaussianPDFReal, Asymptotics.IsBigOTVS.refl, expNegInvGlue.differentiable_polynomial_eval_inv_mul, cfcHom_eq_of_isStarNormal, HasGradientWithinAt.hasFDerivWithinAt, hasFDerivAt_exp, Orientation.volumeForm_comp_linearIsometryEquiv, Pi.orthonormalBasis_repr, Polynomial.hasDerivWithinAt, differentiableAt_iff_comp_sub_const, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, NumberField.Units.basisOfIsMaxRank_fundSystem, LinearMap.isAdjointPair_inner, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, AnalyticOnNhd.eval_mvPolynomial, WithLp.unitization_nnnorm_def, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Affine.Simplex.signedInfDist_apply_of_ne, ContinuousLinearMap.hasStrictDerivAt, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, signedDist_left_lineMap, hasFDerivAt_inv, Real.deriv_mul_log_zero, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, IccRightChart_extend_top, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Asymptotics.IsBigO.isBigOTVS, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, measurableSet_of_differentiableWithinAt_Ici, fderivInnerCLM_apply, ConvexOn.sSup_affine_eq, nndist_self_homothety, boundary_Icc, deriv_sqrt_mul_log', Asymptotics.isLittleOTVS_sup, Real.differentiableAt_binEntropy_iff_ne_zero_one, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, SchwartzMap.integrable_pow_mul_iteratedFDeriv, Real.fderiv_fourierChar_neg_bilinear_left_apply, Real.deriv_tan, isConformalMap_iff_is_complex_or_conj_linear, Asymptotics.isEquivalent_of_tendsto_one', RCLike.span_one_I, Asymptotics.isThetaTVS_iff_isTheta, Real.exists_measure_rpow_eq_integral, Real.fourierIntegral_continuousMultilinearMap_apply', HasGradientAtFilter.hasDerivAtFilter, AddCircle.norm_eq_of_zero, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, MeasureTheory.eLpNorm_conj, ProbabilityTheory.integrable_comp_iff, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, integrable_cexp_neg_mul_sq, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, differentiableAt_comp_sub_const, finrank_euclideanSpace_fin, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, le_egauge_closedBall_one, InformationTheory.deriv_klFun, boundary_product, differentiable_sigmoid, LinearMap.mem_span_iff_continuous, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, NormedField.exists_lt_nnnorm, Asymptotics.isBigOTVS_comm, OrthonormalBasis.repr_reindex, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, AnalyticOnNhd.eval_continuousLinearMap, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, Asymptotics.isLittleOTVS_pi, ProbabilityTheory.integral_tilted_mul_self, integrableOn_Ioi_deriv_norm_ofReal_cpow, integrable_of_le_of_pow_mul_le, nndist_homothety_self, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, Complex.det_conjLIE, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, RCLike.realLinearIsometryEquiv_apply, ProbabilityTheory.mgf_pos_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, ContinuousLinearMap.norm_smulRightL_apply, Asymptotics.IsThetaTVS.rfl, Orientation.areaForm_rightAngleRotation_left, Differentiable.norm, SchwartzMap.smulLeftCLM_smul, differentiableAt_iff_comp_neg, NumberField.mixedEmbedding.disjoint_negAt_plusPart, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, DifferentiableAt.dist, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, ConvexOn.univ_sSup_of_nat_affine_eq, Icc_isBoundaryPoint_top, ConvexOn.slope_le_leftDeriv_of_mem_interior, NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le, NormedSpace.dual_def, RCLike.inner_eq_wInner_one, NumberField.house_eq_sup', fderiv_norm_sq, Seminorm.smul_le_smul, WeakDual.CharacterSpace.instStarHomClass, Int.Matrix.exists_ne_zero_int_vec_norm_le, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', Real.integrableOn_rpowIntegrandββ_Ici, ModularGroup.smul_eq_lcRow0_add, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, hasDerivAt_abs_pos, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', differentiableWithinAt_Ioi_iff_Ici, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, HasCompactSupport.hasFDerivAt_convolution_left, Complex.isEquivalent_sin, differentiableOn_zpow, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, MeasureTheory.integrable_rnDeriv_mul_log_iff, TemperedDistribution.smulLeftCLM_apply_apply, integrableAtFilter_rpow_atTop_iff, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, nndist_lineMap_left, Orientation.inner_mul_areaForm_sub, fderiv_inner_apply, contDiff_one_iff_deriv, deriv2_sqrt_mul_log, Real.hasStrictDerivAt_log_of_pos, contMDiffOn_projIcc, MeasureTheory.SignedMeasure.im_toComplexMeasure, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, MeasureTheory.pdf.hasFiniteIntegral_mul, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, parallelepiped_single, contMDiff_circleExp, Quaternion.nnnorm_coe, Real.deriv2_negMulLog, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Urysohns.CU.lim_eq_midpoint, MeasureTheory.Measure.integrable_pow_neg_integrablePower, HasFDerivAt.const_cpow, norm_jacobiThetaβ_term_fderiv_le, fderiv_eq_smul_deriv, integrableOn_rpow_mul_exp_neg_mul_rpow, MeasureTheory.Measure.integrable_toReal_rnDeriv, Real.isEquivalent_sinh, Int.Matrix.exists_ne_zero_int_vec_norm_le', intervalIntegral.differentiableOn_integral_of_continuous, hasStrictFDerivAt_exp_smul_const_of_mem_ball, differentiable_circleMap, integrableOn_exp_mul_complex_Ioi, NormedSpace.exp_add, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Complex.restrictScalars_toSpanSingleton', Real.differentiableAt_negMulLog_iff, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, BoundedContinuousFunction.integrable_of_nnreal, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, IsLocalMinOn.fderivWithin_eq_zero, Real.deriv2_mul_log, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, Orientation.abs_volumeForm_apply_le, Complex.conjLIE_symm, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding', deriv_id', hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, Affine.Simplex.signedInfDist_incenter, ProbabilityTheory.integrable_rpow_mul_exp_of_mem_interior_integrableExpSet
|
toSeminormedRing π | CompOp | 3578 mathmath: ArithmeticFunction.vonMangoldt.residueClass_eq, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, LinearMap.det_toContinuousLinearMap, ValueDistribution.logCounting_zero, instSeparatingDual, hasFDerivAt_iff_hasDerivAt, ContMDiffAt.coordChangeL, HurwitzZeta.hasSum_int_hurwitzZetaOdd, iteratedDeriv_scomp_two, LinearMap.IsSymmetric.clm_adjoint_eq, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, WeakFEPair.differentiableAt_Ξ, TemperedDistribution.lineDerivOpCLM_eq, continuousSMul_sphere_ball, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, MeasureTheory.Lp.toTemperedDistributionCLM_apply, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Orientation.kahler_map_complex, Polynomial.differentiableWithinAt, MeasureTheory.convolution_flip, FormalMultilinearSeries.comp_rightInv_aux1, tendsto_zero_iff_meromorphicOrderAt_pos, MDifferentiable.coordChangeL, UpperHalfPlane.mdifferentiable_num, Complex.cos_eq_tsum, ContinuousAt.inner, LinearMap.mkContinuousβ_norm_le', NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, Bundle.ContMDiffRiemannianMetric.isVonNBounded, NormedSpace.isBounded_polar_of_mem_nhds_zero, SchwartzMap.lineDerivOpCLM_eq, HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_div, Valued.instIsUltrametricDist, TensorProduct.enorm_lid, differentiableAt_comp_neg, continuousAt_const_cpow, hasDerivWithinAt_Iio_iff_Iic, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, LinearMap.mkContinuousβ_apply, Matrix.frobenius_nnnorm_mul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, Complex.differentiableAt_sin, Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero, Bundle.ContMDiffRiemannianMetric.contMDiff, Complex.norm_circleTransformBoundingFunction_le, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, Seminorm.absorbent_closedBall_zero, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, LeftInvariantDerivation.lift_zero, Complex.isOpen_re_lt_EReal, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcβHom, RCLike.map_apply, differentiable_const_cpow_of_neZero, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, completedZeta_eq_tsum_of_one_lt_re, Complex.continuousOn_exp, ContinuousLinearMap.continuousβ, RCLike.geometric_hahn_banach_point_open, hasDerivWithinAt_add_const_iff, IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, CuspFormClass.holo, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, RCLike.ofRealCLM_apply, SchwartzMap.integral_sesq_fourier_fourier, HurwitzZeta.differentiableAt_hurwitzZeta_sub_one_div, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, ModularFormClass.differentiableAt_comp_ofComplex, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, Real.hasFDerivAt_fourierChar_neg_bilinear_left, hasStrictDerivAt_intCast, LeftInvariantDerivation.leibniz, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.convolution_eq_right', EisensteinSeries.hasSum_e2Summand_symmetricIcc, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, RCLike.reCLM_apply, HurwitzZeta.differentiableAt_hurwitzZetaEven, curveIntegral_smul, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, RCLike.separate_convex_open_set, NumberField.canonicalEmbedding.mem_span_latticeBasis, Real.fderiv_fourierIntegral, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, PeriodPair.hasSumLocallyUniformly_weierstrassP, Subalgebra.spectrum_sUnion_connectedComponentIn, Function.FactorizedRational.divisor, hasDerivAt_sqrt_mul_log, LinearMap.IsSymmetric.restrictScalars, LSeries.term_sum, ContinuousLinearMap.continuous_det, HurwitzZeta.hasSum_int_cosKernelβ, HasFiniteFPowerSeriesAt.neg, Complex.isOpenMap_im, SchwartzMap.norm_le_seminorm, HurwitzZeta.hasSum_int_hurwitzZetaEven, Complex.ofRealCLM_coe, Complex.kahler, Complex.norm_polarCoord_symm, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, ContinuousLinearMap.map_add_add, ContinuousAlternatingMap.isEmbedding_restrictScalars, WeakDual.isCompact_polar, MeromorphicOn.divisor_fun_smul, finrank_real_complex_fact', PeriodPair.deriv_weierstrassP, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, Real.hasDerivAt_sigmoid, PeriodPair.coeff_weierstrassPExceptSeries, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, Matrix.IsHermitian.det_abs, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, RCLike.ofRealLI_apply, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Complex.comap_exp_cobounded, ModularForm.mul_slash, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, differentiableAt_zpow, hasFDerivAt_multiset_prod, Circle.exp_arg, spectrum.subset_closedBall_norm_mul, Circle.injective_arg, OrthonormalBasis.repr_injective, continuousSMul_sphere_sphere, spectrum.instCompactSpace, ContinuousLinearMap.continuousSMul, hasFTaylorSeriesUpToOn_top_iff_right, DirichletCharacter.LSeries_eulerProduct_tprod, smoothSheafCommRing.nonunits_stalk, LSeries.term_convolution', CuspFormClass.zero_at_infty_comp_ofComplex, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, PeriodPair.derivWeierstrassPExcept_sub, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries, deriv_mem_iff, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, Bornology.isVonNBounded_add_of_nonempty, NumberField.canonicalEmbedding.latticeBasis_apply, Complex.integral_comp_pi_polarCoord_symm, FormalMultilinearSeries.radius_pi_eq_iInf, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, Padic.withValUniformEquiv_norm_le_one_iff, ApproximatesLinearOn.lipschitz, summableLocallyUniformlyOn_iteratedDerivWithin_cexp, tendsto_cobounded_iff_meromorphicOrderAt_neg, Real.hasStrictDerivAt_rpow_const_of_ne, Matrix.IsHermitian.cfc_eq, lp.inner_eq_tsum, UpperHalfPlane.image_coe_sphere, Complex.isCoveringMap_exp, StrongDual.polarSubmodule_eq_setOf, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, ContinuousLinearMap.isUniformEmbedding_restrictScalars, PeriodPair.Οβ_div_two_notMem_lattice, OrthonormalBasis.sum_inner_mul_inner, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, range_circleMap, Asymptotics.isLittleOTVS_one, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, ContinuousLinearMap.hasDerivAtFilter, HasFPowerSeriesAt.locally_ne_zero, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, span_fourier_closure_eq_top, Complex.GammaSeq_tendsto_Gamma, PeriodPair.basis_one, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, RCLike.conjCLE_norm, HasFPowerSeriesOnBall.add, Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, SchwartzMap.seminorm_le_bound, Bornology.isVonNBounded_add_self, WeakDual.isClosed_image_polar_of_mem_nhds, one_add_cpow_hasFPowerSeriesAt_zero, RCLike.algebraMap_eq_ofReal, circleIntegrable_iff, LinearMap.polar_eq_iInter, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, MeasureTheory.MemLp.const_inner, DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontriv, Complex.tsum_exp_neg_mul_int_sq, not_integrableOn_Ioi_cpow, Real.fderiv_fourierChar_neg_bilinear_right_apply, WithSeminorms.mem_nhds_iff, BoundedContinuousFunction.char_neg, UpperHalfPlane.isOpenEmbedding_coe, Unitization.real_cfcβ_eq_cfc_inr, ContDiffAt.fderiv_right_succ, flip_innerSL_real, RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, hasFPowerSeriesOnBall_pi_iff, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, Complex.uniformlyContinuous_im, eventually_enorm_mfderivWithin_symm_extChartAt_lt, HasFPowerSeriesWithinAt.const_smul, BoundedContinuousFunction.char_zero_eq_one, SchwartzMap.lineDerivOp_fourier_eq, isClosedEmbedding_cfcβAux, LeftInvariantDerivation.coe_derivation, innerSL_apply_apply, RCLike.norm_expect_le, HasGradientAt.continuousOn, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, SeminormFamily.filter_eq_iInf, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerββ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, inner_sum, HasFTaylorSeriesUpTo.hasFDerivAt, Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_ne, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, UpperHalfPlane.comp_ofComplex_of_im_pos, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContinuousLinearMap.toBilinForm_apply, Seminorm.restrictScalars_closedBall, RCLike.map_same_eq_id, DoubleCentralizer.nnnorm_def', NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, Seminorm.bddAbove_range_iff, Complex.continuousOn_arg, dist_iteratedFDerivWithin_one, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, NormedSpace.image_isVonNBounded_iff, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, UpperHalfPlane.dist_le_iff_dist_coe_center_le, LeftInvariantDerivation.left_invariant', hasDerivAt_bernoulliFun, hasSum_one_div_nat_pow_mul_fourier, derivWithin_fderivWithin, two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even, MultilinearMap.mkContinuousMultilinear_apply, SchwartzMap.instContinuousSMul, Complex.UnitDisc.instSMulCommClass_closedBall_circle, TemperedDistribution.lineDerivOp_fourier_eq, Complex.frontier_setOf_re_le, PadicInt.norm_mahlerTerm, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, ContDiff.differentiable_deriv_two, Seminorm.smul_inf, Submodule.Quotient.instIsBoundedSMul, FormalMultilinearSeries.derivSeries_coeff_one, Polynomial.isCoveringMapOn_eval, Complex.ofRealCLM_norm, Complex.UnitDisc.instSMulCommClass_closedBall_left, MulAlgebraNorm.extends_norm', mdifferentiableOn_symm_coordChangeL, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, StarAlgebra.elemental.characterSpaceToSpectrum_coe, Bornology.IsBounded.reProdIm, Circle.ofConjDivSelf_coe, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, NumberField.mixedEmbedding.mem_idealLattice, MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE, SchwartzMap.bilinLeftCLM_apply, Complex.borelSpace, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, IsConformalMap.is_complex_or_conj_linear, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', AffineMap.hasDerivWithinAt, MeromorphicOn.divisor_const, LeftInvariantDerivation.left_invariant, instSMulCommClass_sphere_sphere_sphere, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, Complex.convexHull_reProdIm, NormedSpace.toIsBoundedSMul, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, Complex.hasStrictDerivAt_tan, Circle.starRingEnd_addChar, ContDiff.continuous_deriv_one, curveIntegralFun_smul, Complex.closure_preimage_im, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasDerivWithinAt_iff_isLittleO, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, mul_comm, RCLike.re_add_im_ax, ContinuousAlternatingMap.piLIE_apply_apply, Matrix.PosSemidef.sqrt_eq_zero_iff, Differentiable.fderiv_norm_rpow, NumberField.InfiniteAdeleRing.algebraMap_apply, UnitAddTorus.mFourierSubalgebra_coe, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, hasDerivWithinAt_zero, iteratedDerivWithin_tsum_cexp_eq, ContDiffAt.hasStrictDerivAt, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, MeasureTheory.integral_const_mul, Complex.continuous_sin, FormalMultilinearSeries.hasSum_of_finite, hasDerivAtFilter_ofNat, Complex.exp_eq_exp_β, FormalMultilinearSeries.changeOriginSeries_summable_auxβ, curveIntegrable_smul_iff, TensorProduct.toLinearEquiv_lidIsometry, HasFPowerSeriesOnBall.restrictScalars, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, ContinuousLinearMap.isometry_mul_flip, PeriodPair.weierstrassP_coe, AnalyticOnNhd.eval_linearMap', HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, ClosedSubmodule.inf_orthogonal, LinearMap.coe_toContinuousLinearMap', balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, ModularForm.prod_slash, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, contDiffOn_iff_continuousOn_differentiableOn, Complex.isQuotientCoveringMap_npow, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, sum_cauchyPowerSeries_eq_integral, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, SchwartzMap.laplacianCLM_eq, CStarModule.innerSL_apply, monomial_has_deriv_aux, continuous_equivFun_basis, DirichletCharacter.LSeries_twist_vonMangoldt_eq, LinearIsometryEquiv.conjStarAlgEquiv_apply, PadicInt.mahlerTerm_apply, LinearMap.toMatrixOrthonormal_reindex, MeasureTheory.integral_div, MeasureTheory.ConvolutionExistsAt.integrable, Matrix.IsHermitian.eigenvalues_eq, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, Filter.tendsto_ofReal_iff', iter_deriv_zpow', PadicInt.coe_sum, Complex.deriv_cos, WithSeminorms.continuousSMul, Matrix.exp_conj', hasLineDerivAt_iff_isLittleO_nhds_zero, Complex.not_differentiableAt_Gamma_neg_nat, RCLike.borelSpace, Real.hasStrictDerivAt_sinh, AddCircle.homeomorphCircle'_symm_apply, TestFunction.continuous_iff_continuous_comp, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, HasFiniteFPowerSeriesOnBall.sum, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, ConvexOn.univ_sSup_of_countable_affine_eq, IsUltrametricDist.of_normedAlgebra', RCLike.hasSum_ofReal, InnerProductSpace.inner_left_rankOne_apply, Matrix.PosSemidef.commute_iff, TestFunction.toBoundedContinuousFunctionCLM_apply, RCLike.continuous_normSq, IsLocalFrameOn.coeff_apply_of_mem, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, Matrix.exp_neg, Manifold.IsImmersionAtOfComplement.ofOpen, HasFPowerSeriesAt.add, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, ContinuousAlternatingMap.curryLeft_smul, continuous_const_cpow, AlgebraNorm.extends_norm, ContinuousLinearMap.hasBasis_nhds_zero, polynomialFunctions.starClosure_topologicalClosure, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerββ_apply_apply, hasFDerivWithinAt_inv, hasSum_nat_jacobiTheta, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, iteratedDeriv_scomp_three, hasDerivWithinAt_pi, differentiableOn_iteratedDerivWithin_cotTerm, smoothSheafCommRing.instLocalRing_stalk, Real.integrable_prod_sub, NormedSpace.isVonNBounded_ball, MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt, ContinuousLinearMap.eq_adjoint_iff, PeriodPair.hasSum_derivWeierstrassPExcept, ContDiffAt.fderiv_succ, rotation_apply, toMatrix_rotation, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, convexHull_union_neg_eq_absConvexHull, RCLike.smul_re, Polynomial.div_tendsto_zero_iff_degree_lt, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, HasFPowerSeriesAt.comp, Complex.differentiableAt_GammaAux, ContinuousLinearMap.IsPositive.smul_of_nonneg, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, EuclideanSpace.nndist_eq, LinearMap.polar_singleton, FormalMultilinearSeries.sum_of_finite, MeromorphicOn.divisor_pow, ModularForm.prod_slash_sum_weights, MeasureTheory.convolution_tendsto_right, gelfandStarTransform_apply_apply, HasFTaylorSeriesUpToOn.zero_eq', HarmonicAt.analyticAt_complex_partial, Complex.instPathConnectedSpaceUnits, ContDiff.continuous_deriv, NormedSpace.Dual.toWeakDual_continuous, WithSeminorms.withSeminorms_eq, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMultilinearMap.norm_smulRightL_le, ContinuousLinearMap.precompL_apply, DoubleCentralizer.nnnorm_snd, differentiableAt_comp_add_const, IsSelfAdjoint.adjoint_eq, Complex.continuousOn_cos, OrthonormalBasis.measurePreserving_repr, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ZMod.completedLFunction_def_even, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, RCLike.geometric_hahn_banach_closed_point, MeasureTheory.AEStronglyMeasurable.inner_const, Real.hasDerivAt_arcosh, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, Complex.isOpen_slitPlane, HasGradientAt.continuousAt, VectorBundleCore.contMDiffOn_coordChange, FormalMultilinearSeries.radius_le_smul, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, MeasureTheory.SignedMeasure.toComplexMeasure_apply, ModularForm.tsum_logDeriv_eta_q, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, CStarMatrix.toCLM_injective, enorm_fderiv_norm_rpow_le, ContinuousLinearMap.isPositive_self_comp_adjoint, dslope_eventuallyEq_slope_nhdsNE, LinearMap.adjoint_toContinuousLinearMap, StrongFEPair.differentiable_Ξ, hasDerivAt_iff_isLittleO, spectrum.isOpen_resolventSet, Polynomial.toAddCircle_X_pow_eq_fourier, HasDerivWithinAt.hasFDerivWithinAt, hasFPowerSeriesAt_const, fderiv_eq_deriv_mul, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, HasFPowerSeriesWithinOnBall.fderivWithin, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, FormalMultilinearSeries.radius_compNeg, SeminormFamily.comp_apply, gelfandTransform_bijective, Polynomial.differentiableOn_aeval, SchwartzMap.integral_bilin_fourierIntegral_eq, NumberField.mixedEmbedding.polarSpaceCoord_target, OnePoint.isZeroAt_iff_exists_SL2Z, LinearIsometryEquiv.adjoint_eq_symm, NumberField.mixedEmbedding.negAt_apply_snd, extDeriv_fun_smul, ContinuousAlternatingMap.toAlternatingMap_curryLeft, MeromorphicAt.inv_iff, Matrix.toEuclideanLin_apply, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, NormedField.discreteTopology_or_nontriviallyNormedField, WithSeminorms.tendsto_nhds', Complex.tendsto_exp_nhds_zero_iff, fourier_norm, ContinuousLinearMap.opNorm_mul, AlgebraNormClass.map_smul_eq_mul, Complex.uniformContinuous_im, Complex.frontier_preimage_re, CuspForm.coe_trace, EisensteinSeries.e2Summand_summable, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, image_circleMap_Ioc, TemperedDistribution.smulLeftCLM_neg, analyticOrderAt_eq_top, Real.hasStrictDerivAt_arccos, AnalyticAt.frequently_zero_iff_eventually_zero, RCLike.conjCLE_apply, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Complex.reCLM_nnnorm, Unitization.nnnorm_def, UpperHalfPlane.coe_pos_real_smul, isScalarTower_closedBall_closedBall_closedBall, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Complex.instContinuousStar, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, NumberField.mixedEmbedding.negAt_preimage, HasLineDerivAt.tendsto_slope_zero_right, isScalarTower_sphere_closedBall_closedBall, Complex.hasDerivAt_GammaIntegral, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, Complex.deriv_ofReal_cpow_const, UpperHalfPlane.comp_ofComplex, Complex.starConvex_ofReal_slitPlane, PiTensorProduct.mapL_smul, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, Real.fderiv_fourier, ApproximatesLinearOn.norm_fderiv_sub_le, ContinuousLinearMap.adjointAux_norm, RCLike.toIsStrictOrderedModule, CStarMatrix.norm_def', NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, HurwitzZeta.hasSum_nat_sinZeta, ValueDistribution.logCounting_top, Quaternion.linearIsometryEquivTuple_symm_apply, LeftInvariantDerivation.lift_add, hasDerivAtFilter_natCast, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, Pi.counit_eq_adjoint, ContinuousAlternatingMap.instContinuousSMul, LinearMap.toMatrixOrthonormal_apply_apply, HasFDerivAt.restrictScalars, balancedHull_subset_convexHull_union_neg, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, Complex.UnitDisc.coe_smul_circle, PiTensorProduct.projectiveSeminorm_apply, Complex.summable_conj, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, HasGradientWithinAt.continuousWithinAt, Complex.continuousAt_arg, PeriodPair.latticeBasis_zero, ZMod.LFunction_def_odd, summable_mul_of_bigO_atTop, SchwartzMap.fourier_lineDerivOp_eq, Complex.starConvex_one_slitPlane, ContinuousLinearMapWOT.inducingFn_apply, TemperedDistribution.instLineDerivLeftSMulReal, meromorphicOrderAt_eq_top_iff, CStarMatrix.inner_toCLM_conjTranspose_left, hasStrictDerivAt_exp_smul_const, ContinuousMap.setOfIdeal_ofSet_of_isOpen, isBoundedBilinearMap_comp, Complex.interior_setOf_le_re, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, Filter.tendsto_ofReal_iff, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, hasStrictDerivAt_add_const_iff, Finsupp.sum_inner, TemperedDistribution.fourierInv_lineDerivOp_eq, UpperHalfPlane.mdifferentiable_inv_denom, multipliable_one_add_of_summable, LeftInvariantDerivation.lift_smul, FormalMultilinearSeries.rightInv_removeZero, WithAbs.uniformSpace_comap_eq_of_comp, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', hasStrictDerivAt_exp_smul_const', Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, Orientation.kahler_eq_zero_iff, AddChar.sum_apply_eq_ite, EulerProduct.eulerProduct_completely_multiplicative, PositiveLinearMap.preGNS_norm_def, contDiff_succ_iff_fderiv, ContinuousLinearMap.opNNNorm_prod, UpperHalfPlane.dist_eq_iff_eq_sinh, hasDerivAtFilter_zero, Complex.integral_comp_polarCoord_symm, Complex.uniformContinuous_re, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, PeriodPair.Οβ_div_two_notMem_lattice, UnitAddTorus.mFourierCoeff_toLp, WeakDual.toStrongDual_inj, ContinuousLinearMap.uniformContinuous_restrictScalars, HurwitzZeta.differentiable_expZeta_of_ne_zero, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, isModuleTopologyOfFiniteDimensional, PeriodPair.hasSum_derivWeierstrassP, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, PeriodPair.compl_lattice_diff_singleton_mem_nhds, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, hasDerivAt_id', integrableOn_Ioi_cpow_iff, ContinuousMultilinearMap.curryRight_norm, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, HurwitzZeta.differentiable_hurwitzZetaOdd, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, MeasureTheory.MemLp.inner_const, LSeries_deriv_eqOn, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, MeasureTheory.convolution_lsmul, HurwitzZeta.differentiable_hurwitzZeta_sub_hurwitzZeta, PeriodPair.hasSumLocallyUniformly_derivWeierstrassP, Complex.sameRay_of_arg_eq, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, SeminormFamily.finset_sup_comp, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, UpperHalfPlane.ofComplex_apply_of_im_nonpos, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, Real.deriv_sqrt_aux, deriv_fderiv, IsOpen.reProdIm, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, RegularNormedAlgebra.isometry_mul', Complex.frontier_setOf_im_lt, cauchyPowerSeries_apply, summable_eisSummand, ContDiffWithinAt.hasFDerivWithinAt_nhds, ModularFormClass.continuous, Matrix.PosSemidef.det_sqrt, Orientation.rotation_map_complex, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, Complex.isConnected_of_lowerHalfPlane, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, tendsto_cobounded_of_meromorphicOrderAt_neg, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, TensorProduct.lidIsometry_apply, ContDiffMapSupportedIn.seminorm_le_iff, MeasureTheory.StronglyMeasurable.inner, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, Complex.tendsto_exp_comap_re_atTop, convex_halfSpace_re_le, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, PadicInt.fwdDiff_tendsto_zero, Complex.deriv_Gamma_add_one, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux', Seminorm.ball_norm_mul_subset, EuclideanSpace.dist_single_same, EulerProduct.eulerProduct_hasProd, Complex.continuous_re, Module.Basis.coe_toOrthonormalBasis_repr, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, Matrix.linfty_opNNNorm_eq_opNNNorm, VectorFourier.fourierIntegral_iteratedFDeriv, UpperHalfPlane.contMDiff_coe, PadicInt.compactSpace, InformationTheory.hasDerivAt_klFun, CuspForm.holo', InnerProductSpace.nnnorm_rankOne, PeriodPair.mem_lattice, BoundedContinuousFunction.mem_charPoly, spectrum.gelfandTransform_eq, Orientation.kahler_comp_rightAngleRotation, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, BoundedContinuousFunction.charAlgHom_apply, LeftInvariantDerivation.comp_L, ArithmeticFunction.vonMangoldt.residueClass_apply, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, FormalMultilinearSeries.continuousOn_of_finite, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, LinearMap.trace_eq_sum_inner, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, MeasureTheory.memLp_haarAddCircle_iff, ContinuousLinearMap.flip_smul, MeromorphicOn.divisor_inv, PadicInt.mahlerSeries_apply, Circle.arg_eq_arg, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, NumberField.mixedEmbedding.convexBodySum_compact, MeromorphicOn.divisor_fun_pow, Bundle.ContinuousRiemannianMetric.continuous, Matrix.IsHermitian.charpoly_cfc_eq, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow, MeasureTheory.ConvolutionExistsAt.integrable_swap, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, spectrum.isCompact, HasFiniteFPowerSeriesOnBall.eq_partialSum, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, IsLocalFrameOn.coeff_congr, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, AffineMap.hasDerivAt_lineMap, FiniteDimensional.rclike_to_real, Complex.comap_exp_nhds_zero, EisensteinSeries.G2_eq_tsum_symmetricIco, Complex.equivRealProdCLM_symm_apply, Seminorm.convexOn, Complex.cos_eq_tsum', ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasDerivWithinAt.norm_sq, HasGradientAtFilter.hasDerivAtFilter', WeakDual.CharacterSpace.continuousMapEval_bijective, cot_series_rep', DirichletCharacter.differentiableAt_LFunction, differentiableOn_dslope_of_notMem, LowerSemicontinuousOn.isClosed_re_epigraph, NumberField.canonicalEmbedding.integralBasis_repr_apply, Complex.interior_preimage_re, Complex.continuous_cosh, fourier_one, Polynomial.ofReal_eval, HasFPowerSeriesOnBall.fderiv_eq, Seminorm.coe_restrictScalars, ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, ContinuousLinearMap.flip_mul, NormedSpace.inclusionInDoubleDual_norm_eq, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, PiTensorProduct.projectiveSeminorm_tprod_le, PadicInt.continuous_choose, AffineMap.hasDerivWithinAt_lineMap, PeriodPair.basis_zero, UpperHalfPlane.image_coe_ball, ContinuousLinearMap.fderiv_of_bilinear, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Complex.closure_setOf_lt_im, Real.Angle.coe_toCircle, Real.hasDerivWithinAt_arccos_Ici, Seminorm.gaugeSeminorm_ball, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ContinuousLinearMap.nnnorm_toSpanSingleton, iteratedFDerivWithin_succ_apply_right, ContinuousAlternatingMap.alternatizeUncurryFin_smul, contDiffAt_map_inverse, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, EulerProduct.eulerProduct, Complex.hasDerivAt_Gammaβ_one, SchwartzMap.toBoundedContinuousFunctionCLM_apply, hasSum_jacobiThetaβ_term, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, deriv_id'', hasFDerivAt_jacobiThetaβ_term, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, Complex.continuousAt_cpow_const_of_re_pos, ContinuousAlternatingMap.norm_restrictScalars, OrthonormalBasis.coe_ofRepr, LSeries_deriv, Submodule.adjoint_subtypeL, MeasureTheory.convolutionExistsAt_flip, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, AbsoluteValue.Completion.locallyCompactSpace, AnalyticOn.fderivWithin, UpperHalfPlane.contMDiff_inv_denom, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, RCLike.conjLIE_apply, Complex.uniformlyContinuous_re, WithAbs.tendsto_one_div_one_add_pow_nhds_one, PadicInt.coe_addChar_of_value_at_one, Complex.map_exp_comap_re_atTop, RCLike.summable_ofReal, Complex.orthonormalBasisOneI_repr_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, PadicInt.mahlerSeries_apply_nat, ContDiffAt.fderiv_right, Complex.differentiable_exp, MeasureTheory.convolution_def, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, Complex.UnitDisc.isEmbedding_coe, HurwitzZeta.hasSum_nat_completedCosZeta, HasDerivAt.hasFDerivAt, tendsto_sub_mul_tsum_nat_cpow, Polynomial.toAddCircle.integrable, fourier_zero, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, RCLike.imLm_coe, fourier_neg', HasFPowerSeriesWithinOnBall.prod, NormedSpace.eq_iff_forall_dual_eq, Function.Periodic.boundedAtFilter_cuspFunction, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, ContinuousLinearMap.continuous_restrictScalars, hasStrictDerivAt_const_add_iff, Summable_cotTerm, isBoundedBilinearMap_compMultilinear, norm_cauchyPowerSeries_le, hasFDerivAt_norm_rpow, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, HasFPowerSeriesOnBall.uniform_geometric_approx, summable_jacobiThetaβ_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, MeromorphicOn.divisor_sub_const_self, Unitization.cobounded_eq_aux, sum_inner, Polynomial.div_tendsto_atBot_zero_of_degree_lt, HurwitzZeta.hasSum_nat_hurwitzZetaEven, HasFPowerSeriesWithinAt.fderivWithin_eq, ContDiffBump.convolution_tendsto_right, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, continuousWithinAt_dslope_of_ne, HurwitzZeta.hasSum_int_cosKernel, ZMod.completedLFunction_def_odd, AnalyticOnNhd.fderiv_of_isOpen, FormalMultilinearSeries.id_comp', Seminorm.rescale_to_shell_zpow, OnePoint.isZeroAt_infty_iff, Circle.smul_def, contDiffOn_infty_iff_fderivWithin, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, Matrix.toEuclideanCLM_toLp, Seminorm.smul_closedBall_zero, WeakDual.CharacterSpace.homeoEval_naturality, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, PeriodPair.isClosed_lattice, BoundedContinuousFunction.innerProbChar_zero, FormalMultilinearSeries.coeff_eq_zero, Complex.tendsto_normSq_cocompact_atTop, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, RCLike.conjCLE_coe, HasFPowerSeriesOnBall.sum, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, LeftInvariantDerivation.evalAt_coe, Matrix.IsHermitian.trace_eq_sum_eigenvalues, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', HasFPowerSeriesOnBall.fderiv, convex_halfSpace_im_gt, contDiffOn_nat_iff_continuousOn_differentiableOn, Matrix.PosSemidef.sqrt_eq_one_iff, EisensteinSeries.tendsto_zero_inv_linear_sub, GaussianFourier.integrable_cexp_neg_mul_sum_add, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Complex.continuousOn_sin, Complex.hasStrictFDerivAt_cpow, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, tendsto_riemannZeta_sub_one_div, ZetaAsymptotics.tendsto_Gamma_term_aux, NumberField.InfinitePlace.Completion.locallyCompactSpace, Seminorm.restrictScalars_ball, InnerProductSpace.rankOne_eq_zero, Polynomial.differentiable_aeval, Complex.polarCoord_apply, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Convex.toWeakSpace_closure, Complex.differentiable_iteratedDeriv_sin, AddChar.expect_apply_eq_zero_iff_ne_zero, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, Complex.hasStrictDerivAt_sinh, tsum_pow_div_one_sub_eq_tsum_sigma, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, ContMDiffOn.coordChangeL, EisensteinSeries.linear_right_summable, InnerProductSpace.inner_right_rankOne_apply, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, spectrum.eventually_isUnit_resolvent, UnitAddTorus.mFourier_add, Bornology.isVonNBounded_sub_of_nonempty, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, PositiveLinearMap.preGNS_inner_def, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, fderivWithin_inv', hasDerivAt_add_const_iff, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, UpperHalfPlane.cosh_dist, LSeries_eq_mul_integral_of_nonneg, UpperHalfPlane.image_coe_closedBall, PeriodPair.periodic_derivWeierstrassP, EisensteinSeries.summable_linear_left_mul_linear_left, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, HasFPowerSeriesOnBall.compContinuousLinearMap, differentiableWithinAt_of_derivWithin_ne_zero, LinearMap.IsSymmetric.coe_toSelfAdjoint, MeromorphicOn.divisor_intCast, Complex.tendsto_one_add_div_pow_exp, quasispectrum.isCompact, TensorProduct.inner_lid_lid, ContDiffMapSupportedIn.uniformSpace_eq_iInf, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, riemannZeta_eulerProduct_exp_log, PiTensorProduct.liftIsometry_tprodL, NormedSpace.inclusionInDoubleDual_norm_le, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, hasDerivWithinAt_one, IsSelfAdjoint.isConnected_spectrum_compl, WeakDual.isCompact_closedBall, PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm, ConvexOn.sSup_of_countable_affine_eq, TestFunction.coe_ofSupportedInCLM, RCLike.reCLM_coe, ContDiffBump.normed_convolution_eq_right, continuousSMul_closedBall_ball, UpperHalfPlane.dist_coe_center, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, HasDerivWithinAt.inner, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, DifferentiableAt.inner, MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, tendsto_logDeriv_euler_sin_div, NormedSpace.exp_continuousMap_eq, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, EisensteinSeries.div_linear_zpow_differentiableOn, Seminorm.comp_smul, UnitAddTorus.mFourier_zero, absorbent_nhds_zero, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, isScalarTower_sphere_sphere_sphere, MeromorphicOn.analyticAt_mem_codiscreteWithin, MeasureTheory.hasFDerivAt_convolution_right_with_param, ContMDiffAt.mfderiv_const, smoothSheafCommRing.isUnit_stalk_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, FormalMultilinearSeries.coeff_ofScalars, UpperHalfPlane.ofComplex_apply_of_im_pos, hasDerivAt_ofNat, iteratedFDerivWithin_eq_equiv_comp, RCLike.isUniformEmbedding_ofReal, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, Orthonormal.inner_left_right_finset, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, ContDiffMapSupportedIn.structureMapCLM_zero_apply, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, differentiableAt_inv_iff, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, SchwartzMap.norm_iteratedFDeriv_le_seminorm, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, Finsupp.inner_sum, LinearMap.deriv, SchwartzMap.seminorm_le_bound', contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, zeta_eq_tsum_one_div_nat_cpow, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, Bornology.IsVonNBounded.restrict_scalars_of_nontrivial, continuousAt_cpow, InnerProductSpace.toDualMap_apply, gelfandTransform_map_star, TotallyBounded.isVonNBounded, NumberField.mixedEmbedding.convexBodySumFun_smul, Complex.interior_preimage_im, NumberField.mixedEmbedding.logMap_real_smul, ContinuousLinearMap.adjoint_inner_left, Complex.isBigO_re_sub_re, AddChar.sum_apply_eq_zero_iff_ne_zero, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, isQuotientCoveringMap_npow, EulerProduct.eulerProduct_tprod, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, Complex.comap_exp_nhdsNE, ContinuousLinearMap.isBoundedBilinearMap, fdifferential_apply, ContinuousMultilinearMap.hasBasis_nhds_zero, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, Real.hasStrictDerivAt_arcosh, LinearMap.extendToπ_apply, UnitAddTorus.coeFn_mFourierLp, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, MeromorphicOn.divisor_sub_const_of_ne, ContinuousMultilinearMap.ofSubsingletonβα΅’_symm_apply, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, totallyBounded_absConvexHull, ProperSpace.of_nontriviallyNormedField_of_weaklyLocallyCompactSpace, NumberField.mixedEmbedding.polarCoord_symm_apply, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, Complex.deriv_Gamma_nat, MDifferentiableOn.coordChangeL, hasDerivAt_update, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, fderiv_pow_ring, Complex.continuous_sinh, constFormalMultilinearSeries_apply_zero, Padic.instCompleteSpace, DifferentiableAt.fderiv_restrictScalars, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, Complex.UnitDisc.coe_closedBall_smul, FormalMultilinearSeries.radius_smul_eq, ContinuousLinearMap.bilinearComp_zero_right, Circle.ext_iff, AlgebraNorm.smul', IsContMDiffRiemannianBundle.exists_contMDiff, ContDiffWithinAt.fderivWithin'', ContinuousMap.ideal_isMaximal_iff, Complex.isOpen_compl_range_intCast, BaireSpace.instBarrelledSpace, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, integral_conj, Complex.hasSum_ofReal, CuspFormClass.zero_at_infty, hasDerivAtFilter_add_const_iff, HurwitzZeta.completedHurwitzZetaEven_residue_one, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, hasDerivAt_jacobiThetaβ_fst, InnerProductSpace.rank_rankOne, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, Module.Basis.coe_toOrthonormalBasis_repr_symm, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, UnitAddTorus.mFourier_neg, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, contMDiffAt_coordChangeL, InnerProductSpace.toDual_apply_apply, Complex.continuousOn_norm_circleTransformBoundingFunction, Complex.continuousAt_Gamma_one, intervalIntegral.intervalIntegrable_cpow, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, Real.hasDerivAt_arcsin, coe_lpBCFβα΅’, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, PeriodPair.differentiableOn_derivWeierstrassP, ProperCone.innerDual_singleton, Complex.hasDerivAt_sinh, PeriodPair.weierstrassPExcept_def, RCLike.ofReal_re_ax, differentiable_inner, LeftInvariantDerivation.coe_sub, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, HasLineDerivAt.tendsto_slope_zero_left, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, tendsto_nhds_iff_meromorphicOrderAt_nonneg, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, LDL.lower_conj_diag, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionβ_apply_apply, hasFDerivAt_list_prod', HurwitzZeta.hasSum_int_cosZeta, hasFDerivAt_integral_of_dominated_loc_of_lip', SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, ArithmeticFunction.IsMultiplicative.eulerProduct_tprod, InnerProductSpace.rankOne_def, MDifferentiableWithinAt.coordChangeL, ContinuousLinearMap.coe_flipβα΅’', PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, deriv_inv, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, contDiff_iff_continuous_differentiable, NumberField.mixedEmbedding.mem_span_latticeBasis, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaβ, hasDerivAt_const, Complex.tendsto_norm_tan_atTop, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, BoundedContinuousFunction.innerProbChar_apply, OrthonormalBasis.repr_apply_apply, UniformSpace.Completion.norm_toComplL, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, instSMulCommClass_sphere_closedBall_closedBall, Circle.coe_inv_eq_conj, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, Complex.hasDerivAt_Gammaβ_one, AnalyticAt.eventually_constant_or_nhds_le_map_nhds, Complex.hasSum_sin, Complex.tendsto_self_mul_Gamma_nhds_zero, SchwartzMap.integral_bilin_fourier_eq, Complex.hasStrictDerivAt_const_cpow, ClosedSubmodule.orthogonal_eq_inter, ContinuousMultilinearMap.prodL_apply, Orientation.kahler_neg_orientation, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, hasFTaylorSeriesUpToOn_succ_iff_right, EisensteinSeries.hasSum_e2Summand_symmetricIco, ContinuousLinearMap.coe_flipMultilinearEquiv, Seminorm.bddAbove_iff, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', intervalIntegral.integrableOn_Ioo_cpow_iff, Circle.coe_mul, SchwartzMap.smulRightCLM_apply_apply, LinearIsometryEquiv.conjStarAlgEquiv_refl, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, contDiff_nat_iff_iteratedDeriv, eventually_singleton_add_smul_subset, LinearMap.IsSymmetric.toSelfAdjoint_apply, hasSum_jacobiThetaβ'_term, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, circleMap_notMem_ball, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, ContinuousLinearMap.coe_restrict_scalarsL', ContinuousLinearMapWOT.isInducing_inducingFn, SlashInvariantFormClass.periodic_comp_ofComplex, fderivWithin_fderivWithin_eq_of_eventuallyEq, integrableOn_Ioi_deriv_ofReal_cpow, NormedField.nhdsNE_neBot, EulerProduct.eulerProduct_completely_multiplicative_tprod, Complex.map_exp_comap_re_atBot, StrongDual.polarSubmodule_eq_polar, fourier_coe_apply, summable_prod_mul_pow, PiTensorProduct.liftEquiv_symm_apply, Complex.interior_setOf_le_im, RCLike.summable_conj, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, RCLike.geometric_hahn_banach_point_point, TestFunction.coe_ofSupportedInLM, extDerivWithin_fun_smul, inner_smul_real_right, fourierSubalgebra_separatesPoints, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Complex.isEquivalent_sinh, AnalyticOnNhd.is_constant_or_isOpenMap, hasFDerivAt_exp_smul_const', Real.Angle.arg_toCircle, MeasureTheory.SignedMeasure.re_toComplexMeasure, TemperedDistribution.smulLeftCLM_sub, Complex.one_add_cpow_hasFPowerSeriesAt_zero, Matrix.exp_zsmul, HurwitzZeta.hasSum_nat_cosZeta, ContinuousLinearMapWOT.hasBasis_seminorms, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, OnePoint.isZeroAt_iff_forall_SL2Z, ContDiff.continuous_iteratedDeriv, LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, WithSeminorms.topology_eq_withSeminorms, hasSum_cauchyPowerSeries_integral, ContinuousLinearMap.aestronglyMeasurable_compβ, continuousSMul_sphere_closedBall, Circle.coe_pow, SchwartzMap.smulLeftCLM_const, UpperHalfPlane.contMDiff_num, UpperHalfPlane.mdifferentiable_denom, LinearMap.toMatrix_innerββ_apply, UpperHalfPlane.dist_self_center, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Complex.continuous_conj, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Function.locallyFinsuppWithin.toClosedBall_divisor, LSeries.term_convolution, PointwiseConvergenceCLM.equivWeakDual_symm_apply, MeasureTheory.ComplexMeasure.integrable_rnDeriv, NumberField.mixedEmbedding.negAt_apply_isComplex, isBigO_riemannZeta_sub_one_div, AffineMap.hasDerivAt, Complex.hasFDerivAt_cpow, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, Complex.differentiableAt_exp, LinearMap.range_toContinuousLinearMap, Complex.not_continuousAt_Gamma_zero, Complex.differentiable_Gammaβ_inv, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, continuous_circleMap, differentiableAt_jacobiThetaβ_fst, AffineMap.differentiableAt, hasStrictDerivAt_finCons', isScalarTower_closedBall_ball_ball, Complex.iter_deriv_exp, MeromorphicOn.meromorphicNFAt_mem_codiscreteWithin, HasProdLocallyUniformlyOn_euler_sin_prod, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, NormedSpace.ofReal_exp_β_β, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMapβ'_zero_iff, convex_halfSpace_im_lt, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, NormedSpace.isVonNBounded_iff', Polynomial.rootSet_derivative_subset_convexHull_rootSet, VonNeumannAlgebra.mem_carrier, WeakDual.isSeqCompact_closedBall, hasStrictDerivAt_finCons, Complex.differentiableAt_tan, PiTensorProduct.liftEquiv_apply, ModularForm.differentiableAt_eta_tprod, has_antideriv_at_fourier_neg, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, PadicInt.denseRange_natCast, UnitAddTorus.mFourier_norm, toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhds, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, LSeriesSummable.sum, Function.Periodic.continuous_qParam, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, HurwitzZeta.hasSum_expZeta_of_one_lt_re, innerSLFlip_apply_apply, UniformContinuousOn.cexp, ContinuousLinearMap.nnnorm_holder_apply_apply_le, Polynomial.hasFDerivAt, RCLike.ofReal_finsupp_sum, tendsto_zero_of_meromorphicOrderAt_pos, finrank_euclideanSpace, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Complex.continuous_exp, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, ConvexOn.sSup_of_nat_affine_eq, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, Complex.frontier_preimage_im, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, Submodule.orthogonal_orthogonal_eq_closure, continuousAt_clog, EisensteinSeries.linear_left_summable, AnalyticOnNhd.preimage_zero_mem_codiscrete, PeriodPair.hasSumLocallyUniformly_weierstrassPExcept, Circle.invOn_arg_exp, contMDiff_smul, MeasureTheory.dist_convolution_le, MeromorphicOn.divisor_ofNat, DoubleCentralizer.nnnorm_fst, with_gaugeSeminormFamily, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Complex.hasDerivAt_cos, Complex.ofRealCLM_apply, contMDiffOn_continuousLinearMapCoordChange, UpperHalfPlane.ofComplex_apply_eq_of_im_nonpos, Complex.log_sub_self_isBigO, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Module.Basis.exists_opNNNorm_le, aestronglyMeasurable_smul_const_iff, absConvexHull_add_subset, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Module.Basis.equivFunL_apply, WithSeminorms.tendsto_nhds, BoundedContinuousFunction.probCharDual_zero, ContinuousMultilinearMap.flipLinear_apply_apply, tendsto_integral_mul_one_add_inv_smul_sq_pow, HasGradientAt.hasFDerivAt, Complex.arg_eq_nhds_of_im_neg, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, LinearMap.hasDerivWithinAt, WithSeminorms.isOpen_iff_mem_balls, CStarMatrix.toCLM_apply_single, MeromorphicOn.inv_iff, MeasureTheory.AEStronglyMeasurable.inner, FormalMultilinearSeries.comp_id, Complex.tendsto_exp_comap_re_atBot, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, ContinuousMap.adjoin_id_eq_span_one_union, IsSelfAdjoint.spectrumRestricts, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, hasFTaylorSeriesUpTo_succ_nat_iff_right, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, HasFDerivWithinAt.norm_sq, tsum_riemannZetaSummand, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, ClosedSubmodule.iInf_orthogonal, Complex.summable_ofReal, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, StrongDual.dualPairing_separatingLeft, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, ContinuousLinearMap.uncurryBilinear_apply, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, Seminorm.sSup_empty, hasStrictDerivAt_abs, fourier_eval_zero, Matrix.PosDef.commute_iff, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, RCLike.finrank_le_two, Complex.tendsto_euler_sin_prod, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, ZMod.completedLFunction_eq, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, iteratedFDeriv_eq_equiv_comp, Complex.hasStrictDerivAt_log, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Unitization.norm_eq_sup, Real.hasDerivAt_cos, Matrix.ofLp_toEuclideanCLM, NumberField.mixedEmbedding.convexBodySumFun_continuous, hasFTaylorSeriesUpToOn_succ_nat_iff_right, hasDerivAtFilter_iff_isLittleO, CStarMatrix.toCLM_apply_eq_sum, HasStrictFDerivAt.restrictScalars, mahler_natCast_eq, PadicInt.coe_adicCompletionIntegersEquiv_apply, MeromorphicAt.eventually_continuousAt, UpperHalfPlane.dist_eq, Circle.star_addChar, HurwitzZeta.hurwitzZeta_residue_one, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, hasDerivAt_exp_smul_const, RCLike.continuous_re, NormedSpace.algebraMap_exp_comm, exists_dual_vector, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, hasFDerivWithinAt_comp_smul_smul_iff, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, RCLike.instContinuousStar, ProbabilityTheory.hasDerivAt_complexMGF, MeromorphicOn.divisor_fun_zpow, LinearMap.isPositive_toContinuousLinearMap_iff, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, Complex.tsum_exp_neg_quadratic, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, FormalMultilinearSeries.changeOrigin_eval_of_finite, RCLike.sqrt_map, iteratedFDerivWithin_two_apply', PadicInt.mahlerTerm_one, Real.hasDerivWithinAt_arcsin_Ici, HasStrictDerivAt.hasStrictFDerivAt, PeriodPair.derivWeierstrassP_sub_coe, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, Matrix.instFiniteElemRealSpectrum, AnalyticAt.analyticOrderAt_eq_natCast, RCLike.smul_im, SpectrumRestricts.real_iff, Matrix.l2_opNNNorm_mul, contDiffWithinAt_succ_iff_hasFDerivWithinAt', HurwitzZeta.differentiableAt_completedHurwitzZetaEven, Complex.cosh_eq_tsum, IsLocalFrameOn.eventually_eq_sum_coeff_smul, contDiffOn_succ_iff_hasFDerivWithinAt, RCLike.tendsto_ofReal_cobounded_cobounded, differentiableWithinAt_euclidean, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, unitary.spectrum_subset_circle, FormalMultilinearSeries.radius_unshift, Complex.frontier_setOf_lt_im, HasFPowerSeriesAt.fderiv_eq, LinearPMap.adjointDomainMkCLM_apply, MeromorphicOn.divisor_apply, Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.coe_restrictScalarsIsometry, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, Polynomial.aeval_conj, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, continuousMultilinearCurryFin0_apply, Complex.interior_reProdIm, HurwitzZeta.differentiableAt_one_completedHurwitzZetaEven_sub_completedHurwitzZetaEven, HasGradientAt.differentiableAt, PiTensorProduct.dualSeminorms_bounded, LinearMap.hasBasis_weakBilin, NormedSpace.exp_sum, FormalMultilinearSeries.radius_neg, extDeriv_smul, Complex.contDiff_exp, spectrum.isClosed, HasDerivAt.norm_sq, WeakBilin.locallyConvexSpace, GromovHausdorff.ghDist_eq_hausdorffDist, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, Complex.closure_preimage_re, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, tendsto_ne_zero_of_meromorphicOrderAt_eq_zero, DoubleCentralizer.algebraMap_snd, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, WeakDual.polar_def, RCLike.wInner_const_left, AnalyticAt.analyticOrderNatAt_eq_iff, Complex.isOpenQuotientMap_pow, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, HurwitzZeta.hasSum_int_sinKernel, MeasureTheory.integrable_smul_const, hasFiniteFPowerSeriesOnBall_const, contDiffAt_inv, iteratedFDerivWithin_succ_apply_left, hasStrictFDerivAt_norm_sq, SchwartzMap.fourier_evalCLM_eq, support_deriv_subset, Bornology.IsVonNBounded.restrict_scalars, LinearMap.adjoint_toSpanSingleton, ContDiff.differentiable_iteratedDeriv, Complex.interior_setOf_im_le, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, ContinuousMultilinearMap.norm_mkPiAlgebra, NontriviallyNormedField.cobounded_neBot, contDiffOn_infty_iff_fderiv_of_isOpen, hasDerivWithinAt_natCast, MeromorphicOn.divisor_fun_mul, Asymptotics.superpolynomialDecay_iff_isLittleO, MeromorphicOn.divisor_zpow, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, QuasispectrumRestricts.real_iff, ContinuousLinearMap.bilinearComp_apply, TemperedDistribution.instLineDerivSMulReal, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, cot_series_rep, SchwartzMap.evalCLM_apply_apply, upperHemicontinuous_quasispectrum, spectrum.isBounded, UpperHalfPlane.ofComplex_apply_eq_ite, Matrix.posDef_iff_eq_conjTranspose_mul_self, Polynomial.differentiableAt_aeval, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, HurwitzZeta.completedCosZeta_residue_zero, hasDerivAt_id, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, CStarMatrix.toCLM_apply, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, MeasureTheory.Integrable.re_im_iff, RCLike.hasSum_conj, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, FormalMultilinearSeries.id_comp, ContinuousLinearMap.norm_map_tail_le, deriv_update, UpperHalfPlane.qParam_tendsto_atImInfty, HasFPowerSeriesAt.restrictScalars, contMDiffOn_symm_coordChangeL, ContinuousLinearMap.instStarModuleId, Polynomial.hasFDerivAt_aeval, Seminorm.convex_ball, NormedField.continuousAt_inv, ContDiffAt.restrictScalars_iteratedFDeriv, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, LeftInvariantDerivation.map_add, Complex.isConnected_of_upperHalfPlane, AnalyticOnNhd.codiscreteWithin_setOf_analyticOrderAt_eq_zero_or_top, norm_fderiv_iteratedFDeriv, Complex.differentiable_sin, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, Complex.continuous_normSq, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, PeriodPair.weierstrassP_add_coe, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, TemperedDistribution.fourier_lineDerivOp_eq, Matrix.l2_opNNNorm_def, hasDerivAtFilter_sub_const_iff, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.adjointAux_adjointAux, PeriodPair.instProperSpaceSubtypeComplexMemSubmoduleIntLattice, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, LinearMap.polar_gc, hasDerivAt_exp, circleMap_mem_sphere, UniformSpace.Completion.Continuous.inner, LeftInvariantDerivation.coe_add, Complex.hasDerivAt_logTaylor, DirichletCharacter.differentiable_LFunction, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow, NumberField.mixedEmbedding.norm_smul, Real.hasStrictDerivAt_arsinh, circleMap_preimage_codiscrete, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', MeasureTheory.AEStronglyMeasurable.const_inner, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, Complex.lintegral_comp_polarCoord_symm, EuclideanSpace.basisFun_repr, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, zero_cpow_eq_nhds, HasFTaylorSeriesUpToOn.hasFDerivAt, RCLike.realLinearIsometryEquiv_symm_apply, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, ContinuousLinearMap.flip_add, hasFiniteFPowerSeriesAt_const, Circle.leftInverse_exp_arg, Complex.continuousAt_ofReal_cpow, Subalgebra.spectrum_isBounded_connectedComponentIn, MeromorphicOn.eventually_codiscreteWithin_analyticAt, ArithmeticFunction.IsMultiplicative.eulerProduct, ContinuousAlternatingMap.hasBasis_nhds_zero, AnalyticAt.eventually_constant_or_nhds_le_map_nhds_aux, Bornology.isBounded_iff_isVonNBounded, circleMap_mem_closedBall, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', HasFDerivWithinAt.restrictScalars, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, RCLike.continuous_ofReal, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, IsLocalFrameOn.coeff_apply_of_notMem, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, GromovHausdorff.eq_toGHSpace, ContinuousMultilinearMap.uncurryRight_apply, NumberField.mixedEmbedding.polarCoord_source, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, fderiv_inv, differentiableWithinAt_iff_restrictScalars, Complex.orthonormalBasisOneI_repr_symm_apply, MeasureTheory.L1.nnnorm_Integral_le_one, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, RCLike.ofReal_alg, ContinuousLinearMap.bilinearComp_zero, isScalarTower_sphere_sphere_closedBall, Complex.UnitDisc.instSMulCommClass_closedBall_right, iteratedDeriv_eq_equiv_comp, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NumberField.mixedEmbedding.continuous_norm, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, Complex.continuousOn_tan, ContinuousLinearMap.norm_extendToπ'_bound, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, hasDerivAt_iff_hasFDerivAt, HasFiniteFPowerSeriesOnBall.neg, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, LinearMap.weakBilin_withSeminorms, RCLike.complexLinearIsometryEquiv_symm_apply, PadicInt.continuous_addChar_of_value_at_one, norm_derivWithin_eq_norm_fderivWithin, ModularForm.differentiableAt_eta_of_mem_upperHalfPlaneSet, differentiableWithinAt_dslope_of_ne, LinearMap.polar_weak_closed, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, hasDerivAt_fourier, Filter.Tendsto.ofReal, Complex.continuousAt_cpow_zero_of_re_pos, Circle.norm_coe, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Complex.UnitDisc.instIsScalarTower_closedBall, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Complex.instCompleteSpace, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, ZMod.LFunction_def_even, Real.fourier_bilin_convolution_eq, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, UpperHalfPlane.le_dist_coe, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, CStarMatrix.mul_entry_mul_eq_inner_toCLM, continuous_inner, ModularFormClass.differentiableAt_cuspFunction, fourier_apply, ContinuousLinearMap.le_opNormβ, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, Seminorm.continuous_iff, ContinuousLinearMap.norm_uncurryMid, QuadraticForm.equivalent_sum_squares, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, LeftInvariantDerivation.coe_injective, ContinuousLinearMap.uncurryLeft_norm, MeromorphicOn.divisor_restrict, ContDiffWithinAt.fderivWithin', hasStrictDerivAt_abs_neg, WithSeminorms.continuous_seminorm, HasFPowerSeriesOnBall.tendstoUniformlyOn', Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, fderiv_apply_one_eq_deriv, HurwitzZeta.hasSum_nat_completedSinZeta, EulerProduct.eulerProduct_hasProd_mulIndicator, isScalarTower_sphere_sphere_ball, integrableOn_exp_mul_complex_Iic, ContinuousAlternatingMap.continuous_restrictScalars, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, Complex.frontier_setOf_le_re, MeasureTheory.Integrable.convolution_integrand, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, LinearMap.toMatrixOrthonormal_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, UpperHalfPlane.contMDiff_denom_zpow, contDiffOn_tsum_cexp, convex_halfSpace_re_ge, OrthogonalFamily.inner_sum, deriv_circleMap, NormedSpace.vonNBornology_eq, PeriodPair.latticeBasis_one, EuclideanSpace.inner_eq_star_dotProduct, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, isCoveringMapOn_npow, OrthonormalBasis.sum_repr_symm, LeftInvariantDerivation.coe_neg, Complex.hasStrictDerivAt_cos, StrongDual.toLpβ_apply, Orientation.kahler_apply_self, Complex.frontier_setOf_re_lt, DifferentiableWithinAt.restrictScalars_fderivWithin, PeriodPair.weierstrassP_sub_coe, isCompact_closedAbsConvexHull_of_totallyBounded, Complex.analyticOn_univ_iff_differentiable, Valued.integer.coe_span_singleton_eq_closedBall, Complex.conjCLE_nnorm, Polynomial.differentiableOn, IsLocalFrameOn.coeff_apply_zero_at, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', isQuotientCoveringMap_zpow, AnalyticOnNhd.eval_polynomial, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, differentiableOn_neg, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, LinearMap.continuous_of_nonzero_on_open, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Complex.isBigO_im_sub_im, InnerProductSpace.innerSL_norm, ArithmeticFunction.LSeries_vonMangoldt_eq, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', SchwartzMap.le_seminorm, DoubleCentralizer.nnnorm_fst_eq_snd, toWeakSpace_closedConvexHull_eq, Unitization.norm_def, EisensteinSeries.qExpansion_identity_pnat, SchwartzMap.eLpNorm_le_seminorm, Complex.isCoveringMapOn_exp, deriv_neg', Orientation.kahler_rotation_left', zeta_eq_tsum_one_div_nat_add_one_cpow, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, Complex.continuous_cos, DirichletCharacter.differentiableAt_completedLFunction, norm_prod, ContinuousAlternatingMap.curryLeft_same, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ContinuousMultilinearMap.curryRight_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, ContMDiffWithinAt.mfderivWithin, convex_halfSpace_im_ge, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, contDiffOn_inv, ContinuousLinearMap.extendToπ_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, UpperHalfPlane.le_dist_iff_le_dist_coe_center, PadicInt.hasSum_mahlerSeries, NumberField.mixedEmbedding.polarCoord_target, Complex.continuousAt_arg_coe_angle, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, CauSeq.cauchySeq, Asymptotics.superpolynomialDecay_iff_isBigO, ContinuousLinearMap.norm_extendToπ', HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, StrongDual.polar_univ, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, PeriodPair.hasSum_weierstrassP, convex_halfSpace_re_lt, differentiableAt_iff_comp_const_sub, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, UpperHalfPlane.ofComplex_apply, ContDiffMapSupportedIn.postcompCLM_apply, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, PeriodPair.coeff_weierstrassPSeries, Complex.ball_one_subset_slitPlane, dslope_eventuallyEq_slope_of_ne, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, PeriodPair.isOpen_compl_lattice_diff, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, Orientation.normSq_kahler, Complex.volume_closedBall, Complex.tendsto_one_add_div_cpow_exp, hasGradientAt_iff_hasFDerivAt, Complex.hasSum_cos', Complex.closure_setOf_re_lt, Complex.deriv_cosh, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, PeriodPair.derivWeierstrassP_coe, HasFPowerSeriesOnBall.tendsto_partialSum, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, Manifold.IsImmersionOfComplement.ofOpen, hasFDerivAt_exp_smul_const_of_mem_ball, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, norm_root_le_spectralValue, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, HasFPowerSeriesWithinAt.prod, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, iteratedFDeriv_succ_apply_right, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, FormalMultilinearSeries.leftInv_coeff_one, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, RCLike.instStarModuleReal, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, Orthonormal.inner_finsupp_eq_sum_left, continuousAt_const_cpow', fderiv_deriv, Complex.hasStrictDerivAt_sin, Complex.polarCoord_source, hasFPowerSeriesAt_pi_iff, Module.Basis.continuous_toMatrix, NormedField.continuousAt_zpow, hasDerivWithinAt_univ, Seminorm.ball_zero_absorbs_ball_zero, RCLike.continuous_conj, NumberField.mixedEmbedding.polarCoord_symm_eq, Matrix.PosSemidef.sq_sqrt, continuous_barycentric_coord, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, Complex.exp_sub_sum_range_succ_isLittleO_pow, ContinuousLinearMapWOT.ext_dual_iff, contDiff_clm_apply_iff, Complex.continuousOn_prod_circle_transform_function, HasFPowerSeriesAt.hasFDerivAt, OrthonormalBasis.measurePreserving_repr_symm, lp.summable_inner, WeakDual.isClosed_polar, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, spec_cfcβAux, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, eventually_enorm_mfderiv_extChartAt_lt, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, hasFDerivAt_exp_smul_const, Differentiable.inner, UpperHalfPlane.dist_center_dist, LinearMap.mkContinuousβ_norm_le, DifferentiableAt.ofReal_cpow_const, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, LeftInvariantDerivation.map_smul, hasFDerivAt_jacobiThetaβ, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, Complex.isHomeomorphicTrivialFiberBundle_re, WithSeminorms.congr_equiv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, NumberField.mixedEmbedding.polarSpaceCoord_target', hasStrictDerivAt_const, rotationOf_coe, NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, HasFPowerSeriesWithinAt.restrictScalars, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, Complex.deriv_tan, contDiffOn_clm_apply, isCauSeq_iff_cauchySeq, MeromorphicAt.frequently_eq_iff_eventuallyEq, UpperHalfPlane.dist_le_dist_coe_div_sqrt, Seminorm.inf_apply, PiTensorProduct.mapLMultilinear_apply_apply, iteratedDeriv_comp_two, LinearMap.mem_polar_singleton, ContinuousMap.setOfIdeal_eq_compl_singleton, Complex.hasDerivAt_cosh, isBoundedBilinearMap_apply, MulAlgebraNormClass.toSeminormClass, FormalMultilinearSeries.analyticOnNhd, EisensteinSeries.tendsto_zero_inv_linear, Unitization.nnreal_cfcβ_eq_cfc_inr, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, RCLike.ofRealCLM_norm, ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, Complex.UnitDisc.coe_smul_closedBall, ContinuousLinearMap.mul_apply', HurwitzZeta.differentiableAt_hurwitzZeta, MeromorphicNFOn.zero_set_eq_divisor_support, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, MeasureTheory.convolution_lsmul_swap, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem, Real.hasStrictDerivAt_arctan, Complex.interior_setOf_re_le, DirichletCharacter.deriv_LFunctionTrivCharβ_apply_of_ne_one, AnalyticAt.hasFPowerSeriesAt, hasDerivAtFilter_finCons', Complex.isOpen_im_gt_EReal, MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero, Matrix.toEuclideanLin_eq_toLin, tendsto_logDeriv_euler_cot_sub, SlashInvariantForm.coe_trace, StrongDual.toLpβ_of_not_memLp, isConformalMap_complex_linear_conj, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, TrivSqZeroExt.instL1IsBoundedSMul, BoundedContinuousFunction.instIsBoundedSMul_1, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, LSeries_differentiableOn, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, MulAlgebraNormClass.map_smul_eq_mul, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, differentiableAt_riemannZeta, Complex.tendsto_partialGamma, Complex.exp_sub_sum_range_isBigO_pow, Matrix.finite_real_spectrum, deriv_zpow, Complex.tendsto_norm_tan_of_cos_eq_zero, riemannZeta_eulerProduct, Complex.isOpenQuotientMap_zpow_compl_zero, UpperHalfPlane.eventuallyEq_coe_comp_ofComplex, InnerProductSpace.rankOne_comp, EisensteinSeries.summable_linear_sub_mul_linear_add, StrongDual.mem_polarSubmodule, exists_dual_vector', FormalMultilinearSeries.apply_eq_prod_smul_coeff, Orientation.kahler_rightAngleRotation_left, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, hasFPowerSeriesWithinAt_pi_iff, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, hasDerivAt_iff_isLittleO_nhds_zero, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, PadicInt.hasSum_mahler, Function.Periodic.invQParam_tendsto, InnerProductSpace.toMatrix_rankOne, cfcβHom_real_eq_restrict, PeriodPair.latticeEquiv_symm_apply, LinearMap.polar_AbsConvex, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, Complex.closure_setOf_lt_re, UnitAddTorus.mFourierSubalgebra_separatesPoints, Complex.betaIntegral_convergent, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, RCLike.geometric_hahn_banach_open, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Real.hasDerivAt_cosh, PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept, continuousMultilinearCurryLeftEquiv_apply, LeftInvariantDerivation.coe_smul, HasFPowerSeriesAt.deriv, ModularForm.summable_logDeriv_one_sub_eta_q, LSeries_sum, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, UpperHalfPlane.comp_ofComplex_of_im_le_zero, Complex.hasDerivAt_sin, fourierCoeff_eq_intervalIntegral, Seminorm.bddBelow_range_add, ContinuousAlternatingMap.restrictScalarsCLM_apply, NumberField.mixedEmbedding.continuous_normAtPlace, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, Manifold.IsImmersionAtOfComplement.of_opens, hfdifferential_apply, MeasureTheory.Integrable.inner_const, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, Complex.closure_reProdIm, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Real.hasDerivAt_fourierChar, AnalyticOnNhd.fderiv, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, hasDerivAt_intCast, Orientation.kahler_rotation_left, multipliable_sineTerm, Seminorm.absorbent_ball_zero, LindemannWeierstrass.integral_exp_mul_eval, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcβHom, ModularFormClass.hasSum_qExpansion_of_abs_lt, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, Complex.isUniformEmbedding_ofReal, Complex.conjCLE_enorm, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, DirichletCharacter.LSeries_eulerProduct_hasProd, spectrum.differentiableOn_inverse_one_sub_smul, Continuous.inner_, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, Complex.hasSum_conj, ContinuousMultilinearMap.changeOriginSeries_support, PeriodPair.deriv_derivWeierstrassPExcept_self, ContDiffMapSupportedIn.seminorm_apply, LinearMap.tripolar_eq_polar, RCLike.toIsOrderedAddMonoid, Complex.hasStrictDerivAt_exp, WithSeminorms.tendsto_nhds_atTop, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Continuous.inner, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, Seminorm.smul_closedBall_subset, Padic.denseRange_ratCast, DoubleCentralizer.algebraMap_fst, AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top, differentiableOn_euclidean, RCLike.reLm_coe, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, nnnorm_fderiv_norm_rpow_le, EisensteinSeries.q_expansion_bernoulli, HasStrictFDerivAt.approximates_deriv_on_open_nhds, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, Complex.hasStrictDerivAt_cosh, ContinuousMultilinearMap.nnnorm_ofSubsingleton, inner_smul_real_left, eigenvalue_mem_ball, ContDiffOn.fderivWithin, tsum_prod_pow_eq_tsum_sigma, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, toSpanSingleton_derivWithin, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, ContinuousLinearMap.isEmbedding_restrictScalars, HasFiniteFPowerSeriesOnBall.eq_partialSum', continuousAt_cpow_const, GaussianFourier.tendsto_verticalIntegral, coe_lpBCFβα΅’_symm, MeromorphicOn.AnalyticOnNhd.divisor_nonneg, MeromorphicOn.eventually_analyticAt_or_mem_compl, IsBoundedBilinearMap.toContinuousLinearMap_apply, Bornology.isVonNBounded_sub, HasFPowerSeriesOnBall.pi, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, HasFPowerSeriesWithinOnBall.fderivWithin_eq, Complex.UnitDisc.continuous_coe, ContinuousMultilinearMap.piβα΅’_symm_apply, RCLike.wInner_one_const_right, AlgHom.coe_toContinuousLinearMap, hahnEmbedding_isOrderedModule_rat, Matrix.posSemidef_iff_eq_sum_vecMulVec, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, AnalyticAt.analyticOrderAt_ne_top, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, differentiableAt_const_cpow_of_neZero, tsum_dirichletSummand, Filter.Tendsto.isVonNBounded_range, AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top, Real.hasFDerivAt_fourierIntegral, SchwartzMap.integralCLM_apply, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, PolynormableSpace.withSeminorms', hasDerivAt_one, Complex.dist_conj_conj, circleIntegrable_sub_zpow_iff, FormalMultilinearSeries.radius_shift, Polynomial.fourierCoeff_toAddCircle_natCast, Complex.conjCLE_apply, ContinuousMap.spectrum_eq_range, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, innerSLFlip_apply, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, fderivWithin_derivWithin, hasDerivAt_const_mul, hasLineDerivAt_iff_tendsto_slope_zero, Circle.coe_eq_one, InnerProductSpace.toContinuousLinearMap_toDualMap, Complex.differentiable_one_div_Gamma, Valued.integer.properSpace_iff_compactSpace_integer, completeSpace_of_cauSeq_isComplete, contDiff_nat_iff_continuous_differentiable, ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, absorbent_ball, UpperHalfPlane.cosh_half_dist, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, DirichletCharacter.LSeries_eulerProduct_exp_log, mdifferentiableOn_coordChangeL, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, Polynomial.hasDerivAt, Complex.not_differentiableAt_Gamma_zero, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, MeasureTheory.Integrable.ofReal, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, ContinuousLinearMap.opNorm_lsmul_le, MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds, OrthonormalBasis.repr_symm_single, Real.fourierChar_apply, MultilinearMap.mkContinuousMultilinear_norm_le, WeakDual.CharacterSpace.norm_le_norm_one, Matrix.linfty_opNorm_toMatrix, hasDerivAt_natCast, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, Seminorm.rescale_to_shell, ProbabilityTheory.differentiableOn_complexMGF, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, closedBall_normSeminorm, Real.hasStrictDerivAt_cos, PeriodPair.deriv_weierstrassPExcept_same, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_symm_apply, ContinuousLinearMap.coe_restrictScalarsL, Function.Periodic.qParam_tendsto, continuousAt_jacobiTheta, iter_deriv_inv, PeriodPair.analyticOnNhd_derivWeierstrassP, Matrix.frobenius_norm_mul, Complex.Gammaβ_residue_zero, Matrix.star_dotProduct_gram_mulVec, ContinuousLinearMap.norm_compL_le, integrableOn_Ioi_cpow_of_lt, RCLike.hasSum_iff, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, ContMDiffVectorBundle.contMDiffOn_coordChangeL, EulerSine.antideriv_cos_comp_const_mul, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Complex.instTietzeExtension, Bornology.isVonNBounded_add, HasFPowerSeriesAt.sub, ProperSpace.of_locallyCompact_module, hasDerivWithinAt_zpow, OrthogonalFamily.range_linearIsometry, NumberField.mixedEmbedding.convexBodyLT_convex, Complex.instT2Space, Monotone.deriv_nonneg, UpperHalfPlane.exp_half_dist, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, Orientation.kahler_mul, innerSL_real_flip, GaussianFourier.integral_cexp_neg_mul_sum_add, Complex.continuous_ofReal_cpow_const, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, TensorProduct.norm_lid, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, Matrix.instIsOrderedAddMonoid, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NormedAlgebra.Real.nonempty_algEquiv_or, HurwitzZeta.differentiableAt_completedCosZeta, fourier_neg, LSeries.tendsto_cpow_mul_atTop, ContinuousMultilinearMap.curryMid_apply, ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, EisensteinSeries.tendsto_double_sum_S_act, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Matrix.PosSemidef.re_dotProduct_nonneg, Complex.sinh_eq_tsum, balanced_closedBall_zero, continuousAt_jacobiThetaβ, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, instSMulCommClass_sphere_ball_ball, PiLp.basis_toMatrix_basisFun_mul, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MDifferentiableAt.coordChangeL, Polynomial.isOpenQuotientMap_eval, EulerSine.antideriv_sin_comp_const_mul, ContinuousLinearMap.norm_restrictScalars, Complex.differentiableAt_cosh, coe_normSeminorm, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NormedSpace.sInter_polar_eq_closedBall, Complex.differentiableAt_Gamma_nat_add_one, ContDiffBump.convolution_eq_right, TemperedDistribution.instFourierInvSMul, PadicInt.totallyBounded_univ, Complex.deriv_cos', Complex.imCLM_coe, lp.hasSum_inner, iteratedDeriv_comp_eq_sum_orderedFinpartition, Complex.isQuotientMap_im, ContinuousLinearMap.opNorm_mul_apply_le, HasFPowerSeriesAt.tendsto_partialSum, circleAverage_log_norm_factorizedRational, Polynomial.aeval_ofReal, deriv_pow_field, ContinuousLinearMap.orthogonal_range, HasFiniteFPowerSeriesAt.add, HasFPowerSeriesAt.hasDerivAt, MeromorphicOn.min_divisor_le_divisor_add, AnalyticAt.eventually_eq_or_eventually_ne, Polynomial.hasDerivAt_aeval, MeasureTheory.stronglyMeasurable_charFun, PeriodPair.instDiscreteTopologySubtypeComplexMemSubmoduleIntLattice, HasFDerivAt.linear_multilinear_comp, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, Complex.continuous_ofReal, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, MeasureTheory.convolutionExistsAt_iff_integrable_swap, Complex.not_continuousAt_Gamma_neg_nat, Polynomial.C_eq_or_isOpenQuotientMap_eval, hasDerivAt_ofReal_cpow_const, EisensteinSeries.summable_e2Summand_symmetricIcc, hasDerivAt_norm_rpow, UnitAddTorus.hasSum_prod_mFourierCoeff, Padic.withValUniformEquiv_cast_apply, NumberField.mixedEmbedding.latticeBasis_apply, LeftInvariantDerivation.map_sub, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, spectrum.exp_mem_exp, Unitization.isUniformEmbedding_addEquiv, ContinuousMultilinearMap.compContinuousLinearMapL_apply, Seminorm.smul_closedBall_preimage, AnalyticAt.eventually_eq_zero_or_eventually_ne_zero, MeromorphicOn.extract_zeros_poles, Matrix.IsHermitian.cfcAux_id, cfcβAux_mem_range_inr, ContinuousLinearMap.norm_bilinearRestrictScalars, eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top, Ideal.Quotient.norm_mk_lt, ContinuousLinearMap.nhds_zero_eq, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, Complex.sin_eq_tsum, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, RCLike.real_smul_ofReal, differentiableAt_jacobiThetaβ_snd, Padic.coe_withValRingEquiv, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, HasFPowerSeriesWithinOnBall.neg, NumberField.mixedEmbedding.measurable_polarCoord_symm, norm_deriv_eq_norm_fderiv, IsUltrametricDist.normedAlgebra_iff, PadicInt.fwdDiff_mahlerSeries, LSeries.tendsto_atTop, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ContinuousLinearMap.bilinearComp_zero_left, one_add_cpow_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, Complex.hasSum_conj', MeasureTheory.L2.mem_L1_inner, withSeminorms_pi, Complex.isOpen_im_lt_EReal, SchwartzMap.derivCLM_apply, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, Seminorm.gauge_ball, Circle.coe_inv, RCLike.map_nonneg_iff, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, MeromorphicOn.negPart_divisor_add_le_max, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, Complex.hasStrictDerivAt_cpow_const, ContDiffBump.dist_normed_convolution_le, WithAbs.isUniformInducing_of_comp, mellin_differentiableAt_of_isBigO_rpow_exp, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', AlgebraNorm.extends_norm', Asymptotics.isEquivalent_iff_tendsto_one, differentiable_neg, hasDerivAt_neg, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, hasFTaylorSeriesUpToOn_succ_iff_left, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Padic.isUniformInducing_cast_withVal, PadicInt.continuous_multichoose, Complex.hasSum_taylorSeries_neg_log, Polynomial.hasStrictDerivAt, VectorFourier.integral_bilin_fourierIntegral_eq_flip, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, NumberField.mixedEmbedding.logMap_real, contDiffOn_succ_iff_fderivWithin, NumberField.mixedEmbedding.commMap_apply_of_isReal, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, NormedSpace.of_real_exp_β_β, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, NumberField.mixedEmbedding.polarCoord_apply, TemperedDistribution.instLineDerivSMulComplex, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, euler_sineTerm_tprod, NormedField.discreteTopology_of_bddAbove_range_norm, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, continuousMultilinearCurryRightEquiv_symm_apply', ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, ContDiffWithinAt.fderivWithin, ContDiffMapSupportedIn.continuousSMul, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, Subalgebra.frontier_spectrum, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, Complex.log_eq_integral, Complex.equivRealProdCLM_symm_apply_re, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, LinearMap.isStarProjection_toContinuousLinearMap_iff, MeromorphicOn.divisor_smul, UpperHalfPlane.sinh_half_dist_add_dist, NumberField.mixedEmbedding.continuous_normAtAllPlaces, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, MeasureTheory.L2.integrable_inner, IsCompact.reProdIm, LinearPMap.adjointDomainMkCLMExtend_apply, WithAbs.pseudoMetricSpace_induced_of_comp, iteratedFDerivWithin_two_apply, extDerivWithin_smul, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, DoubleCentralizer.coe_fst, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, HurwitzZeta.differentiable_cosZeta_of_ne_zero, ContDiffPointwiseHolderAt.fderiv, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, Complex.deriv_cpow_const, ContinuousMapZero.instCStarRing, NormedField.instCompletableTopField, hasFDerivWithinAt_iff_hasGradientWithinAt, CurveIntegrable.smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, FormalMultilinearSeries.min_radius_le_radius_add, hasStrictDerivAt_one, Complex.summable_one_div_nat_cpow, Complex.nndist_conj_comm, ContinuousLinearMap.closed_range_of_antilipschitz, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, logDeriv_prod_sineTerm_eq_sum_cotTerm, Complex.differentiableAt_Gamma_one, Real.differentiable_fourierChar, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, hasFDerivAt_integral_of_dominated_of_fderiv_le, HasFPowerSeriesAt.pi, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, summable_prod_eisSummand, mdifferentiable_jacobiTheta, Matrix.linfty_opNorm_eq_opNorm, ContinuousAlternatingMap.prodLIE_apply, RCLike.ofReal_tsum, hasDerivAt_pow, contDiff_succ_iff_deriv, Complex.instProperSpace, CPolynomialOn.fderiv, max_norm_root_eq_spectralValue, EuclideanSpace.dist_eq, NumberField.mixedEmbedding.normAtPlace_negAt, PadicInt.mahlerEquiv_apply, Complex.nndist_conj_conj, Polynomial.div_tendsto_atTop_zero_of_degree_lt, SchwartzMap.convolution_flip, continuousSMul_closedBall_closedBall, ContinuousLinearMap.opNorm_flip, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, EisensteinSeries.G2_eq_tsum_cexp, IsConformalMap.smul, nndist_lineMap_lineMap, isCoveringMap_npow, Irreducible.maximalIdeal_eq_closedBall, Complex.frontier_setOf_le_re_and_le_im, Complex.sameRay_iff, Circle.normSq_coe, Real.hasStrictDerivAt_sqrt, Complex.hasDerivAt_Gamma_one, NumberField.mixedEmbedding.normAtPlace_smul, PeriodPair.hasSum_weierstrassPExcept, Polynomial.deriv, FormalMultilinearSeries.derivSeries_eq_zero, HilbertBasis.summable_inner_mul_inner, Polynomial.div_tendsto_zero_of_degree_lt, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, Real.hasDerivAt_tan_of_mem_Ioo, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, AffineMap.differentiableOn, Complex.imCLM_nnnorm, ContinuousMultilinearMap.curryLeft_apply, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, EisensteinSeries.qExpansion_identity, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, UpperHalfPlane.contMDiffAt_ofComplex, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, ModularForm.prod_fintype_slash, GaussianFourier.integral_cexp_neg_sum_mul_add, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, circleIntegrable_sub_inv_iff, AlternatingMap.mkContinuousLinear_norm_le, ModularFormClass.bounded_at_infty_comp_ofComplex, ProperCone.hyperplane_separation_of_notMem, NumberField.mixedEmbedding.convexBodySum_isBounded, LinearMap.continuous_of_isClosed_ker, Complex.sameRay_iff_arg_div_eq_zero, Complex.arg_eq_nhds_of_im_pos, ModularForm.holo', FormalMultilinearSeries.radius_le_radius_derivSeries, ContinuousAlternatingMap.curryLeftLI_apply, LDL.diag_eq_lowerInv_conj, eventuallyConst_iff_analyticOrderAt_sub_eq_top, NumberField.mixedEmbedding.polarSpaceCoord_apply, Real.nonempty_algEquiv_or, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, Padic.coe_withValRingEquiv_symm, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, differentiableAt_iff_comp_add_const, Complex.starConvex_slitPlane, ContinuousLinearMap.norm_compSL_le, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, ContDiffMapSupportedIn.withSeminorms, MeasureTheory.withDensityα΅₯_smul, LinearMap.polar_isClosed, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Bornology.isVonNBounded_vadd, innerββ_apply, deriv_inner_apply, Complex.log_sub_logTaylor_isBigO, differentiable_completedZetaβ, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, fourier_zero', HurwitzZeta.hasSum_int_sinZeta, spectrum.resolvent_tendsto_cobounded, Complex.differentiable_sinh, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, ContinuousMultilinearMap.toUniformOnFun_toFun, ZMod.toCircle_intCast, iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum, hasDerivAtFilter_pi, StrongDual.toLp_apply, StrongDual.polar_empty, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, ContinuousLinearMap.coe_flipβα΅’, HasGradientAtFilter.tendsto_nhds, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, ZMod.toCircle_natCast, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, ModularFormClass.hasSum_qExpansion_of_norm_lt, ContMDiffAt.mfderiv, Complex.volume_ball, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, cpow_eq_nhds', Bornology.isVonNBounded_insert, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, instSMulCommClass_closedBall_closedBall_ball, jacobiTheta_eq_tsum_nat, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Complex.UnitDisc.instSMulCommClass_circle_closedBall, Complex.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.changeOrigin_eval, LSeries.term_sum_apply, LinearMap.toSeminorm_ball_zero, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, UpperHalfPlane.contMDiffAt_iff, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet, IsSelfAdjoint.adjoint_conj, closedAbsConvexHull_eq_closure_absConvexHull, Complex.differentiableAt_sinh, HasDerivAt.inner, HasFPowerSeriesAt.prod, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, Function.Periodic.differentiable_qParam, VectorPrebundle.contMDiffOn_contMDiffCoordChange, Complex.continuous_tan, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, LeftInvariantDerivation.toDerivation_injective, PeriodPair.differentiableOn_weierstrassPExcept, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, AlternatingMap.mkContinuousAlternating_norm_le_max, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, Complex.conjCLE_norm, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, SchwartzMap.seminorm_apply, mdifferentiableAt_coordChangeL, hasDerivAt_finCons', MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Complex.differentiableAt_log, LeftInvariantDerivation.evalAt_mul, differentiableAt_completedZeta, isScalarTower_sphere_ball_ball, PeriodPair.derivWeierstrassPExcept_add_coe, HasFPowerSeriesWithinAt.add, MeasureTheory.BoundedContinuousFunction.inner_toLp, Complex.isQuotientMap_re, ContinuousLinearMap.adjoint_inner_right, Circle.coeHom_apply, exists_extension_norm_eq, Complex.dist_conj_comm, hasFDerivAt_integral_of_dominated_of_fderiv_le'', rootsOfUnityCircleEquiv_apply, CuspFormClass.zero_at_infty_slash, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, NormedSpace.closedBall_inv_subset_polar_closedBall, ContDiffMapSupportedIn.postcompLM_apply, PeriodPair.differentiableOn_weierstrassP, UnitAddTorus.span_mFourier_closure_eq_top, ContinuousLinearMap.norm_smulRightL_le, MeasureTheory.withDensityα΅₯_smul', differentiableAt_iff_restrictScalars, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, SchwartzMap.tsupport_derivCLM_subset, hasDerivAt_single, OrthonormalBasis.coe_toBasis_repr_apply, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, PadicInt.norm_mahler_eq, UpperHalfPlane.mdifferentiable_coe, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, Circle.coe_inj, SchwartzMap.le_seminorm', Complex.arg_eq_nhds_of_re_pos, FormalMultilinearSeries.radius_prod_eq_min, ContinuousOn.inner, summable_cotTerm, RCLike.conjAe_coe, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, continuousAt_jacobiThetaβ', VectorFourier.norm_fourierSMulRight_le, Manifold.IsImmersionOfComplement.id, RCLike.wInner_one_eq_sum, ContinuousAlternatingMap.nnnorm_ofSubsingleton, norm_cfcHom, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, KuratowskiEmbedding.embeddingOfSubset_dist_le, EisensteinSeries.eisSummand_extension_differentiableOn, EuclideanSpace.dist_sq_eq, integral_ofReal, HasFiniteFPowerSeriesOnBall.fderiv', Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Complex.isOpenQuotientMap_pow_compl_zero, ContinuousMultilinearMap.currySum_apply, isOpenMap_barycentric_coord, Complex.deriv_sinh, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, intervalIntegral.intervalIntegrable_cpow', Complex.deriv_sin, signedDist_apply, UniformSpace.Completion.inner_coe, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, WeakDual.CharacterSpace.equivAlgHom_coe, Valued.toNormedField.setOf_mem_integer_eq_closedBall, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipβα΅’'_symm, fourier_coe_apply', EuclideanSpace.inner_toLp_toLp, NumberField.mixedEmbedding.polarSpaceCoord_source, TemperedDistribution.lineDerivOp_fourierInv_eq, Complex.hasSum_taylorSeries_log, fourierCoeffOn_eq_integral, MeromorphicOn.negPart_divisor_add_le_add, UpperHalfPlane.dist_coe_le, CompactConvergenceCLM.continuousSMul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, hasStrictDerivAt_zero, PeriodPair.hasSum_sumInvPow, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, DirichletCharacter.LFunctionTrivChar_residue_one, Complex.hasDerivAt_tan, Complex.lintegral_comp_pi_polarCoord_symm, RCLike.instOrderClosedTopology, FormalMultilinearSeries.coeff_iterate_fslope, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, Filter.Tendsto.inner, PadicInt.continuousAddCharEquiv_symm_apply, MeasureTheory.Integrable.const_inner, hasStrictDerivAt_exp_smul_const_of_mem_ball', LSeriesHasSum.sum, ContinuousLinearMap.extendToπ'_apply, continuous_descPochhammer_eval, IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, VectorFourier.norm_fourierPowSMulRight_le, Complex.equivRealProdCLM_symm_apply_im, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, Complex.polarCoord_symm_apply, AnalyticOnNhd.is_constant_or_isOpen, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, summable_bernoulli_fourier, ModularFormClass.differentiableOn_cuspFunction_ball, Unitization.splitMul_injective, Antitone.deriv_nonpos, ZMod.differentiable_completedLFunctionβ, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, ContDiffMapSupportedIn.continuous_iff_comp, PeriodPair.periodic_weierstrassP, ModularFormClass.holo, RCLike.ofReal_im_ax, ZMod.toCircle_apply, Polynomial.differentiable, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, PadicInt.isOpenEmbedding_coe, ContinuousLinearEquiv.coord_norm', completedRiemannZeta_residue_one, EisensteinSeries.summable_e2Summand_symmetricIco, ContinuousLinearMap.nnnorm_id, GaussianFourier.integrable_cexp_neg_sum_mul_add, absConvexHull_eq_convexHull_balancedHull, ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, Complex.hasSum_sinh, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, hasStrictFDerivAt_inv', LinearMap.mem_span_iff_bound, Circle.arg_exp, hasFDerivAt_exp_smul_const_of_mem_ball', WithSeminorms.partial_sups, hasDerivAt_mul_const, TemperedDistribution.smulLeftCLM_const, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, hasStrictFDerivAt_exp_smul_const, dist_algebraMap, SchwartzMap.fourier_convolution_apply, UpperHalfPlane.sinh_half_dist, Seminorm.smul_ball_zero, Complex.hasStrictFDerivAt_log_real, Complex.differentiableAt_Gamma, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, Real.hasStrictDerivAt_tan, UpperHalfPlane.dist_le_iff_le_sinh, RCLike.wInner_cWeight_const_right, TemperedDistribution.smulLeftCLM_sum, mahler_apply, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, iter_deriv_inv_linear, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, HurwitzZeta.differentiableAt_cosZeta, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, Complex.hasSum_sin', jacobiThetaβ_fderiv_undef, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, instPerfectSpace, Complex.arg_eq_nhds_of_re_neg_of_im_pos, Real.differentiable_fourierChar_neg_bilinear_left, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, EisensteinSeries.summable_linear_right_add_one_mul_linear_right, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, PadicAlgCl.instIsUltrametricDist, gelfandTransform_isometry, FormalMultilinearSeries.le_radius_pi, Quaternion.coe_ofComplex, Real.hasDerivAt_arctan, continuousMultilinearCurryLeftEquiv_symm_apply, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, Complex.betaIntegral_convergent_left, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, Complex.continuousAt_cpow_of_re_pos, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, innerββ_apply_coe, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, Complex.sin_eq_tsum', PiLp.inner_apply, mellin_differentiableAt_of_isBigO_rpow, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Complex.reCLM_norm, iteratedFDeriv_succ_eq_comp_left, UpperHalfPlane.dist_coe_center_sq, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, differentiableAt_of_deriv_ne_zero, ZMod.LFunction_residue_one, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NumberField.mixedEmbedding.convexBodySum_convex, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, PeriodPair.mul_Οβ_add_mul_Οβ_mem_lattice, ContinuousLinearMap.opNorm_mulLeftRight_le, Circle.coe_exp, convex_halfSpace_im_le, ClosedSubmodule.orthogonal_closure, riemannZeta_eulerProduct_tprod, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, cpow_eq_nhds, ContDiffMapSupportedIn.structureMapCLM_zero_injective, RCLike.iInter_halfSpaces_eq, StrongDual.polar_zero, ContinuousMultilinearMap.piβα΅’_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, Real.deriv_arcsin_aux, Complex.differentiable_cosh, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonβα΅’_apply, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, fourier_add', RCLike.continuous_im, norm_iteratedFDerivWithin_fderivWithin, MeasureTheory.Integrable.fourier_smul, LinearMap.coe_toContinuousLinearMap_symm, Complex.frontier_setOf_le_re_and_im_le, continuousMultilinearCurryFin1_symm_apply, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, Complex.continuousAt_Gamma, StrongDual.mem_polar_iff, FormalMultilinearSeries.radius_pi_le, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, Submodule.orthogonal_eq_inter, BoundedContinuousFunction.charMonoidHom_apply, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, Complex.differentiable_iteratedDeriv_cos, ContinuousLinearEquiv.coord_self, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, riemannZeta_residue_one, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, Complex.ofReal_tsum, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_apply, ContDiffAt.differentiableAt_iteratedFDeriv, Manifold.IsImmersionOfComplement.of_opens, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, AddChar.coe_complexBasis, Polynomial.toAddCircle_X_eq_fourier_one, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, Complex.differentiable_cos, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, RCLike.geometric_hahn_banach_point_closed, hasDerivWithinAt_intCast, differentiableWithinAt_zpow, CircleIntegrable.out, UniformSpace.Completion.continuous_inner, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, PadicInt.denseRange_intCast, instSMulCommClass_sphere_closedBall_ball, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, LeftInvariantDerivation.commutator_apply, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, UpperHalfPlane.mdifferentiableAt_iff, fourier_add_half_inv_index, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, NormedField.noncompactSpace, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, PeriodPair.analyticOnNhd_weierstrassPExcept, hasStrictFDerivAt_pow, FormalMultilinearSeries.derivSeries_apply_diag, NormedSpace.polar_closedBall, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, AnalyticAt.fderiv, AnalyticOn.eval_polynomial, Matrix.l2_opNNNorm_conjTranspose_mul_self, fderiv_comp_smul, integrable_cexp_quadratic, Complex.image_exp_Ioc_eq_sphere, ContinuousLinearMap.opNorm_lsmul, coe_innerββ_apply, isCoveringMapOn_zpow, FormalMultilinearSeries.norm_changeOriginSeriesTerm, HurwitzZeta.completedHurwitzZetaEven_residue_zero, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, ContinuousWithinAt.inner, Module.Basis.continuous_coe_repr, Unitization.uniformity_eq_aux, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, hasDerivAt_exp_zero, HasFTaylorSeriesUpTo.zero_eq', deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, HurwitzZeta.tendsto_hurwitzZeta_sub_one_div_nhds_one, InnerProductSpace.continuousLinearMapOfBilin_apply, Circle.toUnits_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, instFieldContMDiffRing, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, PeriodPair.indep, UpperHalfPlane.tanh_half_dist, MeasureTheory.convolution_eq_swap, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, ContDiff.fderiv_right, hasDerivAt_const_add_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, ContDiffMapSupportedIn.withSeminorms', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, DFinsupp.inner_sum, SchwartzMap.tsum_eq_tsum_fourierIntegral, Orientation.kahler_rightAngleRotation_right, MeromorphicOn.divisor_def, WeakDual.isSeqCompact_polar, inner_matrix_row_row, ContinuousAlternatingMap.uniformContinuous_restrictScalars, HasFTaylorSeriesUpTo.fderiv, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.intervalIntegrable_charFun, ContinuousMap.idealOf_compl_singleton_isMaximal, Complex.arg_eq_nhds_of_re_neg_of_im_neg, PiTensorProduct.injectiveSeminorm_tprod_le, Complex.hasSum_arctan, ContinuousLinearMap.norm_holderL_le, fourier_add, hasFDerivWithinAt_pow, PolynormableSpace.withSeminorms, contDiff_infty_iff_fderiv, MeasureTheory.charFun_eq_integral_innerProbChar, LinearMap.polar_mem_iff, hasDerivWithinAt_inv, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, gaugeSeminormFamily_ball, hasStrictDerivAt_id, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem_of_analyticOn, instNonemptySeedRatReal, HasGradientAt.fderiv_apply, Seminorm.comp_smul_apply, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, HurwitzZeta.hasSum_int_completedCosZeta, deriv_neg, Complex.hasSum_cosh, RCLike.tendsto_ofReal_atBot_cobounded, LeftInvariantDerivation.ext_iff, Complex.frontier_setOf_lt_re, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, Complex.conj_tsum, Polynomial.hasFDerivWithinAt, LinearMap.hasDerivAt, Real.hasStrictDerivAt_rpow_const, HasFDerivAtFilter.restrictScalars, LinearMap.hasDerivAtFilter, HasFiniteFPowerSeriesOnBall.fderiv_eq, ModularForm.coe_trace, integrable_mul_cexp_neg_mul_sq, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, Complex.frontier_setOf_le_im, Complex.hasDerivAt_log_sub_logTaylor, Complex.GammaIntegral_convergent, hasStrictDerivAt_iff_hasStrictFDerivAt, WithSeminorms.isVonNBounded_iff_seminorm_bounded, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, ContinuousLinearMap.analyticAt_bilinear, Complex.isOpenMap_exp, ConvexOn.exists_affine_le_of_lt, HasFPowerSeriesAt.hasStrictFDerivAt, convex_halfSpace_re_gt, WithSeminorms.hasBasis, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AddChar.complexBasis_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, hasStrictDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, tendsto_algebraMap_cobounded, Real.probChar_apply, StrongDual.polar_singleton, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, hasDerivAt_pi, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, dist_algebraMap', hasFDerivAt_inv', MeasureTheory.dominatedFinMeasAdditive_weightedSMul, tendsto_euler_sin_prod', hasDerivWithinAt_finCons, Ideal.Quotient.norm_mk_le, WeakDual.CharacterSpace.exists_apply_eq_zero, exists_continuousLinearEquiv_fderiv_symm_eq, Complex.polarCoord_target, RCLike.conj_smul, FormalMultilinearSeries.rightInv_coeff, differentiableAt_dslope_of_ne, Complex.hasDerivAt_log, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, hasDerivAt_zpow, AnalyticAt.frequently_eq_iff_eventually_eq, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Circle.coe_injective, Complex.hasSum_cos, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, isClosedMap_smul_left, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, instSMulCommClass_sphere_sphere_closedBall, Complex.isHomeomorphicTrivialFiberBundle_im, ContDiffOn.differentiableOn_iteratedFDerivWithin, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, HurwitzZeta.hasSum_int_completedSinZeta, RCLike.instTietzeExtension, Matrix.IsHermitian.mulVec_eigenvectorBasis, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', zeta_nat_eq_tsum_of_gt_one, Matrix.l2_opNorm_def, UpperHalfPlane.tendsto_comap_im_ofComplex, Circle.coe_zpow, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, Matrix.toEuclideanLin_toLp, ContinuousLinearMapWOT.continuous_dual_apply, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, ContinuousLinearMap.holderL_apply_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, AddChar.expect_apply_eq_ite, LeftInvariantDerivation.toFun_eq_coe, Complex.reCLM_enorm, UpperHalfPlane.contMDiff_denom, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, isClosedEmbedding_smul_left, Polynomial.toAddCircle_C_eq_smul_fourier_zero, isConformalMap_const_smul, Matrix.l2_opNorm_mul, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, riemannZeta_eulerProduct_hasProd, norm_innerSL_le, VectorFourier.hasFDerivAt_fourierChar_smul, BoundedContinuousFunction.separatesPoints_charPoly, Padic.instProperSpace, DirichletCharacter.LSeries_eulerProduct, integrable_cexp_quadratic', Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, PeriodPair.lattice_eq_span_range_basis, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, continuousMultilinearCurryRightEquiv_apply, Seminorm.convex_closedBall, RCLike.real_smul_eq_coe_mul, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, Bornology.isVonNBounded_of_smul_tendsto_zero, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, Complex.frontier_reProdIm, RCLike.ofRealAm_coe, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, ContinuousAlternatingMap.prodLIE_symm_apply, Bornology.sUnion_isVonNBounded_eq_univ, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, PeriodPair.Οβ_mem_lattice, ContDiff.fderiv, SchwartzMap.fourier_convolution, Complex.log_inv_eq_integral, OnePoint.isZeroAt_iff, AnalyticOnNhd.eval_continuousLinearMap', UnitAddTorus.span_mFourierLp_closure_eq_top, fderivWithin_comp_smul, ZMod.LFunction_dft, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, instSMulCommClass_closedBall_closedBall_closedBall, PeriodPair.analyticOnNhd_weierstrassP, ContinuousLinearMap.flipβα΅’_symm, HasFPowerSeriesAt.compContinuousLinearMap, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, EuclideanSpace.nndist_single_same, Complex.differentiableAt_cos, cfcHom_eq_of_isStarNormal, exists_continuousLinearEquiv_fderivWithin_symm_eq, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, UpperHalfPlane.mdifferentiable_denom_zpow, HasGradientWithinAt.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, hasFDerivAt_exp, Pi.orthonormalBasis_repr, RCLike.hasSum_conj', MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, Complex.frontier_setOf_im_le, differentiableAt_iff_comp_sub_const, Complex.range_exp_mul_I, LinearMap.polar_mem, MeromorphicOn.divisor_mul, LinearMap.isAdjointPair_inner, Circle.coe_div, ContinuousLinearMap.norm_holder_apply_apply_le, upperHemicontinuous_spectrum, Complex.isUniformEmbedding_equivRealProd, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, tendsto_nhds_of_meromorphicOrderAt_nonneg, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, Circle.coe_one, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, hasDerivWithinAt_iff_tendsto_slope, constFormalMultilinearSeries_apply_succ, Polynomial.fourierCoeff_toAddCircle, FormalMultilinearSeries.continuousOn, hasFDerivAt_inv, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, Complex.hasSum_iff, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, DoubleCentralizer.toProdHom_apply, HurwitzZeta.differentiable_completedHurwitzZetaEvenβ, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, ContinuousLinearMap.fpowerSeries_apply_one, HurwitzZeta.differentiable_completedHurwitzZetaOdd, summable_pow_mul_cexp, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, WeakFEPair.Ξ_residue_zero, ModularFormClass.hasSum_qExpansion, SchwartzMap.one_add_le_sup_seminorm_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Seminorm.continuous_iff_continuous_comp, BoundedContinuousFunction.char_add_eq_mul, constFormalMultilinearSeries_zero, Complex.isOpenMap_re, HilbertBasis.hasSum_inner_mul_inner, Real.hasDerivWithinAt_arccos_Iic, ContDiffBump.convolution_tendsto_right_of_continuous, Complex.approx_Gamma_integral_tendsto_Gamma_integral, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, ContinuousMultilinearMap.curryFinFinset_apply, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, AlgebraNormClass.toSeminormClass, FormalMultilinearSeries.changeOriginSeriesTerm_bound, spectrum.subset_circle_of_unitary, summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, spectrum.subset_closedBall_norm, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, UpperHalfPlane.continuous_coe, summable_mul_of_bigO_atTop', MeromorphicAt.frequently_zero_iff_eventuallyEq_zero, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Complex.deriv_exp, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, ContinuousLinearMap.apply_apply, RCLike.span_one_I, PeriodPair.Οβ_mem_lattice, DirichletCharacter.differentiable_LFunctionTrivCharβ, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, algebraMap_cobounded_le_cobounded, summable_jacobiThetaβ'_term_iff, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, instSMulCommClass_sphere_sphere_ball, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, PiTensorProduct.mapLMultilinear_opNorm, Convex.instPathConnectedSpace, hasFPowerSeriesAt_iff', RCLike.geometric_hahn_banach_closed_compact, ContDiff.continuous_iteratedDeriv', ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, hasDerivAt_exp_smul_const_of_mem_ball, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, DFinsupp.sum_inner, UpperHalfPlane.mdifferentiable_iff, meromorphicOrderAt_ne_top_iff_eventually_ne_zero, Real.fourierIntegral_iteratedFDeriv, Complex.isOpen_re_gt_EReal, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, WeakFEPair.Ξ_residue_k, integrable_cexp_neg_mul_sq, WithSeminorms.hasBasis_ball, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, Complex.analyticAt_iff_eventually_differentiableAt, differentiableAt_comp_sub_const, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, smooth_functions_tower, RCLike.ofReal_sum, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, UpperHalfPlane.isOpen_upperHalfPlaneSet, Set.Finite.isVonNBounded, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, UpperHalfPlane.isEmbedding_coe, HurwitzZeta.differentiable_completedSinZeta, HurwitzZeta.differentiable_hurwitzZetaEven_sub_hurwitzZetaEven, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, HasCompactSupport.convolution_integrand_bound_right, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, Padic.isDenseInducing_cast_withVal, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, GromovHausdorff.eq_toGHSpace_iff, OrthonormalBasis.repr_reindex, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, MeasureTheory.condExpL2_comp_continuousLinearMap, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, PeriodPair.derivWeierstrassPExcept_def, Complex.continuousAt_ofReal_cpow_const, AnalyticOnNhd.eval_continuousLinearMap, circleMap_mem_sphere', Circle.argEquiv_apply_coe, MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, LSeries.hasDerivAt_term, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, UpperHalfPlane.mdifferentiableAt_ofComplex, LSeries_eq_mul_integral', ContDiffMapSupportedIn.structureMapLM_apply, isBoundedLinearMap_prod_multilinear, Orthonormal.inner_sum, Summable.hasSumUniformlyOn_log_one_add, HasCompactSupport.convolution_integrand_bound_right_of_subset, HasStrictDerivAt_ofNat, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, ContinuousMap.idealOfSet_isMaximal_iff, LeftInvariantDerivation.coeFnAddMonoidHom_apply, hasDerivWithinAt_iff_tendsto, balancedHull_convexHull_subseteq_absConvexHull, WeakFEPair.differentiable_Ξβ, cyclotomicCharacter.continuous, RCLike.realLinearIsometryEquiv_apply, TemperedDistribution.laplacianCLM_apply, Unitary.spectrum_subset_circle, continuousAt_gaussian_integral, mem_contMDiffFiberwiseLinear_iff, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, coeFn_fourierLp, RCLike.tendsto_ofReal_atTop_cobounded, differentiableAt_iff_comp_neg, DoubleCentralizer.coe_snd, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NumberField.mixedEmbedding.disjoint_negAt_plusPart, Matrix.IsHermitian.instContinuousFunctionalCalculus, MeasureTheory.integral_convolution, Complex.UnitDisc.coe_circle_smul, fderiv_norm_sq_apply, RCLike.imCLM_apply, ZMod.stdAddChar_apply, DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivCharβ, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, DirichletCharacter.differentiable_completedLFunction, Complex.continuousAt_tan, PositiveLinearMap.preGNS_norm_sq, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, HurwitzZeta.differentiableAt_expZeta, Submodule.starProjection_tendsto_closure_iSup, MulAlgebraNorm.smul', norm_iteratedFDeriv_fderiv, MeasureTheory.MemLp.ofReal, StrongDual.polar_nonempty, NormedSpace.dual_def, MulAlgebraNorm.extends_norm, RCLike.geometric_hahn_banach_open_open, MeasureTheory.integral_mul_const, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, HasMFDerivAt.const_smul, Complex.continuous_im, WeakDual.CharacterSpace.instStarHomClass, Complex.equivRealProdCLM_apply, Circle.argPartialEquiv_apply, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulβα΅’, MeasureTheory.charFun_eq_integral_probChar, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', EulerProduct.exp_tsum_primes_log_eq_tsum, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, PeriodPair.finrank_lattice, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, PeriodPair.derivWeierstrassP_add_coe, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Complex.orderClosedTopology, CStarMatrix.norm_def, ContinuousLinearMap.coe_derivβ, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, differentiableWithinAt_Ioi_iff_Ici, HurwitzZeta.differentiableAt_sinZeta, ModularForm.multipliableLocallyUniformlyOn_eta, contDiff_succ_iff_hasFDerivAt, dist_lineMap_lineMap, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, balanced_iff_neg_mem, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, Complex.isEquivalent_sin, NumberField.mixedEmbedding.convexBodyLT'_convex, differentiableOn_zpow, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, summable_jacobiThetaβ_term_iff, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, WithSeminorms.hasBasis_zero_ball, fderiv_inner_apply, contDiff_one_iff_deriv, inner_matrix_col_col, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, ContMDiff.coordChangeL, Real.hasStrictDerivAt_log_of_pos, BoundedContinuousFunction.char_mem_charPoly, MeasureTheory.SignedMeasure.im_toComplexMeasure, differentiableAt_jacobiTheta, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, ContinuousLinearMap.orthogonal_ker, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ContDiffWithinAt.fderivWithin_right, Complex.rotation, AnalyticAt.hasStrictDerivAt, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, SchwartzMap.norm_pow_mul_le_seminorm, pi_mul_cot_pi_q_exp, contDiffWithinAt_succ_iff_hasFDerivWithinAt, BoundedContinuousFunction.probCharDual_apply, PeriodPair.weierstrassPExcept_add, InnerProductSpace.norm_rankOne, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Complex.hasDerivAt_Gamma_nat, hasFDerivAt_integral_of_dominated_loc_of_lip, IsClosed.reProdIm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, PiTensorProduct.mapLMultilinear_toFun_apply, CStarMatrix.inner_toCLM_conjTranspose_right, norm_jacobiThetaβ_term_fderiv_le, HasFiniteFPowerSeriesOnBall.fderiv, Matrix.PosDef.re_dotProduct_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Summable.tendstoUniformlyOn_tsum_nat_log_one_add, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, quasispectrum.instCompactSpace, fderiv_eq_smul_deriv, CStarMatrix.toCLM_apply_single_apply, BoundedContinuousFunction.char_apply, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, LinearMap.ker_toContinuousLinearMap, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Complex.tendsto_exp_comap_re_atBot_nhdsNE, differentiable_circleMap, HurwitzZeta.tendsto_hurwitzZetaEven_sub_one_div_nhds_one, integrableOn_exp_mul_complex_Ioi, NormedSpace.exp_add, Complex.isClosed_range_intCast, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, WithSeminorms.finset_sups, hasDerivWithinAt_sub_const_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, HurwitzZeta.differentiable_completedCosZetaβ, Complex.restrictScalars_toSpanSingleton', NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, fderiv_inv', ContinuousLinearMapWOT.ext_inner_iff, Complex.differentiable_iteratedDeriv_cosh, Complex.closedEmbedding_intCast, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, HurwitzZeta.hurwitzZetaEven_residue_one, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, FormalMultilinearSeries.comp_assoc, HasFPowerSeriesWithinAt.comp, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, continuousAt_dslope_of_ne, Complex.closure_setOf_im_lt, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, PeriodPair.differentiableOn_derivWeierstrassPExcept, continuousMultilinearCurryFin1_apply, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, hasFDerivAt_finset_prod, fourierCoeff_fourier, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, HilbertBasis.finite_spans_dense, toMeromorphicNFOn_eqOn_codiscrete
|
| Name | Category | Theorems |
|---|
induced π | CompOp | 2 mathmath: NormOneClass.induced, NormMulClass.induced
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toNonUnitalSeminormedRing π | CompOp | 64 mathmath: RingHom.compLeftContinuousBounded_apply_apply, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, List.nnnorm_prod, List.nnnorm_prod_le', ContinuousLinearMap.opNorm_lsmul_apply_le, nndist_smulβ, norm_sub_mul_le', nnnorm_algebraMap_nnreal, isBoundedBilinearMap_mul, ContinuousLinearMap.mulLeftRight_apply, hasFDerivAt_ringInverse, nnnorm_smul, List.nnnorm_prod_le, RingHomIsometric.enorm_map, NormedAlgebra.exists_isMinOn_norm_sub_smul, ContinuousLinearMap.lsmul_flip_inj, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, fderiv_inverse, fderivWithin_inv', nnnorm_natAbs, nnnorm_algebraMap, nnnorm_pow, ContinuousLinearMap.lsmul_apply, nnnorm_pow_le, RingHomIsometric.nnnorm_map, FormalMultilinearSeries.ofScalars_norm_le, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, ContinuousMap.nnnorm_smul_const, IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, nnnorm_intCast_abs, edist_smulβ, NormedAlgebra.instRegularNormedAlgebra, hasStrictFDerivAt_ringInverse, nnnorm_pow_le', TrivSqZeroExt.nnnorm_def, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, nnnorm_algebraMap', ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, ContinuousLinearMap.opNorm_lsmul_le, instENormSMulClass, TrivSqZeroExt.nnnorm_inl, Matrix.linfty_opNormOneClass, isBoundedBilinearMap_smul, IsUltrametricDist.nnnorm_intCast_le_one, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, nnnormHom_apply, nnnorm_commutator_units_sub_one_le, IsUltrametricDist.nnnorm_natCast_le_one, norm_commutator_units_sub_one_le, hasStrictFDerivAt_inv', ContinuousMap.norm_smul_const, ContinuousLinearMap.opNorm_mulLeftRight_le, enorm_pow, ContinuousLinearMap.opNorm_lsmul, norm_sub_mul_le, hasFDerivAt_inv', BoundedContinuousFunction.coe_npowRec, toRingSeminorm_apply, FormalMultilinearSeries.ofScalars_norm_eq_mul, ContinuousMultilinearMap.norm_mkPiAlgebraFin, HolderWith.smul_iff, FormalMultilinearSeries.ofScalars_norm, fderiv_inv'
|
toNorm π | CompOp | 91 mathmath: List.norm_prod_le, norm_natCast_eq_mul_norm_one, Polynomial.exists_eq_supNorm, IsUltrametricDist.norm_intCast_le_one, MulAlgebraNorm.extends_norm', ContinuousLinearMap.opNorm_lsmul_apply_le, IsUltrametricDist.norm_add_one_le_max_norm_one, Asymptotics.isBigO_const_mul_left_iff', Asymptotics.IsBigOWith.const_smul_self, TrivSqZeroExt.instNormOneClass, AlgebraNorm.extends_norm, norm_pow, Multipliable.norm, List.norm_prod_le', AlgebraNormClass.map_smul_eq_mul, norm_algebraMap_nnreal, Asymptotics.isBigOWith_self_const_mul', NormMulClass.toNormSMulClass_op, norm_pow_le, ContinuousMultilinearMap.opNorm_smul_le, normHom_apply, Asymptotics.IsBigOWith.const_smul_left, NormedAlgebra.exists_isMinOn_norm_sub_smul, TrivSqZeroExt.norm_def, norm_natCast, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, Seminorm.smul', Polynomial.le_supNorm, AlgebraNorm.smul', NormSMulClass.of_nnnorm_smul, SubringClass.toNormMulClass, norm_natAbs, dist_eq, norm_intCast_abs, eventually_norm_pow_le, mem_balancedHull_iff, PadicInt.mahlerTerm_one, NormOneClass.induced, RingHomIsometric.ids, Multipliable.norm_tprod, NormMulClass.induced, Polynomial.supNorm_monomial, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, Polynomial.supNorm_C, Matrix.linftyOpNormSMulClass, Polynomial.supNorm_def', WithLp.normSMulClassSeminormedAddCommGroupToProd, norm_prod, norm_algebraMap, Prod.instNormSMulClass, TrivSqZeroExt.norm_inl, Asymptotics.isBigO_const_mul_right_iff', MulAlgebraNormClass.map_smul_eq_mul, SeminormClass.map_smul_eq_mul, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Asymptotics.isBigO_self_const_mul', norm_mul_le, WithLp.instProdNormSMulClass, Matrix.normSMulClass, NormedAlgebra.norm_smul_le, Ideal.Quotient.norm_mk_lt, Asymptotics.isLittleO_const_mul_left_iff', AlgebraNorm.extends_norm', spectralValue_X_sub_C, Asymptotics.isBigO_const_mul_self, IsUltrametricDist.norm_natCast_le_one, Nat.norm_cast_le, SubringClass.toNormOneClass, Matrix.frobeniusNormSMulClass, dist_smulβ, norm_pow_le', norm_intCast_eq_abs_mul_norm_one, Asymptotics.isBigOWith_const_mul_self, Polynomial.isGreatest_supNorm, norm_commutator_units_sub_one_le, Algebra.norm_smul_one_eq_norm, RingHomIsometric.inv, dist_algebraMap, List.norm_prod, norm_algebraMap', Polynomial.supNorm_eq_iSup, Seminorm.comp_smul_apply, spectralValueTerms_of_lt_natDegree, Ideal.Quotient.norm_mk_le, ULift.instNormSMulClass, toRingSeminorm_apply, Asymptotics.isLittleO_const_mul_right_iff', HasProd.norm, MulAlgebraNorm.smul', MulAlgebraNorm.extends_norm
|
