Basic

📁 Source: Mathlib/Analysis/Normed/Module/Basic.lean

Statistics

Metric	Count
Definitions normedAlgebraOrig, normedSpaceOrig, instNormedAlgebra, instNormedSpace, ofCore, ofCoreReplaceAll, ofCoreReplaceTopology, ofCoreReplaceUniformity, NormedAlgebra, id, induced, restrictScalars, toAlgebra, toNormedSpace, toNormedSpace, induced, ofCore, restrictScalars, toModule, normedAlgebra, normedAlgebra, normedSpace, normedAlgebra, normedSpace, ofSeminormedSpaceCore, ofSeminormedSpaceCore, ofSeminormedSpaceCoreReplaceAll, ofSeminormedSpaceCoreReplaceTopology, ofSeminormedSpaceCoreReplaceUniformity, normedAlgebra, normedSpace, ofCore, ofCoreReplaceAll, ofCoreReplaceTopology, ofCoreReplaceUniformity, instNormedAlgebra, instNormedSpace, toNormedAlgebra, toNormedAlgebra, normedSpace, toNormedSpace, normedSpace, instNonUnitalNormedCommRingRestrictScalars, instNonUnitalNormedRingRestrictScalars, instNonUnitalSeminormedCommRingRestrictScalars, instNonUnitalSeminormedRingRestrictScalars, instNormedAddCommGroupRestrictScalars, instNormedAlgebraULift, instNormedCommRingRestrictScalars, instNormedRingRestrictScalars, instSeminormedAddCommGroupRestrictScalars, instSeminormedCommRingRestrictScalars, instSeminormedRingRestrictScalars, normedAlgebraRat	54
Theorems continuous_of_isBounded_nhds_zero, norm_smul_one_eq_norm, smul_tendsto_zero, zero_smul_isBoundedUnder_le, diam_ball_eq, diam_closedBall_eq, diam_sphere_eq, cobounded_neBot, infinite, norm_smul_le, noncompactSpace, norm_eq_zero_iff, toCore, cobounded_neBot, discreteTopology_zmultiples, exists_lt_norm, ext, ext_iff, noncompactSpace, norm_smul_le, restrictScalars_eq, toIsBoundedSMul, toNormSMulClass, unbounded_univ, cobounded_neBot, noncompactSpace, norm_nonneg, norm_smul, norm_triangle, algebraMap_cobounded_le_cobounded, algebraMap_isometry, dist_algebraMap, dist_algebraMap', eventually_nhds_norm_smul_sub_lt, nnnorm_algebraMap, nnnorm_algebraMap', nnnorm_algebraMap_nnreal, norm_algebraMap, norm_algebraMap', norm_algebraMap_nnreal, norm_intCast_eq_abs_mul_norm_one, norm_natCast, norm_natCast_eq_mul_norm_one, norm_zsmul, tendsto_algebraMap_cobounded	45
Total	99

AddMonoidHom

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuous_of_isBounded_nhds_zero 📖	mathematical	Set Filter Filter.instMembership nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid SeminormedAddCommGroup.toAddCommGroup Bornology.IsBounded PseudoMetricSpace.toBornology Set.image DFunLike.coe AddMonoidHom AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup instFunLike	Continuous UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe AddMonoidHom AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup instFunLike	—	Metric.mem_nhds_iff Metric.isBounded_iff_subset_ball Bornology.IsBounded.subset Set.image_mono continuous_of_continuousAt_zero SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd instAddMonoidHomClass Metric.continuousAt_iff dist_zero_right map_zero AddMonoidHomClass.toZeroHomClass LE.le.trans_lt norm_nonneg norm_zero exists_nat_gt Real.instIsStrictOrderedRing Real.instArchimedean LT.lt.trans div_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Nat.cast_zero map_nsmul Nat.cast_smul_eq_nsmul inv_smul_smul₀ IsStrictOrderedRing.toCharZero norm_smul_le NormedSpace.toIsBoundedSMul mul_lt_mul_of_pos_left norm_nsmul_le lt_div_iff₀ MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE IsStrictOrderedRing.toMulPosStrictMono mul_comm norm_inv Nat.abs_cast Real.instIsOrderedRing Real.instNontrivial Nat.instCanonicallyOrderedAdd mul_lt_mul_of_pos_right inv_strictAnti₀ inv_div IsUnit.div_mul_cancel LT.lt.ne'

Algebra

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
norm_smul_one_eq_norm 📖	mathematical	—	Norm.norm SeminormedRing.toNorm toSMul Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedField.toNorm	—	norm_smul NormedSpace.toNormSMulClass NormOneClass.norm_one mul_one

Filter.IsBoundedUnder

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
smul_tendsto_zero 📖	mathematical	Filter.IsBoundedUnder Real Real.instLE Norm.norm NormedField.toNorm Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid SeminormedAddCommGroup.toAddCommGroup	Filter.Tendsto SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup NormedSpace.toModule nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	Filter.Tendsto.op_zero_isBoundedUnder_le LE.le.trans_eq norm_smul_le NormedSpace.toIsBoundedSMul mul_comm

Filter.Tendsto

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zero_smul_isBoundedUnder_le 📖	mathematical	Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing Filter.IsBoundedUnder Real Real.instLE Norm.norm SeminormedAddCommGroup.toNorm	Filter.Tendsto SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup NormedSpace.toModule nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	op_zero_isBoundedUnder_le norm_smul_le NormedSpace.toIsBoundedSMul

Metric

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
diam_ball_eq 📖	mathematical	Real Real.instLE Real.instZero	diam SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ball Real Real.instMul instOfNatAtLeastTwo Real.instNatCast Nat.instAtLeastTwoHAddOfNat	—	le_antisymm Nat.instAtLeastTwoHAddOfNat diam_ball mul_le_of_forall_lt_of_nonneg Real.instIsStrictOrderedRing le_of_lt Mathlib.Meta.Positivity.pos_of_isNat Real.instIsOrderedRing Real.instNontrivial Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Meta.NormNum.instAtLeastTwo diam_nonneg mul_le_mul_of_nonneg_right IsOrderedRing.toMulPosMono diam_sphere_eq GE.ge.le diam_mono sphere_subset_ball isBounded_ball
diam_closedBall_eq 📖	mathematical	Real Real.instLE Real.instZero	diam SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup closedBall Real Real.instMul instOfNatAtLeastTwo Real.instNatCast Nat.instAtLeastTwoHAddOfNat	—	le_antisymm Nat.instAtLeastTwoHAddOfNat diam_closedBall LE.le.trans Eq.le diam_sphere_eq diam_mono sphere_subset_closedBall isBounded_closedBall
diam_sphere_eq 📖	mathematical	Real Real.instLE Real.instZero	diam SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup sphere Real Real.instMul instOfNatAtLeastTwo Real.instNatCast Nat.instAtLeastTwoHAddOfNat	—	le_antisymm Nat.instAtLeastTwoHAddOfNat LE.le.trans diam_mono sphere_subset_closedBall isBounded_closedBall diam_closedBall exists_ne IsScalarTower.left dist_eq_norm add_sub_sub_cancel AddCommMonoid.nat_isScalarTower nsmul_eq_mul norm_smul NormedSpace.toNormSMulClass norm_mul NormedDivisionRing.toNormMulClass Real.norm_ofNat abs_of_nonneg IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid norm_inv norm_norm mul_assoc inv_mul_cancel_right₀ dist_le_diam_of_mem isBounded_sphere add_sub_cancel_left inv_mul_cancel₀ mul_one sub_sub_cancel_left norm_neg

Module.RestrictScalars

Definitions

Name	Category	Theorems
normedAlgebraOrig 📖	CompOp	—
normedSpaceOrig 📖	CompOp	—

MulOpposite

Definitions

Name	Category	Theorems
instNormedAlgebra 📖	CompOp	—
instNormedSpace 📖	CompOp	—

NontriviallyNormedField

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cobounded_neBot 📖	mathematical	—	Filter.NeBot Bornology.cobounded PseudoMetricSpace.toBornology SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing toNormedField	—	NormedSpace.cobounded_neBot IsSimpleRing.instNontrivial DivisionRing.isSimpleRing
infinite 📖	mathematical	—	Infinite	—	NormedSpace.unbounded_univ IsSimpleRing.instNontrivial DivisionRing.isSimpleRing Set.Finite.isBounded Set.toFinite Subtype.finite

NormedAddCommGroup

Definitions

Name	Category	Theorems
ofCore 📖	CompOp	—
ofCoreReplaceAll 📖	CompOp	—
ofCoreReplaceTopology 📖	CompOp	—
ofCoreReplaceUniformity 📖	CompOp	—

NormedAlgebra

Definitions

Name	Category	Theorems
id 📖	CompOp	32 math math: logDeriv_tprod_eq_tsum, AnalyticAt.tendsto_mul_logDeriv_simple_zero, logDeriv_comp, Complex.logDeriv_tendsto, MeasureTheory.convolution_lsmul, BoundedContinuousFunction.mem_charPoly, BoundedContinuousFunction.charAlgHom_apply, WeakDual.CharacterSpace.homeoEval_naturality, tendsto_logDeriv_euler_sin_div, logDeriv_sin_div_eq_cot, Complex.logDeriv_sin, Complex.logDeriv_exp, logDeriv_id, logDeriv_id', Complex.digamma_def, MeasureTheory.convolution_lsmul_swap, logDeriv_inv, Complex.LogDeriv_exp, BoundedContinuousFunction.star_mem_range_charAlgHom, logDeriv_prod_sineTerm_eq_sum_cotTerm, Complex.logDeriv_cos, ContinuousLinearMap.lsmul_flip_apply, ContinuousMapZero.elemental_eq_top, BoundedContinuousFunction.separatesPoints_charPoly, logDeriv_sineTerm_eq_cotTerm, logDeriv_pow, logDeriv_zpow, Real.fourier_smul_convolution_eq, Complex.deriv_log_comp_eq_logDeriv, Complex.logDeriv_cosh, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, BoundedContinuousFunction.char_mem_charPoly
induced 📖	CompOp	—
restrictScalars 📖	CompOp	—
toAlgebra 📖	CompOp	661 math math: IsKrasner.of_completeSpace_of_normal, HasStrictFDerivAt.fun_mul', unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, HasMFDerivAt.mul, ModularForm.smul_slash, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, IsSelfAdjoint.quasispectrumRestricts, IsStarNormal.spectralRadius_eq_nnnorm, Matrix.IsHermitian.isClosedEmbedding_cfcAux, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, NormedSpace.hasFPowerSeriesAt_exp_zero_of_radius_pos, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, hasStrictFDerivAt_list_prod_finRange', Filter.Tendsto.cfc, Subalgebra.spectrum_sUnion_connectedComponentIn, ContMDiffMap.coeFnAlgHom_apply, NormedSpace.expSeries_summable_of_mem_ball, LinearMap.IsSymmetric.restrictScalars, ContinuousAlternatingMap.isEmbedding_restrictScalars, HasFDerivWithinAt.pow, nnnorm_cfc_lt, fderivWithin_fun_smul, PositiveLinearMap.apply_le_of_isSelfAdjoint, Matrix.IsHermitian.det_abs, ModularForm.mul_slash, hasFDerivAt_multiset_prod, BoundedContinuousFunction.algebraMap_apply, spectrum.subset_closedBall_norm_mul, spectrum.instCompactSpace, CFC.tendsto_cfc_rpow_sub_one_log, SchwartzMap.pairing_apply_apply, Matrix.IsHermitian.cfc_eq, ContinuousLinearMap.isUniformEmbedding_restrictScalars, HasDerivAtFilter.comp_hasFDerivAtFilter, ordinaryHypergeometric_radius_top_of_neg_nat₃, integrableOn_cfc', ContinuousLinearMap.integral_apply, RCLike.algebraMap_eq_ofReal, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, Unitization.real_cfcₙ_eq_cfc_inr, fderivWithin_fun_pow', norm_cfc_lt_iff, Module.Dual.extendRCLikeₗ_symm_apply, SchwartzMap.lineDerivOp_fourier_eq, fderiv_multiset_prod, HasFPowerSeriesWithinOnBall.restrictScalars, HasFDerivAt.fun_mul, selfAdjoint.expUnitaryPathToOne_apply, CStarAlgebra.norm_or_neg_norm_mem_spectrum, StarAlgebra.elemental.characterSpaceToSpectrum_coe, SchwartzMap.bilinLeftCLM_apply, HasDerivAt.comp_hasFDerivAt_of_eq, IsConformalMap.is_complex_or_conj_linear, ContinuousAt.cfc, RCLike.re_add_im_ax, UpperHalfPlane.σ_sq, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, HasStrictFDerivAt.mul', fderiv_fun_pow, ModularForm.prod_slash, hasStrictFDerivAt_exp_smul_const_of_mem_ball', SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, HasStrictFDerivAt.pow, norm_cfc_le_iff, HasStrictFDerivAt.const_mul, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, Complex.conjCAE_apply, HasFDerivAt.finset_prod, fderiv_fun_pow', RCLike.smul_re, Continuous.cfc', gelfandStarTransform_naturality, ModularForm.prod_slash_sum_weights, gelfandStarTransform_apply_apply, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, HasFDerivWithinAt.const_mul, ContinuousMultilinearMap.norm_mkPiAlgebra_le, spectrum.isOpen_resolventSet, Unitization.sqrt_inr, Continuous.cfc_nnreal', spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, gelfandTransform_bijective, ordinaryHypergeometricSeries_radius_eq_one, nnnorm_algebraMap_nnreal, HasFDerivWithinAt.mul, fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, UpperHalfPlane.coe_pos_real_smul, CFC.continuousOn_log, HasFDerivAt.fun_smul, NormedSpace.exp_hasFPowerSeriesOnBall, NormedSpace.expSeries_summable, Complex.starConvex_ofReal_slitPlane, BoundedContinuousFunction.coe_toContinuousMapStarₐ, cfcL_integrable, RCLike.toIsStrictOrderedModule, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, binomialSeries_radius_eq_one, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, HasDerivAt.comp_hasFDerivWithinAt, HasFDerivAt.restrictScalars, UpperHalfPlane.denom_cocycle_σ, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, ContinuousOn.cfc, HasStrictFDerivAt.list_prod', SchwartzMap.fourier_lineDerivOp_eq, Complex.starConvex_one_slitPlane, TemperedDistribution.instLineDerivLeftSMulReal, hasStrictDerivAt_exp_smul_const, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, norm_algebraMap_nnreal, ContinuousMultilinearMap.isEmbedding_restrictScalars, hasStrictDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_real_smul, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, ContinuousLinearMap.uniformContinuous_restrictScalars, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, hasStrictFDerivAt_multiset_prod, Polynomial.exists_aroots_norm_sub_lt_of_norm_coeff_sub_lt, fderivWithin_finset_prod, Matrix.PosSemidef.det_sqrt, convex_halfSpace_re_le, hasFDerivAt_ringInverse, MeasureTheory.convolution_precompR_apply, SchwartzMap.compSubConstCLM_apply, fderiv_smul, spectrum.gelfandTransform_eq, Unitary.norm_sub_one_lt_two_iff, Matrix.IsHermitian.charpoly_cfc_eq, NormedSpace.norm_expSeries_summable, spectrum.isCompact, CStarAlgebra.nnnorm_le_iff_of_nonneg, Polynomial.ofReal_eval, SchwartzMap.smulLeftCLM_sum, UpperHalfPlane.σ_mul, continuousOn_cfc_setProd, fderiv_mul_const', spectrum.spectralRadius_lt_of_forall_lt, ContinuousAlternatingMap.norm_restrictScalars, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, IsGreatest.norm_cfc, hasStrictFDerivAt_exp, IsSelfAdjoint.neg_algebraMap_norm_le_self, gelfandStarTransform_symm_apply, HasFDerivWithinAt.fun_smul, exists_isMinOn_norm_sub_smul, ContinuousLinearMap.continuous_restrictScalars, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, UpperHalfPlane.norm_σ, NormedSpace.expSeries_hasSum_exp, IsSelfAdjoint.val_re_map_spectrum, RCLike.conjCLE_coe, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, convex_halfSpace_im_gt, ContinuousMultilinearMap.restrictScalarsLinear_apply, fderiv_pow, IsGreatest.nnnorm_cfc, SchwartzMap.pairing_apply, HasFDerivAt.pow, spectrum.eventually_isUnit_resolvent, fderivWithin_inv', NormedSpace.norm_expSeries_summable_of_mem_ball', spectrum.gelfand_formula, HasStrictFDerivAt.cexp, IsSelfAdjoint.isConnected_spectrum_compl, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, HasFDerivWithinAt.mul_const, MeasureTheory.hasFDerivAt_convolution_right_with_param, fderiv_pow', fderiv_mul, SchwartzMap.postcompCLM_apply, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, gelfandTransform_map_star, NumberField.mixedEmbedding.convexBodySumFun_smul, continuousOn_cfc_nnreal, NumberField.mixedEmbedding.logMap_real_smul, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, NormedSpace.hasFPowerSeriesOnBall_exp_of_radius_pos, nnnorm_algebraMap, cfcHom_integral, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, spectrum.map_pow, fderiv_pow_ring, DifferentiableAt.fderiv_restrictScalars, selfAdjoint.unitarySelfAddISMul_coe, HasDerivWithinAt.complexToReal_fderiv, IsometricContinuousFunctionalCalculus.toNonUnital, fderivWithin_fun_mul', algebraMap_isometry, RCLike.ofReal_re_ax, CFC.exp_eq_normedSpace_exp, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, hasFDerivAt_list_prod', hasFDerivAt_integral_of_dominated_loc_of_lip', Real.spectralRadius_mem_spectrum, spectrum.spectralRadius_lt_of_forall_lt_of_nonempty, norm_eq_spectralNorm, fderiv_mul', HasFDerivWithinAt.cexp, IsSelfAdjoint.cfc_arg, SchwartzMap.compCLMOfAntilipschitz_apply, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', NormedSpace.norm_expSeries_summable_of_mem_ball, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, ContinuousLinearMap.coe_restrict_scalarsL', HasDerivAt.complexToReal_fderiv, inner_smul_real_right, hasFDerivAt_exp_smul_const', FormalMultilinearSeries.ofScalars_norm_le, SchwartzMap.postcompCLM_postcompCLM, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, SchwartzMap.smulLeftCLM_const, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, UpperHalfPlane.σ_num, hasFDerivWithinAt_pow', Continuous.cfc_nnreal_of_mem_nhdsSet, convex_halfSpace_im_lt, Subalgebra.spectrum_eq_of_isPreconnected_compl, HasFDerivAt.cexp, StarSubalgebra.spectrum_eq, UpperHalfPlane.coe_smul, fderivWithin_mul_const', fderivWithin_smul, cfcHom_real_eq_restrict, SchwartzMap.fourierMultiplierCLM_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, hasFDerivAt_list_prod_finRange', IsSelfAdjoint.spectrumRestricts, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, SchwartzMap.compSubConstCLM_zero, ordinaryHypergeometric_radius_top_of_neg_nat₂, StrongDual.extendRCLikeₗ_apply, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, CFC.log_monotoneOn, ContinuousMultilinearMap.uniformContinuous_restrictScalars, HasStrictFDerivAt.restrictScalars, hasDerivAt_exp_smul_const, NormedSpace.algebraMap_exp_comm, IsSelfAdjoint.toReal_spectralRadius_complex_eq_norm, CFC.monotone_rpow, fderivWithin_fun_pow, Matrix.instFiniteElemRealSpectrum, CFC.rpow_neg_one_eq_cfc_inv, RCLike.smul_im, HasFDerivAt.multiset_prod, SpectrumRestricts.real_iff, HasFDerivAt.mul_const, NormedSpace.expSeries_radius_eq_top, unitary.spectrum_subset_circle, ContinuousLinearMap.coe_restrictScalarsIsometry, nnnorm_cfc_le_iff, Polynomial.aeval_conj, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, CommCStarAlgebra.toStarModule, HasFDerivWithinAt.mul_const', HasDerivAt.comp_hasFDerivWithinAt_of_eq, spectrum.isClosed, fderiv_const_mul, RCLike.wInner_const_left, Real.spectralRadius_mem_spectrum_or, ContinuousMultilinearMap.norm_mkPiAlgebra, algebraMap_memℓp_infty, fderiv_pow_ring', QuasispectrumRestricts.real_iff, TemperedDistribution.instLineDerivSMulReal, spectrum.isBounded, ContinuousMultilinearMap.norm_restrictScalars, IsSelfAdjoint.sq_spectrumRestricts, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, HasFPowerSeriesAt.restrictScalars, continuous_cfcHomSuperset_left, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, ContDiffAt.restrictScalars_iteratedFDeriv, Continuous.cfc_of_mem_nhdsSet, Module.Dual.extendRCLikeₗ_apply, binomialSeries_radius_eq_top_of_nat, hasFDerivAt_pow, spectrum.hasDerivAt_resolvent, ContinuousOn.cfc_nnreal, NumberField.mixedEmbedding.norm_smul, PositiveLinearMap.gnsStarAlgHom_apply, cfc_integral, toMulAlgebraNorm_apply, ConvexOn.convex_re_epigraph, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, spectrum.nonempty, Subalgebra.spectrum_isBounded_connectedComponentIn, HasFDerivWithinAt.restrictScalars, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, nnnorm_cfc_nnreal_lt, SchwartzMap.fourierMultiplierCLM_ofReal, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, differentiableWithinAt_iff_restrictScalars, RCLike.ofReal_alg, HasFDerivAt.fun_pow', SchwartzMap.smulLeftCLM_add, HasMFDerivWithinAt.mul', CFC.rpow_le_rpow, ContinuousMultilinearMap.integral_apply, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, StrongDual.extendRCLikeₗᵢ_symm_apply, nnnorm_cfc_nnreal_le, RCLike.wInner_const_right, Continuous.cfc_nnreal, NormedSpace.exp_hasFPowerSeriesAt_zero, ContinuousOn.cfc_of_mem_nhdsSet, nnnorm_cfc_nnreal_le_iff, ContinuousAlternatingMap.continuous_restrictScalars, convex_halfSpace_re_ge, NormedRing.algEquivComplexOfComplete_symm_apply, HasFDerivAt.const_mul, DifferentiableWithinAt.restrictScalars_fderivWithin, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, StrongDual.extendRCLikeₗ_symm_apply, NormedSpace.norm_expSeries_summable', formalMultilinearSeries_geometric_eq_ofScalars, fderivWithin_multiset_prod, HasFDerivAt.mul, selfAdjoint.star_coe_unitarySelfAddISMul, UpperHalfPlane.σ_ofReal, convex_halfSpace_im_ge, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, hasStrictFDerivAt_pow', instRegularNormedAlgebra, convex_halfSpace_re_lt, NNReal.spectralRadius_mem_spectrum, SchwartzMap.compSubConstCLM_comp, CStarAlgebra.mul_star_le_algebraMap_norm_sq, ContinuousAlternatingMap.restrictScalarsLI_apply, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, RCLike.instStarModuleReal, SpectrumRestricts.spectralRadius_eq, upperHemicontinuous_spectrum_nnreal, norm_algebraMap, spectrum.exists_nnnorm_eq_spectralRadius_of_nonempty, StrongDual.extendRCLikeₗᵢ_apply, hasFDerivAt_exp_smul_const, Matrix.IsHermitian.instContinuousFunctionalCalculusIsClosedEmbedding, fderiv_finset_prod, hasStrictFDerivAt_list_prod_attach', HasFPowerSeriesWithinAt.restrictScalars, nnnorm_cfc_le, Unitization.nnreal_cfcₙ_eq_cfc_inr, hasStrictFDerivAt_ringInverse, integrable_cfc', CStarAlgebra.norm_le_iff_le_algebraMap, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, nnnorm_apply_le_nnnorm_cfc, CFC.log_smul', isConformalMap_complex_linear_conj, Continuous.cfc, Matrix.PosSemidef.inv_sqrt, IsSelfAdjoint.spectralRadius_eq_nnnorm, Matrix.IsHermitian.cfcHom_eq_cfcAux, hasStrictFDerivAt_finset_prod, Matrix.finite_real_spectrum, HasDerivWithinAt.comp_hasFDerivAt, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, SchwartzMap.tsupport_smulLeftCLM_subset, cfcₙHom_real_eq_restrict, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, ContinuousLinearMap.intervalIntegral_apply, LindemannWeierstrass.integral_exp_mul_eval, SchwartzMap.smulLeftCLM_neg, CFC.nnnorm_rpow, spectrum.differentiableOn_inverse_one_sub_smul, NormedRing.algEquivComplexOfComplete_apply, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, IsStarNormal.instContinuousFunctionalCalculus, inner_smul_real_left, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, CStarAlgebra.star_mul_le_algebraMap_norm_sq, ContinuousLinearMap.isEmbedding_restrictScalars, spectrum.hasFDerivAt_resolvent, apply_le_nnnorm_cfc_nnreal, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, AlgHom.coe_toContinuousLinearMap, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, SchwartzMap.integralCLM_apply, nnnorm_algebraMap', HasFDerivAt.list_prod', hasFDerivAt_pow', SchwartzMap.lineDerivOp_fourierInv_eq, cfcL_integral, StarSubalgebra.mem_spectrum_iff, ContinuousLinearMap.coe_restrictScalarsL, spectrum.algebraMap_eq_of_mem, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, NumberField.mixedEmbedding.convexBodyLT_convex, Real.nonempty_algEquiv_or, HasMFDerivAt.prod, norm_cfc_le, SchwartzMap.compCLM_apply, TemperedDistribution.fourierMultiplierCLM_apply_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, BoundedContinuousFunction.toContinuousMapStarₐ_apply_apply, CStarAlgebra.rpow_neg_one_le_one, ContinuousLinearMap.norm_restrictScalars, norm_smul_le, Polynomial.aeval_ofReal, ordinaryHypergeometricSeries_eq_zero_iff, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, IsSelfAdjoint.map_spectrum_real, spectrum.exp_mem_exp, Matrix.IsHermitian.cfcAux_id, ContinuousOn.cfc', RCLike.real_smul_ofReal, SchwartzMap.fderivCLM_fourier_eq, SchwartzMap.derivCLM_apply, hasDerivAt_exp_smul_const_of_mem_ball', SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.logMap_real, HasMFDerivWithinAt.mul, Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapₐ, Complex.log_eq_integral, Filter.Tendsto.cfc_nnreal, HasStrictFDerivAt.fun_smul, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, fderiv_fun_mul, HasFDerivAt.pow', HasStrictFDerivAt.pow', HasStrictFDerivAt.multiset_prod, hasFDerivAt_integral_of_dominated_of_fderiv_le, HasFDerivWithinAt.smul, nnnorm_cfc_lt_iff, StarSubalgebra.coe_isUnit, spectrum.spectralRadius_le_nnnorm, spectrum.isCompact_nnreal, HasStrictFDerivAt.mul_const', NumberField.mixedEmbedding.normAtPlace_smul, ModularForm.prod_fintype_slash, selfAdjoint.val_re_map_spectrum, fderivWithin_list_prod', Real.nonempty_algEquiv_or, Complex.starConvex_slitPlane, HasFDerivWithinAt.fun_mul', Matrix.IsHermitian.eigenvalues_mem_spectrum_real, BoundedContinuousFunction.toContinuousMapₐ_apply, NormedSpace.continuousOn_exp, hasStrictFDerivAt_list_prod, CFC.log_le_log, spectrum.resolvent_tendsto_cobounded, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, fderivWithin_pow_ring', Orientation.kahler_apply_apply, ModularForm.slash_def, norm_apply_le_norm_cfc, spectrum.instCompactSpaceNNReal, HasFDerivWithinAt.fun_pow', integrable_cfc, IsSelfAdjoint.toReal_spectralRadius_eq_norm, differentiableAt_iff_restrictScalars, NormedSpace.expSeries_radius_pos, SchwartzMap.tsupport_derivCLM_subset, nnnorm_cfc_nnreal_lt_iff, RCLike.conjAe_coe, fderivWithin_mul_const, NormedSpace.algebraMap_exp_comm_of_mem_ball, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, HasFDerivAt.mul_const', norm_cfcHom, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', CFC.norm_rpow, spectrum.exists_nnnorm_eq_spectralRadius, ordinaryHypergeometric_radius_top_of_neg_nat₁, Algebra.norm_smul_one_eq_norm, hasStrictDerivAt_exp_smul_const_of_mem_ball', Real.hasFDerivAt_fourierChar_neg_bilinear_right, MonotoneOn.nnnorm_cfc, RCLike.ofReal_im_ax, unitary.norm_sub_one_lt_two_iff, cfc_setIntegral', hasStrictFDerivAt_inv', hasFDerivAt_exp_smul_const_of_mem_ball', SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, SchwartzMap.fourier_fderivCLM_eq, hasStrictFDerivAt_exp_smul_const, dist_algebraMap, HasStrictFDerivAt.mul, gelfandTransform_isometry, Quaternion.coe_ofComplex, UpperHalfPlane.σ_conj, hasDerivAt_exp_smul_const', WeakDual.CharacterSpace.compContinuousMap_comp, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, continuousOn_cfc_nnreal_setProd, Complex.nonempty_algEquiv, norm_algebraMap', NumberField.mixedEmbedding.convexBodySum_convex, convex_halfSpace_im_le, nnnorm_cfcHom, integrableOn_cfc, WeakDual.CharacterSpace.equivAlgHom_symm_coe, continuousOn_cfc, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', spectrum.mem_resolventSet_of_norm_lt, SchwartzMap.smulLeftCLM_ofReal, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, CStarAlgebra.norm_mem_spectrum_of_nonneg, spectrum.hasDerivAt_resolvent_const_right, NormedSpace.expSeries_hasSum_exp_of_mem_ball', fderivWithin_pow, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, hasStrictFDerivAt_pow, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, CFC.log_algebraMap, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, UpperHalfPlane.denom_cocycle', CStarAlgebra.toStarModule, isConformalMap_complex_linear, SchwartzMap.smulLeftCLM_apply, Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero, ContinuousAlternatingMap.uniformContinuous_restrictScalars, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, HasFDerivWithinAt.mul', UpperHalfPlane.σ_eventuallyEq, TemperedDistribution.derivCLM_apply_apply, spectrum.hasDerivAt_resolvent_const_left, UpperHalfPlane.σ_mul_comm, HasFDerivAtFilter.restrictScalars, IsStarNormal.instIsometricContinuousFunctionalCalculus, RCLike.ofRealCLM_coe, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.integral_unitInterval_deriv_eq_sub, convex_halfSpace_re_gt, ContinuousAt.cfc_nnreal, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, fderivWithin_mul', hasStrictDerivAt_exp_smul_const_of_mem_ball, HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, tendsto_algebraMap_cobounded, Unitary.argSelfAdjoint_coe, ContinuousWithinAt.cfc, dist_algebraMap', hasFDerivAt_inv', RCLike.conj_smul, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, NormedSpace.expSeries_summable_of_mem_ball', Matrix.IsHermitian.mulVec_eigenvectorBasis, spectrum.map_polynomial_aeval, IsKrasner.of_completeSpace, Subalgebra.SeparatesPoints.rclike_to_real, BoundedContinuousFunction.separatesPoints_charPoly, ContinuousWithinAt.cfc_nnreal, CStarAlgebra.exists_sum_four_unitary, RCLike.real_smul_eq_coe_mul, RCLike.ofRealAm_coe, IsSelfAdjoint.le_algebraMap_norm_self, Complex.conjCAE_toAlgEquiv, fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, Complex.log_inv_eq_integral, HasMFDerivAt.mul', cfcHom_eq_of_isStarNormal, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, hasFDerivAt_exp, CFC.real_exp_eq_normedSpace_exp, CFC.continuousOn_rpow, upperHemicontinuous_spectrum, fderivWithin_pow_ring, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, HasFDerivAt.fun_mul', HasStrictFDerivAt.mul_const, spectrum.subset_circle_of_unitary, spectrum.subset_closedBall_norm, HasFTaylorSeriesUpToOn.restrictScalars, algebraMap_cobounded_le_cobounded, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, fderivWithin_restrictScalars_comp, hasDerivAt_exp_smul_const_of_mem_ball, HasFDerivAt.mul', Matrix.PosDef.posDef_sqrt, continuousFunctionalCalculus_map_id, Complex.exists_norm_sub_smul_one_eq_zero, hasFDerivAt_list_prod_attach', CFC.conjugate_rpow_neg_one_half, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, FormalMultilinearSeries.ofScalars_norm_eq_mul, CFC.log_smul, NormedSpace.expSeries_hasSum_exp_of_mem_ball, HasDerivWithinAt.comp_hasFDerivAt_of_eq, binomialSeries_radius_ge_one, fderivWithin_fun_mul, CFC.complex_exp_eq_normedSpace_exp, le_iff_norm_sqrt_mul_rpow, UpperHalfPlane.σ_denom, Unitary.path_apply, CStarAlgebra.nnnorm_mem_spectrum_of_nonneg, SpectrumRestricts.nnreal_iff_nnnorm, Unitary.spectrum_subset_circle, HasFDerivAt.smul, SchwartzMap.smulLeftCLM_smul, Matrix.IsHermitian.instContinuousFunctionalCalculus, cfc_setIntegral, ContinuousMultilinearMap.norm_mkPiAlgebraFin, ContinuousMultilinearMap.isUniformEmbedding_restrictScalars, hasFDerivAt_exp_of_mem_ball, SchwartzMap.laplacian_eq_fourierMultiplierCLM, SpectrumRestricts.nnreal_add, spectrum.mem_resolventSet_of_norm_lt_mul, norm_cfc_lt, ContinuousMultilinearMap.continuous_restrictScalars, cfc_integral', HasCompactSupport.hasFDerivAt_convolution_left, NumberField.mixedEmbedding.convexBodyLT'_convex, selfAdjoint.expUnitary_coe, fderivWithin_mul, TemperedDistribution.smulLeftCLM_apply_apply, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, FormalMultilinearSeries.ofScalars_norm, HasFDerivWithinAt.fun_mul, HasStrictFDerivAt.smul, HasStrictFDerivAt.finset_prod, Nonneg.instIsometricContinuousFunctionalCalculus, hasFDerivAt_integral_of_dominated_loc_of_lip, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Complex.conjCAE_toLinearMap, ModularForm.slash_apply, le_iff_norm_sqrt_mul_sqrt_inv, HasFDerivWithinAt.list_prod', fderiv_inv', unitary.spectrum_subset_slitPlane_iff_norm_lt_two, fderivWithin_pow', UpperHalfPlane.petersson_slash, hasFDerivAt_finset_prod
toNormedSpace 📖	CompOp	734 math math: HasStrictDerivAt.fun_pow', cfcₙL_integral, HasStrictFDerivAt.fun_mul', unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, HasMFDerivAt.mul, contDiffAt_prod', ContinuousLinearMap.mulLeftRight_isBoundedBilinear, RCLike.map_apply, Meromorphic.mul, RCLike.ofRealCLM_apply, Ideal.toCharacterSpace_apply_eq_zero_of_mem, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, RCLike.reCLM_apply, NormedSpace.hasFPowerSeriesAt_exp_zero_of_radius_pos, AnalyticOn.aeval_polynomial, derivWithin_smul, Differentiable.fun_div, hasStrictFDerivAt_list_prod_finRange', Finset.analyticOnNhd_prod, ContMDiffMap.coeFnAlgHom_apply, MDifferentiableAt.prod, iteratedDerivWithin_const_mul_field, HasFDerivWithinAt.pow, ContDiff.div_const, HasDerivWithinAt.div_const, fderivWithin_fun_smul, RCLike.ofRealLI_apply, hasFDerivAt_multiset_prod, DifferentiableAt.mul, SchwartzMap.pairing_apply_apply, norm_iteratedFDerivWithin_smul_le, Meromorphic.fun_inv, derivWithin_mul_const, logDeriv_comp, HasStrictDerivAt.pow, DifferentiableAt.div, ContDiffWithinAt.cexp, Function.HasTemperateGrowth.fun_pow, HasDerivAtFilter.comp_hasFDerivAtFilter, MeromorphicAt.finsum, HasDerivWithinAt.fun_div, RCLike.conjCLE_norm, ordinaryHypergeometric_radius_top_of_neg_nat₃, DifferentiableAt.fun_inv, AnalyticWithinAt.fun_zpow, ContinuousLinearMap.integral_apply, HasDerivAt.fun_finset_prod, norm_iteratedFDeriv_mul_le, fderivWithin_fun_pow', deriv_fun_finset_prod, analyticOnNhd_inverse, Module.Dual.extendRCLikeₗ_symm_apply, SchwartzMap.lineDerivOp_fourier_eq, fderiv_multiset_prod, RCLike.map_same_eq_id, HasFDerivAt.fun_mul, deriv_mul_const_field, MeromorphicAt.mul, deriv_fun_pow', MDifferentiableWithinAt.mul, intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivAt, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiff.pow, SchwartzMap.bilinLeftCLM_apply, HasDerivAt.comp_hasFDerivAt_of_eq, deriv_mul_const, Differentiable.fun_inv, HasStrictDerivAt.pow', MeasureTheory.integral_const_mul, iteratedDeriv_div_const, differentiableWithinAt_inv, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, analyticAt_iff_analytic_mul, DifferentiableOn.fun_mul, AnalyticOnNhd.eval_linearMap', HasStrictFDerivAt.mul', fderiv_fun_pow, hasStrictFDerivAt_exp_smul_const_of_mem_ball', DifferentiableWithinAt.inverse, fderiv_fun_smul, AnalyticOn.fun_inv, MeasureTheory.integral_div, HasStrictFDerivAt.pow, derivWithin_fun_mul, deriv.scomp_of_eq, HasStrictFDerivAt.const_mul, integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable, HasFDerivAt.finset_prod, Meromorphic.finsum, Manifold.IsImmersionAtOfComplement.ofOpen, derivWithin.scomp_of_eq, fderiv_fun_pow', derivWithin.scomp, gelfandStarTransform_naturality, HasFDerivWithinAt.const_mul, cfcₙ_integral, ContinuousMultilinearMap.norm_mkPiAlgebra_le, RCLike.reCLM_norm, cfcₙ_setIntegral, formalMultilinearSeries_geometric_apply_norm_le, DifferentiableAt.fun_finset_prod, ordinaryHypergeometricSeries_radius_eq_one, MeromorphicAt.inv_iff, HasFDerivWithinAt.mul, fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, DifferentiableOn.mul, AnalyticOn.pow, RCLike.conjCLE_apply, HasDerivAt.fun_pow', isScalarTower_closedBall_closedBall_closedBall, HasFDerivAt.fun_smul, NormedSpace.exp_hasFPowerSeriesOnBall, isScalarTower_sphere_closedBall_closedBall, iteratedDerivWithin_mul_const, DifferentiableAt.fun_div, binomialSeries_radius_eq_one, ContDiffAt.inv, HasDerivAt.comp_hasFDerivWithinAt, deriv_fun_mul, ContDiffOn.pow, MeasureTheory.integral_Ioi_deriv_mul_eq_sub, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, iteratedDeriv_smul_const, HasStrictFDerivAt.list_prod', Meromorphic.prod, SchwartzMap.fourier_lineDerivOp_eq, hasStrictDerivAt_exp_smul_const, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeromorphicOn.prod, HasDerivWithinAt.comp, hasStrictDerivAt_exp_smul_const', iteratedDeriv_const_mul, MDifferentiableAt.mul, SchwartzMap.smulLeftCLM_real_smul, Differentiable.cexp, HasStrictDerivAt.div, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Meromorphic.div, MDifferentiableAt.pow, MeasureTheory.integral_Ioi_mul_deriv_eq_deriv_mul, Differentiable.pow, deriv_fun_smul, HasStrictDerivAt.mul, hasStrictFDerivAt_multiset_prod, ContDiff.cexp, fderivWithin_finset_prod, HasDerivAt.pow, integral_smul_const, HasStrictDerivAt.const_mul, intervalIntegral.integral_mul_deriv_eq_deriv_mul, hasFDerivAt_ringInverse, DifferentiableWithinAt.mul, fderiv_smul, HasDerivAt.fun_pow, ContDiffAt.div_const, HasDerivWithinAt.fun_pow', DifferentiableWithinAt.const_mul, differentiableWithinAt_pow, DifferentiableWithinAt.fun_pow, contDiffOn_prod', FiniteDimensional.rclike_to_real, ContDiffAt.pow, HasDerivWithinAt.fun_finset_prod, SchwartzMap.smulLeftCLM_sum, DifferentiableAt.inverse, cfcₙHom_integral, fderiv_mul_const', hasStrictFDerivAt_exp, AnalyticOn.fun_zpow, deriv_const_mul_field', RCLike.conjLIE_apply, deriv_fun_div, HasFDerivWithinAt.fun_smul, ContinuousMapZero.integral_apply, Complex.differentiable_exp, RCLike.imLm_coe, Meromorphic.zpow, Finset.analyticWithinAt_fun_prod, contDiffWithinAt_prod', ContinuousLinearMap.lsmul_flip_inj, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, contDiffOn_prod, derivWithin_fun_div, HasDerivAt.comp, WeakDual.CharacterSpace.homeoEval_naturality, RCLike.conjCLE_coe, HasDerivWithinAt.mul, Units.instIsManifoldModelWithCornersSelf, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, deriv_pow, analyticAt_smul, fderiv_pow, AnalyticWithinAt.inv, SchwartzMap.pairing_apply, HasFDerivAt.pow, NormedSpace.analyticAt_exp_of_mem_ball, Finset.analyticWithinAt_prod, fderivWithin_inv', derivWithin_div_const, iteratedFDerivWithin_smul_const_apply, HasStrictFDerivAt.cexp, AnalyticOnNhd.eval_linearMap, RCLike.rank_le_two, FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto, RCLike.reCLM_coe, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable, HasFDerivWithinAt.mul_const, iteratedDerivWithin_smul_const, isScalarTower_sphere_sphere_sphere, DifferentiableOn.inv, MeasureTheory.integral_deriv_mul_eq_sub, fderiv_pow', fderiv_mul, NormedSpace.hasFPowerSeriesOnBall_exp_