toPseudoMetricSpace π | CompOp | 3512 mathmath: ArithmeticFunction.vonMangoldt.residueClass_eq, Unitary.openPartialHomeomorph_source, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, LinearMap.det_toContinuousLinearMap, ValueDistribution.logCounting_zero, instSeparatingDual, hasFDerivAt_iff_hasDerivAt, absorbent_iff_eventually_nhdsNE_zero, HurwitzZeta.hasSum_int_hurwitzZetaOdd, iteratedDeriv_scomp_two, LinearMap.IsSymmetric.clm_adjoint_eq, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, ContinuousMap.toLp_inj, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, WeakFEPair.differentiableAt_Ξ, TemperedDistribution.lineDerivOpCLM_eq, continuousSMul_sphere_ball, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, MeasureTheory.Lp.toTemperedDistributionCLM_apply, fderiv_iteratedFDeriv, Orientation.kahler_map_complex, Polynomial.differentiableWithinAt, FormalMultilinearSeries.comp_rightInv_aux1, tendsto_zero_iff_meromorphicOrderAt_pos, UpperHalfPlane.mdifferentiable_num, Complex.cos_eq_tsum, ContinuousAt.inner, LinearMap.mkContinuousβ_norm_le', NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, NormedSpace.exp_continuous, NormedSpace.isBounded_polar_of_mem_nhds_zero, HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_div, Valued.instIsUltrametricDist, TensorProduct.enorm_lid, differentiableAt_comp_neg, continuousAt_const_cpow, hasDerivWithinAt_Iio_iff_Iic, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, LinearMap.mkContinuousβ_apply, Matrix.frobenius_nnnorm_mul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, Complex.differentiableAt_sin, Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero, Bundle.ContMDiffRiemannianMetric.contMDiff, Complex.norm_circleTransformBoundingFunction_le, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, Seminorm.absorbent_closedBall_zero, LeftInvariantDerivation.lift_zero, Complex.isOpen_re_lt_EReal, hasSum_geometric_of_norm_lt_one, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcβHom, RCLike.map_apply, MDifferentiableOn.clm_postcomp, differentiable_const_cpow_of_neZero, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', Matrix.frobeniusIsBoundedSMul, HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, completedZeta_eq_tsum_of_one_lt_re, Complex.continuousOn_exp, ContinuousLinearMap.continuousβ, RCLike.geometric_hahn_banach_point_open, hasDerivWithinAt_add_const_iff, IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, CuspFormClass.holo, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, RCLike.ofRealCLM_apply, SchwartzMap.integral_sesq_fourier_fourier, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, PowerSeries.IsRestricted.smul, HurwitzZeta.differentiableAt_hurwitzZeta_sub_one_div, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, ModularFormClass.differentiableAt_comp_ofComplex, PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, Real.hasFDerivAt_fourierChar_neg_bilinear_left, hasStrictDerivAt_intCast, NormedRing.inverse_one_sub_norm, LeftInvariantDerivation.leibniz, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.convolution_eq_right', EisensteinSeries.hasSum_e2Summand_symmetricIcc, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, RCLike.reCLM_apply, HurwitzZeta.differentiableAt_hurwitzZetaEven, curveIntegral_smul, NormedSpace.exp_zsmul, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, RCLike.separate_convex_open_set, NumberField.canonicalEmbedding.mem_span_latticeBasis, hasStrictFDerivAt_list_prod_finRange', InnerProductSpace.rankOne_one_left_eq_innerSL, PeriodPair.hasSumLocallyUniformly_weierstrassP, Subalgebra.spectrum_sUnion_connectedComponentIn, ContMDiffMap.coeFnAlgHom_apply, Function.FactorizedRational.divisor, hasDerivAt_sqrt_mul_log, LSeries.term_sum, ContinuousLinearMap.continuous_det, HurwitzZeta.hasSum_int_cosKernelβ, HasFiniteFPowerSeriesAt.neg, Complex.isOpenMap_im, HurwitzZeta.hasSum_int_hurwitzZetaEven, Complex.ofRealCLM_coe, Complex.kahler, Complex.norm_polarCoord_symm, ContinuousLinearMap.map_add_add, SeminormFamily.basisSets_smul_right, WeakDual.isCompact_polar, MeromorphicOn.divisor_fun_smul, finrank_real_complex_fact', PeriodPair.deriv_weierstrassP, nnnorm_cfc_lt, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, Real.hasDerivAt_sigmoid, PeriodPair.coeff_weierstrassPExceptSeries, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, Metric.unitSphere.coe_one, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, PositiveLinearMap.apply_le_of_isSelfAdjoint, Matrix.IsHermitian.det_abs, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Complex.comap_exp_cobounded, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, differentiableAt_zpow, hasFDerivAt_multiset_prod, MDifferentiableAt.cle_arrowCongr, BoundedContinuousFunction.algebraMap_apply, spectrum.subset_closedBall_norm_mul, continuousSMul_sphere_sphere, spectrum.instCompactSpace, geom_series_mul_shift, ContinuousLinearMap.continuousSMul, hasFTaylorSeriesUpToOn_top_iff_right, DirichletCharacter.LSeries_eulerProduct_tprod, MeasureTheory.Lp.const_smul_mem_Lp, smoothSheafCommRing.nonunits_stalk, LSeries.term_convolution', CuspFormClass.zero_at_infty_comp_ofComplex, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, PeriodPair.derivWeierstrassPExcept_sub, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries, deriv_mem_iff, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, NumberField.canonicalEmbedding.latticeBasis_apply, Complex.integral_comp_pi_polarCoord_symm, FormalMultilinearSeries.radius_pi_eq_iInf, CFC.tendsto_cfc_rpow_sub_one_log, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, Padic.withValUniformEquiv_norm_le_one_iff, hasSum_choose_mul_geometric_of_norm_lt_one, summableLocallyUniformlyOn_iteratedDerivWithin_cexp, tendsto_cobounded_iff_meromorphicOrderAt_neg, Real.hasStrictDerivAt_rpow_const_of_ne, Matrix.IsHermitian.cfc_eq, tsum_coe_mul_geometric_of_norm_lt_one', lp.inner_eq_tsum, UpperHalfPlane.image_coe_sphere, Complex.isCoveringMap_exp, StrongDual.polarSubmodule_eq_setOf, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, PeriodPair.Οβ_div_two_notMem_lattice, OrthonormalBasis.sum_inner_mul_inner, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, range_circleMap, Asymptotics.isLittleOTVS_one, Filter.inv_nhdsWithin_ne_zero, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, ContinuousLinearMap.hasDerivAtFilter, HasFPowerSeriesAt.locally_ne_zero, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, span_fourier_closure_eq_top, Complex.GammaSeq_tendsto_Gamma, PeriodPair.basis_one, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, RCLike.conjCLE_norm, ordinaryHypergeometric_radius_top_of_neg_natβ, HasFPowerSeriesOnBall.add, Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, tendsto_zpow_nhdsNE_zero_cobounded, ContinuousMap.toLp_denseRange, WeakDual.isClosed_image_polar_of_mem_nhds, Seminorm.ball_smul_closedBall, ContinuousLinearMap.integral_apply, one_add_cpow_hasFPowerSeriesAt_zero, Unitary.mem_pathComponentOne_iff, circleIntegrable_iff, LinearMap.polar_eq_iInter, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, MeasureTheory.MemLp.const_inner, DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontriv, Complex.tsum_exp_neg_mul_int_sq, not_integrableOn_Ioi_cpow, Real.fderiv_fourierChar_neg_bilinear_right_apply, BoundedContinuousFunction.char_neg, UpperHalfPlane.isOpenEmbedding_coe, RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, Quaternion.continuous_imI, hasFPowerSeriesOnBall_pi_iff, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Units.nhds, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, Complex.uniformlyContinuous_im, HasFPowerSeriesWithinAt.const_smul, BoundedContinuousFunction.char_zero_eq_one, SchwartzMap.lineDerivOp_fourier_eq, isClosedEmbedding_cfcβAux, LeftInvariantDerivation.coe_derivation, innerSL_apply_apply, RCLike.norm_expect_le, HasGradientAt.continuousOn, HasFPowerSeriesWithinOnBall.restrictScalars, SeminormFamily.filter_eq_iInf, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerββ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, inner_sum, HasFTaylorSeriesUpTo.hasFDerivAt, Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_ne, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, UpperHalfPlane.comp_ofComplex_of_im_pos, hasDerivAt_neg', Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContMDiffOn.clm_postcomp, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, Complex.continuousOn_arg, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, ContinuousMap.range_toLp, deriv_mul_const_field, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, UpperHalfPlane.dist_le_iff_dist_coe_center_le, LeftInvariantDerivation.left_invariant', selfAdjoint.expUnitaryPathToOne_apply, NormedRing.inverse_add_norm_diff_nth_order, hasDerivAt_bernoulliFun, Unitary.continuousOn_argSelfAdjoint, hasSum_one_div_nat_pow_mul_fourier, derivWithin_fderivWithin, two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even, WithLp.isBoundedSMulSeminormedAddCommGroupToProd, MultilinearMap.mkContinuousMultilinear_apply, SchwartzMap.instContinuousSMul, Complex.UnitDisc.instSMulCommClass_closedBall_circle, TemperedDistribution.lineDerivOp_fourier_eq, Complex.frontier_setOf_re_le, PadicInt.norm_mahlerTerm, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, ContDiff.differentiable_deriv_two, Submodule.Quotient.instIsBoundedSMul, Polynomial.isCoveringMapOn_eval, Complex.ofRealCLM_norm, Complex.UnitDisc.instSMulCommClass_closedBall_left, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, StarAlgebra.elemental.characterSpaceToSpectrum_coe, Bornology.IsBounded.reProdIm, tsum_choose_mul_geometric_of_norm_lt_one', OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, NumberField.mixedEmbedding.mem_idealLattice, MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE, SchwartzMap.bilinLeftCLM_apply, Complex.borelSpace, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, IsConformalMap.is_complex_or_conj_linear, HasGradientAt.hasDerivAt', hasSum_coe_mul_geometric_of_norm_lt_one', AffineMap.hasDerivWithinAt, MeromorphicOn.divisor_const, LeftInvariantDerivation.left_invariant, isUltrametricDist_iff_forall_norm_natCast_le_one, instSMulCommClass_sphere_sphere_sphere, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, tsum_coe_mul_geometric_of_norm_lt_one, Complex.convexHull_reProdIm, NormedSpace.toIsBoundedSMul, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, Complex.hasStrictDerivAt_tan, ContDiff.continuous_deriv_one, curveIntegralFun_smul, Complex.closure_preimage_im, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasDerivWithinAt_iff_isLittleO, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, Filter.map_mul_left_cobounded, ContinuousAlternatingMap.piLIE_apply_apply, Matrix.PosSemidef.sqrt_eq_zero_iff, Differentiable.fderiv_norm_rpow, NumberField.InfiniteAdeleRing.algebraMap_apply, UnitAddTorus.mFourierSubalgebra_coe, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, hasDerivWithinAt_zero, iteratedDerivWithin_tsum_cexp_eq, ContDiffAt.hasStrictDerivAt, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, Complex.continuous_sin, FormalMultilinearSeries.hasSum_of_finite, differentiableWithinAt_inv, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, hasDerivAtFilter_ofNat, CFC.exp_log, Complex.exp_eq_exp_β, FormalMultilinearSeries.changeOriginSeries_summable_auxβ, curveIntegrable_smul_iff, TensorProduct.toLinearEquiv_lidIsometry, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, LinearMap.toContinuousLinearMapβ_coe, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, ContinuousLinearMap.isometry_mul_flip, PeriodPair.weierstrassP_coe, AnalyticOnNhd.eval_linearMap', HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, ClosedSubmodule.inf_orthogonal, LinearMap.coe_toContinuousLinearMap', HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, contDiffOn_iff_continuousOn_differentiableOn, Complex.isQuotientCoveringMap_npow, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, sum_cauchyPowerSeries_eq_integral, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, SchwartzMap.laplacianCLM_eq, CStarModule.innerSL_apply, monomial_has_deriv_aux, continuous_equivFun_basis, DirichletCharacter.LSeries_twist_vonMangoldt_eq, LinearIsometryEquiv.conjStarAlgEquiv_apply, PadicInt.mahlerTerm_apply, LinearMap.toMatrixOrthonormal_reindex, MeasureTheory.ConvolutionExistsAt.integrable, Matrix.IsHermitian.eigenvalues_eq, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, Filter.tendsto_ofReal_iff', iter_deriv_zpow', PadicInt.coe_sum, Complex.deriv_cos, WithSeminorms.continuousSMul, Matrix.exp_conj', hasLineDerivAt_iff_isLittleO_nhds_zero, Complex.not_differentiableAt_Gamma_neg_nat, RCLike.borelSpace, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, MeasureTheory.integrable_const_mul_iff, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, HasFiniteFPowerSeriesOnBall.sum, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, ConvexOn.univ_sSup_of_countable_affine_eq, IsUltrametricDist.of_normedAlgebra', RCLike.hasSum_ofReal, InnerProductSpace.inner_left_rankOne_apply, Matrix.PosSemidef.commute_iff, TestFunction.toBoundedContinuousFunctionCLM_apply, RCLike.continuous_normSq, IsLocalFrameOn.coeff_apply_of_mem, hasStrictDerivAt_abs_pos, ContinuousLinearMap.smul_compLp, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendToπ, Matrix.exp_neg, HasFPowerSeriesAt.add, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, ContinuousAlternatingMap.curryLeft_smul, continuous_const_cpow, polynomialFunctions.starClosure_topologicalClosure, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerββ_apply_apply, hasFDerivWithinAt_inv, hasSum_nat_jacobiTheta, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, NumberField.InfinitePlace.Completion.norm_coe, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, iteratedDeriv_scomp_three, hasDerivWithinAt_pi, differentiableOn_iteratedDerivWithin_cotTerm, smoothSheafCommRing.instLocalRing_stalk, Real.integrable_prod_sub, MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt, ContinuousLinearMap.eq_adjoint_iff, PeriodPair.hasSum_derivWeierstrassPExcept, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, Polynomial.div_tendsto_zero_iff_degree_lt, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, HasFPowerSeriesAt.comp, Complex.differentiableAt_GammaAux, ContinuousLinearMap.IsPositive.smul_of_nonneg, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, EuclideanSpace.nndist_eq, LinearMap.polar_singleton, FormalMultilinearSeries.sum_of_finite, MeromorphicOn.divisor_pow, gelfandStarTransform_apply_apply, Filter.map_mul_right_cobounded, HasFTaylorSeriesUpToOn.zero_eq', HarmonicAt.analyticAt_complex_partial, Complex.instPathConnectedSpaceUnits, Filter.inv_nhdsNE_zero, ContDiff.continuous_deriv, NormedSpace.Dual.toWeakDual_continuous, WithSeminorms.withSeminorms_eq, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, ContinuousMultilinearMap.norm_smulRightL_le, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, tsum_geometric_of_norm_lt_one, ContinuousLinearMap.precompL_apply, Seminorm.closedBall_smul_ball, differentiableAt_comp_add_const, IsSelfAdjoint.adjoint_eq, Complex.continuousOn_cos, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ZMod.completedLFunction_def_even, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, RCLike.geometric_hahn_banach_closed_point, MeasureTheory.AEStronglyMeasurable.inner_const, Real.hasDerivAt_arcosh, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, Complex.isOpen_slitPlane, HasGradientAt.continuousAt, FormalMultilinearSeries.radius_le_smul, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, MeasureTheory.SignedMeasure.toComplexMeasure_apply, MDifferentiable.clm_postcomp, ModularForm.tsum_logDeriv_eta_q, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, dist_inv_invβ, CStarMatrix.toCLM_injective, ContinuousLinearMap.isPositive_self_comp_adjoint, tendsto_norm_inv_nhdsNE_zero_atTop, dslope_eventuallyEq_slope_nhdsNE, formalMultilinearSeries_geometric_apply_norm_le, LinearMap.adjoint_toContinuousLinearMap, StrongFEPair.differentiable_Ξ, hasDerivAt_iff_isLittleO, spectrum.isOpen_resolventSet, Polynomial.toAddCircle_X_pow_eq_fourier, HasDerivWithinAt.hasFDerivWithinAt, hasFPowerSeriesAt_const, fderiv_eq_deriv_mul, UniformOnFun.continuousSMul_induced_of_image_bounded, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, FormalMultilinearSeries.radius_compNeg, gelfandTransform_bijective, Polynomial.differentiableOn_aeval, SchwartzMap.integral_bilin_fourierIntegral_eq, NormedRing.inverse_one_sub_nth_order, NumberField.mixedEmbedding.polarSpaceCoord_target, OnePoint.isZeroAt_iff_exists_SL2Z, LinearIsometryEquiv.adjoint_eq_symm, NumberField.mixedEmbedding.negAt_apply_snd, extDeriv_fun_smul, ContinuousAlternatingMap.toAlternatingMap_curryLeft, ordinaryHypergeometricSeries_radius_eq_one, Matrix.toEuclideanLin_apply, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, NormedField.discreteTopology_or_nontriviallyNormedField, Complex.tendsto_exp_nhds_zero_iff, fourier_norm, ContinuousLinearMap.opNorm_mul, Complex.uniformContinuous_im, Complex.frontier_preimage_re, CuspForm.coe_trace, EisensteinSeries.e2Summand_summable, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, image_circleMap_Ioc, TemperedDistribution.smulLeftCLM_neg, analyticOrderAt_eq_top, Real.hasStrictDerivAt_arccos, AnalyticAt.frequently_zero_iff_eventually_zero, RCLike.conjCLE_apply, MDifferentiable.cle_arrowCongr, Complex.reCLM_nnnorm, Unitization.nnnorm_def, Unitization.dist_inr, CFC.continuousOn_log, isScalarTower_closedBall_closedBall_closedBall, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Complex.instContinuousStar, NormedSpace.exp_hasFPowerSeriesOnBall, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, NumberField.mixedEmbedding.negAt_preimage, HasLineDerivAt.tendsto_slope_zero_right, isScalarTower_sphere_closedBall_closedBall, Complex.hasDerivAt_GammaIntegral, NormedSpace.expSeries_summable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, Complex.deriv_ofReal_cpow_const, UpperHalfPlane.comp_ofComplex, Complex.starConvex_ofReal_slitPlane, PiTensorProduct.mapL_smul, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, BoundedContinuousFunction.coe_toContinuousMapStarβ, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, ContinuousLinearMap.adjointAux_norm, CStarMatrix.norm_def', IsGreatest.nnnorm_cfc_nnreal, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, HurwitzZeta.hasSum_nat_sinZeta, ValueDistribution.logCounting_top, LeftInvariantDerivation.lift_add, hasDerivAtFilter_natCast, binomialSeries_radius_eq_one, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, Pi.counit_eq_adjoint, ContinuousAlternatingMap.instContinuousSMul, LinearMap.toMatrixOrthonormal_apply_apply, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, Complex.summable_conj, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, HasGradientWithinAt.continuousWithinAt, Complex.continuousAt_arg, PeriodPair.latticeBasis_zero, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, ZMod.LFunction_def_odd, Asymptotics.IsLittleO.tendsto_div_nhds_zero, summable_mul_of_bigO_atTop, SchwartzMap.fourier_lineDerivOp_eq, Complex.starConvex_one_slitPlane, ContinuousLinearMapWOT.inducingFn_apply, meromorphicOrderAt_eq_top_iff, CStarMatrix.inner_toCLM_conjTranspose_left, hasStrictDerivAt_exp_smul_const, ContinuousMap.setOfIdeal_ofSet_of_isOpen, isBoundedBilinearMap_comp, Complex.interior_setOf_le_re, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Filter.tendsto_ofReal_iff, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, hasStrictDerivAt_add_const_iff, Finsupp.sum_inner, TemperedDistribution.fourierInv_lineDerivOp_eq, UpperHalfPlane.mdifferentiable_inv_denom, multipliable_one_add_of_summable, LeftInvariantDerivation.lift_smul, FormalMultilinearSeries.rightInv_removeZero, WithAbs.uniformSpace_comap_eq_of_comp, geom_series_succ, Asymptotics.isLittleO_pow_pow, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ClosedSubmodule.orthogonal_closure'', hasStrictDerivAt_exp_smul_const', Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, Real.fourier_iteratedFDeriv, SchwartzMap.smulLeftCLM_real_smul, uniqueDiffWithinAt_iff_accPt, InnerProductSpace.toDualMap_apply_apply, Orientation.kahler_eq_zero_iff, AddChar.sum_apply_eq_ite, EulerProduct.eulerProduct_completely_multiplicative, PositiveLinearMap.preGNS_norm_def, tsum_geometric_le_of_norm_lt_one, UpperHalfPlane.dist_eq_iff_eq_sinh, hasDerivAtFilter_zero, Complex.integral_comp_polarCoord_symm, Complex.uniformContinuous_re, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, PeriodPair.Οβ_div_two_notMem_lattice, UnitAddTorus.mFourierCoeff_toLp, WeakDual.toStrongDual_inj, Metric.unitSphere.coe_mul, HurwitzZeta.differentiable_expZeta_of_ne_zero, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, isModuleTopologyOfFiniteDimensional, PeriodPair.hasSum_derivWeierstrassP, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, PeriodPair.compl_lattice_diff_singleton_mem_nhds, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, hasDerivAt_id', integrableOn_Ioi_cpow_iff, ContinuousMultilinearMap.curryRight_norm, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, HurwitzZeta.differentiable_hurwitzZetaOdd, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, MeasureTheory.MemLp.inner_const, LSeries_deriv_eqOn, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, MDifferentiableAt.clm_postcomp, HurwitzZeta.differentiable_hurwitzZeta_sub_hurwitzZeta, PeriodPair.hasSumLocallyUniformly_derivWeierstrassP, Complex.sameRay_of_arg_eq, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, Bornology.isVonNBounded_iff_absorbing_le, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, UpperHalfPlane.ofComplex_apply_of_im_nonpos, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, Real.deriv_sqrt_aux, deriv_fderiv, summable_mul_of_summable_norm, IsOpen.reProdIm, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, RegularNormedAlgebra.isometry_mul', Complex.frontier_setOf_im_lt, cauchyPowerSeries_apply, summable_eisSummand, ModularFormClass.continuous, Matrix.PosSemidef.det_sqrt, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcβHom, Complex.isConnected_of_lowerHalfPlane, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, tendsto_cobounded_of_meromorphicOrderAt_neg, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, TensorProduct.lidIsometry_apply, ContDiffMapSupportedIn.seminorm_le_iff, Unitary.openPartialHomeomorph_symm_apply, MeasureTheory.StronglyMeasurable.inner, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, Complex.tendsto_exp_comap_re_atTop, convex_halfSpace_re_le, Complex.reCLM_coe, PadicInt.fwdDiff_tendsto_zero, Complex.deriv_Gamma_add_one, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux', EuclideanSpace.dist_single_same, EulerProduct.eulerProduct_hasProd, Complex.continuous_re, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, ContinuousMultilinearMap.opNorm_smul_le, MeasureTheory.convolution_precompR_apply, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, Filter.inv_coboundedβ, Matrix.linfty_opNNNorm_eq_opNNNorm, VectorFourier.fourierIntegral_iteratedFDeriv, UpperHalfPlane.contMDiff_coe, PadicInt.compactSpace, InformationTheory.hasDerivAt_klFun, CuspForm.holo', InnerProductSpace.nnnorm_rankOne, PeriodPair.mem_lattice, BoundedContinuousFunction.mem_charPoly, spectrum.gelfandTransform_eq, Orientation.kahler_comp_rightAngleRotation, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, BoundedContinuousFunction.charAlgHom_apply, LeftInvariantDerivation.comp_L, ArithmeticFunction.vonMangoldt.residueClass_apply, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, FormalMultilinearSeries.continuousOn_of_finite, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, LinearMap.trace_eq_sum_inner, ContinuousAlternatingMap.curryLeft_apply_apply, BoundedContinuousFunction.coe_intCast, MeasureTheory.memLp_haarAddCircle_iff, ContinuousLinearMap.flip_smul, MeromorphicOn.divisor_inv, ContinuousMap.spectrum_eq_preimage_range, PadicInt.mahlerSeries_apply, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, NumberField.mixedEmbedding.convexBodySum_compact, MeromorphicOn.divisor_fun_pow, differentiableWithinAt_pow, Bundle.ContinuousRiemannianMetric.continuous, Matrix.IsHermitian.charpoly_cfc_eq, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow, NormedSpace.norm_expSeries_summable, MeasureTheory.ConvolutionExistsAt.integrable_swap, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, spectrum.isCompact, HasFiniteFPowerSeriesOnBall.eq_partialSum, tsum_mul_tsum_of_summable_norm, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, IsUltrametricDist.isUltrametricDist_of_forall_norm_sub_one_of_norm_le_one, IsLocalFrameOn.coeff_congr, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, AffineMap.hasDerivAt_lineMap, Complex.comap_exp_nhds_zero, EisensteinSeries.G2_eq_tsum_symmetricIco, Complex.equivRealProdCLM_symm_apply, nndist_inv_invβ, Complex.cos_eq_tsum', ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasDerivWithinAt.norm_sq, HasGradientAtFilter.hasDerivAtFilter', WeakDual.CharacterSpace.continuousMapEval_bijective, cot_series_rep', DirichletCharacter.differentiableAt_LFunction, differentiableOn_dslope_of_notMem, LowerSemicontinuousOn.isClosed_re_epigraph, NumberField.canonicalEmbedding.integralBasis_repr_apply, Complex.interior_preimage_re, Complex.continuous_cosh, fourier_one, Polynomial.isClosedMap_eval, HasFPowerSeriesOnBall.fderiv_eq, ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, NormedSpace.inclusionInDoubleDual_norm_eq, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, SchwartzMap.smulLeftCLM_sum, PadicInt.continuous_choose, AffineMap.hasDerivWithinAt_lineMap, PeriodPair.basis_zero, UpperHalfPlane.image_coe_ball, ContinuousLinearMap.fderiv_of_bilinear, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Complex.closure_setOf_lt_im, Real.hasDerivWithinAt_arccos_Ici, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ContinuousLinearMap.nnnorm_toSpanSingleton, ContinuousAlternatingMap.alternatizeUncurryFin_smul, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Matrix.linftyOpIsBoundedSMul, EulerProduct.eulerProduct, Complex.hasDerivAt_Gammaβ_one, SchwartzMap.toBoundedContinuousFunctionCLM_apply, hasSum_jacobiThetaβ_term, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, deriv_id'', hasFDerivAt_jacobiThetaβ_term, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, Complex.continuousAt_cpow_const_of_re_pos, LSeries_deriv, Submodule.adjoint_subtypeL, hasStrictFDerivAt_exp, NormedSpace.exp_conj, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, AbsoluteValue.Completion.locallyCompactSpace, UpperHalfPlane.contMDiff_inv_denom, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, mul_neg_geom_series, deriv_const_mul_field', unitSphereToUnits_apply_coe, Complex.uniformlyContinuous_re, WithAbs.tendsto_one_div_one_add_pow_nhds_one, Complex.map_exp_comap_re_atTop, RCLike.summable_ofReal, PadicInt.mahlerSeries_apply_nat, Complex.differentiable_exp, MeasureTheory.convolution_def, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, Complex.UnitDisc.isEmbedding_coe, HurwitzZeta.hasSum_nat_completedCosZeta, HasDerivAt.hasFDerivAt, tendsto_sub_mul_tsum_nat_cpow, Polynomial.toAddCircle.integrable, fourier_zero, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MDifferentiableWithinAt.cle_arrowCongr, RCLike.imLm_coe, fourier_neg', HasFPowerSeriesWithinOnBall.prod, MDifferentiableWithinAt.clm_precomp, IsUltrametricDist.isUltrametricDist_of_forall_pow_norm_le_nsmul_pow_max_one_norm, NormedSpace.eq_iff_forall_dual_eq, Matrix.isBoundedSMul, Function.Periodic.boundedAtFilter_cuspFunction, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, hasStrictDerivAt_const_add_iff, Summable_cotTerm, isBoundedBilinearMap_compMultilinear, norm_cauchyPowerSeries_le, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_le_max_norm_one, Filter.tendsto_invβ_cobounded, hasFDerivAt_norm_rpow, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, tendsto_intCast_atBot_sup_atTop_cobounded, HasFPowerSeriesOnBall.uniform_geometric_approx, summable_jacobiThetaβ_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, MeromorphicOn.divisor_sub_const_self, Unitization.cobounded_eq_aux, sum_inner, Polynomial.div_tendsto_atBot_zero_of_degree_lt, HurwitzZeta.hasSum_nat_hurwitzZetaEven, HasFPowerSeriesWithinAt.fderivWithin_eq, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, continuousWithinAt_dslope_of_ne, HurwitzZeta.hasSum_int_cosKernel, ZMod.completedLFunction_def_odd, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, FormalMultilinearSeries.id_comp', OnePoint.isZeroAt_infty_iff, NormedSpace.expSeries_hasSum_exp, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, PeriodPair.isClosed_lattice, BoundedContinuousFunction.innerProbChar_zero, FormalMultilinearSeries.coeff_eq_zero, Complex.tendsto_normSq_cocompact_atTop, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, RCLike.conjCLE_coe, HasFPowerSeriesOnBall.sum, contDiffOn_stereoToFun, absorbs_iff_eventually_nhdsNE_zero, Units.instIsManifoldModelWithCornersSelf, LeftInvariantDerivation.evalAt_coe, Matrix.IsHermitian.trace_eq_sum_eigenvalues, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, convex_halfSpace_im_gt, ContMDiffOn.clm_precomp, BoundedContinuousFunction.toLp_inj, contDiffOn_nat_iff_continuousOn_differentiableOn, Matrix.PosSemidef.sqrt_eq_one_iff, BoundedContinuousFunction.coe_natCast, EisensteinSeries.tendsto_zero_inv_linear_sub, GaussianFourier.integrable_cexp_neg_mul_sum_add, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Complex.continuousOn_sin, Complex.hasStrictFDerivAt_cpow, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, tendsto_riemannZeta_sub_one_div, ZetaAsymptotics.tendsto_Gamma_term_aux, NumberField.InfinitePlace.Completion.locallyCompactSpace, InnerProductSpace.rankOne_eq_zero, Polynomial.differentiable_aeval, Complex.polarCoord_apply, BoundedContinuousFunction.toLp_injective, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Convex.toWeakSpace_closure, Unitary.instLocPathConnectedSpace, Complex.differentiable_iteratedDeriv_sin, AddChar.expect_apply_eq_zero_iff_ne_zero, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, ContinuousMap.isUnit_iff_forall_isUnit, Complex.hasStrictDerivAt_sinh, tsum_pow_div_one_sub_eq_tsum_sigma, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, EisensteinSeries.linear_right_summable, InnerProductSpace.inner_right_rankOne_apply, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, spectrum.eventually_isUnit_resolvent, UnitAddTorus.mFourier_add, Real.hasDerivAt_qaryEntropy, innerSL_inj, continuousAt_dslope_same, PositiveLinearMap.preGNS_inner_def, hasDerivAt_add_const_iff, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, UpperHalfPlane.cosh_dist, Asymptotics.isLittleO_pow_id, LSeries_eq_mul_integral_of_nonneg, Ideal.IsMaximal.isClosed, UpperHalfPlane.image_coe_closedBall, PeriodPair.periodic_derivWeierstrassP, EisensteinSeries.summable_linear_left_mul_linear_left, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, HasFPowerSeriesOnBall.compContinuousLinearMap, Quaternion.expSeries_odd_of_imaginary, differentiableWithinAt_of_derivWithin_ne_zero, MeromorphicOn.divisor_intCast, unitSphereToUnits_injective, Complex.tendsto_one_add_div_pow_exp, quasispectrum.isCompact, TensorProduct.inner_lid_lid, ContDiffMapSupportedIn.uniformSpace_eq_iInf, derivWithin_div_const, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, iteratedFDerivWithin_smul_const_apply, tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, cfcβAux_id, riemannZeta_eulerProduct_exp_log, PiTensorProduct.liftIsometry_tprodL, NormedSpace.inclusionInDoubleDual_norm_le, AnalyticOnNhd.eval_linearMap, UniformConvergenceCLM.continuousSMul, RCLike.rank_le_two, hasDerivWithinAt_one, IsSelfAdjoint.isConnected_spectrum_compl, WeakDual.isCompact_closedBall, Quaternion.continuous_imJ, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, ConvexOn.sSup_of_countable_affine_eq, TestFunction.coe_ofSupportedInCLM, RCLike.reCLM_coe, isClosedMap_pow, continuousSMul_closedBall_ball, UpperHalfPlane.dist_coe_center, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, HasDerivWithinAt.inner, Bornology.isVonNBounded_iff, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, DifferentiableAt.inner, MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, tendsto_logDeriv_euler_sin_div, NormedSpace.exp_continuousMap_eq, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, EisensteinSeries.div_linear_zpow_differentiableOn, UnitAddTorus.mFourier_zero, absorbent_nhds_zero, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, isScalarTower_sphere_sphere_sphere, MeromorphicOn.analyticAt_mem_codiscreteWithin, MeasureTheory.hasFDerivAt_convolution_right_with_param, smoothSheafCommRing.isUnit_stalk_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, FormalMultilinearSeries.coeff_ofScalars, UpperHalfPlane.ofComplex_apply_of_im_pos, hasDerivAt_ofNat, iteratedFDerivWithin_eq_equiv_comp, RCLike.isUniformEmbedding_ofReal, summable_norm_sum_mul_range_of_summable_norm, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, Orthonormal.inner_left_right_finset, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, ContDiffMapSupportedIn.structureMapCLM_zero_apply, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, differentiableAt_inv_iff, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, Finsupp.inner_sum, LinearMap.deriv, contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, zeta_eq_tsum_one_div_nat_cpow, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, continuousAt_cpow, InnerProductSpace.toDualMap_apply, gelfandTransform_map_star, Quaternion.instCompleteSpaceReal, Complex.interior_preimage_im, continuousOn_cfc_nnreal, selfAdjoint.continuous_expUnitary, ContinuousLinearMap.adjoint_inner_left, Complex.isBigO_re_sub_re, AddChar.sum_apply_eq_zero_iff_ne_zero, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, isQuotientCoveringMap_npow, EulerProduct.eulerProduct_tprod, Complex.comap_exp_nhdsNE, ContinuousLinearMap.isBoundedBilinearMap, fdifferential_apply, HasFPowerSeriesWithinOnBall.sum, Real.hasStrictDerivAt_arcosh, UnitAddTorus.coeFn_mFourierLp, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, MeromorphicOn.divisor_sub_const_of_ne, ContinuousMultilinearMap.ofSubsingletonβα΅’_symm_apply, nonunits.isClosed, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, ProperSpace.of_nontriviallyNormedField_of_weaklyLocallyCompactSpace, NumberField.mixedEmbedding.polarCoord_symm_apply, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, Complex.deriv_Gamma_nat, hasDerivAt_update, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, fderiv_pow_ring, Complex.continuous_sinh, constFormalMultilinearSeries_apply_zero, Padic.instCompleteSpace, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, Complex.UnitDisc.coe_closedBall_smul, FormalMultilinearSeries.radius_smul_eq, selfAdjoint.unitarySelfAddISMul_coe, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, ContinuousLinearMap.bilinearComp_zero_right, IsContMDiffRiemannianBundle.exists_contMDiff, ContinuousMap.ideal_isMaximal_iff, Complex.isOpen_compl_range_intCast, deriv_const_mul_field, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, Complex.hasSum_ofReal, CuspFormClass.zero_at_infty, hasDerivAtFilter_add_const_iff, HurwitzZeta.completedHurwitzZetaEven_residue_one, Matrix.exp_nsmul, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, hasDerivAt_jacobiThetaβ_fst, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, UnitAddTorus.mFourier_neg, InnerProductSpace.toDual_apply_apply, Complex.continuousOn_norm_circleTransformBoundingFunction, Complex.continuousAt_Gamma_one, intervalIntegral.intervalIntegrable_cpow, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, Real.hasDerivAt_arcsin, coe_lpBCFβα΅’, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, PeriodPair.differentiableOn_derivWeierstrassP, ProperCone.innerDual_singleton, Complex.hasDerivAt_sinh, PeriodPair.weierstrassPExcept_def, algebraMap_isometry, differentiable_inner, LeftInvariantDerivation.coe_sub, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, HasLineDerivAt.tendsto_slope_zero_left, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, tendsto_nhds_iff_meromorphicOrderAt_nonneg, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, LDL.lower_conj_diag, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionβ_apply_apply, hasFDerivAt_list_prod', HurwitzZeta.hasSum_int_cosZeta, hasFDerivAt_integral_of_dominated_loc_of_lip', ArithmeticFunction.IsMultiplicative.eulerProduct_tprod, InnerProductSpace.rankOne_def, ContinuousLinearMap.coe_flipβα΅’', stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, deriv_inv, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, PointwiseConvergenceCLM.equivWeakDual_apply, hasSum_jacobiThetaβ_term_fderiv, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, Real.hasStrictDerivAt_cosh, contDiff_iff_continuous_differentiable, NumberField.mixedEmbedding.mem_span_latticeBasis, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaβ, hasDerivAt_const, Complex.tendsto_norm_tan_atTop, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, BoundedContinuousFunction.innerProbChar_apply, IsUltrametricDist.of_normedAlgebra, UniformSpace.Completion.norm_toComplL, Bornology.IsVonNBounded.tendsto_smallSets_nhds, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, instSMulCommClass_sphere_closedBall_closedBall, ContinuousMap.toLp_def, Units.instLieGroupModelWithCornersSelf, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, Complex.hasDerivAt_Gammaβ_one, AnalyticAt.eventually_constant_or_nhds_le_map_nhds, Complex.hasSum_sin, Complex.tendsto_self_mul_Gamma_nhds_zero, SchwartzMap.integral_bilin_fourier_eq, Complex.hasStrictDerivAt_const_cpow, ClosedSubmodule.orthogonal_eq_inter, ContinuousMultilinearMap.prodL_apply, Orientation.kahler_neg_orientation, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, IsSelfAdjoint.cfc_arg, hasFTaylorSeriesUpToOn_succ_iff_right, EisensteinSeries.hasSum_e2Summand_symmetricIco, RingHom.isometry, ContinuousLinearMap.coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', intervalIntegral.integrableOn_Ioo_cpow_iff, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', LinearIsometryEquiv.conjStarAlgEquiv_refl, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, hasStrictFDerivAt_iff_hasStrictDerivAt, contDiff_nat_iff_iteratedDeriv, eventually_singleton_add_smul_subset, hasSum_jacobiThetaβ'_term, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, circleMap_notMem_ball, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, ContinuousLinearMapWOT.isInducing_inducingFn, SlashInvariantFormClass.periodic_comp_ofComplex, fderivWithin_fderivWithin_eq_of_eventuallyEq, integrableOn_Ioi_deriv_ofReal_cpow, NormedField.nhdsNE_neBot, EulerProduct.eulerProduct_completely_multiplicative_tprod, Complex.map_exp_comap_re_atBot, StrongDual.polarSubmodule_eq_polar, fourier_coe_apply, summable_prod_mul_pow, PiTensorProduct.liftEquiv_symm_apply, Complex.interior_setOf_le_im, RCLike.summable_conj, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, RCLike.geometric_hahn_banach_point_point, iteratedDeriv_mul, TestFunction.coe_ofSupportedInLM, extDerivWithin_fun_smul, fourierSubalgebra_separatesPoints, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Complex.isEquivalent_sinh, AnalyticOnNhd.is_constant_or_isOpenMap, hasFDerivAt_exp_smul_const', Quaternion.exp_of_re_eq_zero, MeasureTheory.SignedMeasure.re_toComplexMeasure, TemperedDistribution.smulLeftCLM_sub, Complex.one_add_cpow_hasFPowerSeriesAt_zero, FormalMultilinearSeries.ofScalars_norm_le, Matrix.exp_zsmul, HurwitzZeta.hasSum_nat_cosZeta, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, ContinuousLinearMapWOT.hasBasis_seminorms, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, OnePoint.isZeroAt_iff_forall_SL2Z, ContDiff.continuous_iteratedDeriv, LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, WithSeminorms.topology_eq_withSeminorms, hasSum_cauchyPowerSeries_integral, ContinuousLinearMap.aestronglyMeasurable_compβ, continuousSMul_sphere_closedBall, SchwartzMap.smulLeftCLM_const, UpperHalfPlane.contMDiff_num, UpperHalfPlane.mdifferentiable_denom, LinearMap.toMatrix_innerββ_apply, UpperHalfPlane.dist_self_center, Matrix.exp_sum_of_commute, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Complex.continuous_conj, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Function.locallyFinsuppWithin.toClosedBall_divisor, LSeries.term_convolution, PointwiseConvergenceCLM.equivWeakDual_symm_apply, MeasureTheory.ComplexMeasure.integrable_rnDeriv, Polynomial.isProperMap_eval, NumberField.mixedEmbedding.negAt_apply_isComplex, isBigO_riemannZeta_sub_one_div, AffineMap.hasDerivAt, Complex.hasFDerivAt_cpow, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, Complex.differentiableAt_exp, LinearMap.range_toContinuousLinearMap, Complex.not_continuousAt_Gamma_zero, Complex.differentiable_Gammaβ_inv, Quaternion.re_exp, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, hasFDerivWithinAt_pow', ContDiffMapSupportedIn.structureMapLM_apply_withOrder, continuous_circleMap, differentiableAt_jacobiThetaβ_fst, AffineMap.differentiableAt, hasStrictDerivAt_finCons', isScalarTower_closedBall_ball_ball, Complex.iter_deriv_exp, MeromorphicOn.meromorphicNFAt_mem_codiscreteWithin, HasProdLocallyUniformlyOn_euler_sin_prod, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, NormedSpace.ofReal_exp_β_β, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMapβ'_zero_iff, convex_halfSpace_im_lt, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, Polynomial.rootSet_derivative_subset_convexHull_rootSet, VonNeumannAlgebra.mem_carrier, WeakDual.isSeqCompact_closedBall, hasStrictDerivAt_finCons, Complex.differentiableAt_tan, PiTensorProduct.liftEquiv_apply, ModularForm.differentiableAt_eta_tprod, has_antideriv_at_fourier_neg, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, fderivWithin_iteratedFDerivWithin, PadicInt.denseRange_natCast, UnitAddTorus.mFourier_norm, toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhds, MultilinearMap.mkContinuousLinear_norm_le, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, LSeriesSummable.sum, Function.Periodic.continuous_qParam, Orientation.areaForm'_apply, hasFDerivAtFilter_iff_hasDerivAtFilter, HurwitzZeta.hasSum_expZeta_of_one_lt_re, innerSLFlip_apply_apply, UniformContinuousOn.cexp, ContinuousLinearMap.nnnorm_holder_apply_apply_le, Polynomial.hasFDerivAt, RCLike.ofReal_finsupp_sum, tendsto_zero_of_meromorphicOrderAt_pos, finrank_euclideanSpace, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Complex.continuous_exp, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, ConvexOn.sSup_of_nat_affine_eq, dist_eq, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, Complex.frontier_preimage_im, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, Submodule.orthogonal_orthogonal_eq_closure, continuousAt_clog, EisensteinSeries.linear_left_summable, AnalyticOnNhd.preimage_zero_mem_codiscrete, PeriodPair.hasSumLocallyUniformly_weierstrassPExcept, contMDiff_smul, MeromorphicOn.divisor_ofNat, UniformFun.continuousSMul_induced_of_range_bounded, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Complex.hasDerivAt_cos, Complex.ofRealCLM_apply, contMDiffOn_continuousLinearMapCoordChange, UpperHalfPlane.ofComplex_apply_eq_of_im_nonpos, Complex.log_sub_self_isBigO, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, aestronglyMeasurable_smul_const_iff, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, Module.Basis.equivFunL_apply, hasFDerivAt_list_prod_finRange', BoundedContinuousFunction.probCharDual_zero, ContinuousMultilinearMap.flipLinear_apply_apply, Asymptotics.isLittleO_iff_tendsto', HasGradientAt.hasFDerivAt, Complex.arg_eq_nhds_of_im_neg, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, LinearMap.hasDerivWithinAt, summable_choose_mul_geometric_of_norm_lt_one, CStarMatrix.toCLM_apply_single, Real.fourier_fderiv, MeasureTheory.AEStronglyMeasurable.inner, FormalMultilinearSeries.comp_id, ContinuousMap.nnnorm_smul_const, Complex.tendsto_exp_comap_re_atBot, ContinuousMap.adjoin_id_eq_span_one_union, IsSelfAdjoint.spectrumRestricts, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, hasFTaylorSeriesUpTo_succ_nat_iff_right, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, HasFDerivWithinAt.norm_sq, tsum_riemannZetaSummand, ordinaryHypergeometric_radius_top_of_neg_natβ, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, ClosedSubmodule.iInf_orthogonal, Complex.summable_ofReal, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, StrongDual.dualPairing_separatingLeft, HasFPowerSeriesOnBall.neg, ContinuousLinearMap.uncurryBilinear_apply, Asymptotics.continuousAt_iff_isLittleO, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, hasStrictDerivAt_abs, fourier_eval_zero, Matrix.PosDef.commute_iff, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, RCLike.finrank_le_two, Complex.tendsto_euler_sin_prod, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, ZMod.completedLFunction_eq, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, iteratedFDeriv_eq_equiv_comp, Complex.hasStrictDerivAt_log, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, CFC.log_monotoneOn, Unitization.norm_eq_sup, Real.hasDerivAt_cos, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, NumberField.mixedEmbedding.convexBodySumFun_continuous, hasFTaylorSeriesUpToOn_succ_nat_iff_right, hasDerivAtFilter_iff_isLittleO, NormedSpace.expSeries_div_summable, CStarMatrix.toCLM_apply_eq_sum, mahler_natCast_eq, PadicInt.coe_adicCompletionIntegersEquiv_apply, MeromorphicAt.eventually_continuousAt, summable_descFactorial_mul_geometric_of_norm_lt_one, UpperHalfPlane.dist_eq, differentiableOn_pow, HurwitzZeta.hurwitzZeta_residue_one, tsum_choose_mul_geometric_of_norm_lt_one, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, hasDerivAt_exp_smul_const, RCLike.continuous_re, NormedSpace.algebraMap_exp_comm, exists_dual_vector, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, hasFDerivWithinAt_comp_smul_smul_iff, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, RCLike.instContinuousStar, ProbabilityTheory.hasDerivAt_complexMGF, MeromorphicOn.divisor_fun_zpow, LinearMap.isPositive_toContinuousLinearMap_iff, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, Complex.tsum_exp_neg_quadratic, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', CFC.monotone_rpow, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', derivWithin_mul_const_field, logDeriv_apply, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, FormalMultilinearSeries.changeOrigin_eval_of_finite, RCLike.sqrt_map, iteratedFDerivWithin_two_apply', Real.hasDerivWithinAt_arcsin_Ici, HasStrictDerivAt.hasStrictFDerivAt, PeriodPair.derivWeierstrassP_sub_coe, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, AnalyticAt.analyticOrderAt_eq_natCast, CFC.rpow_neg_one_eq_cfc_inv, SpectrumRestricts.real_iff, Matrix.l2_opNNNorm_mul, HurwitzZeta.differentiableAt_completedHurwitzZetaEven, Complex.cosh_eq_tsum, IsLocalFrameOn.eventually_eq_sum_coeff_smul, NormedSpace.expSeries_radius_eq_top, RCLike.tendsto_ofReal_cobounded_cobounded, differentiableWithinAt_euclidean, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, unitary.spectrum_subset_circle, Complex.frontier_setOf_lt_im, HasFPowerSeriesAt.fderiv_eq, LinearPMap.adjointDomainMkCLM_apply, MeasureTheory.integrable_mul_const_iff, MeromorphicOn.divisor_apply, Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, NormedRing.inverse_add, continuousMultilinearCurryFin0_apply, Complex.interior_reProdIm, HurwitzZeta.differentiableAt_one_completedHurwitzZetaEven_sub_completedHurwitzZetaEven, HasGradientAt.differentiableAt, PiTensorProduct.dualSeminorms_bounded, LinearMap.hasBasis_weakBilin, NormedSpace.exp_sum, FormalMultilinearSeries.radius_neg, extDeriv_smul, spectrum.isClosed, HasDerivAt.norm_sq, WeakBilin.locallyConvexSpace, GromovHausdorff.ghDist_eq_hausdorffDist, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, nonunits.subset_compl_ball, Complex.closure_preimage_re, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, tendsto_ne_zero_of_meromorphicOrderAt_eq_zero, DoubleCentralizer.algebraMap_snd, WeakDual.polar_def, RCLike.wInner_const_left, AnalyticAt.analyticOrderNatAt_eq_iff, Complex.isOpenQuotientMap_pow, RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, HurwitzZeta.hasSum_int_sinKernel, MeasureTheory.integrable_smul_const, NormedSpace.invOf_exp, hasFiniteFPowerSeriesOnBall_const, iteratedFDerivWithin_succ_apply_left, hasStrictFDerivAt_norm_sq, support_deriv_subset, LinearMap.adjoint_toSpanSingleton, ContDiff.differentiable_iteratedDeriv, Complex.interior_setOf_im_le, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, ContinuousMultilinearMap.norm_mkPiAlgebra, NontriviallyNormedField.cobounded_neBot, hasDerivWithinAt_natCast, MeromorphicOn.divisor_fun_mul, Asymptotics.superpolynomialDecay_iff_isLittleO, MeromorphicOn.divisor_zpow, EulerProduct.eulerProduct_completely_multiplicative_hasProd, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, fderiv_pow_ring', QuasispectrumRestricts.real_iff, ContinuousLinearMap.bilinearComp_apply, NormedSpace.exp_conj', cot_series_rep, upperHemicontinuous_quasispectrum, spectrum.isBounded, NormedRing.inverse_add_norm, UpperHalfPlane.ofComplex_apply_eq_ite, Matrix.posDef_iff_eq_conjTranspose_mul_self, Polynomial.differentiableAt_aeval, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, HurwitzZeta.completedCosZeta_residue_zero, hasDerivAt_id, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, CStarMatrix.toCLM_apply, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, MeasureTheory.Integrable.re_im_iff, RCLike.hasSum_conj, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, FormalMultilinearSeries.id_comp, ContinuousLinearMap.norm_map_tail_le, deriv_update, UpperHalfPlane.qParam_tendsto_atImInfty, HasFPowerSeriesAt.restrictScalars, ContinuousLinearMap.instStarModuleId, Polynomial.hasFDerivAt_aeval, NormedField.continuousAt_inv, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, LeftInvariantDerivation.map_add, Complex.isConnected_of_upperHalfPlane, AnalyticOnNhd.codiscreteWithin_setOf_analyticOrderAt_eq_zero_or_top, NormedSpace.exp_units_conj', norm_fderiv_iteratedFDeriv, Complex.differentiable_sin, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, Complex.continuous_normSq, binomialSeries_radius_eq_top_of_nat, PeriodPair.weierstrassP_add_coe, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, TemperedDistribution.fourier_lineDerivOp_eq, Matrix.l2_opNNNorm_def, ContinuousMultilinearMap.instIsBoundedSMul, hasDerivAtFilter_sub_const_iff, Filter.tendsto_invβ_nhdsWithin_ne_zero, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.adjointAux_adjointAux, PeriodPair.instProperSpaceSubtypeComplexMemSubmoduleIntLattice, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, LinearMap.polar_gc, hasDerivAt_exp, circleMap_mem_sphere, UniformSpace.Completion.Continuous.inner, LeftInvariantDerivation.coe_add, ContMDiffAt.clm_precomp, Complex.hasDerivAt_logTaylor, DirichletCharacter.differentiable_LFunction, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow, Real.hasStrictDerivAt_arsinh, circleMap_preimage_codiscrete, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', MeasureTheory.AEStronglyMeasurable.const_inner, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, Complex.lintegral_comp_polarCoord_symm, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, zero_cpow_eq_nhds, HasFTaylorSeriesUpToOn.hasFDerivAt, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, BoundedContinuousFunction.coeFn_toLp, ContinuousLinearMap.flip_add, hasFiniteFPowerSeriesAt_const, Complex.continuousAt_ofReal_cpow, Subalgebra.spectrum_isBounded_connectedComponentIn, MeromorphicOn.eventually_codiscreteWithin_analyticAt, ArithmeticFunction.IsMultiplicative.eulerProduct, AnalyticAt.eventually_constant_or_nhds_le_map_nhds_aux, circleMap_mem_closedBall, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, RCLike.continuous_ofReal, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, NormedRing.inverse_add_norm_diff_second_order, IsLocalFrameOn.coeff_apply_of_notMem, GromovHausdorff.eq_toGHSpace, ContinuousMultilinearMap.uncurryRight_apply, NumberField.mixedEmbedding.polarCoord_source, nnnorm_cfc_nnreal_lt, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, fderiv_inv, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, ContinuousLinearMap.bilinearComp_zero, isScalarTower_sphere_sphere_closedBall, Complex.UnitDisc.instSMulCommClass_closedBall_right, Unitary.openPartialHomeomorph_target, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, CFC.rpow_le_rpow, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NumberField.mixedEmbedding.continuous_norm, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, Complex.continuousOn_tan, ContinuousLinearMap.norm_extendToπ'_bound, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, Quaternion.normSq_exp, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, unitary.joined, SeminormFamily.basisSets_smul, hasDerivAt_iff_hasFDerivAt, IsSelfAdjoint.exp_nonneg, HasFiniteFPowerSeriesOnBall.neg, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, LinearMap.weakBilin_withSeminorms, norm_derivWithin_eq_norm_fderivWithin, ModularForm.differentiableAt_eta_of_mem_upperHalfPlaneSet, differentiableWithinAt_dslope_of_ne, LinearMap.polar_weak_closed, Submonoid.coe_unitSphere, WeakDual.isClosed_closedBall, hasDerivAt_fourier, Filter.Tendsto.ofReal, Complex.continuousAt_cpow_zero_of_re_pos, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Complex.UnitDisc.instIsScalarTower_closedBall, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Complex.instCompleteSpace, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, Metric.sphere.instContinuousMul, nnnorm_cfc_nnreal_le, ZMod.LFunction_def_even, Real.fourier_bilin_convolution_eq, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, UpperHalfPlane.le_dist_coe, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, CStarMatrix.mul_entry_mul_eq_inner_toCLM, continuous_inner, ModularFormClass.differentiableAt_cuspFunction, fourier_apply, ContinuousLinearMap.le_opNormβ, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ContinuousLinearMap.norm_uncurryMid, QuadraticForm.equivalent_sum_squares, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, LeftInvariantDerivation.coe_injective, ContinuousLinearMap.uncurryLeft_norm, MeromorphicOn.divisor_restrict, hasStrictDerivAt_abs_neg, NormedSpace.exp_hasFPowerSeriesAt_zero, HasFPowerSeriesOnBall.tendstoUniformlyOn', Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, fderiv_apply_one_eq_deriv, HurwitzZeta.hasSum_nat_completedSinZeta, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, EulerProduct.eulerProduct_hasProd_mulIndicator, absorbs_iff_norm, isScalarTower_sphere_sphere_ball, nnnorm_cfc_nnreal_le_iff, integrableOn_exp_mul_complex_Iic, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, Complex.frontier_setOf_le_re, MeasureTheory.Integrable.convolution_integrand, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, Quaternion.im_exp, LinearMap.toMatrixOrthonormal_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, UpperHalfPlane.contMDiff_denom_zpow, contDiffOn_tsum_cexp, convex_halfSpace_re_ge, OrthogonalFamily.inner_sum, NormedDivisionRing.to_continuousInvβ, deriv_circleMap, NormedSpace.vonNBornology_eq, PeriodPair.latticeBasis_one, EuclideanSpace.inner_eq_star_dotProduct, CauSeq.tendsto_limit, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, isCoveringMapOn_npow, LeftInvariantDerivation.coe_neg, Complex.hasStrictDerivAt_cos, StrongDual.toLpβ_apply, Orientation.kahler_apply_self, Complex.frontier_setOf_re_lt, PeriodPair.weierstrassP_sub_coe, NormedSpace.exp_nsmul, formalMultilinearSeries_geometric_apply_norm, Complex.analyticOn_univ_iff_differentiable, Valued.integer.coe_span_singleton_eq_closedBall, Complex.conjCLE_nnorm, Polynomial.differentiableOn, hasSum_geom_series_inverse, IsLocalFrameOn.coeff_apply_zero_at, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', formalMultilinearSeries_geometric_eq_ofScalars, isQuotientCoveringMap_zpow, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, differentiableOn_neg, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, LinearMap.continuous_of_nonzero_on_open, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Complex.isBigO_im_sub_im, hasSum_coe_mul_geometric_of_norm_lt_one, Metric.unitSphere.coe_inv, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, ArithmeticFunction.LSeries_vonMangoldt_eq, MultilinearMap.mkContinuousMultilinear_norm_le', toWeakSpace_closedConvexHull_eq, Unitization.norm_def, BoundedContinuousFunction.coe_ofNat, EisensteinSeries.qExpansion_identity_pnat, Complex.isCoveringMapOn_exp, selfAdjoint.star_coe_unitarySelfAddISMul, deriv_neg', Orientation.kahler_rotation_left', zeta_eq_tsum_one_div_nat_add_one_cpow, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, Complex.continuous_cos, DirichletCharacter.differentiableAt_completedLFunction, ContinuousAlternatingMap.curryLeft_same, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ContinuousMultilinearMap.curryRight_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Units.isOpen, convex_halfSpace_im_ge, Balanced.absorbs_self, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, hasSum_choose_mul_geometric_of_norm_lt_one', ContinuousLinearMap.extendToπ_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, UpperHalfPlane.le_dist_iff_le_dist_coe_center, PadicInt.hasSum_mahlerSeries, NumberField.mixedEmbedding.polarCoord_target, hasStrictFDerivAt_pow', Complex.continuousAt_arg_coe_angle, isScalarTower_sphere_closedBall_ball, Polynomial.hasStrictDerivAt_aeval, IsBoundedSMul.of_enorm_smul_le, CauSeq.cauchySeq, Asymptotics.superpolynomialDecay_iff_isBigO, ContinuousLinearMap.norm_extendToπ', HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, StrongDual.polar_univ, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, PeriodPair.hasSum_weierstrassP, convex_halfSpace_re_lt, differentiableAt_iff_comp_const_sub, MDifferentiableAt.clm_precomp, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, UpperHalfPlane.ofComplex_apply, Quaternion.summable_coe, ContDiffMapSupportedIn.postcompCLM_apply, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, PeriodPair.coeff_weierstrassPSeries, Complex.ball_one_subset_slitPlane, dslope_eventuallyEq_slope_of_ne, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, PeriodPair.isOpen_compl_lattice_diff, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, Orientation.normSq_kahler, Complex.volume_closedBall, Complex.tendsto_one_add_div_cpow_exp, hasGradientAt_iff_hasFDerivAt, Complex.hasSum_cos', NormedDivisionRing.unitClosedBall_eq_univ_of_discrete, Complex.closure_setOf_re_lt, Complex.deriv_cosh, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, PeriodPair.derivWeierstrassP_coe, HasFPowerSeriesOnBall.tendsto_partialSum, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, HasFPowerSeriesWithinAt.prod, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, FormalMultilinearSeries.leftInv_coeff_one, Matrix.exp_conj, Polynomial.toAddCircle_monomial_eq_smul_fourier, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, Orthonormal.inner_finsupp_eq_sum_left, continuousAt_const_cpow', fderiv_deriv, Complex.hasStrictDerivAt_sin, Complex.polarCoord_source, hasFPowerSeriesAt_pi_iff, Module.Basis.continuous_toMatrix, NormedField.continuousAt_zpow, hasDerivWithinAt_univ, Seminorm.ball_zero_absorbs_ball_zero, RCLike.continuous_conj, NumberField.mixedEmbedding.polarCoord_symm_eq, upperHemicontinuous_spectrum_nnreal, Matrix.PosSemidef.sq_sqrt, continuous_barycentric_coord, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, Complex.exp_sub_sum_range_succ_isLittleO_pow, ContinuousLinearMapWOT.ext_dual_iff, Complex.continuousOn_prod_circle_transform_function, HasFPowerSeriesAt.hasFDerivAt, lp.summable_inner, WeakDual.isClosed_polar, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, spec_cfcβAux, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, hasSum_sum_range_mul_of_summable_norm, DifferentiableOn.inner, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, hasFDerivAt_exp_smul_const, Differentiable.inner, UpperHalfPlane.dist_center_dist, LinearMap.mkContinuousβ_norm_le, DifferentiableAt.ofReal_cpow_const, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, LeftInvariantDerivation.map_smul, hasFDerivAt_jacobiThetaβ, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, Complex.isHomeomorphicTrivialFiberBundle_re, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, NumberField.mixedEmbedding.polarSpaceCoord_target', hasStrictDerivAt_const, Metric.unitSphere.coe_zpow, hasStrictFDerivAt_list_prod_attach', NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, StrongDual.norm_toLpβ_le, hasFDerivWithinAt_euclidean, HasFPowerSeriesWithinAt.restrictScalars, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, Complex.deriv_tan, nnnorm_cfc_le, isCauSeq_iff_cauchySeq, MeromorphicAt.frequently_eq_iff_eventuallyEq, UpperHalfPlane.dist_le_dist_coe_div_sqrt, PiTensorProduct.mapLMultilinear_apply_apply, iteratedDeriv_comp_two, LinearMap.mem_polar_singleton, ContinuousMap.setOfIdeal_eq_compl_singleton, Complex.hasDerivAt_cosh, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, EisensteinSeries.tendsto_zero_inv_linear, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, RCLike.ofRealCLM_norm, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, Complex.UnitDisc.coe_smul_closedBall, ContinuousLinearMap.mul_apply', HurwitzZeta.differentiableAt_hurwitzZeta, MeromorphicNFOn.zero_set_eq_divisor_support, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_of_norm_le_one, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, Real.hasStrictDerivAt_arctan, Complex.interior_setOf_re_le, Quaternion.tsum_coe, DirichletCharacter.deriv_LFunctionTrivCharβ_apply_of_ne_one, AnalyticAt.hasFPowerSeriesAt, hasDerivAtFilter_finCons', Complex.isOpen_im_gt_EReal, Prod.fst_exp, MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero, ContinuousMap.toLp_injective, Matrix.toEuclideanLin_eq_toLin, tendsto_logDeriv_euler_cot_sub, SlashInvariantForm.coe_trace, StrongDual.toLpβ_of_not_memLp, isConformalMap_complex_linear_conj, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, TrivSqZeroExt.instL1IsBoundedSMul, Quaternion.continuous_im, BoundedContinuousFunction.instIsBoundedSMul_1, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, LSeries_differentiableOn, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, instContMDiffInvβModelWithCornersSelf, differentiableAt_riemannZeta, Complex.tendsto_partialGamma, Complex.exp_sub_sum_range_isBigO_pow, deriv_zpow, Complex.tendsto_norm_tan_of_cos_eq_zero, riemannZeta_eulerProduct, Complex.isOpenQuotientMap_zpow_compl_zero, UpperHalfPlane.eventuallyEq_coe_comp_ofComplex, InnerProductSpace.rankOne_comp, Unitary.joined, EisensteinSeries.summable_linear_sub_mul_linear_add, StrongDual.mem_polarSubmodule, exists_dual_vector', FormalMultilinearSeries.apply_eq_prod_smul_coeff, Orientation.kahler_rightAngleRotation_left, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, hasFPowerSeriesWithinAt_pi_iff, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, hasDerivAt_iff_isLittleO_nhds_zero, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, PadicInt.hasSum_mahler, Real.fourierIntegral_fderiv, Function.Periodic.invQParam_tendsto, InnerProductSpace.toMatrix_rankOne, cfcβHom_real_eq_restrict, PeriodPair.latticeEquiv_symm_apply, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, Complex.closure_setOf_lt_re, geom_series_mul_one_add, iteratedFDeriv_smul_const_apply, UnitAddTorus.mFourierSubalgebra_separatesPoints, Complex.betaIntegral_convergent, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, RCLike.geometric_hahn_banach_open, Asymptotics.isLittleO_iff_exists_eq_mul, MeasureTheory.Lp.instIsBoundedSMul, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, Seminorm.ball_smul_ball, ContinuousMap.coe_toLp, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Real.hasDerivAt_cosh, PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept, continuousMultilinearCurryLeftEquiv_apply, LeftInvariantDerivation.coe_smul, HasFPowerSeriesAt.deriv, ModularForm.summable_logDeriv_one_sub_eta_q, differentiable_pow, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, LSeries_sum, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, UpperHalfPlane.comp_ofComplex_of_im_le_zero, Complex.hasDerivAt_sin, fourierCoeff_eq_intervalIntegral, NumberField.mixedEmbedding.continuous_normAtPlace, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, hfdifferential_apply, MeasureTheory.Integrable.inner_const, Complex.closure_reProdIm, ContinuousMap.canLift, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Real.hasDerivAt_fourierChar, ContinuousLinearMap.intervalIntegral_apply, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, hasDerivAt_intCast, Orientation.kahler_rotation_left, multipliable_sineTerm, Seminorm.absorbent_ball_zero, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcβHom, ModularFormClass.hasSum_qExpansion_of_abs_lt, SchwartzMap.smulLeftCLM_neg, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, Complex.isUniformEmbedding_ofReal, differentiableOn_inverse, Complex.conjCLE_enorm, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, CFC.nnnorm_rpow, IsUltrametricDist.isUltrametricDist_of_forall_norm_natCast_le_one, DirichletCharacter.LSeries_eulerProduct_hasProd, spectrum.differentiableOn_inverse_one_sub_smul, Continuous.inner_, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, Complex.hasSum_conj, ContinuousMultilinearMap.changeOriginSeries_support, PeriodPair.deriv_derivWeierstrassPExcept_self, ContDiffMapSupportedIn.seminorm_apply, LinearMap.tripolar_eq_polar, RCLike.toIsOrderedAddMonoid, Complex.hasStrictDerivAt_exp, Matrix.exp_units_conj', ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Continuous.inner, MeasureTheory.Lp.simpleFunc.isBoundedSMul, Padic.denseRange_ratCast, DoubleCentralizer.algebraMap_fst, AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top, differentiableOn_euclidean, RCLike.reLm_coe, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, EisensteinSeries.q_expansion_bernoulli, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, IsStarNormal.instContinuousFunctionalCalculus, ContinuousLinearMap.toBilinForm_injective, Complex.hasStrictDerivAt_cosh, eigenvalue_mem_ball, tsum_prod_pow_eq_tsum_sigma, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, toSpanSingleton_derivWithin, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, HasFiniteFPowerSeriesOnBall.eq_partialSum', continuousAt_cpow_const, GaussianFourier.tendsto_verticalIntegral, apply_le_nnnorm_cfc_nnreal, coe_lpBCFβα΅’_symm, MeromorphicOn.AnalyticOnNhd.divisor_nonneg, MeromorphicOn.eventually_analyticAt_or_mem_compl, IsBoundedBilinearMap.toContinuousLinearMap_apply, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, HasFPowerSeriesOnBall.pi, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, HasFPowerSeriesWithinOnBall.fderivWithin_eq, Complex.UnitDisc.continuous_coe, ContinuousMultilinearMap.piβα΅’_symm_apply, RCLike.wInner_one_const_right, AlgHom.coe_toContinuousLinearMap, Matrix.posSemidef_iff_eq_sum_vecMulVec, AnalyticAt.analyticOrderAt_ne_top, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, differentiableAt_const_cpow_of_neZero, tsum_dirichletSummand, AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top, SchwartzMap.integralCLM_apply, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, hasDerivAt_one, Complex.dist_conj_conj, circleIntegrable_sub_zpow_iff, Polynomial.fourierCoeff_toAddCircle_natCast, IsBoundedSMul.of_nnnorm_smul_le, Complex.conjCLE_apply, ContinuousMap.spectrum_eq_range, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, innerSLFlip_apply, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, fderivWithin_derivWithin, hasDerivAt_const_mul, hasLineDerivAt_iff_tendsto_slope_zero, InnerProductSpace.toContinuousLinearMap_toDualMap, Complex.differentiable_one_div_Gamma, Valued.integer.properSpace_iff_compactSpace_integer, completeSpace_of_cauSeq_isComplete, contDiff_nat_iff_continuous_differentiable, hasFDerivAt_pow', absorbent_ball, UpperHalfPlane.cosh_half_dist, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, DirichletCharacter.LSeries_eulerProduct_exp_log, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, Polynomial.hasDerivAt, Complex.not_differentiableAt_Gamma_zero, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, MeasureTheory.Integrable.ofReal, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, ContinuousLinearMap.opNorm_lsmul_le, MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds, MultilinearMap.mkContinuousMultilinear_norm_le, WeakDual.CharacterSpace.norm_le_norm_one, Matrix.linfty_opNorm_toMatrix, hasDerivAt_natCast, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ContinuousMap.coeFn_toLp, ProbabilityTheory.differentiableOn_complexMGF, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, Real.hasStrictDerivAt_cos, PeriodPair.deriv_weierstrassPExcept_same, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_symm_apply, Function.Periodic.qParam_tendsto, Unitary.isPathConnected_ball, continuousAt_jacobiTheta, iter_deriv_inv, PeriodPair.analyticOnNhd_derivWeierstrassP, Matrix.frobenius_norm_mul, Complex.Gammaβ_residue_zero, Matrix.star_dotProduct_gram_mulVec, hasStrictFDerivAt_exp_zero, ContinuousLinearMap.norm_compL_le, integrableOn_Ioi_cpow_of_lt, RCLike.hasSum_iff, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, EulerSine.antideriv_cos_comp_const_mul, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Complex.instTietzeExtension, AccPt.uniqueDiffWithinAt, HasFPowerSeriesAt.sub, ProperSpace.of_locallyCompact_module, hasDerivWithinAt_zpow, OrthogonalFamily.range_linearIsometry, NumberField.mixedEmbedding.convexBodyLT_convex, Complex.instT2Space, Monotone.deriv_nonneg, UpperHalfPlane.exp_half_dist, Orientation.kahler_mul, GaussianFourier.integral_cexp_neg_mul_sum_add, Complex.continuous_ofReal_cpow_const, ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, TensorProduct.norm_lid, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, Matrix.instIsOrderedAddMonoid, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, egauge_eq_zero_iff, HurwitzZeta.differentiableAt_completedCosZeta, fourier_neg, LSeries.tendsto_cpow_mul_atTop, ContinuousMultilinearMap.curryMid_apply, norm_cfc_le, ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, EisensteinSeries.tendsto_double_sum_S_act, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, ContinuousMap.toLp_comp_toContinuousMap, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Matrix.PosSemidef.re_dotProduct_nonneg, ContMDiff.clm_postcomp, Complex.sinh_eq_tsum, BoundedContinuousFunction.toContinuousMapStarβ_apply_apply, continuousAt_jacobiThetaβ, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, instSMulCommClass_sphere_ball_ball, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, Metric.unitSphere.coe_pow, Polynomial.isOpenQuotientMap_eval, CStarAlgebra.rpow_neg_one_le_one, EulerSine.antideriv_sin_comp_const_mul, Complex.differentiableAt_cosh, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, MDifferentiableWithinAt.clm_postcomp, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NormedSpace.sInter_polar_eq_closedBall, Complex.differentiableAt_Gamma_nat_add_one, TemperedDistribution.instFourierInvSMul, MeasureTheory.AEEqFun.Integrable.smul, PadicInt.totallyBounded_univ, Complex.deriv_cos', Complex.imCLM_coe, lp.hasSum_inner, iteratedDeriv_comp_eq_sum_orderedFinpartition, Complex.isQuotientMap_im, ContinuousLinearMap.opNorm_mul_apply_le, HasFPowerSeriesAt.tendsto_partialSum, circleAverage_log_norm_factorizedRational, deriv_pow_field, ContinuousLinearMap.orthogonal_range, HasFiniteFPowerSeriesAt.add, HasFPowerSeriesAt.hasDerivAt, MeromorphicOn.min_divisor_le_divisor_add, AnalyticAt.eventually_eq_or_eventually_ne, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, MeasureTheory.stronglyMeasurable_charFun, PeriodPair.instDiscreteTopologySubtypeComplexMemSubmoduleIntLattice, HasFDerivAt.linear_multilinear_comp, Quaternion.norm_exp, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, Quaternion.continuous_coe, Complex.continuous_ofReal, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, MeasureTheory.convolutionExistsAt_iff_integrable_swap, Complex.not_continuousAt_Gamma_neg_nat, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, Polynomial.C_eq_or_isOpenQuotientMap_eval, hasDerivAt_ofReal_cpow_const, EisensteinSeries.summable_e2Summand_symmetricIcc, hasDerivAt_norm_rpow, UnitAddTorus.hasSum_prod_mFourierCoeff, Padic.withValUniformEquiv_cast_apply, NumberField.mixedEmbedding.latticeBasis_apply, LeftInvariantDerivation.map_sub, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, spectrum.exp_mem_exp, Unitization.isUniformEmbedding_addEquiv, differentiableWithinAt_inverse, ContinuousMultilinearMap.compContinuousLinearMapL_apply, NormedSpace.exp_neg, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, AnalyticAt.eventually_eq_zero_or_eventually_ne_zero, MeromorphicOn.extract_zeros_poles, cfcβAux_mem_range_inr, ContinuousLinearMap.norm_bilinearRestrictScalars, eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, Complex.sin_eq_tsum, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, differentiableAt_jacobiThetaβ_snd, Padic.coe_withValRingEquiv, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, HasFPowerSeriesWithinOnBall.neg, NumberField.mixedEmbedding.measurable_polarCoord_symm, norm_deriv_eq_norm_fderiv, IsUltrametricDist.normedAlgebra_iff, PadicInt.fwdDiff_mahlerSeries, LSeries.tendsto_atTop, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ContinuousLinearMap.bilinearComp_zero_left, one_add_cpow_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, Complex.hasSum_conj', MeasureTheory.L2.mem_L1_inner, Complex.isOpen_im_lt_EReal, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, RCLike.map_nonneg_iff, NormedSpace.exp_smul, MeromorphicOn.negPart_divisor_add_le_max, LinearMap.toContinuousLinearMapβ_apply, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, Complex.hasStrictDerivAt_cpow_const, MDifferentiableOn.clm_precomp, WithAbs.isUniformInducing_of_comp, mellin_differentiableAt_of_isBigO_rpow_exp, Real.hasDerivAt_arctan', ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, Asymptotics.isEquivalent_iff_tendsto_one, differentiable_neg, hasDerivAt_neg, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, hasFTaylorSeriesUpToOn_succ_iff_left, Padic.isUniformInducing_cast_withVal, PadicInt.continuous_multichoose, Complex.hasSum_taylorSeries_neg_log, Polynomial.hasStrictDerivAt, VectorFourier.integral_bilin_fourierIntegral_eq_flip, Real.hasStrictDerivAt_arcsin, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, Metric.unitClosedBall.coe_one, HasFPowerSeriesWithinOnBall.add, NumberField.mixedEmbedding.commMap_apply_of_isReal, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, NormedSpace.of_real_exp_β_β, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, NumberField.mixedEmbedding.polarCoord_apply, TemperedDistribution.instLineDerivSMulComplex, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, euler_sineTerm_tprod, NormedField.discreteTopology_of_bddAbove_range_norm, summable_geometric_iff_norm_lt_one, ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, continuousMultilinearCurryRightEquiv_symm_apply', ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, ContDiffMapSupportedIn.continuousSMul, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, summable_pow_mul_geometric_of_norm_lt_one, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapβ, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, Complex.equivRealProdCLM_symm_apply_re, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, LinearMap.isStarProjection_toContinuousLinearMap_iff, MeromorphicOn.divisor_smul, UpperHalfPlane.sinh_half_dist_add_dist, NumberField.mixedEmbedding.continuous_normAtAllPlaces, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, MeasureTheory.L2.integrable_inner, IsCompact.reProdIm, LinearPMap.adjointDomainMkCLMExtend_apply, WithAbs.pseudoMetricSpace_induced_of_comp, BoundedContinuousFunction.toLp_norm_le, iteratedFDerivWithin_two_apply, extDerivWithin_smul, NormedSpace.expSeries_div_hasSum_exp, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, DoubleCentralizer.coe_fst, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, HurwitzZeta.differentiable_cosZeta_of_ne_zero, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, Complex.deriv_cpow_const, ContinuousMapZero.instCStarRing, NormedField.instCompletableTopField, hasFDerivWithinAt_iff_hasGradientWithinAt, CurveIntegrable.smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, FormalMultilinearSeries.min_radius_le_radius_add, hasStrictDerivAt_one, Complex.summable_one_div_nat_cpow, tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm, Complex.nndist_conj_comm, Filter.tendsto_mul_left_cobounded, ContinuousLinearMap.closed_range_of_antilipschitz, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, logDeriv_prod_sineTerm_eq_sum_cotTerm, Complex.differentiableAt_Gamma_one, Real.differentiable_fourierChar, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, hasFDerivAt_integral_of_dominated_of_fderiv_le, HasFPowerSeriesAt.pi, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', Filter.HasBasis.isVonNBounded_iff, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, summable_prod_eisSummand, mdifferentiable_jacobiTheta, Matrix.linfty_opNorm_eq_opNorm, ContinuousAlternatingMap.prodLIE_apply, RCLike.ofReal_tsum, hasDerivAt_pow, contDiff_succ_iff_deriv, NormedRing.inverse_add_norm_diff_first_order, Complex.instProperSpace, EuclideanSpace.dist_eq, NumberField.mixedEmbedding.normAtPlace_negAt, PadicInt.mahlerEquiv_apply, Complex.nndist_conj_conj, Polynomial.div_tendsto_atTop_zero_of_degree_lt, SchwartzMap.convolution_flip, continuousSMul_closedBall_closedBall, ContinuousLinearMap.opNorm_flip, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, EisensteinSeries.G2_eq_tsum_cexp, IsConformalMap.smul, nndist_lineMap_lineMap, isCoveringMap_npow, Irreducible.maximalIdeal_eq_closedBall, Complex.frontier_setOf_le_re_and_le_im, Complex.sameRay_iff, Real.hasStrictDerivAt_sqrt, Complex.hasDerivAt_Gamma_one, PeriodPair.hasSum_weierstrassPExcept, Polynomial.deriv, FormalMultilinearSeries.derivSeries_eq_zero, HilbertBasis.summable_inner_mul_inner, Polynomial.div_tendsto_zero_of_degree_lt, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, Real.hasDerivAt_tan_of_mem_Ioo, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, AffineMap.differentiableOn, Complex.imCLM_nnnorm, ContinuousMultilinearMap.curryLeft_apply, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, EisensteinSeries.qExpansion_identity, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, UpperHalfPlane.contMDiffAt_ofComplex, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, GaussianFourier.integral_cexp_neg_sum_mul_add, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, hasStrictDerivAt_inv, RCLike.wInner_one_const_left, circleIntegrable_sub_inv_iff, AlternatingMap.mkContinuousLinear_norm_le, ModularFormClass.bounded_at_infty_comp_ofComplex, ProperCone.hyperplane_separation_of_notMem, NumberField.mixedEmbedding.convexBodySum_isBounded, LinearMap.continuous_of_isClosed_ker, Complex.sameRay_iff_arg_div_eq_zero, Complex.arg_eq_nhds_of_im_pos, ModularForm.holo', ContinuousAlternatingMap.curryLeftLI_apply, LDL.diag_eq_lowerInv_conj, eventuallyConst_iff_analyticOrderAt_sub_eq_top, NumberField.mixedEmbedding.polarSpaceCoord_apply, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, Padic.coe_withValRingEquiv_symm, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, differentiableAt_iff_comp_add_const, Complex.starConvex_slitPlane, ContinuousLinearMap.norm_compSL_le, BoundedContinuousFunction.toContinuousMapβ_apply, ContDiffMapSupportedIn.withSeminorms, MeasureTheory.withDensityα΅₯_smul, LinearMap.polar_isClosed, NumberField.mixedEmbedding.negAt_apply_norm_isReal, innerββ_apply, deriv_inner_apply, NormedSpace.continuousOn_exp, Complex.log_sub_logTaylor_isBigO, differentiable_completedZetaβ, innerSL_apply, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, Metric.unitSphere.coe_div, HurwitzZeta.hasSum_int_sinZeta, CFC.log_le_log, spectrum.resolvent_tendsto_cobounded, Complex.differentiable_sinh, Seminorm.absorbent_closedBall, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Matrix.isUnit_exp, fderivWithin_continuousLinearEquiv_comp, iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum, hasDerivAtFilter_pi, StrongDual.toLp_apply, StrongDual.polar_empty, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, ContinuousLinearMap.coe_flipβα΅’, HasGradientAtFilter.tendsto_nhds, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, ModularFormClass.hasSum_qExpansion_of_norm_lt, Complex.volume_ball, Real.deriv_fourierChar, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, cpow_eq_nhds', MeasureTheory.Lp.coe_LpSubmodule, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, StieltjesFunction.ae_hasDerivAt, NormedDivisionRing.to_isTopologicalDivisionRing, instSMulCommClass_closedBall_closedBall_ball, jacobiTheta_eq_tsum_nat, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, PositiveLinearMap.norm_apply_le_of_nonneg, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Complex.UnitDisc.instSMulCommClass_circle_closedBall, Complex.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.changeOrigin_eval, Unitization.nndist_inr, LSeries.term_sum_apply, NormedRing.inverse_continuousAt, LinearMap.toSeminorm_ball_zero, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, UpperHalfPlane.contMDiffAt_iff, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet, IsSelfAdjoint.adjoint_conj, Complex.differentiableAt_sinh, HasDerivAt.inner, HasFPowerSeriesAt.prod, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, Function.Periodic.differentiable_qParam, Complex.continuous_tan, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, LeftInvariantDerivation.toDerivation_injective, PeriodPair.differentiableOn_weierstrassPExcept, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, AlternatingMap.mkContinuousAlternating_norm_le_max, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, Complex.conjCLE_norm, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, hasDerivAt_finCons', MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Complex.differentiableAt_log, LeftInvariantDerivation.evalAt_mul, absorbs_iff_eventually_nhds_zero, differentiableAt_completedZeta, isScalarTower_sphere_ball_ball, Absorbs.of_norm, PeriodPair.derivWeierstrassPExcept_add_coe, HasFPowerSeriesWithinAt.add, MeasureTheory.BoundedContinuousFunction.inner_toLp, Complex.isQuotientMap_re, ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, Complex.dist_conj_comm, CuspFormClass.zero_at_infty_slash, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, NormedSpace.closedBall_inv_subset_polar_closedBall, ContDiffMapSupportedIn.postcompLM_apply, PeriodPair.differentiableOn_weierstrassP, UnitAddTorus.span_mFourier_closure_eq_top, ContinuousLinearMap.norm_smulRightL_le, MeasureTheory.withDensityα΅₯_smul', NormedSpace.expSeries_radius_pos, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, SchwartzMap.tsupport_derivCLM_subset, hasDerivAt_single, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, PadicInt.norm_mahler_eq, UpperHalfPlane.mdifferentiable_coe, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, nnnorm_cfc_nnreal_lt_iff, Complex.arg_eq_nhds_of_re_pos, FormalMultilinearSeries.radius_prod_eq_min, ContinuousOn.inner, summable_cotTerm, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, continuousAt_jacobiThetaβ', RCLike.wInner_one_eq_sum, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, Asymptotics.isLittleO_iff_tendsto, norm_cfcHom, KuratowskiEmbedding.embeddingOfSubset_dist_le, EisensteinSeries.eisSummand_extension_differentiableOn, EuclideanSpace.dist_sq_eq, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Complex.isOpenQuotientMap_pow_compl_zero, ContinuousMultilinearMap.currySum_apply, isOpenMap_barycentric_coord, NormSMulClass.toIsBoundedSMul, Complex.deriv_sinh, MeasureTheory.ComplexMeasure.re_apply, Polynomial.differentiableWithinAt_aeval, intervalIntegral.intervalIntegrable_cpow', Complex.deriv_sin, signedDist_apply, UniformSpace.Completion.inner_coe, Unitization.norm_splitMul_snd_sq, geom_series_mul_neg, WeakDual.CharacterSpace.equivAlgHom_coe, Valued.toNormedField.setOf_mem_integer_eq_closedBall, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipβα΅’'_symm, EuclideanSpace.inner_toLp_toLp, NumberField.mixedEmbedding.polarSpaceCoord_source, TemperedDistribution.lineDerivOp_fourierInv_eq, CFC.norm_rpow, Complex.hasSum_taylorSeries_log, fourierCoeffOn_eq_integral, MeromorphicOn.negPart_divisor_add_le_add, UpperHalfPlane.dist_coe_le, CompactConvergenceCLM.continuousSMul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, ordinaryHypergeometric_radius_top_of_neg_natβ, hasStrictDerivAt_zero, PeriodPair.hasSum_sumInvPow, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, Units.contMDiff_val, DirichletCharacter.LFunctionTrivChar_residue_one, Complex.hasDerivAt_tan, Complex.lintegral_comp_pi_polarCoord_symm, IsBoundedSMul.of_norm_smul_le, RCLike.instOrderClosedTopology, FormalMultilinearSeries.coeff_iterate_fslope, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, Filter.Tendsto.inner, MeasureTheory.Integrable.const_inner, LSeriesHasSum.sum, ContinuousLinearMap.extendToπ'_apply, continuous_descPochhammer_eval, IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, Complex.equivRealProdCLM_symm_apply_im, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, Complex.polarCoord_symm_apply, AnalyticOnNhd.is_constant_or_isOpen, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, summable_bernoulli_fourier, ModularFormClass.differentiableOn_cuspFunction_ball, Unitization.splitMul_injective, Antitone.deriv_nonpos, ZMod.differentiable_completedLFunctionβ, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, ContDiffMapSupportedIn.continuous_iff_comp, PeriodPair.periodic_weierstrassP, MonotoneOn.nnnorm_cfc, ModularFormClass.holo, Metric.unitClosedBall.coe_pow, Polynomial.differentiable, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, PadicInt.isOpenEmbedding_coe, ContinuousLinearEquiv.coord_norm', completedRiemannZeta_residue_one, EisensteinSeries.summable_e2Summand_symmetricIco, GaussianFourier.integrable_cexp_neg_sum_mul_add, ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, Metric.unitClosedBall.instIsCancelMulZero, Complex.hasSum_sinh, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, hasStrictFDerivAt_inv', LinearMap.mem_span_iff_bound, hasDerivAt_mul_const, SchwartzMap.smulLeftCLM_sub, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, hasStrictFDerivAt_exp_smul_const, dist_algebraMap, SchwartzMap.fourier_convolution_apply, UpperHalfPlane.sinh_half_dist, Complex.hasStrictFDerivAt_log_real, Complex.differentiableAt_Gamma, iteratedFDeriv_two_apply, Real.hasStrictDerivAt_tan, UpperHalfPlane.dist_le_iff_le_sinh, RCLike.wInner_cWeight_const_right, TemperedDistribution.smulLeftCLM_sum, mahler_apply, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, iter_deriv_inv_linear, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, HurwitzZeta.differentiableAt_cosZeta, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, Complex.hasSum_sin', jacobiThetaβ_fderiv_undef, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, instPerfectSpace, MDifferentiable.clm_precomp, Complex.arg_eq_nhds_of_re_neg_of_im_pos, Metric.unitClosedBall.coe_eq_one, Real.differentiable_fourierChar_neg_bilinear_left, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, EisensteinSeries.summable_linear_right_add_one_mul_linear_right, PadicAlgCl.instIsUltrametricDist, gelfandTransform_isometry, FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, continuousMultilinearCurryLeftEquiv_symm_apply, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, Complex.betaIntegral_convergent_left, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, Complex.continuousAt_cpow_of_re_pos, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, innerββ_apply_coe, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, Complex.sin_eq_tsum', PiLp.inner_apply, mellin_differentiableAt_of_isBigO_rpow, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Complex.reCLM_norm, ContinuousMap.norm_smul_const, iteratedFDeriv_succ_eq_comp_left, UpperHalfPlane.dist_coe_center_sq, ContinuousLinearMap.smul_compLpL, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, summable_geometric_of_norm_lt_one, unitary.isPathConnected_ball, continuousOn_cfc_nnreal_setProd, differentiableAt_of_deriv_ne_zero, ZMod.LFunction_residue_one, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NumberField.mixedEmbedding.convexBodySum_convex, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, PeriodPair.mul_Οβ_add_mul_Οβ_mem_lattice, ContinuousLinearMap.opNorm_mulLeftRight_le, convex_halfSpace_im_le, ClosedSubmodule.orthogonal_closure, riemannZeta_eulerProduct_tprod, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, cpow_eq_nhds, ContDiffMapSupportedIn.structureMapCLM_zero_injective, RCLike.iInter_halfSpaces_eq, StrongDual.polar_zero, ContinuousMultilinearMap.piβα΅’_apply, nnnorm_cfcHom, Module.Basis.opNNNorm_le, Matrix.PosSemidef.sqrt_mul_self, ContMDiffWithinAt.clm_precomp, NormedRing.inverse_one_sub_nth_order', NormedSpace.exp_add_of_commute, Real.deriv_arcsin_aux, Complex.differentiable_cosh, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonβα΅’_apply, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, fourier_add', RCLike.continuous_im, MeasureTheory.Integrable.fourier_smul, LinearMap.coe_toContinuousLinearMap_symm, hasStrictFDerivAt_list_prod', Complex.frontier_setOf_le_re_and_im_le, continuousMultilinearCurryFin1_symm_apply, Quaternion.hasSum_expSeries_of_imaginary, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, Complex.continuousAt_Gamma, StrongDual.mem_polar_iff, FormalMultilinearSeries.radius_pi_le, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, Prod.snd_exp, Submodule.orthogonal_eq_inter, BoundedContinuousFunction.charMonoidHom_apply, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, Complex.differentiable_iteratedDeriv_cos, ContinuousLinearEquiv.coord_self, UniformOnFun.continuousSMul_submodule_of_image_bounded, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, riemannZeta_residue_one, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, Complex.ofReal_tsum, MeasureTheory.ComplexMeasure.equivSignedMeasureβ_apply, ContDiffAt.differentiableAt_iteratedFDeriv, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, tendsto_intCast_atTop_cobounded, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, AddChar.coe_complexBasis, NormedSpace.isUnit_exp, Polynomial.toAddCircle_X_eq_fourier_one, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, Complex.differentiable_cos, ContinuousLinearMap.norm_adjoint_comp_self, summable_norm_sum_mul_antidiagonal_of_summable_norm, LinearPMap.mem_adjoint_domain_iff, RCLike.geometric_hahn_banach_point_closed, hasDerivWithinAt_intCast, differentiableWithinAt_zpow, CircleIntegrable.out, ContMDiff.clm_precomp, UniformSpace.Completion.continuous_inner, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, PadicInt.denseRange_intCast, instSMulCommClass_sphere_closedBall_ball, CFC.log_exp, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, LeftInvariantDerivation.commutator_apply, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, UpperHalfPlane.mdifferentiableAt_iff, fourier_add_half_inv_index, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, NormedField.noncompactSpace, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, PeriodPair.analyticOnNhd_weierstrassPExcept, hasStrictFDerivAt_pow, FormalMultilinearSeries.derivSeries_apply_diag, NormedSpace.polar_closedBall, Matrix.l2_opNNNorm_conjTranspose_mul_self, iteratedDeriv_fun_mul, fderiv_comp_smul, integrable_cexp_quadratic, Complex.image_exp_Ioc_eq_sphere, ContinuousLinearMap.opNorm_lsmul, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, coe_innerββ_apply, isCoveringMapOn_zpow, FormalMultilinearSeries.norm_changeOriginSeriesTerm, HurwitzZeta.completedHurwitzZetaEven_residue_zero, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, ContinuousWithinAt.inner, Module.Basis.continuous_coe_repr, NormedRing.inverse_add_nth_order, Filter.tendsto_mul_right_cobounded, Unitization.uniformity_eq_aux, isScalarTower_closedBall_closedBall_ball, HasGradientAt.hasDerivAt, hasDerivAt_exp_zero, HasFTaylorSeriesUpTo.zero_eq', deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, HurwitzZeta.tendsto_hurwitzZeta_sub_one_div_nhds_one, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, instFieldContMDiffRing, NormedDivisionRing.to_hasContinuousInvβ, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, PeriodPair.indep, UpperHalfPlane.tanh_half_dist, MeasureTheory.convolution_eq_swap, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, hasDerivAt_const_add_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, DFinsupp.inner_sum, SchwartzMap.tsum_eq_tsum_fourierIntegral, Orientation.kahler_rightAngleRotation_right, MeromorphicOn.divisor_def, WeakDual.isSeqCompact_polar, inner_matrix_row_row, HasFTaylorSeriesUpTo.fderiv, MeasureTheory.intervalIntegrable_charFun, ContinuousMap.idealOf_compl_singleton_isMaximal, Complex.arg_eq_nhds_of_re_neg_of_im_neg, Filter.tendsto_invβ_nhdsNE_zero, Complex.hasSum_arctan, ContinuousLinearMap.norm_holderL_le, fourier_add, hasFDerivWithinAt_pow, MeasureTheory.charFun_eq_integral_innerProbChar, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, coe_algEquiv_lpBCF_symm, LinearMap.polar_mem_iff, hasDerivWithinAt_inv, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, hasStrictDerivAt_id, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, HurwitzZeta.hasSum_int_completedCosZeta, deriv_neg, Complex.hasSum_cosh, RCLike.tendsto_ofReal_atBot_cobounded, LeftInvariantDerivation.ext_iff, Complex.frontier_setOf_lt_re, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, Complex.conj_tsum, Polynomial.hasFDerivWithinAt, LinearMap.hasDerivAt, Real.hasStrictDerivAt_rpow_const, NormedSpace.exp_analytic, LinearMap.hasDerivAtFilter, differentiableAt_inv, HasFiniteFPowerSeriesOnBall.fderiv_eq, NormedSpace.exp_sum_of_commute, ModularForm.coe_trace, integrable_mul_cexp_neg_mul_sq, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, Complex.frontier_setOf_le_im, Complex.hasDerivAt_log_sub_logTaylor, Complex.GammaIntegral_convergent, hasStrictDerivAt_iff_hasStrictFDerivAt, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, ContinuousLinearMap.analyticAt_bilinear, Complex.isOpenMap_exp, ConvexOn.exists_affine_le_of_lt, HasFPowerSeriesAt.hasStrictFDerivAt, convex_halfSpace_re_gt, tendsto_pow_cobounded_cobounded, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AddChar.complexBasis_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, innerSL_apply_coe, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, tendsto_algebraMap_cobounded, Unitary.openPartialHomeomorph_apply, StrongDual.polar_singleton, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, Unitary.argSelfAdjoint_coe, hasDerivAt_pi, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, dist_algebraMap', hasFDerivAt_inv', tendsto_euler_sin_prod', Matrix.exp_units_conj, hasDerivWithinAt_finCons, WeakDual.CharacterSpace.exists_apply_eq_zero, exists_continuousLinearEquiv_fderiv_symm_eq, Complex.polarCoord_target, Units.isOpenEmbedding_val, FormalMultilinearSeries.rightInv_coeff, Seminorm.absorbent_ball, differentiableAt_dslope_of_ne, Complex.hasDerivAt_log, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, NormedSpace.exp_units_conj, hasDerivAt_zpow, AnalyticAt.frequently_eq_iff_eventually_eq, MeasureTheory.AEStronglyMeasurable.convolution_integrand', tangentConeAt_eq_univ, Complex.hasSum_cos, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, isClosedMap_smul_left, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, instSMulCommClass_sphere_sphere_closedBall, Complex.isHomeomorphicTrivialFiberBundle_im, ContDiffOn.differentiableOn_iteratedFDerivWithin, TensorProduct.nnnorm_lid, differentiableAt_iff_comp_const_add, HurwitzZeta.hasSum_int_completedSinZeta, RCLike.instTietzeExtension, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', zeta_nat_eq_tsum_of_gt_one, differentiableAt_inverse, Matrix.l2_opNorm_def, Quaternion.hasSum_coe, UpperHalfPlane.tendsto_comap_im_ofComplex, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Matrix.toEuclideanLin_toLp, ContinuousLinearMapWOT.continuous_dual_apply, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, ContinuousLinearMap.holderL_apply_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, AddChar.expect_apply_eq_ite, LeftInvariantDerivation.toFun_eq_coe, Complex.reCLM_enorm, UpperHalfPlane.contMDiff_denom, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, isClosedEmbedding_smul_left, Polynomial.toAddCircle_C_eq_smul_fourier_zero, isConformalMap_const_smul, tendsto_pow_atTop_nhds_zero_of_norm_lt_one, Matrix.l2_opNorm_mul, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, riemannZeta_eulerProduct_hasProd, norm_innerSL_le, VectorFourier.hasFDerivAt_fourierChar_smul, BoundedContinuousFunction.separatesPoints_charPoly, Padic.instProperSpace, DirichletCharacter.LSeries_eulerProduct, integrable_cexp_quadratic', Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, ContMDiffWithinAt.cle_arrowCongr, PeriodPair.lattice_eq_span_range_basis, Quaternion.continuous_imK, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, CStarAlgebra.exists_sum_four_unitary, continuousMultilinearCurryRightEquiv_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, Complex.frontier_reProdIm, Units.chartAt_source, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, ContinuousAlternatingMap.prodLIE_symm_apply, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, PeriodPair.Οβ_mem_lattice, SchwartzMap.fourier_convolution, OnePoint.isZeroAt_iff, AnalyticOnNhd.eval_continuousLinearMap', UnitAddTorus.span_mFourierLp_closure_eq_top, fderivWithin_comp_smul, tendsto_intCast_atBot_cobounded, ZMod.LFunction_dft, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, instSMulCommClass_closedBall_closedBall_closedBall, PeriodPair.analyticOnNhd_weierstrassP, ContinuousLinearMap.flipβα΅’_symm, HasFPowerSeriesAt.compContinuousLinearMap, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, EuclideanSpace.nndist_single_same, Complex.differentiableAt_cos, cfcHom_eq_of_isStarNormal, DoubleCentralizer.instCompleteSpace, exists_continuousLinearEquiv_fderivWithin_symm_eq, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, UpperHalfPlane.mdifferentiable_denom_zpow, BoundedContinuousFunction.coe_npowRec, NormedSpace.exp_mem_unitary_of_mem_skewAdjoint, HasGradientWithinAt.