of_radius_pos, cfcHom_integral, MeromorphicAt.fun_pow, Differentiable.fun_pow, MeromorphicOn.fun_pow, fderiv_pow_ring, ContinuousLinearMap.lsmul_apply, MeromorphicOn.div, deriv_const_mul_field, integral_conj, Differentiable.inverse, IsometricContinuousFunctionalCalculus.toNonUnital, DifferentiableOn.div_const, AlgHom.instContinuousLinearMapClassOfAlgHomClass, fderivWithin_fun_mul', analyticAt_iff_analytic_fun_mul, hasFDerivAt_list_prod', ContDiffWithinAt.mul, fderiv_mul', Units.instLieGroupModelWithCornersSelf, HasFDerivWithinAt.cexp, HasStrictDerivAt.mul_const, SchwartzMap.smulRightCLM_apply_apply, DifferentiableAt.const_mul, iteratedDeriv_mul, HasStrictDerivAt.cexp, intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDeriv_right, DifferentiableWithinAt.fun_mul, AnalyticOn.zpow_nonneg, hasFDerivAt_exp_smul_const', FormalMultilinearSeries.ofScalars_norm_le, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, SchwartzMap.smulLeftCLM_const, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, MDifferentiableOn.prod, Complex.differentiableAt_exp, HasStrictDerivAt.fun_finset_prod, hasFDerivWithinAt_pow', isScalarTower_closedBall_ball_ball, HasFDerivAt.cexp, AnalyticWithinAt.aeval_polynomial, norm_iteratedFDerivWithin_prod_le, ContDiffWithinAt.inv, HasStrictDerivAt.comp_of_eq, AnalyticOnNhd.aeval_mvPolynomial, fderivWithin_mul_const', fderivWithin_smul, AnalyticWithinAt.fun_inv, HasStrictDerivAt.fun_div, derivWithin_comp_of_eq, SchwartzMap.fourierMultiplierCLM_apply, hasFDerivAt_list_prod_finRange', MeromorphicOn.inv_iff, ordinaryHypergeometric_radius_top_of_neg_nat₂, DifferentiableWithinAt.div_const, StrongDual.extendRCLikeₗ_apply, HasFDerivWithinAt.smul_const, SchwartzMap.fourierInv_lineDerivOp_eq, RCLike.finrank_le_two, DifferentiableAt.inv, HasDerivWithinAt.comp_hasDerivAt_of_eq, AnalyticAt.fun_zpow, DifferentiableWithinAt.inv, deriv_comp, derivWithin_cexp, differentiableOn_pow, hasDerivAt_exp_smul_const, DifferentiableAt.fun_pow, derivWithin_mul_const_field, logDeriv_apply, DifferentiableWithinAt.fun_div, fderivWithin_fun_pow, RCLike.sqrt_map, deriv.scomp, HasFDerivAt.multiset_prod, Differentiable.mul_const, HasFDerivAt.mul_const, NormedSpace.expSeries_radius_eq_top, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, HasFDerivWithinAt.mul_const', HasDerivAt.comp_hasFDerivWithinAt_of_eq, Complex.contDiff_exp, fderiv_const_mul, contDiffAt_inv, ContinuousMultilinearMap.norm_mkPiAlgebra, contDiffAt_prod, fderiv_pow_ring', Function.HasTemperateGrowth.pow, WeakDual.CharacterSpace.compContinuousMap_apply, HasDerivAt.fun_div, contDiff_smul_const, deriv_cexp, DifferentiableWithinAt.finset_prod, HasDerivWithinAt.const_mul, Module.Dual.extendRCLikeₗ_apply, binomialSeries_radius_eq_top_of_nat, HasDerivWithinAt.div, hasFDerivAt_pow, MeromorphicOn.inv, spectrum.hasDerivAt_resolvent, deriv_smul, cfc_integral, RCLike.realLinearIsometryEquiv_symm_apply, AnalyticAt.aeval_polynomial, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, derivWithin_fun_smul, HasFDerivAt.fun_pow', isScalarTower_sphere_sphere_closedBall, SchwartzMap.smulLeftCLM_add, HasMFDerivWithinAt.mul', MeromorphicOn.logDeriv, ContinuousMultilinearMap.integral_apply, RCLike.complexLinearIsometryEquiv_symm_apply, Meromorphic.fun_zpow, AnalyticOn.inv, Meromorphic.fun_mul, intervalIntegral.integral_deriv_mul_eq_sub, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, StrongDual.extendRCLikeₗᵢ_symm_apply, HasFDerivAt.smul_const, NormedSpace.exp_hasFPowerSeriesAt_zero, isScalarTower_sphere_sphere_ball, AnalyticAt.fun_mul, Function.HasTemperateGrowth.fun_mul, DifferentiableAt.mul_const, HasFDerivAt.const_mul, Meromorphic.pow, formalMultilinearSeries_geometric_apply_norm, StrongDual.extendRCLikeₗ_symm_apply, DifferentiableOn.fun_inv, AnalyticOnNhd.eval_polynomial, fderivWithin_multiset_prod, HasFDerivAt.mul, MDifferentiable.mul, hasFDerivAt_exp_zero, MeromorphicOn.fun_zpow, contDiffOn_inv, MeromorphicAt.pow, hasStrictFDerivAt_pow', isScalarTower_sphere_closedBall_ball, AnalyticWithinAt.div_const, DifferentiableWithinAt.pow, instRegularNormedAlgebra, MeromorphicOn.zpow, intervalIntegral.integral_deriv_mul_eq_sub_of_hasDeriv_right, HasDerivWithinAt.fun_mul, Manifold.IsImmersionOfComplement.ofOpen, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', AnalyticOnNhd.mul, HasDerivWithinAt.pow', AnalyticOnNhd.fun_zpow, MeromorphicAt.prod, DifferentiableOn.finset_prod, AnalyticWithinAt.pow, AnalyticWithinAt.fun_zpow_nonneg, StrongDual.extendRCLikeₗᵢ_apply, DifferentiableOn.fun_finset_prod, hasFDerivAt_exp_smul_const, AnalyticOn.zpow, fderiv_finset_prod, hasStrictFDerivAt_list_prod_attach', hasFPowerSeriesOnBall_inv_one_sub, hasFPowerSeriesOnBall_inverse_one_sub, RCLike.ofRealCLM_norm, HasStrictDerivAt.comp, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, DifferentiableOn.fun_pow, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, HasDerivAtFilter.comp_of_eq, AnalyticOnNhd.zpow, fderiv_smul_const, hasStrictFDerivAt_finset_prod, HasDerivWithinAt.comp_hasFDerivAt, MeromorphicAt.fun_prod, DifferentiableWithinAt.div, SchwartzMap.tsupport_smulLeftCLM_subset, iteratedFDeriv_smul_const_apply, AnalyticAt.fun_pow, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, differentiable_pow, DifferentiableOn.div, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, Manifold.IsImmersionAtOfComplement.of_opens, Differentiable.const_mul, MeromorphicAt.fun_mul, iteratedDerivWithin_mul, SchwartzMap.smulLeftCLM_neg, differentiableOn_inverse, spectrum.differentiableOn_inverse_one_sub_smul, derivWithin_comp, RCLike.reLm_coe, hasStrictFDerivAt_exp_zero_of_radius_pos, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, spectrum.hasFDerivAt_resolvent, deriv_comp_of_eq, contDiff_prod', HasDerivAt.comp_hasDerivWithinAt, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, integral_coe_re_add_coe_im, AlgHom.coe_toContinuousLinearMap, hahnEmbedding_isOrderedModule_rat, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, HasDerivAt.const_mul, AnalyticWithinAt.div, HasFDerivAt.list_prod', AnalyticWithinAt.fun_pow, norm_iteratedFDeriv_prod_le, hasFDerivAt_pow', SchwartzMap.lineDerivOp_fourierInv_eq, Finset.analyticAt_prod, ContinuousLinearMap.opNorm_lsmul_le, WeakDual.CharacterSpace.norm_le_norm_one, cfcL_integral, hasStrictFDerivAt_exp_zero, formalMultilinearSeries_geometric_radius, ContDiff.inv, MeromorphicOn.fun_mul, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, derivWithin_fun_finset_prod, DifferentiableOn.pow, iteratedDerivWithin_smul, HasDerivWithinAt.fun_pow, HasDerivWithinAt.finset_prod, HasMFDerivAt.prod, AnalyticOnNhd.zpow_nonneg, TemperedDistribution.fourierMultiplierCLM_apply_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, analyticOn_inv, HasDerivAt.mul, AnalyticOnNhd.fun_pow, intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivAt, AnalyticWithinAt.zpow_nonneg, instSMulCommClass_sphere_ball_ball, AnalyticOn.div, Finset.analyticOn_fun_prod, AnalyticAt.zpow_nonneg, Differentiable.fun_finset_prod, deriv_smul_const, contDiff_mul, deriv_finset_prod, deriv_div, AnalyticOnNhd.div, differentiableWithinAt_inverse, Meromorphic.logDeriv, DifferentiableOn.inverse, SchwartzMap.fderivCLM_fourier_eq, RCLike.map_nonneg_iff, AnalyticOn.fun_zpow_nonneg, AnalyticWithinAt.zpow, hasDerivAt_exp_smul_const_of_mem_ball', HasDerivWithinAt.mul_const, deriv_const_mul, HasDerivWithinAt.cexp, contDiffWithinAt_prod, contDiff_smul, derivWithin_fun_pow, HasMFDerivWithinAt.mul, AnalyticAt.fun_inv, DifferentiableOn.cexp, HasStrictFDerivAt.fun_smul, iteratedDeriv_mul_const_field, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, fderiv_fun_mul, HasFDerivAt.pow', HasStrictFDerivAt.pow', MeromorphicOn.fun_div, HasStrictFDerivAt.multiset_prod, HasDerivAt.div_const, HasFDerivWithinAt.smul, HasDerivAt.cexp, AnalyticAt.fun_div, HasStrictFDerivAt.mul_const', HasDerivAt.div, HasDerivWithinAt.pow, differentiableAt_pow, AnalyticOnNhd.div_const, AlgHom.toContinuousLinearMap_norm, ContDiffWithinAt.pow, Meromorphic.fun_prod, Differentiable.div_const, fderivWithin_list_prod', HasFDerivWithinAt.fun_mul', ContDiffOn.div_const, MeromorphicAt.zpow, fderivWithin_smul_const, NormedSpace.continuousOn_exp, hasStrictFDerivAt_list_prod, DifferentiableWithinAt.fun_finset_prod, analyticAt_finprod, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, fderivWithin_pow_ring', DifferentiableAt.cexp, ContDiffAt.cexp, MeromorphicOn.pow, RCLike.imCLM_coe, DifferentiableOn.const_mul, Meromorphic.finprod, isScalarTower_sphere_ball_ball, HasFDerivWithinAt.fun_pow', AnalyticAt.div_const, MeromorphicAt.div, NormedSpace.expSeries_radius_pos, Function.HasTemperateGrowth.mul, MDifferentiableOn.mul, analyticAt_mul, fderivWithin_mul_const, Manifold.IsImmersionOfComplement.id, derivWithin_finset_prod, derivWithin_div, ContDiffOn.inv, HasFDerivAt.mul_const', RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, integral_ofReal, DifferentiableOn.mul_const, analyticAt_inv, AnalyticAt.aeval_mvPolynomial, contDiffAt_ringInverse, HasDerivAt.pow', Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', ordinaryHypergeometric_radius_top_of_neg_nat₁, Units.contMDiff_val, AnalyticOnNhd.aeval_polynomial, hasStrictDerivAt_exp_smul_const_of_mem_ball', Differentiable.fun_mul, MeromorphicAt.inv, DifferentiableWithinAt.cexp, MeromorphicOn.fun_inv, analyticAt_inverse_one_sub, Meromorphic.inv, norm_iteratedFDerivWithin_mul_le, HasStrictDerivAt.div_const, HasStrictDerivAt.fun_mul, deriv_fun_pow, cfc_setIntegral', DifferentiableAt.div_const, AnalyticOnNhd.fun_zpow_nonneg, cfcₙ_setIntegral', hasStrictFDerivAt_inv', hasFDerivAt_exp_smul_const_of_mem_ball', SchwartzMap.smulLeftCLM_sub, SchwartzMap.smulLeftCLM_apply_apply, analyticAt_inv_one_sub, Differentiable.mul, iteratedDerivWithin_const_mul, iteratedDeriv_const_mul_field, SchwartzMap.fourier_fderivCLM_eq, intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivWithinAt, hasStrictFDerivAt_exp_smul_const, AnalyticAt.mul, derivWithin_mul, HasStrictFDerivAt.mul, AnalyticAt.div, MeromorphicAt.fun_zpow, DifferentiableAt.finset_prod, DifferentiableOn.fun_div, hasDerivAt_exp_smul_const', WeakDual.CharacterSpace.compContinuousMap_comp, HasStrictDerivAt.finset_prod, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, MeasureTheory.integral_mul_deriv_eq_deriv_mul_of_integrable, HasDerivAt.comp_hasDerivWithinAt_of_eq, WeakDual.CharacterSpace.equivAlgHom_symm_coe, HasDerivAtFilter.comp, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', HasDerivAt.comp_of_eq, Differentiable.finset_prod, MeromorphicOn.mul, HasStrictFDerivAt.smul_const, setIntegral_re_add_im, SchwartzMap.smulLeftCLM_ofReal, norm_iteratedFDeriv_smul_le, Manifold.IsImmersionOfComplement.of_opens, HasDerivAt.finset_prod, MeromorphicAt.fun_div, fderivWithin_pow, hasFDerivAt_exp_zero_of_radius_pos, AnalyticAt.fun_zpow_nonneg, hasStrictFDerivAt_pow, HasDerivWithinAt.comp_of_eq, AnalyticOn.eval_polynomial, iteratedDeriv_fun_mul, ContinuousLinearMap.opNorm_lsmul, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, AnalyticOn.div_const, isScalarTower_closedBall_closedBall_ball, analyticOnNhd_inv, DifferentiableAt.pow, MeromorphicOn.fun_prod, SchwartzMap.smulLeftCLM_apply, MeromorphicOn.finsum, MeasureTheory.integral_Iic_mul_deriv_eq_deriv_mul, DifferentiableWithinAt.fun_inv, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, MeasureTheory.integral_mul_deriv_eq_deriv_mul, HasFDerivWithinAt.mul', instNonemptySeedRatReal, AnalyticAt.pow, integral_re, DifferentiableAt.fun_mul, spectrum.hasDerivAt_resolvent_const_left, deriv_mul, NormedSpace.exp_analytic, differentiableAt_inv, deriv_pow', AnalyticAt.inv, AnalyticOnNhd.pow, RCLike.ofRealCLM_coe, DifferentiableWithinAt.mul_const, HasDerivWithinAt.comp_hasDerivAt, fderivWithin_mul', hasStrictDerivAt_exp_smul_const_of_mem_ball, HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivWithinAt, Meromorphic.fun_div, Meromorphic.fun_pow, hasFDerivAt_inv', HasDerivAt.fun_mul, WeakDual.CharacterSpace.exists_apply_eq_zero, WeakDual.CharacterSpace.compContinuousMap_id, differentiableAt_inverse, AnalyticOn.fun_pow, integral_re_add_im, ContDiffOn.mul, AnalyticOn.mul, fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', ContDiffOn.cexp, HasMFDerivAt.mul', MDifferentiableWithinAt.pow, hasFDerivAt_exp, deriv_mul_const_field', WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, fderivWithin_pow_ring, Differentiable.inv, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, derivWithin_pow, HasFDerivAt.fun_mul', HasStrictFDerivAt.mul_const, MeromorphicAt.fun_inv, derivWithin_smul_const, derivWithin_const_mul_field, AnalyticOnNhd.fun_inv, RCLike.span_one_I, MDifferentiable.prod, hasDerivAt_exp_smul_const_of_mem_ball, analyticAt_inverse, MeasureTheory.integral_Iic_deriv_mul_eq_sub, HasFDerivAt.mul', hasFDerivAt_list_prod_attach', iteratedDerivWithin_mul_const_field, AnalyticAt.zpow, Finset.analyticAt_fun_prod, FormalMultilinearSeries.ofScalars_norm_eq_mul, AnalyticOnNhd.eval_continuousLinearMap, HasDerivWithinAt.comp_hasFDerivAt_of_eq, MDifferentiableOn.pow, binomialSeries_radius_ge_one, fderivWithin_fun_mul, Differentiable.div, deriv_div_const, MeromorphicAt.finprod, MeromorphicOn.finprod, ContDiffWithinAt.div_const, RCLike.realLinearIsometryEquiv_apply, HasFDerivAt.smul, SchwartzMap.smulLeftCLM_smul, one_le_formalMultilinearSeries_geometric_radius, RCLike.imCLM_apply, cfc_setIntegral, differentiableOn_inv, ContinuousMultilinearMap.norm_mkPiAlgebraFin, hasFDerivAt_exp_of_mem_ball, MeasureTheory.integral_mul_const, contDiff_prod, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, derivWithin_fun_pow', integral_im, cfc_integral', fderivWithin_mul, intervalIntegral.integral_const_mul, TemperedDistribution.smulLeftCLM_apply_apply, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, Finset.analyticOnNhd_fun_prod, ContDiff.mul, MDifferentiableWithinAt.prod, Finset.analyticOn_prod, FormalMultilinearSeries.ofScalars_norm, HasFDerivWithinAt.fun_mul, derivWithin_pow', HasStrictFDerivAt.smul, RCLike.complexLinearIsometryEquiv_apply, HasStrictFDerivAt.finset_prod, MDifferentiable.pow, AnalyticWithinAt.mul, AnalyticOnNhd.inv, hasStrictFDerivAt_exp_smul_const_of_mem_ball, HasDerivAt.mul_const, derivWithin_const_mul, ContDiffAt.mul, HasFDerivWithinAt.list_prod', fderiv_inv', cfcₙ_integral', fderivWithin_pow', hasFDerivAt_finset_prod, HasStrictDerivAt.fun_pow