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, hasFDerivAt_exp, deriv_mul_const_field', WithLp.instProdIsBoundedSMul, RCLike.hasSum_conj', MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, Complex.frontier_setOf_im_le, differentiableAt_iff_comp_sub_const, Complex.range_exp_mul_I, LinearMap.polar_mem, CFC.real_exp_eq_normedSpace_exp, MeromorphicOn.divisor_mul, LinearMap.isAdjointPair_inner, CFC.continuousOn_rpow, ContinuousLinearMap.norm_holder_apply_apply_le, upperHemicontinuous_spectrum, Complex.isUniformEmbedding_equivRealProd, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, Asymptotics.IsLittleO.exists_eq_mul, tendsto_nhds_of_meromorphicOrderAt_nonneg, BoundedContinuousFunction.range_toLp, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, hasDerivWithinAt_iff_tendsto_slope, constFormalMultilinearSeries_apply_succ, Polynomial.fourierCoeff_toAddCircle, FormalMultilinearSeries.continuousOn, hasFDerivAt_inv, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, Complex.hasSum_iff, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, HurwitzZeta.differentiable_completedHurwitzZetaEvenβ, ContinuousMap.isUnit_iff_forall_ne_zero, VectorFourier.fourierIntegral_fderiv, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, HurwitzZeta.differentiable_completedHurwitzZetaOdd, summable_pow_mul_cexp, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, WeakFEPair.Ξ_residue_zero, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, ModularFormClass.hasSum_qExpansion, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, BoundedContinuousFunction.char_add_eq_mul, constFormalMultilinearSeries_zero, Complex.isOpenMap_re, Ring.inverse_exp, HilbertBasis.hasSum_inner_mul_inner, Real.hasDerivWithinAt_arccos_Iic, Complex.approx_Gamma_integral_tendsto_Gamma_integral, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, ContinuousMultilinearMap.curryFinFinset_apply, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, unitary.mem_pathComponentOne_iff, FormalMultilinearSeries.changeOriginSeriesTerm_bound, spectrum.subset_circle_of_unitary, summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, spectrum.subset_closedBall_norm, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, UpperHalfPlane.continuous_coe, summable_mul_of_bigO_atTop', derivWithin_const_mul_field, MeromorphicAt.frequently_zero_iff_eventuallyEq_zero, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Complex.deriv_exp, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, Units.isOpenMap_val, ContinuousLinearMap.apply_apply, RCLike.span_one_I, PeriodPair.Οβ_mem_lattice, DirichletCharacter.differentiable_LFunctionTrivCharβ, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, algebraMap_cobounded_le_cobounded, summable_jacobiThetaβ'_term_iff, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, instSMulCommClass_sphere_sphere_ball, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, PiTensorProduct.mapLMultilinear_opNorm, Convex.instPathConnectedSpace, hasFPowerSeriesAt_iff', RCLike.geometric_hahn_banach_closed_compact, ContDiff.continuous_iteratedDeriv', ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, DFinsupp.sum_inner, UpperHalfPlane.mdifferentiable_iff, meromorphicOrderAt_ne_top_iff_eventually_ne_zero, Real.fourierIntegral_iteratedFDeriv, Complex.isOpen_re_gt_EReal, hasStrictDerivAt_exp_zero, Matrix.PosDef.posDef_sqrt, WeakFEPair.Ξ_residue_k, integrable_cexp_neg_mul_sq, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, Complex.analyticAt_iff_eventually_differentiableAt, differentiableAt_comp_sub_const, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, smooth_functions_tower, RCLike.ofReal_sum, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, UpperHalfPlane.isOpen_upperHalfPlaneSet, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, coe_algEquiv_lpBCF, Quaternion.continuous_normSq, UpperHalfPlane.isEmbedding_coe, HurwitzZeta.differentiable_completedSinZeta, HurwitzZeta.differentiable_hurwitzZetaEven_sub_hurwitzZetaEven, hasFDerivAt_list_prod_attach', Quaternion.continuous_re, CFC.conjugate_rpow_neg_one_half, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, geom_series_eq_inverse, HasCompactSupport.convolution_integrand_bound_right, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, Padic.isDenseInducing_cast_withVal, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, GromovHausdorff.eq_toGHSpace_iff, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendToπ'β, InnerProductSpace.symm_toEuclideanLin_rankOne, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, balanced_iff_closedBall_smul, PeriodPair.derivWeierstrassPExcept_def, Complex.continuousAt_ofReal_cpow_const, ContMDiffAt.cle_arrowCongr, AnalyticOnNhd.eval_continuousLinearMap, circleMap_mem_sphere', MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, LSeries.hasDerivAt_term, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, UpperHalfPlane.mdifferentiableAt_ofComplex, LSeries_eq_mul_integral', ContDiffMapSupportedIn.structureMapLM_apply, CStarAlgebra.span_unitary, binomialSeries_radius_ge_one, isBoundedLinearMap_prod_multilinear, Orthonormal.inner_sum, Summable.hasSumUniformlyOn_log_one_add, HasCompactSupport.convolution_integrand_bound_right_of_subset, CFC.complex_exp_eq_normedSpace_exp, HasStrictDerivAt_ofNat, le_iff_norm_sqrt_mul_rpow, deriv_div_const, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, ContinuousMap.idealOfSet_isMaximal_iff, LeftInvariantDerivation.coeFnAddMonoidHom_apply, BoundedContinuousFunction.toLp_denseRange, hasDerivWithinAt_iff_tendsto, Unitary.path_apply, WeakFEPair.differentiable_Ξβ, cyclotomicCharacter.continuous, TemperedDistribution.laplacianCLM_apply, Unitary.spectrum_subset_circle, continuousAt_gaussian_integral, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, coeFn_fourierLp, RCLike.tendsto_ofReal_atTop_cobounded, SchwartzMap.smulLeftCLM_smul, differentiableAt_iff_comp_neg, DoubleCentralizer.coe_snd, Quaternion.exp_coe, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NumberField.mixedEmbedding.disjoint_negAt_plusPart, Matrix.IsHermitian.instContinuousFunctionalCalculus, MeasureTheory.integral_convolution, fderiv_norm_sq_apply, RCLike.imCLM_apply, DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivCharβ, hasStrictDerivAt_pow, Derivation.evalAt_apply, derivWithin_mem_iff, DirichletCharacter.differentiable_completedLFunction, Complex.continuousAt_tan, PositiveLinearMap.preGNS_norm_sq, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, differentiableOn_inv, HurwitzZeta.differentiableAt_expZeta, ContinuousMultilinearMap.norm_mkPiAlgebraFin, Submodule.starProjection_tendsto_closure_iSup, Ideal.IsMaximal.closure_eq, Quaternion.exp_eq, MeasureTheory.MemLp.ofReal, StrongDual.polar_nonempty, NormedSpace.dual_def, RCLike.geometric_hahn_banach_open_open, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, HasMFDerivAt.const_smul, Complex.continuous_im, WeakDual.CharacterSpace.instStarHomClass, Complex.equivRealProdCLM_apply, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulβα΅’, tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm, Filter.tendsto_invβ_cobounded', Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', EulerProduct.exp_tsum_primes_log_eq_tsum, norm_cfc_lt, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, PeriodPair.finrank_lattice, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, PeriodPair.derivWeierstrassP_add_coe, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Complex.orderClosedTopology, CStarMatrix.norm_def, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_derivβ, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, differentiableWithinAt_Ioi_iff_Ici, HurwitzZeta.differentiableAt_sinZeta, ModularForm.multipliableLocallyUniformlyOn_eta, dist_lineMap_lineMap, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, Complex.isEquivalent_sin, NumberField.mixedEmbedding.convexBodyLT'_convex, differentiableOn_zpow, selfAdjoint.expUnitary_coe, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, summable_jacobiThetaβ_term_iff, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, fderiv_inner_apply, contDiff_one_iff_deriv, inner_matrix_col_col, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, Real.hasStrictDerivAt_log_of_pos, FormalMultilinearSeries.ofScalars_norm, BoundedContinuousFunction.char_mem_charPoly, MeasureTheory.SignedMeasure.im_toComplexMeasure, differentiableAt_jacobiTheta, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, ContinuousLinearMap.orthogonal_ker, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, AnalyticAt.hasStrictDerivAt, iter_deriv_pow, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, pi_mul_cot_pi_q_exp, BoundedContinuousFunction.probCharDual_apply, PeriodPair.weierstrassPExcept_add, InnerProductSpace.norm_rankOne, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Complex.hasDerivAt_Gamma_nat, hasFDerivAt_integral_of_dominated_loc_of_lip, IsClosed.reProdIm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, Units.chartAt_apply, PiTensorProduct.mapLMultilinear_toFun_apply, CStarMatrix.inner_toCLM_conjTranspose_right, norm_jacobiThetaβ_term_fderiv_le, Matrix.PosDef.re_dotProduct_pos, Seminorm.closedBall_smul_closedBall, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Summable.tendstoUniformlyOn_tsum_nat_log_one_add, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, quasispectrum.instCompactSpace, fderiv_eq_smul_deriv, CStarMatrix.toCLM_apply_single_apply, BoundedContinuousFunction.char_apply, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, LinearMap.ker_toContinuousLinearMap, Metric.sphere.instIsTopologicalGroup, Complex.tendsto_exp_comap_re_atBot_nhdsNE, differentiable_circleMap, HurwitzZeta.tendsto_hurwitzZetaEven_sub_one_div_nhds_one, selfAdjoint.joined_one_expUnitary, integrableOn_exp_mul_complex_Ioi, NormedSpace.exp_add, Complex.isClosed_range_intCast, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, le_iff_norm_sqrt_mul_sqrt_inv, hasDerivWithinAt_sub_const_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, HurwitzZeta.differentiable_completedCosZetaβ, Complex.restrictScalars_toSpanSingleton', Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, fderiv_inv', ContinuousLinearMapWOT.ext_inner_iff, Complex.differentiable_iteratedDeriv_cosh, unitary.continuousOn_argSelfAdjoint, Complex.closedEmbedding_intCast, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, HurwitzZeta.hurwitzZetaEven_residue_one, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, FormalMultilinearSeries.comp_assoc, HasFPowerSeriesWithinAt.comp, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, continuousAt_dslope_of_ne, Complex.closure_setOf_im_lt, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, PeriodPair.differentiableOn_derivWeierstrassPExcept, continuousMultilinearCurryFin1_apply, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, deriv_id', hasStrictFDerivAt_euclidean, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, hasFDerivAt_finset_prod, fourierCoeff_fourier, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, HilbertBasis.finite_spans_dense, tendsto_natCast_atTop_cobounded, toMeromorphicNFOn_eqOn_codiscrete
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toRing π | CompOp | 650 mathmath: List.norm_prod_le, SchwartzMap.norm_toLp_le_seminorm, OrthonormalBasis.singleton_repr, TemperedDistribution.lineDerivOpCLM_eq, Seminorm.isBounded_const, HasStrictFDerivAt.fun_mul', unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, HasMFDerivAt.mul, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, List.nnnorm_prod, Matrix.frobeniusIsBoundedSMul, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Real.hasFDerivAt_fourierChar_neg_bilinear_left, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, hasStrictFDerivAt_list_prod_finRange', Seminorm.le_finset_sup_apply, LinearMap.IsSymmetric.restrictScalars, Seminorm.norm_sub_map_le_sub, ContinuousAlternatingMap.isEmbedding_restrictScalars, SeminormFamily.basisSets_smul_right, HasFDerivWithinAt.pow, Metric.unitSphere.coe_one, ModularForm.mul_slash, hasFDerivAt_multiset_prod, Filter.BoundedAtFilter.mul, BoundedContinuousFunction.algebraMap_apply, Circle.exp_arg, Circle.injective_arg, OrthonormalBasis.repr_injective, Seminorm.bot_eq_zero, Seminorm.smul_comp, norm_natCast_eq_mul_norm_one, ContinuousLinearMap.isUniformEmbedding_restrictScalars, Seminorm.finset_sup_apply, Polynomial.exists_eq_supNorm, Asymptotics.IsBigO.mul_atTop_rpow_natCast_of_isBigO_rpow, HasDerivAtFilter.comp_hasFDerivAtFilter, Seminorm.ball_smul_closedBall, Real.fderiv_fourierChar_neg_bilinear_right_apply, WithSeminorms.mem_nhds_iff, fderivWithin_fun_pow', Asymptotics.IsBigOWith.pow, fderiv_multiset_prod, HasFPowerSeriesWithinOnBall.restrictScalars, SeminormFamily.filter_eq_iInf, Seminorm.restrictScalars_closedBall, HasFDerivAt.fun_mul, selfAdjoint.expUnitaryPathToOne_apply, WithLp.isBoundedSMulSeminormedAddCommGroupToProd, IsUltrametricDist.norm_intCast_le_one, List.nnnorm_prod_le', ContinuousLinearMap.opNorm_lsmul_apply_le, IsUltrametricDist.norm_add_one_le_max_norm_one, Circle.ofConjDivSelf_coe, Asymptotics.IsBigO.const_mul_left, HasDerivAt.comp_hasFDerivAt_of_eq, IsConformalMap.is_complex_or_conj_linear, Circle.starRingEnd_addChar, SeminormedCommRing.mul_comm, AbsolutelyContinuousOnInterval.const_smul, Seminorm.neg_ball, Asymptotics.IsLittleO.mul, Asymptotics.IsBigO.smul, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, LinearMap.toContinuousLinearMapβ_coe, HasStrictFDerivAt.mul', fderiv_fun_pow, Complex.hasStrictFDerivAt_exp_real, ModularForm.prod_slash, hasStrictFDerivAt_exp_smul_const_of_mem_ball', HasStrictFDerivAt.pow, Asymptotics.IsBigOWith.const_smul_self, nndist_smulβ, AddCircle.homeomorphCircle'_symm_apply, HasStrictFDerivAt.const_mul, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, Bornology.isVonNBounded_neg, HasFDerivAt.finset_prod, TrivSqZeroExt.instNormOneClass, OrthonormalBasis.repr_self, norm_pow, fderiv_fun_pow', norm_sub_mul_le', rotation_apply, toMatrix_rotation, Polynomial.supNorm_zero, RCLike.smul_re, gelfandStarTransform_naturality, ModularForm.prod_slash_sum_weights, gelfandStarTransform_apply_apply, HasFDerivWithinAt.const_mul, balancedCore_nonempty_iff, List.norm_prod_le', Seminorm.closedBall_smul_ball, OrthonormalBasis.measurePreserving_repr, nnnorm_algebraMap_nnreal, HasFDerivWithinAt.mul, WithSeminorms.tendsto_nhds', fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, Seminorm.pullback_apply, Asymptotics.IsLittleO.pow, isBoundedBilinearMap_mul, UpperHalfPlane.coe_pos_real_smul, Complex.starConvex_ofReal_slitPlane, RCLike.toIsStrictOrderedModule, Asymptotics.IsBigO.listProd, Quaternion.linearIsometryEquivTuple_symm_apply, HasDerivAt.comp_hasFDerivWithinAt, HasFDerivAt.restrictScalars, Complex.UnitDisc.coe_smul_circle, HasStrictFDerivAt.list_prod', Complex.starConvex_one_slitPlane, hasStrictDerivAt_exp_smul_const, Asymptotics.IsBigO.const_smul_left, norm_algebraMap_nnreal, isCompactOperator_iff_isCompact_closure_image_ball, Asymptotics.isBigOWith_self_const_mul', hasStrictDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_real_smul, NormMulClass.toNormSMulClass_op, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Metric.unitSphere.coe_mul, ContinuousLinearMap.uniformContinuous_restrictScalars, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, Seminorm.ball_eq_emptyset, Polynomial.supNorm_X, hasStrictFDerivAt_multiset_prod, SeminormFamily.finset_sup_comp, fderivWithin_finset_prod, Orientation.rotation_map_complex, norm_pow_le, convex_halfSpace_re_le, Module.Basis.coe_toOrthonormalBasis_repr, hasFDerivAt_ringInverse, ContinuousMultilinearMap.opNorm_smul_le, Seminorm.closedBall_zero_eq_preimage_closedBall, BoundedContinuousFunction.mem_charPoly, Filter.BoundedAtFilter.smul, BoundedContinuousFunction.charAlgHom_apply, BoundedContinuousFunction.coe_intCast, Circle.arg_eq_arg, normHom_apply, List.nnnorm_prod_le, Seminorm.balanced_closedBall_zero, fourier_one, Seminorm.coe_restrictScalars, RingHomIsometric.enorm_map, Real.Angle.coe_toCircle, Seminorm.gaugeSeminorm_ball, fderiv_mul_const', Matrix.linftyOpIsBoundedSMul, ContinuousAlternatingMap.norm_restrictScalars, OrthonormalBasis.coe_ofRepr, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, gelfandStarTransform_symm_apply, Asymptotics.IsBigOWith.const_smul_left, Complex.orthonormalBasisOneI_repr_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, Seminorm.ball_zero_eq_preimage_ball, NormedAlgebra.exists_isMinOn_norm_sub_smul, fourier_neg', Matrix.isBoundedSMul, ContinuousLinearMap.continuous_restrictScalars, norm_natCast, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, Circle.smul_def, Seminorm.balanced_ball_zero, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', convex_halfSpace_im_gt, BoundedContinuousFunction.coe_natCast, Seminorm.restrictScalars_ball, fderiv_pow, HasFDerivAt.pow, Asymptotics.IsLittleO.smul, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, fderivWithin_inv', NormedSpace.norm_expSeries_summable_of_mem_ball', tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, HasStrictFDerivAt.cexp, OrthonormalBasis.tensorProduct_repr_tmul_apply', nnnorm_natAbs, Seminorm.comp_smul, HasFDerivWithinAt.mul_const, fderiv_pow', fderiv_mul, NumberField.mixedEmbedding.convexBodySumFun_smul, NumberField.mixedEmbedding.logMap_real_smul, Seminorm.comp_zero, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, nnnorm_algebraMap, nnnorm_pow, Asymptotics.IsBigOWith.pow', Polynomial.le_supNorm, Seminorm.neg_mem_ball_zero, OrthonormalBasis.equiv_apply, Seminorm.bound_of_continuous, fderiv_pow_ring, DifferentiableAt.fderiv_restrictScalars, ContinuousLinearMap.lsmul_apply, nnnorm_pow_le, selfAdjoint.unitarySelfAddISMul_coe, HasDerivWithinAt.complexToReal_fderiv, Circle.ext_iff, Module.Basis.coe_toOrthonormalBasis_repr_symm, IsometricContinuousFunctionalCalculus.toNonUnital, subset_balancedHull, fderivWithin_fun_mul', algebraMap_isometry, Asymptotics.IsLittleO.smul_isBigO, hasFDerivAt_list_prod', SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, SubringClass.toNormMulClass, fderiv_mul', OrthonormalBasis.repr_apply_apply, Circle.coe_inv_eq_conj, Seminorm.add_comp, HasFDerivWithinAt.cexp, RingHom.isometry, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, Circle.coe_mul, NormedSpace.expSeries_summable', MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, RingHomIsometric.nnnorm_map, ContinuousLinearMap.coe_restrict_scalarsL', HasDerivAt.complexToReal_fderiv, inner_smul_real_right, hasFDerivAt_exp_smul_const', Real.Angle.arg_toCircle, Seminorm.closedBall_finset_sup, FormalMultilinearSeries.ofScalars_norm_le, IsBoundedLinearMap.smul, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, Circle.coe_pow, LinearMap.toMatrix_innerββ_apply, Asymptotics.IsBigO.mul, hasFDerivWithinAt_pow', convex_halfSpace_im_lt, Asymptotics.IsLittleO.const_mul_left, HasFDerivAt.cexp, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, balanced_neg, norm_natAbs, dist_eq, Circle.invOn_arg_exp, fderivWithin_mul_const', CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, WithSeminorms.tendsto_nhds, hasFDerivAt_list_prod_finRange', WithSeminorms.isOpen_iff_mem_balls, ContinuousMap.nnnorm_smul_const, Seminorm.const_isBounded, Seminorm.preimage_metric_closedBall, IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one, Complex.restrictScalars_one_smulRight, StrongDual.dualPairing_separatingLeft, Seminorm.sSup_empty, norm_intCast_abs, eventually_norm_pow_le, HasStrictFDerivAt.restrictScalars, balancedHull_add_subset, isCompactOperator_iff_image_closedBall_subset_compact, Circle.star_addChar, hasDerivAt_exp_smul_const, Asymptotics.IsBigOWith.smul, fderivWithin_fun_pow, PadicInt.mahlerTerm_one, RCLike.smul_im, HasFDerivAt.multiset_prod, MemHolder.smul, HasFDerivAt.mul_const, ContinuousLinearMap.coe_restrictScalarsIsometry, PiTensorProduct.dualSeminorms_bounded, CommCStarAlgebra.toStarModule, HasFDerivWithinAt.mul_const', HasDerivAt.comp_hasFDerivWithinAt_of_eq, fderiv_const_mul, NormOneClass.induced, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, RCLike.wInner_const_left, RingHomIsometric.ids, fderiv_pow_ring', nnnorm_intCast_abs, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, HasFPowerSeriesAt.restrictScalars, edist_smulβ, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, ContDiffAt.restrictScalars_iteratedFDeriv, PiTensorProduct.injectiveSeminorm_apply, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, hasFDerivAt_pow, ContinuousMultilinearMap.instIsBoundedSMul, Seminorm.exists_apply_eq_finset_sup, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, NumberField.mixedEmbedding.norm_smul, ConvexOn.convex_re_epigraph, EuclideanSpace.basisFun_repr, NormMulClass.induced, Circle.leftInverse_exp_arg, HasFDerivWithinAt.restrictScalars, convex_absConvexHull, differentiableWithinAt_iff_restrictScalars, Complex.orthonormalBasisOneI_repr_symm_apply, Seminorm.coe_bot, RCLike.ofReal_alg, HasFDerivAt.fun_pow', Asymptotics.IsBigO.mul_atTop_rpow_of_isBigO_rpow, HasMFDerivWithinAt.mul', SeminormFamily.basisSets_smul, Submonoid.coe_unitSphere, Circle.norm_coe, Polynomial.supNorm_monomial, Seminorm.neg_closedBall, Metric.sphere.instContinuousMul, fourier_apply, RCLike.wInner_const_right, WithSeminorms.continuous_seminorm, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, Polynomial.supNorm_C, ContinuousAlternatingMap.continuous_restrictScalars, convex_halfSpace_re_ge, Seminorm.comp_apply, OrthonormalBasis.sum_repr_symm, HasFDerivAt.const_mul, DifferentiableWithinAt.restrictScalars_fderivWithin, NormedSpace.norm_expSeries_summable', Matrix.linftyOpNormSMulClass, fderivWithin_multiset_prod, Polynomial.supNorm_def', WithLp.normSMulClassSeminormedAddCommGroupToProd, HasFDerivAt.mul, SchwartzMap.eLpNorm_le_seminorm, selfAdjoint.star_coe_unitarySelfAddISMul, Orientation.kahler_rotation_left', convex_halfSpace_im_ge, Seminorm.closedBall_eq_emptyset, hasStrictFDerivAt_pow', Asymptotics.IsBigO.mul_isLittleO, NormedAlgebra.instRegularNormedAlgebra, convex_halfSpace_re_lt, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', NumberField.finite_of_discr_bdd, RCLike.instStarModuleReal, norm_algebraMap, OrthonormalBasis.measurePreserving_repr_symm, hasFDerivAt_exp_smul_const, WithSeminorms.congr_equiv, fderiv_finset_prod, hasStrictFDerivAt_list_prod_attach', rotationOf_coe, HasFPowerSeriesWithinAt.restrictScalars, hasStrictFDerivAt_ringInverse, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, CFC.log_smul', nnnorm_pow_le', TrivSqZeroExt.instL1IsBoundedSMul, hasStrictFDerivAt_finset_prod, HasDerivWithinAt.comp_hasFDerivAt, isCompactOperator_iff_isCompact_closure_image_closedBall, InnerProductSpace.toMatrix_rankOne, Seminorm.ball_smul_ball, isClosed_nullSubmodule, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, Real.hasDerivAt_fourierChar, Orientation.kahler_rotation_left, LindemannWeierstrass.integral_exp_mul_eval, spectrum.differentiableOn_inverse_one_sub_smul, WithSeminorms.tendsto_nhds_atTop, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, inner_smul_real_left, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, ContinuousLinearMap.isEmbedding_restrictScalars, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, HasFDerivWithinAt.pow', mem_nullSubmodule_iff, nnnorm_algebraMap', norm_mul_le, Circle.coe_eq_one, HasFDerivAt.list_prod', hasFDerivAt_pow', Seminorm.zero_or_exists_apply_eq_finset_sup, ContinuousLinearMap.opNorm_lsmul_le, Seminorm.ball_comp, OrthonormalBasis.repr_symm_single, Real.fourierChar_apply, WithLp.instProdNormSMulClass, ContinuousLinearMap.coe_restrictScalarsL, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, Matrix.normSMulClass, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, NumberField.mixedEmbedding.convexBodyLT_convex, HasMFDerivAt.prod, zero_mem_absConvexHull, toMatrix_innerSL_apply, Matrix.linfty_opNormOneClass, PiLp.basis_toMatrix_basisFun_mul, Metric.unitSphere.coe_pow, isBoundedBilinearMap_smul, ContinuousLinearMap.norm_restrictScalars, NormedAlgebra.norm_smul_le, Asymptotics.IsBigOWith.const_mul_right', Ideal.Quotient.norm_mk_lt, RCLike.real_smul_ofReal, Circle.coe_inv, LinearMap.toContinuousLinearMapβ_apply, Seminorm.coe_comp, isCompactOperator_iff_image_ball_subset_compact, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Metric.unitClosedBall.coe_one, NumberField.mixedEmbedding.logMap_real, Seminorm.finset_sup_smul, HasMFDerivWithinAt.mul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Seminorm.isBounded_sup, Asymptotics.IsLittleO.listProd, Seminorm.comp_id, spectralValue_X_sub_C, Complex.log_eq_integral, Asymptotics.isBigO_const_mul_self, IsUltrametricDist.norm_natCast_le_one, IsUltrametricDist.nnnorm_intCast_le_one, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, fderiv_fun_mul, Nat.norm_cast_le, Seminorm.closedBall_bot, HasFDerivAt.pow', HasStrictFDerivAt.pow', SubringClass.toNormOneClass, HasStrictFDerivAt.multiset_prod, Matrix.frobeniusNormSMulClass, SeminormFamily.basisSets_singleton_mem, Real.differentiable_fourierChar, dist_smulβ, norm_pow_le', nnnormHom_apply, HasStrictFDerivAt.mul_const', Circle.normSq_coe, NumberField.mixedEmbedding.normAtPlace_smul, norm_intCast_eq_abs_mul_norm_one, ModularForm.prod_fintype_slash, fderivWithin_list_prod', Complex.starConvex_slitPlane, HasFDerivWithinAt.fun_mul', nnnorm_commutator_units_sub_one_le, Asymptotics.isBigOWith_const_mul_self, OrthonormalBasis.coe_toBasis_repr, hasStrictFDerivAt_list_prod, fourier_zero', ZMod.toCircle_intCast, IsUltrametricDist.nnnorm_natCast_le_one, ZMod.toCircle_natCast, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, fderivWithin_pow_ring', Orientation.kahler_apply_apply, Polynomial.isGreatest_supNorm, Real.differentiable_fourierChar_neg_bilinear_right, nnnorm_sub_mul_le, Circle.coeHom_apply, HasFDerivWithinAt.fun_pow', rootsOfUnityCircleEquiv_apply, differentiableAt_iff_restrictScalars, OrthonormalBasis.coe_toBasis_repr_apply, Circle.coe_inj, fderivWithin_mul_const, Seminorm.preimage_metric_ball, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, HasFDerivAt.mul_const', Orientation.kahler_rotation_right, norm_commutator_units_sub_one_le, NormSMulClass.toIsBoundedSMul, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, HasStrictFDerivAt.fun_pow', fourier_coe_apply', TrivSqZeroExt.nnnorm_inr, AbsolutelyContinuousOnInterval.fun_smul, Algebra.norm_smul_one_eq_norm, RingHomIsometric.inv, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Metric.unitClosedBall.coe_pow, ZMod.toCircle_apply, Metric.unitClosedBall.instIsCancelMulZero, hasStrictFDerivAt_inv', Circle.arg_exp, hasFDerivAt_exp_smul_const_of_mem_ball', WithSeminorms.partial_sups, hasStrictFDerivAt_exp_smul_const, dist_algebraMap, Complex.hasStrictFDerivAt_log_real, HasStrictFDerivAt.mul, List.norm_prod, Seminorm.comp_comp, Metric.unitClosedBall.coe_eq_one, Real.differentiable_fourierChar_neg_bilinear_left, hasDerivAt_exp_smul_const', HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, ContinuousMap.norm_smul_const, AbsConvexOpenSets.coe_convex, norm_algebraMap', NumberField.mixedEmbedding.convexBodySum_convex, Circle.coe_exp, convex_halfSpace_im_le, LinearMap.toSeminormFamily_apply, Seminorm.ball_finset_sup_eq_iInter, enorm_pow, fourier_add', Asymptotics.IsLittleO.mul_isBigO, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', balancedHull.balanced, balancedCore_zero_mem, BoundedContinuousFunction.charMonoidHom_apply, Asymptotics.IsBigO.pow, Polynomial.supNorm_eq_iSup, Asymptotics.IsBigO.const_smul_self, NormedSpace.expSeries_hasSum_exp_of_mem_ball', fderivWithin_pow, hasStrictFDerivAt_pow, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, ContinuousLinearMap.opNorm_lsmul, Seminorm.zero_comp, Circle.toUnits_apply, CStarAlgebra.toStarModule, PointwiseConvergenceCLM.withSeminorms, ContinuousAlternatingMap.uniformContinuous_restrictScalars, Quaternion.linearIsometryEquivTuple_apply, Seminorm.ball_finset_sup, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, gaugeSeminormFamily_ball, HasFDerivWithinAt.mul', Asymptotics.IsBigOWith.const_mul_left, Seminorm.comp_smul_apply, HasFDerivAtFilter.restrictScalars, WithSeminorms.isVonNBounded_iff_seminorm_bounded, norm_sub_mul_le, HasStrictDerivAt.complexToReal_fderiv, convex_halfSpace_re_gt, tendsto_pow_cobounded_cobounded, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, fderivWithin_mul', HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, tendsto_algebraMap_cobounded, Real.probChar_apply, dist_algebraMap', hasFDerivAt_inv', SeminormFamily.basisSets_mem, Ideal.Quotient.norm_mk_le, RCLike.conj_smul, nnnorm_sub_mul_le', Circle.coe_injective, NormedSpace.expSeries_summable_of_mem_ball', Matrix.IsHermitian.mulVec_eigenvectorBasis, Circle.coe_zpow, Seminorm.closedBall_comp, tendsto_pow_atTop_nhds_zero_of_norm_lt_one, Subalgebra.SeparatesPoints.rclike_to_real, SeminormFamily.basisSets_iff, CStarAlgebra.exists_sum_four_unitary, RCLike.real_smul_eq_coe_mul, fderiv_list_prod', HasMFDerivWithinAt.prod, Complex.log_inv_eq_integral, HasMFDerivAt.mul', Asymptotics.IsBigOWith.mul, spectralValue_X_pow, BoundedContinuousFunction.coe_npowRec, hasFDerivAt_exp, Pi.orthonormalBasis_repr, WithLp.instProdIsBoundedSMul, Circle.coe_div, toRingSeminorm_apply, Circle.coe_one, fderivWithin_pow_ring, HasFDerivAt.fun_mul', Seminorm.continuous_iff_continuous_comp, HasStrictFDerivAt.mul_const, Real.fderiv_fourierChar_neg_bilinear_left_apply, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, AbsolutelyContinuousOnInterval.smul, algebraMap_cobounded_le_cobounded, fderivWithin_restrictScalars_comp, HasFDerivAt.mul', WithSeminorms.hasBasis_ball, hasFDerivAt_list_prod_attach', Seminorm.finset_sup_le_sum, OrthonormalBasis.repr_reindex, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendToπ'β, FormalMultilinearSeries.ofScalars_norm_eq_mul, CFC.log_smul, balanced_iff_closedBall_smul, HasDerivWithinAt.comp_hasFDerivAt_of_eq, Circle.argEquiv_apply_coe, fderivWithin_fun_mul, le_iff_norm_sqrt_mul_rpow, Unitary.path_apply, MemHolder.smul_iff, Seminorm.closedBall_finset_sup_eq_iInter, Complex.UnitDisc.coe_circle_smul, Seminorm.comp_add_le, ZMod.stdAddChar_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply, ContinuousMultilinearMap.norm_mkPiAlgebraFin, hasFDerivAt_exp_of_mem_ball, Circle.argPartialEquiv_apply, MeasureTheory.charFun_eq_integral_probChar, Seminorm.ball_bot, Asymptotics.IsBigO.smul_isLittleO, PiTensorProduct.injectiveSeminorm_def, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, NumberField.mixedEmbedding.convexBodyLT'_convex, HolderWith.smul_iff, selfAdjoint.expUnitary_coe, fderivWithin_mul, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, WithSeminorms.hasBasis_zero_ball, FormalMultilinearSeries.ofScalars_norm, HasFDerivWithinAt.fun_mul, Complex.rotation, Asymptotics.IsLittleO.const_smul_left, HasStrictFDerivAt.finset_prod, Seminorm.neg_mem_closedBall_zero, TrivSqZeroExt.norm_inr, Seminorm.closedBall_smul_closedBall, BoundedContinuousFunction.char_apply, hasStrictFDerivAt_exp_smul_const_of_mem_ball, WithSeminorms.finset_sups, le_iff_norm_sqrt_mul_sqrt_inv, HasFDerivWithinAt.list_prod', NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, fderiv_inv', fderivWithin_pow', balanced_zero, hasFDerivAt_finset_prod
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