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
norm_smul_le 📖	mathematical	—	Real Real.instLE Norm.norm SeminormedRing.toNorm Algebra.toSMul Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing toAlgebra Real.instMul NormedField.toNorm	—	—

NormedField

Definitions

Name	Category	Theorems
toNormedSpace 📖	CompOp	1676 math math: MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact, Polynomial.fderiv, IsLocalMaxOn.fderivWithin_nonpos, hasFDerivAt_iff_hasDerivAt, MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnreal, iteratedDeriv_scomp_two, Real.differentiableOn_arcosh, Real.hasDerivAt_arccos, Differentiable.arsinh, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, MeasureTheory.tendsto_integral_thickenedIndicator_of_isClosed, MeasureTheory.integral_eq_iff_of_ae_le, Polynomial.differentiableWithinAt, ContDiffAt.csin, fun_meromorphicOrderAt_pow_id_sub_const, DifferentiableOn.zpow, MeasureTheory.setIntegral_tilted, Seminorm.isBounded_const, isConformalMap_conj, HasDerivWithinAt.clog_real, ContinuousMultilinearMap.norm_mkPiRing, NormedSpace.isBounded_polar_of_mem_nhds_zero, meromorphicNFOn_mul_iff_right_of_analyticOnNhd, differentiableAt_comp_neg, Real.iteratedDerivWithin_cos_Ioo, deriv_exp, HasDerivAt.const_rpow, LeftInvariantDerivation.lift_zero, Real.differentiable_arctan, contDiffOn_nat_succ_iff_contDiffOn_one_iteratedDerivWithin, Real.differentiableAt_mulExpNegMulSq, Complex.restrictScalars_one_smulRight', MeasureTheory.setIntegral_nonpos_ae, Complex.meromorphicOrderAt_canonicalFactor, fun_meromorphicOrderAt_div, IsSelfAdjoint.quasispectrumRestricts, ContDiffOn.cos, LinearMap.coe_toSeminorm, HasStrictDerivAt.to_localInverse, RCLike.ofRealCLM_apply, deriv_arctan, Real.iteratedDeriv_odd_cos, Real.hasFDerivAt_fourierChar_neg_bilinear_left, Real.differentiableAt_arcsin, Complex.linearEquiv_det_conjLIE, LeftInvariantDerivation.leibniz, DifferentiableWithinAt.log, ConvexOn.le_slope_of_hasDerivAt, HasStrictDerivAt.rpow, smooth_barycentric_coord, StrictConvexOn.slope_lt_leftDeriv, ContDiffOn.rpow_const_of_le, Real.contDiffOn_log, Differentiable.fun_div, Complex.iteratedDeriv_even_cosh, ConvexOn.rightDeriv_le_slope_of_mem_interior, Function.FactorizedRational.divisor, hasDerivAt_sqrt_mul_log, StrongDual.norm_extendRCLike, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, ContinuousLinearMap.opNorm_bound_of_ball_bound, Complex.ofRealCLM_coe, MeromorphicAt.analyticAt, RightDerivMeasurableAux.D_subset_differentiable_set, MeromorphicOn.divisor_fun_smul, Real.deriv_negMulLog, meromorphicOrderAt_const_ofNat, Real.analyticOn_cos, Polynomial.derivWithin_aeval, complexOfReal_hasDerivWithinAt, AffineMap.hasDerivAtFilter, Complex.analyticAt_cosh, MeasureTheory.exists_notMem_null_le_integral, Real.contDiffAt_arcosh, RCLike.ofRealLI_apply, differentiableAt_zpow, Real.nnnorm_deriv_mulExpNegMulSq_le_one, derivWithin_id', Real.deriv_binEntropy, not_differentiableAt_of_local_left_inverse_hasDerivAt_zero, HasDerivWithinAt.liminf_right_slope_le, smoothSheafCommRing.nonunits_stalk, MeasureTheory.convolution_mul, Complex.ofRealLI_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, DifferentiableOn.sqrt, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, deriv_mem_iff, not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioi, Real.analyticOnNhd_sin, HasDerivWithinAt.cosh, Real.hasStrictDerivAt_rpow_const_of_ne, StrongDual.polarSubmodule_eq_setOf, DifferentiableAt.div, ContinuousLinearMap.hasDerivAtFilter, StrictConvexOn.deriv_lt_slope, HasDerivWithinAt.complexToReal_fderiv', Differentiable.cosh, mdifferentiableAt_iff_localFrame_coeff, OpenPartialHomeomorph.hasDerivAt_symm, PMF.bernoulli_expectation, ContDiffBumpBase.smooth, Real.analyticOn_cosh, continuousOn_dslope, StrictConcaveOn.lt_slope_of_hasDerivAt, ContDiffOn.ccosh, Module.Dual.extendRCLikeₗ_symm_apply, ValueDistribution.logCounting_zero_mul_le, Complex.analyticOn_sin, isClosedEmbedding_cfcₙAux, LeftInvariantDerivation.coe_derivation, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, DifferentiableWithinAt.sqrt, LinearMap.adjoint_innerₛₗ_apply, Real.differentiable_sinh, hasDerivAt_neg', AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ContinuousLinearMap.toBilinForm_apply, iteratedDerivWithin_comp_two, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, expNegInvGlue.not_analyticAt_zero, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, LeftInvariantDerivation.left_invariant', StrictConcaveOn.slope_lt_rightDeriv, derivWithin_fderivWithin, ContDiffOn.cosh, StrongDual.norm_extendRCLike_bound, Real.deriv_log, ContDiff.differentiable_deriv_two, StrictConvexOn.rightDeriv_lt_slope, derivWithin_arctan, FormalMultilinearSeries.derivSeries_coeff_one, Complex.ofRealCLM_norm, HasDerivAt.comp_ofReal, rotation_injective, IsConformalMap.is_complex_or_conj_linear, AkraBazziRecurrence.isBigO_apply_r_sub_b, iteratedDeriv_pow, AffineMap.hasDerivWithinAt, LeftInvariantDerivation.left_invariant, Complex.iteratedDeriv_odd_sinh, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, MeasureTheory.toReal_rnDeriv_tilted_left, meromorphicOrderAt_mul, HasStrictDerivAt.of_local_left_inverse, Complex.convexHull_reProdIm, Complex.conjLIE_apply, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, CPolynomialOn.iterated_deriv, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, Bundle.Trivialization.localFrame_coeff_apply_of_notMem_baseSet, hasDerivAt_exp_zero_of_radius_pos, Real.differentiableOn_log, Set.OrdConnected.image_deriv, Real.iteratedDeriv_even_cosh, iteratedDeriv_comp_const_mul, VectorField.mlieBracket_smul_left, Complex.meromorphicOn_canonicalFactor, Real.differentiableOn_arcsin, Complex.hasStrictFDerivAt_exp_real, NumberField.natAbs_discr_eq_natAbs_discr_pow_mul_natAbs_discr_pow, DiffContOnCl.inv, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, ContDiffWithinAt.cosh, StrictConvexOn.strictMonoOn_deriv, DifferentiableAt.zpow, Real.contDiffAt_tan, Real.hasDerivAt_mul_log, derivWithin_cosh, fderivWithin_sinh, iter_deriv_zpow', ValueDistribution.logCounting_pow_top, MeasureTheory.integral_tilted, Real.deriv_arccos, Real.hasStrictDerivAt_sinh, deriv_conj_conj, ConvexOn.univ_sSup_of_countable_affine_eq, contDiff_nat_succ_iff_contDiff_one_iteratedDeriv, ContDiffOn.sqrt, Real.analyticWithinAt_sinh, cfcₙHom_nnreal_eq_restrict, IsLocalFrameOn.coeff_apply_of_mem, OpenPartialHomeomorph.contDiffAt_symm_deriv, Real.contDiffAt_rpow_const_of_le, deriv_sqrt_mul_log, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, Bundle.Trivialization.localFrame_coeff_congr, StrictConcaveOn.slope_lt_derivWithin, differentiable_descPochhammer_eval, innerₛₗ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, iteratedDeriv_scomp_three, smoothSheafCommRing.instLocalRing_stalk, Real.analyticAt_cos, rotation_apply, toMatrix_rotation, Differentiable.zpow, Real.differentiableWithinAt_arccos_Ici, Real.sinc_eq_dslope, MeromorphicOn.divisor_pow, AnalyticOn.rexp, deriv.log, AnalyticAt.rexp, ConcaveOn.slope_le_of_hasDerivAt, deriv_fun_inv'', MeasureTheory.measure_integral_le_pos, AnalyticOn.hasFPowerSeriesOnSubball, exists_deriv_eq_zero, contMDiffOn_localFrame_coeff, contDiffOn_nat_iff_continuousOn_differentiableOn_deriv, ContinuousMultilinearMap.norm_smulRightL_le, differentiableAt_comp_add_const, QuadraticForm.equivalent_signType_weighted_sum_squared, AnalyticOnNhd.rexp, RCLike.reCLM_norm, HasDerivWithinAt.sin, Real.hasDerivAt_arcosh, Complex.analyticWithinAt_cosh, ContDiffAt.arsinh, ConvexOn.monotoneOn_rightDeriv, ContDiffOn.rpow, ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin, Real.iteratedDerivWithin_cos_Icc, iteratedDeriv_scomp_eq_sum_orderedFinpartition, DifferentiableAt.fun_finset_prod, HasDerivAt.arctan, contMDiffOn_baseSet_iff_localFrame_coeff, HasDerivAt.sqrt, fderiv_eq_deriv_mul, MeasureTheory.exists_average_le, Polynomial.differentiableOn_aeval, Bundle.Trivialization.localFrame_coeff_eq_coeff, IsLocalExtr.lineDeriv_eq_zero, MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_part, analyticAt_rexp, StrictConvexOn.lt_slope_of_hasDerivAt, Complex.contDiff_cosh, IsExtrOn.lineDerivWithin_eq_zero, iteratedDerivWithin_eq_iteratedFDerivWithin, VectorFourier.fourierPowSMulRight_eq_comp, Complex.analyticOn_cosh, Real.analyticAt_sinh, ContDiff.arctan, Real.hasStrictDerivAt_arccos, not_differentiableWithinAt_of_deriv_tendsto_atBot_Ioi, MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le, Complex.reCLM_nnnorm, ContDiff.ccos, MeasureTheory.integral_norm_eq_lintegral_enorm, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, MeromorphicOn.divisor_natCast, Complex.deriv_ofReal_cpow_const, PiTensorProduct.mapL_smul, DifferentiableAt.fun_div, ValueDistribution.logCounting_mul_zero_eventuallyLE, Real.norm_deriv_mulExpNegMulSq_le_one, LeftInvariantDerivation.lift_add, meromorphicOrderAt_ne_top_iff, MeasureTheory.integrable_sum_measure_iff, StrictConcaveOn.deriv_lt_slope, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, Real.not_continuousAt_deriv_mul_log_zero, Complex.analyticOn_sinh, ContinuousLinearMapWOT.inducingFn_apply, fderivWithin_sin, StrictConcaveOn.slope_lt_deriv, ConvexOn.slope_le_deriv, LeftInvariantDerivation.lift_smul, DifferentiableOn.rpow, MeasureTheory.Measure.integral_toReal_rnDeriv', analyticOnNhd_rexp, ValueDistribution.logCounting_mul_top_eventuallyLE, HasMFDerivAt.smul, meromorphicOrderAt_mul_of_ne_zero, BoundedContinuousFunction.integral_const_sub, DifferentiableAt.rpow_const, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, Real.differentiableAt_rpow_const_of_ne, derivWithin_zpow, WeakDual.toStrongDual_inj, ContDiff.cos, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, fromTangentSpace_mfderiv_smul_apply, hasDerivAt_id', HasDerivWithinAt.cos, Differentiable.sinh, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, fderiv.log, HasStrictDerivAt.arctan, ContinuousLinearMap.deriv, deriv_norm_ofReal_cpow, Bundle.Trivialization.eq_sum_localFrame_coeff_smul, MeasureTheory.convolution_lsmul, Real.contDiffAt_sqrt, MeasureTheory.L1.dist_eq_integral_dist, Real.deriv_sqrt_aux, deriv_fderiv, meromorphicNFAt_mul_iff_left, MeasureTheory.integral_eq_zero_iff_of_nonneg, HasStrictDerivAt.real_of_complex, Real.deriv_rpow_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, range_cfcₙHom, fun_meromorphicOrderAt_smul, Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzero, HasDerivAt.differentiableAt, StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iio, fun_meromorphicOrderAt_zpow, ContinuousLinearMap.hasDerivAt, DifferentiableAt.star_conj, AnalyticWithinAt.cexp, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, meromorphicNFOn_fun_prod, Complex.reCLM_coe, ContDiffAt.sinh, MeasureTheory.ofReal_setAverage, Real.deriv_sinh, exists_ratio_deriv_eq_ratio_slope, WeakDual.coe_toStrongDual, ContMDiff.piecewise_Iic, Matrix.linfty_opNNNorm_eq_opNNNorm, ModularGroup.lcRow0Extend_symm_apply, Complex.analyticAt_sin, contDiffOn_one_iff_derivWithin, StrictConvexOn.slope_lt_deriv, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, Seminorm.ball_smul, LeftInvariantDerivation.comp_L, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, MeromorphicOn.divisor_inv, MeromorphicOn.id, hasDerivWithinAt_neg, MeasureTheory.integral_exp_tilted, MeromorphicOn.divisor_fun_pow, AnalyticAt.deriv, MeasureTheory.llr_tilted_right, Polynomial.deriv_aeval, ContDiff.log, IsLocalFrameOn.coeff_congr, LinearMap.hasStrictDerivAt, real_linearMap_map_smul_complex, Complex.equivRealProdCLM_symm_apply, CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, IsLocalExtr.fderiv_eq_zero, MeromorphicOn.divisor_fun_prod, Real.differentiableOn_rpow_const, NormedSpace.inclusionInDoubleDual_norm_eq, Meromorphic.MeromorphicOn.countable_compl_analyticAt, Real.smoothTransition.contDiffAt, ContDiffBump.contDiff, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, Seminorm.gaugeSeminorm_ball, ContinuousLinearMap.nnnorm_toSpanSingleton, deriv_id'', ContinuousLinearMap.norm_smulRightL, NormedSpace.inclusionInDoubleDualWeak_apply_apply, MeasureTheory.lpNorm_one_eq_integral_norm, ContDiffOn.rpow_const_of_ne, HasDerivAtFilter.iterate, RCLike.imLm_coe, Real.differentiable_cos, HasDerivWithinAt.const_rpow, Function.FactorizedRational.meromorphicOrderAt_eq, iteratedDeriv_fun_id_zero, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, MeromorphicOn.divisor_sub_const_self, NormedSpace.toLinearMap_inclusionInDoubleDualWeak, Matrix.linfty_opNNNorm_toMatrix, AnalyticAt.rexp', mdifferentiableOn_localFrame_coeff, analyticOrderAt_ne_zero, derivWithin_inv, WeakDual.CharacterSpace.homeoEval_naturality, StrictMonoOn.exists_slope_lt_deriv_aux, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, Complex.contDiffAt_log, HasDerivAt.log, Real.analyticAt_sin, LeftInvariantDerivation.evalAt_coe, Differentiable.sin, MeasureTheory.integral_tendsto_of_tendsto_of_antitone, ContDiffOn.csin, MeasureTheory.integral_tendsto_of_tendsto_of_monotone, Polynomial.differentiable_aeval, meromorphicNFAt_finprod, hasDerivAt_deriv_iff, Complex.differentiable_iteratedDeriv_sin, hasDerivAtFilter_neg, Real.analyticOnNhd_cosh, HasStrictDerivAt.sin, Real.hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, HasStrictDerivAt.clog_real, MeasureTheory.norm_integral_le_integral_norm, HasDerivWithinAt.sqrt, meromorphicOrderAt_const_natCast, Real.hasDerivAt_qaryEntropy, continuousAt_dslope_same, hasDerivWithinAt_pow, differentiableAt_star_conj_iff, MeromorphicOn.divisor_prod, differentiableWithinAt_of_derivWithin_ne_zero, one_mem_posTangentConeAt_iff_mem_closure, MeromorphicOn.divisor_intCast, RealRMK.rieszMeasure_le_of_eq_one, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendsto, DifferentiableAt.log, cfcₙAux_id, NormedSpace.inclusionInDoubleDual_norm_le, Set.OrdConnected.image_derivWithin, LinearIsometry.re_apply_eq_re_of_add_conj_eq, Bundle.Trivialization.eventually_eq_localFrame_sum_coeff_smul, ConcaveOn.slope_le_of_hasDerivWithinAt_Ioi, WeakDual.isCompact_closedBall, Real.abs_iteratedDeriv_cos_le_one, ConvexOn.sSup_of_countable_affine_eq, Real.differentiableAt_rpow_of_ne, Complex.iteratedDeriv_odd_sin, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, HasStrictDerivAt.to_local_left_inverse, ContinuousLinearMap.derivWithin, MeasureTheory.norm_integral_le_of_norm_le, MeasureTheory.Measure.integral_toReal_rnDeriv, Seminorm.comp_smul, ContDiff.sin, MeromorphicOn.analyticAt_mem_codiscreteWithin, deriv_neg_left_of_sign_deriv, Real.deriv_inv_log, smoothSheafCommRing.isUnit_stalk_iff, Real.iteratedDeriv_add_one_cosh, FormalMultilinearSeries.coeff_ofScalars, MeasureTheory.exists_notMem_null_le_average, iteratedFDerivWithin_eq_equiv_comp, CompactlySupportedContinuousMap.toRealLinearMap_apply, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, meromorphicOrderAt_id, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, differentiableAt_inv_iff, Real.iteratedDeriv_add_one_sinh, HasStrictDerivAt.exp, RealRMK.integral_rieszMeasure, ContDiffAt.rpow, LinearMap.deriv, contDiff_iff_iteratedDeriv, LeftInvariantDerivation.map_zero, NormedSpace.polar_ball_subset_closedBall_div, ContDiffWithinAt.arctan, HasDerivAt.cosh, DifferentiableAt.conj_conj, Real.differentiable_exp, fderivWithin_cos, Polynomial.derivWithin, fdifferential_apply, Real.hasStrictDerivAt_arcosh, MeromorphicOn.divisor_sub_const_of_ne, Real.differentiableAt_cos, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, innerₗ_apply, ModularGroup.lcRow0Extend_apply, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral, Real.deriv_log', VectorField.lieBracketWithin_smul_left, hasDerivAt_update, iteratedDeriv_fun_id, Seminorm.bound_of_continuous, DifferentiableOn.log, StrictMonoOn.exists_deriv_lt_slope_aux, DifferentiableAt.comp_ringHom, HasDerivWithinAt.complexToReal_fderiv, ContDiffOn.ccos, HasDerivWithinAt.arsinh, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, Real.deriv2_binEntropy, LinearMap.toSeminorm_comp, HasDerivAt.exp, IsExtrOn.lineDeriv_eq_zero, MeasureTheory.measure_le_setAverage_pos, meromorphicNFAt_inv, DifferentiableAt.sqrt, DifferentiableOn.div_const, AlgHom.instContinuousLinearMapClassOfAlgHomClass, Real.hasDerivAt_arcsin, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, MeasureTheory.integral_llr_tilted_left, LeftInvariantDerivation.coe_sub, Real.analyticOn_arcosh, VitaliFamily.ae_tendsto_average_norm_sub, Real.hasDerivAt_tan, Real.deriv_tan_sub_id, Meromorphic.countable_compl_analyticAt, Real.contDiffAt_log, Real.leftDeriv_mul_log, deriv_inv, PointwiseConvergenceCLM.equivWeakDual_apply, HasDerivAt.cos, Polynomial.fderiv_aeval, orthogonalBilin_innerₗ, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, ConvexOn.real_univ_sSup_of_countable_affine_eq, iteratedDerivWithin_comp_three, Module.Basis.equivFunL_symm_apply_repr, meromorphicOrderAt_pow_id_sub_const, MeasureTheory.integral_pos_iff_support_of_nonneg_ae, iter_deriv_zpow, HasStrictDerivAt.cosh, natCast_le_analyticOrderAt, ContDiffAt.cosh, VectorField.lieBracket_fmul_left, Complex.analyticOnNhd_sin, MeasureTheory.integral_indicator_one, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, DifferentiableWithinAt.arctan, Real.hasStrictDerivAt_log, IsMinOn.lineDerivWithin_eq_zero, hasFDerivWithinAt_iff_hasDerivWithinAt, Real.iteratedDeriv_add_one_cos, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, LeftInvariantDerivation.left_invariant'', Real.differentiableOn_mul_log, Complex.conjCLE_toLinearEquiv, HasDerivAt.complexToReal_fderiv', hasStrictFDerivAt_iff_hasStrictDerivAt, contDiff_nat_iff_iteratedDeriv, ConvexOn.slope_le_leftDeriv, meromorphicNFOn_fun_inv, HasDerivAt.complexToReal_fderiv, ContinuousLinearMapWOT.isInducing_inducingFn, Real.deriv_mulExpNegMulSq, StrongDual.polarSubmodule_eq_polar, MeasureTheory.Integrable.exists_boundedContinuous_integral_sub_le, meromorphicOrderAt_inv, meromorphicOrderAt_fun_prod, MeasureTheory.SignedMeasure.re_toComplexMeasure, fromTangentSpace_mfderiv_smul', iteratedDerivWithin_scomp_eq_sum_orderedFinpartition, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_qaryEntropy, Real.deriv_arctan, LinearMap.coe_complexOfReal, monotoneOn_deriv_descPochhammer_eval, HasDerivWithinAt.rpow, Differentiable.arctan, ContDiffWithinAt.ccos, LinearMap.toMatrix_innerₛₗ_apply, MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, PointwiseConvergenceCLM.equivWeakDual_symm_apply, ConvexOn.le_slope_of_hasDerivWithinAt_Ioi, ContDiffAt.div, AffineMap.hasDerivAt, ContDiffAt.rpow_const_of_ne, Real.iteratedDerivWithin_sinh_Icc, iteratedDerivWithin_zpow, meromorphicOrderAt_eq_int_iff, AffineMap.differentiableAt, contMDiffOn_baseSet_localFrame_coeff, meromorphicNFAt_iff_analyticAt_or, WeakDual.isSeqCompact_closedBall, extDerivFun_zero, WeakDual.isBounded_iff_isVonNBounded, Real.differentiableAt_log_iff, hasStrictDerivAt_zpow, fromTangentSpace_mfderiv_smul_apply', LinearIsometry.toSpanSingleton_apply, DifferentiableWithinAt.sin, hasFDerivAtFilter_iff_hasDerivAtFilter, Polynomial.hasFDerivAt, StrictConcaveOn.slope_lt_of_hasDerivAt, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, UpperHalfPlane.smulFDeriv_J_mul, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, Real.contDiff_arsinh, HasDerivAt.sinh, MeasureTheory.tilted_apply_eq_ofReal_integral, ContDiffAt.derivWithin, contMDiff_smul, MeromorphicOn.divisor_ofNat, Real.contDiffAt_arcsin_iff, ContDiffAt.arctan, ContDiffOn.derivWithin, Complex.ofRealCLM_apply, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, Function.FactorizedRational.meromorphicNFOn_univ, MeasureTheory.setIntegral_eq_zero_iff_of_nonneg_ae, differentiableAt_complex_iff_differentiableAt_real, cfcHom_real_eq_restrict, ContinuousLinearMap.toLinearMap_innerSL_apply, differentiableAt_comp_const_sub, meromorphicNFOn_mul_iff_left_of_analyticOnNhd, HasFPowerSeriesAt.hasStrictDerivAt, derivWithin_comp_of_eq, MeasureTheory.Measure.setIntegral_toReal_rnDeriv', analyticOrderAt_mul, Module.Basis.equivFunL_apply, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, derivWithin_cos, ContDiffOn.log, LinearMap.hasDerivWithinAt, ContDiffOn.differentiableOn_iteratedDerivWithin, ContinuousMap.adjoin_id_eq_span_one_union, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, IsSelfAdjoint.spectrumRestricts, Seminorm.const_isBounded, IsCovariantDerivativeOn.leibniz, meromorphicTrailingCoeffAt_const, ConvexOn.monotoneOn_deriv, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, DifferentiableWithinAt.div_const, ContDiffWithinAt.sinh, derivWithin_const_rpow, iteratedDerivWithin_scomp_three, range_cfcₙHom_le, StrongDual.extendRCLikeₗ_apply, LinearMap.bound_of_ball_bound', HasDerivWithinAt.differentiableWithinAt, ZSpan.coe_floor_self, Real.iteratedDerivWithin_sin_Icc, NormedSpace.inclusionInDoubleDualWeak_apply, Real.iteratedDeriv_odd_sinh, iteratedFDeriv_eq_equiv_comp, linear_isometry_complex, deriv_rpow_const, meromorphicTrailingCoeffAt_inv, MeromorphicAt.id, Real.hasDerivAt_cos, AnalyticOnNhd.cexp, deriv_comp, analyticOnNhd_cexp, StrictConvexOn.strictMonoOn_derivWithin, fderiv_cos, ContDiff.rpow, exists_dual_vector, MeromorphicOn.divisor_fun_zpow, meromorphicNFOn_inv, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, Real.differentiableWithinAt_arcsin_Ici, iteratedDerivWithin_one_div, DifferentiableWithinAt.fun_div, ContDiffWithinAt.derivWithin, ContDiff.exp, derivWithin_exp, Real.hasDerivWithinAt_arcsin_Ici, AnalyticAt.analyticOrderAt_eq_natCast, rotationOf_rotation, IsMIntegralCurveAt.hasMFDerivAt, extDerivFun_add, deriv_neg_right_of_sign_deriv, SpectrumRestricts.real_iff, IsLocalFrameOn.eventually_eq_sum_coeff_smul, iteratedDerivWithin_fun_id, MeasureTheory.tilted_apply, MeasureTheory.lpNorm_nnreal_eq_integral_norm_rpow, derivWithin_rpow_const, DifferentiableOn.sinh, VectorField.mlieBracketWithin_smul_left, Function.FactorizedRational.analyticAt, Real.differentiableAt_cosh, complexOfReal_deriv, MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm, ValueDistribution.logCounting_mul_top_le, Polynomial.hermite_eq_deriv_gaussian', BoundedContinuousFunction.tendsto_integral_of_forall_integral_le_liminf_integral, fderiv_exp, ContDiffAt.log, Differentiable.log, Real.analyticOnNhd_arsinh, AnalyticAt.analyticOrderNatAt_eq_iff, fderiv_arctan, MonotoneOn.derivWithin_nonneg, MeasureTheory.log_rnDeriv_tilted_left_self, CompactlySupportedContinuousMap.integralLinearMap_apply, Real.analyticAt_arcosh, ContDiffAt.real_of_complex, MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le, LinearMap.adjoint_toSpanSingleton, ContDiff.differentiable_iteratedDeriv, ContDiffOn.sin, WeakDual.withSeminorms, MeromorphicOn.divisor_fun_mul, Real.deriv_exp, MeromorphicOn.divisor_zpow, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, Real.contDiff_sin, QuasispectrumRestricts.real_iff, derivWithin_pow_field, deriv_sinh, StrictConcaveOn.derivWithin_lt_slope, HasStrictDerivAt.log, Polynomial.differentiableAt_aeval, DifferentiableAt.cosh, hasDerivAt_id, StrictConvexOn.slope_lt_derivWithin, Real.hasDerivAt_rpow_const, IsMinOn.lineDeriv_eq_zero, ConvexOn.slope_le_of_hasDerivWithinAt, fderivWithin.log, deriv_update, Real.iter_deriv_exp, DifferentiableWithinAt.finset_prod, Real.differentiable_iteratedDeriv_cos, Polynomial.hasFDerivAt_aeval, VectorField.mlieBracketWithin_smul_right, meromorphicOrderAt_div, exists_dual_vector'', ContDiff.ccosh, deriv_zpow', LeftInvariantDerivation.map_add, MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part, LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re, MeasureTheory.exists_integral_le, Module.Dual.extendRCLikeₗ_apply, meromorphicOrderAt_smul, isTheta_deriv_rpow_const_atTop, StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iio, ContDiffAt.ccosh, HasDerivWithinAt.arctan, ValueDistribution.logCounting_top_mul_eventually_le, mdifferentiableOn_baseSet_localFrame_coeff, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.conjCLE_coe_toLinearMap, hasDerivAt_exp, Complex.analyticOn_cos, contDiffOn_succ_iff_deriv_of_isOpen, LeftInvariantDerivation.coe_add, DifferentiableOn.cos, Real.tendsto_rightDeriv_mul_log_atTop, Real.hasStrictDerivAt_arsinh, iter_deriv_pow', RCLike.realLinearIsometryEquiv_symm_apply, hasStrictFDerivAt_inv, MeromorphicAt.eventually_analyticAt, MeromorphicOn.eventually_codiscreteWithin_analyticAt, not_differentiableWithinAt_of_deriv_tendsto_atTop_Iio, LinearIsometry.coe_toSpanSingleton, ConcaveOn.le_slope_of_hasDerivWithinAt, Real.contDiff_cos, deriv_neg'', IsLocalFrameOn.coeff_apply_of_notMem, Seminorm.closedBall_smul, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, fderiv_inv, meromorphicNFAt_fun_prod, MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction, contMDiffAt_localFrame_coeff, MeasureTheory.L1.integral_eq_norm_posPart_sub, IsOpen.measure_eq_biSup_integral_continuous, iteratedDeriv_eq_equiv_comp, Real.iteratedDeriv_even_cos, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, ContDiffOn.div, MeasureTheory.SimpleFunc.norm_integral_le_integral_norm, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, ContDiff.iterate_deriv, ContinuousLinearMap.norm_extendTo𝕜'_bound, Complex.iteratedDeriv_add_one_sinh, HasFDerivWithinAt.hasDerivWithinAt, Real.differentiableAt_arctan, ContDiffWithinAt.rpow, ContDiffOn.fun_div, ContDiff.deriv', MeasureTheory.integral_pos_iff_support_of_nonneg, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, Complex.iteratedDeriv_even_cos, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, WeakDual.isClosed_closedBall, AffineMap.derivWithin, HasDerivAt.arsinh, complexOfReal_fderivWithin, Complex.iteratedDeriv_add_one_sin, StrongDual.extendRCLikeₗᵢ_symm_apply, Real.rightDeriv_mul_log, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, fdifferential_comp, ContDiffWithinAt.ccosh, LeftInvariantDerivation.coe_injective, MeasureTheory.setIntegral_nonpos, fderiv_apply_one_eq_deriv, ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero, DifferentiableWithinAt.cosh, HasDerivAt.rpow, meromorphicTrailingCoeffAt_id_sub_const, fderivWithin_exp, deriv_inv'', Real.analyticWithinAt_cos, cfcₙAux_injective, MeromorphicNFAt.zpow, Complex.analyticAt_sinh, LeftInvariantDerivation.coe_neg, StrongDual.toLpₗ_apply, Real.differentiableWithinAt_arcsin_Iic, Polynomial.hermite_eq_deriv_gaussian, Complex.conjCLE_nnorm, Polynomial.differentiableOn, StrongDual.extendRCLikeₗ_symm_apply, HasStrictDerivAt.complexToReal_fderiv', StrictConcaveOn.strictAntiOn_deriv, Orientation.inner_mul_areaForm_sub', ConcaveOn.slope_le_derivWithin, DifferentiableAt.of_dslope, differentiableOn_neg, LinearMap.continuous_of_nonzero_on_open, ConvexOn.real_univ_sSup_affine_eq, Complex.iteratedDeriv_add_one_cos, Real.deriv_arcsin, ConvexOn.monotoneOn_leftDeriv, linear_isometry_complex_aux, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, deriv_neg', Real.differentiable_sin, AnalyticAt.of_meromorphicOrderAt_pos, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.hasDerivWithinAt_aeval, derivWithin_sin, rotation_trans, CPolynomialOn.deriv, deriv_const_rpow, Real.not_differentiableAt_inv_log_zero, ContDiffAt.rpow_const_of_le, Real.deriv_mul_log, Real.contDiffAt_rpow_const, AnalyticAt.iterated_deriv, Polynomial.hasStrictDerivAt_aeval, MeasureTheory.integral_rnDeriv_mul_log, ContinuousLinearMap.norm_extendTo𝕜', HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, AnalyticOnNhd.deriv_of_isOpen, Convex.image_derivWithin, differentiableAt_iff_comp_const_sub, Complex.restrictScalars_toSpanSingleton, MeasureTheory.SimpleFunc.integral_eq_lintegral, ContDiff.rpow_const_of_le, MeromorphicOn.countable_compl_analyticAt_inter, IsMaxOn.lineDerivWithin_eq_zero, MeasureTheory.setIntegral_nonneg_of_ae_restrict, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, ContDiffOn.arctan, Real.differentiableAt_tan, Real.differentiable_cosh, DifferentiableAt.rpow, MeasureTheory.setLIntegral_tilted, ConcaveOn.leftDeriv_le_slope, NumberField.finite_of_discr_bdd, HasDerivWithinAt.sinh, cfcHom_nnreal_eq_restrict, fderiv_deriv, DifferentiableOn.finset_prod, MeasureTheory.integral_le_measure, meromorphicOrderAt_zpow_id_sub_const, ConcaveOn.derivWithin_le_slope, ValueDistribution.logCounting_zero_mul_eventually_le, MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt, Complex.contDiffAt_tan, Complex.analyticWithinAt_sinh, Complex.analyticOnNhd_cosh, ContDiff.rpow_const_of_ne, coord_norm', spec_cfcₙAux, iteratedDerivWithin_pow, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, MeasureTheory.ofReal_integral_norm_eq_lintegral_enorm, StrongDual.extendRCLikeₗᵢ_apply, DifferentiableOn.fun_finset_prod, HasDerivAt.ofReal_comp, DifferentiableAt.sin, DifferentiableAt.ofReal_cpow_const, LeftInvariantDerivation.map_smul, Real.hasDerivAt_log, analyticOrderAt_pow, ConcaveOn.deriv_le_slope, MeasureTheory.ofReal_setIntegral_one, rotationOf_coe, AnalyticWithinAt.rexp, ContDiffWithinAt.csin, deriv_single, StrongDual.norm_toLpₗ_le, Module.Basis.parallelepiped_eq_map, WeakDual.isBounded_toWeakDual_preimage_iff_isBounded, MeasureTheory.toReal_laverage, iteratedDeriv_comp_two, ContDiffWithinAt.cos, meromorphicNFOn_prod, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational, MeromorphicOn.divisor_fun_inv, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, deriv_cos, DifferentiableAt.arsinh, fromTangentSpace_mfderiv_smul, ContDiffBump.contDiffAt, ContDiffAt.ccos, MeasureTheory.rnDeriv_tilted_left, MeasureTheory.convolution_lsmul_swap, Real.hasStrictDerivAt_arctan, Complex.contDiff_sinh, AnalyticAt.hasFPowerSeriesAt, StrictConcaveOn.strictAntiOn_derivWithin, DifferentiableAt.comp_semilinear₁, StrongDual.toLpₗ_of_not_memLp, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, analyticOrderAt_id, IsLocalMax.lineDeriv_eq_zero, AnalyticOnNhd.deriv, instContMDiffInv₀ModelWithCornersSelf, MeasureTheory.setIntegral_nonpos_le, Real.iteratedDeriv_odd_cosh, deriv_zpow, StrongDual.mem_polarSubmodule, exists_dual_vector', derivWithin_inv', FormalMultilinearSeries.apply_eq_prod_smul_coeff, Real.analyticOn_sin, ConcaveOn.slope_le_of_hasDerivWithinAt, MeromorphicNFOn.fun_zpow, DifferentiableWithinAt.div, Real.hasDerivAt_mulExpNegMulSq, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, cfcₙHom_real_eq_restrict, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, MeasureTheory.ComplexMeasure.im_apply, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, Real.differentiableOn_arccos, HasFPowerSeriesOnBall.r_eq_top_of_exists, IsLocalMin.deriv_eq_zero, Real.hasDerivAt_cosh, ConcaveOn.le_slope_of_hasDerivWithinAt_Iio, Real.tendsto_deriv_mul_log_atTop, LeftInvariantDerivation.coe_smul, HasFPowerSeriesAt.deriv, innerₗ_apply_apply, DifferentiableOn.div, MeasureTheory.integral_eq_zero_iff_of_nonneg_ae, StrictConvexOn.lt_slope_of_hasDerivWithinAt, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity', hfdifferential_apply, AnalyticAt.exists_eq_sum_add_pow_mul, analyticOn_cexp, CompactlySupportedContinuousMap.toNNRealLinear_apply, bilinFormOfRealInner_orthogonal, HasDerivWithinAt.inv, Complex.conjCLE_enorm, Real.differentiableWithinAt_arccos_Iic, spectrum.differentiableOn_inverse_one_sub_smul, derivWithin_comp, AnalyticAt.analyticOrderAt_comp, HasDerivWithinAt.limsup_slope_le', analyticAt_comp_iff_of_deriv_ne_zero, Real.iteratedDerivWithin_sinh_Ioo, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, expNegInvGlue.contDiff, VectorField.lieBracket_smul_left, RCLike.reLm_coe, Differentiable.exp, ContinuousLinearMap.toBilinForm_injective, Real.contDiffOn_arccos, HasStrictDerivAt.arsinh, toSpanSingleton_derivWithin, meromorphicNFAt_prod, deriv_comp_of_eq, MeromorphicOn.eventually_analyticAt_or_mem_compl, StrictConcaveOn.slope_lt_of_hasDerivWithinAt, MeasureTheory.setIntegral_gt_gt, ConvexOn.derivWithin_le_slope, MeasureTheory.setIntegral_nonneg_ae, MeasureTheory.setIntegral_nonpos_of_ae, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Real.iteratedDeriv_even_sinh, AnalyticAt.analyticOrderAt_ne_top, ConvexOn.univ_sSup_affine_eq, linearEquiv_det_rotation, Real.differentiable_mulExpNegMulSq, HasStrictFDerivAt.hasStrictDerivAt, Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, fderivWithin_sqrt, Complex.conjCLE_apply, NormedSpace.polar_ball, Real.not_DifferentiableAt_log_mul_zero, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, fderivWithin_derivWithin, hasDerivAt_const_mul, MeasureTheory.ofReal_integral_eq_lintegral_ofReal, Real.contDiff_sinh, meromorphicNFOn_finprod, MeasureTheory.Measure.exists_regular_eq_of_compactSpace, Polynomial.fderivWithin_aeval, fderiv_sinh, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, Polynomial.fderivWithin, contDiffOn_of_differentiableOn_deriv, IsLocalFrameOn.eq_iff_coeff, Polynomial.hasDerivAt, WeakDual.CharacterSpace.norm_le_norm_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, StrictConcaveOn.slope_lt_of_hasDerivWithinAt_Ioi, Real.hasStrictDerivAt_cos, ContDiffWithinAt.exp, iter_deriv_inv, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, MeasureTheory.setIntegral_nonneg, Differentiable.sqrt, RightDerivMeasurableAux.differentiable_set_eq_D, MeasureTheory.mul_meas_ge_le_integral_of_nonneg, hasDerivWithinAt_zpow, Monotone.deriv_nonneg, Real.contDiff_arctan, MeasureTheory.setIntegral_tilted', fderivWithin_inv, HasDerivAt.real_of_complex, DifferentiableWithinAt.rpow_const, NormedSpace.isEmbedding_inclusionInDoubleDualWeak, measurableSet_of_differentiableWithinAt_Ioi, Real.iteratedDeriv_add_one_sin, Real.differentiable_iteratedDeriv_sin, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, exists_ratio_deriv_eq_ratio_slope', iteratedDeriv_eq_iteratedFDeriv, ProperCone.dual_dual_flip, flip_innerₗ, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, iter_deriv_inv', toMatrix_innerSL_apply, MeasureTheory.integral_eq_lintegral_of_nonneg_ae, Complex.analyticOnNhd_canonicalFactor, Real.iteratedDeriv_even_sin, MeasureTheory.setIntegral_ge_of_const_le_real, DifferentiableOn.arctan, Real.analyticOnNhd_cos, ModularGroup.tendsto_lcRow0, Differentiable.fun_finset_prod, ContDiffOn.exp, NormedSpace.sInter_polar_eq_closedBall, Complex.imCLM_coe, iteratedDeriv_comp_eq_sum_orderedFinpartition, DifferentiableOn.cosh, expNegInvGlue.contDiff_polynomial_eval_inv_mul, DoubleCentralizer.coe_eq_algebraMap, deriv_pow_field, HasFPowerSeriesAt.hasDerivAt, Complex.meromorphicNFOn_canonicalFactor, HasDerivWithinAt.rpow_const, meromorphicOrderAt_pow, Polynomial.hasDerivAt_aeval, DifferentiableWithinAt.arsinh, hasDerivAt_gronwallBound, isBigO_deriv_ofReal_cpow_const_atTop, ContDiffWithinAt.rpow_const_of_ne, meromorphicTrailingCoeffAt_prod, exists_deriv_eq_slope', MeasureTheory.exists_le_setAverage, hasDerivAt_ofReal_cpow_const, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, HasFDerivAt.hasDerivAt, LeftInvariantDerivation.map_sub, MeasureTheory.L1.SimpleFunc.integral_eq_lintegral, AnalyticAt.analyticAt_localInverse, Real.contDiff_cosh, MeromorphicOn.extract_zeros_poles, cfcₙAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, LeftInvariantDerivation.map_neg, meromorphicAt_mul_iff_of_ne_zero, BoundedContinuousFunction.integral_add_const, MeasureTheory.L1.norm_of_fun_eq_integral_norm, Real.analyticAt_arsinh, contDiffOn_of_continuousOn_differentiableOn_deriv, norm_deriv_eq_norm_fderiv, Seminorm.bound_of_shell_sup, AkraBazziRecurrence.differentiableAt_smoothingFn, ContinuousLinearMap.nnnorm_smulRight_apply, MeasureTheory.setIntegral_one_eq_measureReal, deriv_id, Matrix.toLin_finTwoProd_toContinuousLinearMap, Convex.image_deriv, StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioi, MeasureTheory.setIntegral_toReal_rnDeriv_mul', Real.deriv_cos, fun_meromorphicOrderAt_zpow_id_sub_const, iteratedDeriv_exp_const_mul, ContDiffWithinAt.rpow_const_of_le, Real.differentiableAt_binEntropy, VectorField.lieBracketWithin_smul_right, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, ContDiffWithinAt.div, Real.hasDerivAt_arctan', ContDiff.iterate_deriv', differentiable_neg, hasDerivAt_neg, LinearMap.derivWithin, BoundedContinuousFunction.toReal_lintegral_coe_eq_integral, Polynomial.hasStrictDerivAt, Real.deriv2_qaryEntropy, Real.differentiableAt_exp, Real.hasStrictDerivAt_arcsin, ConvexOn.slope_le_of_hasDerivAt, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, Real.abs_iteratedDeriv_sin_le_one, VectorField.mpullback_mfderivWithin_apply_smul, Seminorm.finset_sup_smul, Complex.iteratedDeriv_odd_cos, MeasureTheory.abs_integral_le_integral_abs, Real.contDiff_rpow_const_of_le, Seminorm.isBounded_sup, Real.contDiffOn_arcosh, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, Complex.equivRealProdCLM_symm_apply_re, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_integral, MeromorphicOn.divisor_smul, iteratedDerivWithin_eq_equiv_comp, Polynomial.differentiableAt, DifferentiableAt.cos, LinearIsometry.im_apply_eq_im, MeasureTheory.exists_setAverage_le, CompactlySupportedContinuousMap.toReal_smul, MeasureTheory.lintegral_tilted, Real.analyticAt_cosh, derivWithin_sqrt, Real.contDiffAt_rpow_const_of_ne, ConvexOn.deriv_le_slope, ValueDistribution.logCounting_top_mul_le, MeasureTheory.L1.SimpleFunc.norm_eq_integral, contMDiffAt_iff_localFrame_coeff, ConvexOn.rightDeriv_le_slope, MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top, MeasureTheory.llr_tilted_left, DifferentiableOn.sin, Matrix.linfty_opNorm_eq_opNorm, MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction, ValueDistribution.logCounting_pow_zero, Real.deriv_cos', MeasureTheory.measure_le_integral_pos, isBigO_deriv_rpow_const_atTop, hasDerivAt_pow, contDiff_succ_iff_deriv, Real.deriv_rpow_const', MeromorphicNFOn.zpow, StrictConcaveOn.lt_slope_of_hasDerivWithinAt, MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg, Real.differentiableAt_arcosh, StrictConvexOn.derivWithin_lt_slope, HasDerivAt.rpow_const, contDiffOn_succ_iff_derivWithin, IsLocalMaxOn.fderivWithin_eq_zero, Seminorm.bound_of_shell_smul, WeakDual.isBounded_toStrongDual_preimage_iff_isBounded, LinearMap.isSymmetric_iff_sesqForm, hasDerivWithinAt_derivWithin_iff, hasStrictDerivAt_exp, MeasureTheory.lintegral_coe_le_coe_iff_integral_le, LinearMap.bound_of_sphere_bound, Real.hasStrictDerivAt_sqrt, DifferentiableOn.rpow_const, Polynomial.deriv, Real.hasDerivAt_tan_of_mem_Ioo, MeasureTheory.integral_pos_of_integrable_nonneg_nonzero, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, AlgHom.toContinuousLinearMap_norm, iteratedDeriv_comp_three, MeasureTheory.exists_notMem_null_integral_le, Polynomial.hasFDerivWithinAt_aeval, Complex.iteratedDeriv_even_sin, Real.hasDerivAt_exp, Differentiable.div_const, fderiv_sqrt, hasStrictDerivAt_inv, MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae, Polynomial.contDiff_aeval, fun_meromorphicOrderAt_mul, LinearMap.continuous_of_isClosed_ker, iteratedDerivWithin_id, HasDerivAt.iterate, differentiableAt_iff_comp_add_const, Real.iteratedDerivWithin_cosh_Icc, innerₛₗ_apply, analyticWithinAt_rexp, ContMDiffMap.smul_comp', Complex.iteratedDeriv_even_sinh, IsCompact.measure_eq_biInf_integral_hasCompactSupport, DifferentiableWithinAt.fun_finset_prod, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, LinearMap.continuous_iff_isClosed_ker, HasStrictDerivAt.sinh, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, Complex.differentiable_iteratedDeriv_sinh, Real.contDiffAt_arccos, LinearMap.toSeminorm_ball_zero, Real.differentiableAt_negMulLog, iter_deriv_inv_linear_sub, not_differentiableWithinAt_of_deriv_tendsto_atBot_Iio, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, MeasureTheory.exists_le_integral, DifferentiableWithinAt.zpow, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', ContDiff.sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, LeftInvariantDerivation.toDerivation_injective, Real.analyticOn_arsinh, StrictConvexOn.slope_lt_of_hasDerivWithinAt, Real.analyticWithinAt_sin, Complex.conjCLE_norm, ContDiffAt.csinh, LeftInvariantDerivation.evalAt_mul, ConvexOn.monotoneOn_derivWithin, iteratedDeriv_id, ContDiffWithinAt.arsinh, meromorphicOrderAt_zpow, ConcaveOn.slope_le_rightDeriv, exists_extension_norm_eq, AnalyticOn.hasFPowerSeriesOnBall, Complex.iteratedDeriv_add_one_cosh, contDiff_of_differentiable_iteratedDeriv, ConcaveOn.antitoneOn_derivWithin, DifferentiableAt.sinh, hasStrictDerivAt_exp_zero_of_radius_pos, ContDiff.csinh, differentiableAt_conj_conj_iff, NormedSpace.closedBall_inv_subset_polar_closedBall, MeasureTheory.convolution_mul_swap, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, derivWithin_neg, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, analyticOrderAt_mul_eq_top_of_left, Complex.imCLM_enorm, analyticOrderAt_eq_zero, hasDerivAt_single, det_rotation, IsMaxOn.lineDeriv_eq_zero, hasStrictDerivAt_exp_of_mem_ball, integral_complex_ofReal, complexOfReal_fderiv, continuous_cfcₙAux, ConvexOn.le_slope_of_hasDerivWithinAt, ConvexOn.slope_le_derivWithin, ContDiffAt.sin, Real.iteratedDeriv_odd_sin, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, integral_ofReal, Complex.ofRealCLM_enorm, not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, WeakDual.isBounded_closedBall, Polynomial.differentiableWithinAt_aeval, MeasureTheory.measure_average_le_pos, Real.analyticOn_sinh, mfderiv_smul, Real.differentiableAt_sinh, Real.differentiable_iteratedDeriv_sinh, FormalMultilinearSeries.coeff_iterate_fslope, Complex.analyticWithinAt_sin, HasFPowerSeriesAt.eq_zero, MeasureTheory.measure_setAverage_le_pos, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, MeasureTheory.Integrable.measure_le_integral, Real.instStrictConvexSpace, rotation_symm, fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, ContDiff.differentiable_iteratedDeriv', ContinuousLinearMap.isAdjointPair_inner, deriv_pos_left_of_sign_deriv, Complex.equivRealProdCLM_symm_apply_im, analyticOrderNatAt_pow, meromorphicOrderAt_id_sub_const, complexOfReal_hasDerivAt, Real.hasFDerivAt_fourierChar_neg_bilinear_right, MeasureTheory.measure_le_average_pos, Antitone.deriv_nonpos, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_le, differentiable_tsum', MeasureTheory.setLIntegral_tilted', Polynomial.differentiable, ContinuousLinearEquiv.coord_norm', HasDerivAt.fun_inv, iteratedDerivWithin_comp_eq_sum_orderedFinpartition, DifferentiableAt.div_const, HasFPowerSeriesAt.eq_zero_of_eventually, analyticOrderNatAt_mul, LinearMap.mem_span_iff_bound, MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap, hasDerivAt_mul_const, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, ContDiff.contDiffBump, derivWithin_id, iteratedDeriv_cexp_const_mul, ContDiff.sinh, iteratedDeriv_fun_pow_zero, exists_deriv_eq_slope, Homeomorph.contDiff_symm_deriv, ContDiffAt.cos, Complex.hasStrictFDerivAt_log_real, Real.analyticWithinAt_arcosh, Real.hasStrictDerivAt_tan, iter_deriv_inv_linear, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_integral, DifferentiableOn.exp, AffineMap.differentiable, WeakDual.toStrongDual_apply, DifferentiableAt.finset_prod, meromorphicNFAt_mul_iff_right, DifferentiableOn.fun_div, MeasureTheory.lpNorm_eq_integral_norm_rpow_toReal, Real.hasDerivAt_arctan, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, innerₛₗ_apply_coe, iteratedDerivWithin_scomp_two, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, Real.analyticWithinAt_arsinh, ContinuousMapZero.toNNReal_neg_smul, ContDiffWithinAt.csinh, differentiableAt_of_deriv_ne_zero, MeasureTheory.exists_upperSemicontinuous_le_integral_le, Real.iteratedDerivWithin_cosh_Ioo, ContDiffWithinAt.contDiffBump, meromorphicOrderAt_const_intCast, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, exists_eq_const_mul_setIntegral_of_nonneg, deriv_sin, Module.Basis.opNNNorm_le, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Real.deriv_arcsin_aux, IsLocalMin.fderiv_eq_zero, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity, IsLocalMin.lineDeriv_eq_zero, MeasureTheory.tilted_eq_withDensity_nnreal, ContinuousLinearMap.coe_complexOfReal, Real.differentiableAt_qaryEntropy, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, DifferentiableAt.exp, ContinuousLinearMap.lsmul_flip_apply, Differentiable.finset_prod, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, Complex.differentiable_iteratedDeriv_cos, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_integral_norm, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, setIntegral_re_add_im, MeasureTheory.exists_eq_setAverage, ContinuousLinearEquiv.coord_norm, ContinuousMultilinearMap.nnnorm_smulRight, isTheta_deriv_ofReal_cpow_const_atTop, Real.hasStrictDerivAt_const_rpow, MeasureTheory.FiniteMeasure.continuous_integral_continuousMap, HasStrictDerivAt.cos, LinearPMap.mem_adjoint_domain_iff, spectrum.hasDerivAt_resolvent_const_right, differentiableWithinAt_zpow, contDiffOn_infty_iff_deriv_of_isOpen, ContinuousMultilinearMap.norm_smulRight, DifferentiableAt.conformalAt, Real.analyticOnNhd_sinh, MeasureTheory.rnDeriv_tilted_right, LeftInvariantDerivation.commutator_apply, HasFPowerSeriesAt.has_fpower_series_dslope_fslope, NNRealRMK.integral_rieszMeasure, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, HasStrictDerivAt.iterate, StrictMonoOn.exists_slope_lt_deriv, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, NormedSpace.polar_closedBall, HasDerivAt.conj_conj, ContinuousMapZero.toNNReal_smul, MeasureTheory.setIntegral_nonneg_of_ae, deriv_pos_right_of_sign_deriv, coe_innerₛₗ_apply, fderivWithin_arctan, Complex.analyticAt_cos, StrictMonoOn.exists_deriv_lt_slope, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_integral, ModularGroup.lcRow0_apply, Complex.analyticOnNhd_cos, hasDerivAt_exp_zero, Complex.imCLM_apply, Real.contDiff_exp, NormedSpace.double_dual_bound, instFieldContMDiffRing, HasDerivAt.comp_ringHom, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, Module.Basis.opNorm_le, Real.differentiable_rpow_const, fun_meromorphicOrderAt_inv, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, ContDiffOn.deriv_of_isOpen, MeasureTheory.ofReal_average, analyticWithinAt_cexp, WeakDual.seminormFamily_apply, Real.analyticWithinAt_cosh, fderiv_cosh, hasDerivWithinAt_inv, hasStrictDerivAt_id, MeromorphicNFAt.fun_zpow, Complex.iteratedDeriv_odd_cosh, differentiableWithinAt_complex_iff_differentiableWithinAt_real, IsExtrFilter.lineDeriv_eq_zero, Complex.contDiff_sin, Differentiable.rpow_const, Complex.contDiff_cos, deriv_neg, OpenPartialHomeomorph.hasStrictDerivAt_symm, integral_re, LeftInvariantDerivation.ext_iff, MeromorphicOn.countable_compl_analyticAt, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Real.hasStrictDerivAt_rpow_const, VectorField.lieBracket_smul_right, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, MeasureTheory.exists_le_average, MeasureTheory.setIntegral_le_nonneg, MeasureTheory.integral_toReal_rnDeriv_mul, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, analyticOrderAt_mul_eq_top_of_right, DifferentiableAt.arctan, HasFPowerSeriesAt.locally_zero_iff, HasStrictDerivAt.complexToReal_fderiv, MeromorphicNFAt.inv, ConvexOn.exists_affine_le_of_lt, RealRMK.le_rieszMeasure_tsupport_subset, hasDerivAt_exp_of_mem_ball, mdifferentiableAt_localFrame_coeff, ContDiffWithinAt.sin, AnalyticAt.cexp', derivWithin_fun_inv', ConvexOn.real_sSup_of_nat_affine_eq, MeasureTheory.integral_norm_eq_pos_sub_neg, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, derivWithin_sinh, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, MeasureTheory.tilted_apply_eq_ofReal_integral', hasDerivAt_zpow, HasDerivAt.sin, MeasureTheory.exists_upperSemicontinuous_lt_integral_gt, HasDerivWithinAt.exp, MeasureTheory.integral_llr_tilted_right, Real.contDiffAt_arcsin, differentiableAt_iff_comp_const_add, signedDist_apply_linear, Real.differentiableAt_sin, StrictConcaveOn.leftDeriv_lt_slope, ContDiff.real_of_complex, integral_re_add_im, ZSpan.coe_fract_self, MeasureTheory.tendsto_integral_norm_approxOn_sub, LeftInvariantDerivation.toFun_eq_coe, Complex.reCLM_enorm, Real.hasDerivAt_sinh, Real.deriv_log_comp_eq_logDeriv, MeasureTheory.rnDeriv_tilted_left_self, Real.deriv_cosh, Real.exists_extension_norm_eq, meromorphicOrderAt_prod, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sin, AffineMap.deriv, DifferentiableWithinAt.sinh, DifferentiableOn.arsinh, contDiffOn_infty_iff_derivWithin, MeasureTheory.SimpleFunc.integral_eq_lintegral', AnalyticOnNhd.iterated_deriv, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, contDiffOn_iff_continuousOn_differentiableOn_deriv, DifferentiableWithinAt.exp, ContDiff.csin, expNegInvGlue.differentiable_polynomial_eval_inv_mul, MeromorphicAt.meromorphicTrailingCoeffAt_mul, DifferentiableWithinAt.rpow, ValueDistribution.logCounting_isBigO_one_iff_analyticOnNhd, Differentiable.rpow, ContDiffAt.exp, MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, differentiableAt_iff_comp_sub_const, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support, complexOfReal_derivWithin, MeromorphicOn.divisor_mul, LinearMap.isAdjointPair_inner, HasDerivWithinAt.log, Real.analyticOnNhd_arcosh, AnalyticOnNhd.eval_mvPolynomial, hasDerivAt_conj_conj_iff, ContinuousLinearMap.hasStrictDerivAt, ContDiffWithinAt.log, ContDiffOn.csinh, MeasureTheory.setIntegral_nonpos_of_ae_restrict, hasFDerivAt_inv, Real.deriv_mul_log_zero, MeasureTheory.Measure.setIntegral_toReal_rnDeriv, MeromorphicAt.meromorphicTrailingCoeffAt_zpow, ContinuousLinearMap.smulRightL_apply_apply, Real.hasDerivAt_sqrt, analyticOn_rexp, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, ValueDistribution.logCounting_inv, Bundle.Trivialization.localFrame_coeff_apply_of_mem_baseSet, Real.hasDerivWithinAt_arccos_Iic, ConcaveOn.slope_le_deriv, measurableSet_of_differentiableWithinAt_Ici, ConvexOn.slope_le_of_hasDerivWithinAt_Iio, Real.contDiffOn_arcsin, ConvexOn.sSup_affine_eq, Real.contDiffAt_arccos_iff, deriv_sqrt_mul_log', LinearIsometry.re_apply_eq_re, Real.differentiableAt_binEntropy_iff_ne_zero_one, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, Real.deriv_tan, ConcaveOn.antitoneOn_deriv, isConformalMap_iff_is_complex_or_conj_linear, BoundedContinuousFunction.tendsto_integral_of_forall_limsup_integral_le_integral, hasFPowerSeriesAt_iff', hasStrictDerivAt_exp_zero, MeasureTheory.Integrable.summable_integral, Differentiable.cos, differentiableAt_comp_sub_const, smooth_functions_tower, Real.contDiffAt_rpow_of_ne, ConcaveOn.le_slope_of_hasDerivAt, Real.hasStrictDerivAt_exp, Complex.conjLIE_toCLE, MeasureTheory.setIntegral_toReal_rnDeriv_mul, MeasureTheory.integral_exp_pos, MeromorphicAt.meromorphicTrailingCoeffAt_pow, LinearMap.mem_span_iff_continuous, Complex.analyticOnNhd_sinh, Complex.analyticWithinAt_cos, ConvexOn.real_sSup_affine_eq, isBoundedBilinearMap_smulRight, HasDerivAt.clog_real, MeasureTheory.lintegral_coe_eq_integral, MeasureTheory.integral_coe_le_of_lintegral_coe_le, HasDerivAt.of_local_left_inverse, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, DifferentiableOn.of_dslope, HasDerivWithinAt.iterate, MeasureTheory.toReal_rnDeriv_tilted_right, AnalyticAt.cexp, Differentiable.div, ContDiffBump.contDiffWithinAt, ContDiff.arsinh, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, LeftInvariantDerivation.coeFnAddMonoidHom_apply, Complex.det_conjLIE, ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero, RCLike.realLinearIsometryEquiv_apply, derivWithin.log, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, ContinuousLinearMap.norm_smulRightL_apply, differentiableAt_iff_comp_neg, ContDiffWithinAt.sqrt, hasFPowerSeriesAt_iff, DifferentiableWithinAt.of_dslope, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, fderiv_sin, HasFPowerSeriesOnBall.exchange_radius, hasStrictDerivAt_pow, Derivation.evalAt_apply, derivWithin_mem_iff, ConvexOn.univ_sSup_of_nat_affine_eq, ContDiffAt.sqrt, ConvexOn.slope_le_leftDeriv_of_mem_interior, MeasureTheory.integral_toReal, ContDiffAt.contDiffBump, NormedSpace.dual_def, HasFDerivAtFilter.hasDerivAtFilter, HasDerivAt.inv, Seminorm.smul_le_smul, exists_eq_const_mul_setIntegral_of_ae_nonneg, HasStrictDerivAt.sqrt, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ModularGroup.smul_eq_lcRow0_add, deriv_cosh, MeasureTheory.tilted_apply', Real.hasDerivWithinAt_arcsin_Iic, MeasureTheory.exists_notMem_null_average_le, differentiableWithinAt_Ioi_iff_Ici, integral_im, fun_meromorphicOrderAt_pow, MeromorphicAt.meromorphicOrderAt_comp, differentiableOn_zpow, Real.iteratedDerivWithin_sin_Ioo, HasDerivWithinAt.fun_inv, deriv_sqrt, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto, Function.FactorizedRational.meromorphicNFOn, contDiff_one_iff_deriv, deriv2_sqrt_mul_log, Real.hasStrictDerivAt_log_of_pos, ValueDistribution.logCounting_mul_zero_le, ContDiff.cosh, MeasureTheory.SignedMeasure.im_toComplexMeasure, ContDiff.div, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, HasDerivWithinAt.limsup_slope_le, DifferentiableWithinAt.cos, Real.deriv2_negMulLog, ContDiffOn.sinh, Urysohns.CU.lim_eq_midpoint, VectorField.mlieBracket_smul_right, fderiv_eq_smul_deriv, ContDiffOn.arsinh, MeasureTheory.toReal_setLAverage, Real.smoothTransition.contDiff, contMDiffOn_iff_localFrame_coeff, AnalyticOn.cexp, Complex.restrictScalars_toSpanSingleton', Real.differentiableAt_negMulLog_iff, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, Complex.differentiable_iteratedDeriv_cosh, Complex.rectangle_eq_convexHull, analyticAt_cexp, IsLocalMinOn.fderivWithin_eq_zero, Real.deriv2_mul_log, Complex.reCLM_apply, Real.hasDerivAt_negMulLog, Complex.conjLIE_symm, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, StrictConvexOn.slope_lt_of_hasDerivAt, deriv_id', MeasureTheory.L1.norm_eq_integral_norm

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
noncompactSpace 📖	mathematical	—	NoncompactSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing toNormedCommRing	—	NormedSpace.noncompactSpace IsSimpleRing.instNontrivial DivisionRing.isSimpleRing

NormedSpace

Definitions

Name	Category	Theorems
induced 📖	CompOp	—
ofCore 📖	CompOp	—
restrictScalars 📖	CompOp	5 math math: Convex.convex_isRCLikeNormedField, curveIntegralFun_def', ModelWithCorners.convex_range', curveIntegral_def', restrictScalars_eq
toModule 📖	CompOp	8719 math, 1 bridge math: Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, HasDerivAt.fun_neg, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, MeasureTheory.L1.setToL1_eq_setToL1', instSeparatingDual, TangentBundle.continuousLinearMapAt_model_space, hasFDerivWithinAt_pi'', hasFDerivAt_iff_hasDerivAt, TestFunction.lineDerivCLM_apply_of_le, ContinuousLinearEquiv.antilipschitz, EuclideanGeometry.Sphere.vadd_mem_inter_orthRadius_iff_norm_sq, MeasureTheory.Measure.integral_comp_inv_smul, VectorBundleCore.toFiberBundleCore_coordChange, ContMDiffAt.coordChangeL, iteratedDeriv_scomp_two, HasDerivAt.isLittleO, MeromorphicOn.deriv, TensorProduct.mapInclIsometry_apply, ContinuousOn.clm_apply, LinearMap.IsSymmetric.clm_adjoint_eq, ContinuousLinearMap.rayleigh_smul, Real.differentiableOn_arcosh, Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, Real.hasDerivAt_fourier, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, WeakFEPair.differentiableAt_Λ, Differentiable.arsinh, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, HasStrictFDerivAt.log, LinearIsometryEquiv.strictConvex_preimage, TemperedDistribution.lineDerivOpCLM_eq, Bundle.Trivialization.symm_continuousLinearEquivAt_eq, PiTensorProduct.mapL_id, HasStrictFDerivAt.map_implicitFunctionOfComplemented_eq, IsIntegralCurve.comp_mul, closure_diff_intrinsicFrontier, Submodule.starProjection_apply_eq_isComplProjection, Orientation.oangle_sign_smul_add_right, DiffContOnCl.smul, MeasureTheory.Lp.toTemperedDistributionCLM_apply, fderiv_iteratedFDeriv, Orientation.kahler_map_complex, Polynomial.differentiableWithinAt, ContinuousLinearMap.inner_map_map_of_mem_unitary, HasStrictDerivAt.fun_pow', DifferentiableOn.zpow, MeasureTheory.setIntegral_tilted, FormalMultilinearSeries.comp_rightInv_aux1, integrableOn_cfcₙ', ContinuousLinearMap.hasFPowerSeriesOnBall, MDifferentiable.coordChangeL, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, Differentiable.const_sub, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, IsBoundedLinearMap.differentiableAt, MeasureTheory.setToFun_add_left, hasStrictFDerivAt_const_add_iff, Seminorm.isBounded_const, Affine.Simplex.altitudeFoot_restrict, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, isConformalMap_conj, LinearMap.mkContinuous₂_norm_le', FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_changeOrigin, LinearMap.IsStarProjection.ext_iff, hasStrictFDerivAt_apply, differentiableWithinAt_finCons', Orthonormal.linearIndependent, HasDerivWithinAt.clog_real, ContinuousMultilinearMap.norm_mkPiRing, differentiableAt_comp_const_add, taylor_integral_remainder, fderiv_snd, LinearIsometryEquiv.hasStrictFDerivAt, Bundle.Trivial.continuousLinearEquivAt_trivialization, ContinuousLinearMap.derivWithin_of_bilinear, DifferentiableWithinAt.const_sub, EuclideanGeometry.dist_smul_vadd_sq, Bundle.ContMDiffRiemannianMetric.isVonNBounded, HasDerivWithinAt.clm_comp, isBounded_polar_of_mem_nhds_zero, SchwartzMap.lineDerivOpCLM_eq, deriv_sub_const_fun, real_inner_div_norm_mul_norm_eq_neg_one_iff, SchauderBasis.norm_proj_le_nnnormProjBound, TensorProduct.enorm_lid, EuclideanGeometry.euclideanHausdorffMeasure_eq, HasDerivWithinAt.congr_of_mem, ConformalAt.differentiableAt, Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent, differentiableAt_comp_neg, continuous_cfcₙHomSuperset_left, MeasureTheory.condExpInd_of_measurable, deriv_exp, MeromorphicAt.fun_iterated_deriv, hasDerivWithinAt_Iio_iff_Iic, cfcₙL_integral, HasStrictFDerivAt.fun_mul', unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, LinearMap.mkContinuous₂_apply, isNonneg_inner, ContinuousLinearMap.le_of_opNorm_le_of_le, TensorProduct.inner_tmul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, HasMFDerivAt.mul, extDerivWithin_fun_add, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, LinearIsometryEquiv.comp_fderiv, MeasureTheory.condExpL1_smul, AffineIsometry.image_intrinsicClosure, ContinuousLinearMap.isBigO_comp, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, ContinuousAlternatingMap.opNorm_prod, MonotoneOn.intervalIntegral_slope_le, HasDerivAt.const_rpow, Distribution.delta_apply, Submodule.IsCompl.projection_isSymmetricProjection_iff, Orthonormal.inner_left_finsupp, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, StandardSubspace.toClosedSubmodule_injective, Real.differentiable_arctan, norm_cfcₙHom, ProperCone.innerDual_le_innerDual, HasFDerivWithinAt.continuousMultilinearMap_apply, Filter.EventuallyEq.derivWithin_eq_of_nhds, Bundle.Trivialization.symm_continuousLinearEquivAt_eq', RCLike.map_apply, LinearMap.bound_of_shell, AffineIsometryEquiv.coe_mk, MDifferentiableOn.clm_postcomp, Real.differentiableAt_mulExpNegMulSq, EuclideanGeometry.Cospherical.subtype_val_iff, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, OrthonormalBasis.orthogonalProjection_eq_sum, hasDerivWithinAt_ofNat, Collinear.wbtw_of_dist_eq_of_dist_le, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', MeasureTheory.aestronglyMeasurable_condExpInd, Differentiable.csin, HasCompactSupport.convolution_integrand_bound_left, HasStrictFDerivAt.abs_of_pos, ContinuousLinearMap.compSL_apply, HasStrictFDerivAt.implicitToOpenPartialHomeomorphOfComplemented_fst, ContinuousLinearMap.continuous₂, MeasureTheory.Martingale.smul, LinearMap.IsSymmetric.inner_map_polarization, Distribution.dsupport_delta, fderivWithin_comp_derivWithin_of_eq, HasDerivAt.const_sub, ContinuousLinearEquiv.differentiable, ContinuousLinearMap.opNorm_prod, hasDerivWithinAt_add_const_iff, IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, ContinuousLinearMap.integral_compLp, FormalMultilinearSeries.comp_partialSum, MeasureTheory.integral_convexOn_of_integrand_ae, mellin_eq_fourier, Affine.Triangle.oangle_excenter_singleton_eq_add_pi, SchwartzMap.instLineDerivLeftSMulReal, tendsto_birkhoffAverage_apply_sub_birkhoffAverage', LinearMap.adjoint_adjoint, HasFTaylorSeriesUpTo.differentiable, Complex.cderiv_eq_deriv, DoubleCentralizer.star_snd, ContinuousLinearMap.norm_inr_le_one, HasDerivAtFilter.sum, Affine.Simplex.orthogonalProjectionSpan_map, taylorWithin_succ, TensorProduct.ext_iff_inner_left, MeasureTheory.Measure.addHaar_image_continuousLinearMap, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, HasFDerivWithinAt.ccos, differentiableOn_star_iff, derivWithin_zero_of_frequently_mem, Continuous.clm_comp_const, InnerProductSpace.toLinearIsometry_toDual, HasStrictDerivAt.to_localInverse, RCLike.ofRealCLM_apply, SchwartzMap.integral_sesq_fourier_fourier, HasMFDerivAt.add, deriv_arctan, Real.dimH_of_mem_nhds, AnalyticOn.exists_hasFTaylorSeriesUpToOn, Filter.IsBoundedUnder.smul_tendsto_zero, MeasureTheory.charFun_eq_fourierIntegral', HasFDerivAt.const_add, DiffContOnCl.circleAverage_poissonKernel_smul', hasFDerivAt_comp_add_right, Real.hasFDerivAt_fourierChar_neg_bilinear_left, HasDerivWithinAt.Iio_of_Iic, InnerProductSpace.span_gramSchmidtNormed, Real.differentiableAt_arcsin, LinearIsometryEquiv.analyticOnNhd, LinearMap.toLinearMap_tracePositiveLinearMap, QuadraticMap.lineDeriv, hasStrictDerivAt_intCast, measurable_lineDeriv, segment_subset_closedBall_right, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, Complex.linearEquiv_det_conjLIE, ContinuousWithinAt.cfcₙ, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, MeasureTheory.convolution_eq_right', Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, DifferentiableWithinAt.log, hasFDerivAt_iff_hasGradientAt, ConvexOn.le_slope_of_hasDerivAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, Isometry.preimage_perpBisector, RCLike.reCLM_apply, ContinuousLinearMap.opNorm_le_of_unit_norm, HasStrictDerivAt.rpow, smooth_barycentric_coord, NumberField.Units.finrank_eq_rank, StrictConvexOn.slope_lt_leftDeriv, ContinuousMultilinearMap.cpolynomialOn, LinearIsometry.norm_compContinuousAlternatingMap, MeasureTheory.hausdorffMeasure_segment, ClosedSubmodule.sub_mem_orthogonal_of_inner_right, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, IsHilbertSum.surjective_isometry, curveIntegral_smul, InnerProductSpace.volume_closedBall_of_dim_even, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face, MeasureTheory.L1.setToL1_indicatorConstLp, fun_iteratedFDeriv_add_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, Submodule.reflection_trans_reflection, dist_midpoint_right, HasLineDerivWithinAt.mono_of_mem_nhdsWithin, Orientation.inner_rotation_pi_div_two_right_smul, extDeriv_constOfIsEmpty, Orientation.oangle_add_left_smul_rotation_pi_div_two, ContinuousLinearMap.exists_preimage_norm_le, Convex.norm_image_sub_le_of_norm_fderivWithin_le', CFC.monotoneOn_one_sub_one_add_inv, Bundle.Trivial.symmL_trivialization, Real.fourierIntegral_comp_linearIsometry, SchauderBasis.RankOneDecomposition.proj_tendsto, derivWithin_smul, Real.fderiv_fourierIntegral, Differentiable.fun_div, Submodule.orthogonalDecomposition_symm_apply, hasStrictFDerivAt_list_prod_finRange', Affine.Simplex.sSameSide_excenter_singleton_point, MeasureTheory.integral_smul_nnreal_measure, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, OrthogonalFamily.linearIsometry_apply_single, DifferentiableOn.fun_add, LinearIsometry.nnnorm_toContinuousLinearMap, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, ConvexOn.rightDeriv_le_slope_of_mem_interior, Submodule.IsOrtho.starProjection_comp_starProjection, IsHilbertSum.mkInternal, AffineIsometryEquiv.coe_symm_toAffineEquiv, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, ContDiffAt.implicitFunction_def, NonUnitalCStarAlgebra.toStarModule, Complex.circleTransformDeriv_eq, AnalyticOn.domDomCongr_iteratedFDerivWithin, hasDerivAt_sqrt_mul_log, LinearMap.IsSymmetric.restrictScalars, ContinuousAffineMap.fderiv, StrongDual.norm_extendRCLike, Affine.Triangle.oangle_incenter_eq, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, ContinuousLinearMap.continuous_det, HasFiniteFPowerSeriesAt.neg, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, HasStrictFDerivAt.csin, nnnorm_cfcₙ_nnreal_le_iff, ZSpan.volume_real_fundamentalDomain, isSeparable_range_derivWithin, PiTensorProduct.mapLMonoidHom_apply, ContinuousLinearMap.opNorm_bound_of_ball_bound, Complex.ofRealCLM_coe, Complex.kahler, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, ClosedSubmodule.toSubmodule_orthogonal_eq, ContinuousLinearMap.map_add_add, ContinuousAlternatingMap.norm_constOfIsEmpty, IsBoundedBilinearMap.hasFDerivAt, fderivWithin_comp_add_left, MeasureTheory.Measure.integral_comp_mul_right, HasFDerivWithinAt.pow, RightDerivMeasurableAux.D_subset_differentiable_set, ContinuousLinearMap.sSup_unit_ball_eq_norm, Convex.convex_isRCLikeNormedField, Complex.areaForm, intervalIntegral.inv_smul_integral_comp_div_add, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, LinearMap.instIsOrderedAddMonoidId, WeakDual.isCompact_polar, MeromorphicOn.divisor_fun_smul, finrank_real_complex_fact', intervalIntegral.derivWithin_integral_of_tendsto_ae_left, ClosedSubmodule.mem_iff, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, HasDerivWithinAt.div_const, Real.deriv_negMulLog, Real.hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, ContDiffMapSupportedIn.seminorm_monoLM_eq, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, fderivWithin_fun_smul, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, Polynomial.derivWithin_aeval, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Dual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.analyticWithinAt, ContinuousAffineMap.differentiableWithinAt, Complex.hasSum_deriv_of_summable_norm, HasDerivWithinAt.congr_mono, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, complexOfReal_hasDerivWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, Real.fourierIntegralInv_eq', AffineMap.hasDerivAtFilter, HasFDerivWithinAt.add, PositiveLinearMap.apply_le_of_isSelfAdjoint, Matrix.IsHermitian.det_abs, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_le, RCLike.ofRealLI_apply, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, LinearMap.IsPositive.ne_zero_iff, HasCompactSupport.integral_Ioi_deriv_eq, hasDerivAt_integral_of_dominated_loc_of_lip, hasFDerivAtFilter_pi, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, deriv_abs, curveIntegrable_segment, differentiableAt_zpow, hasFDerivAt_multiset_prod, Affine.Simplex.finiteDimensional_direction_altitude, MDifferentiableAt.cle_arrowCongr, ContinuousLinearMap.frontier_preimage, LinearMap.isPositive_adjoint_comp_self, ProbabilityTheory.covarianceBilinDual_apply', Manifold.IsImmersionAt.map_target_subset_target, DifferentiableAt.finCons, Real.nnnorm_deriv_mulExpNegMulSq_le_one, Submodule.toLinearEquiv_orthogonalDecomposition_symm, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, OrthonormalBasis.repr_injective, LinearMap.IsSymmetric.isFinitelySemisimple, derivWithin_id', iteratedDeriv_succ, Real.deriv_binEntropy, CFC.monotone_nnrpow, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', intervalIntegral.integral_derivWithin_uIcc_of_contDiffOn_uIcc, measurable_deriv_with_param, not_differentiableAt_of_local_left_inverse_hasDerivAt_zero, HasDerivWithinAt.liminf_right_slope_le, Complex.integral_boundary_rect_eq_zero_of_differentiableOn, hasFTaylorSeriesUpToOn_top_iff_right, MeasureTheory.charFunDual_apply, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, DifferentiableAt.mul, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Differentiable.fun_sub_iff_right, Complex.ofRealLI_apply, fderivWithin_extChartAt_comp_extChartAt_symm_range, DifferentiableOn.restrictScalars, Affine.Simplex.circumcenter_map, conformalAt_iff, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, DifferentiableOn.sqrt, HasFPowerSeriesWithinOnBall.hasSum_sub, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, MDifferentiableWithinAt.differentiableWithinAt_mpullbackWithin_vectorField, intervalIntegral.integral_hasDerivWithinAt_right, deriv_mem_iff, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, Matrix.spectrum_toEuclideanLin, ContDiff.iteratedFDeriv_right, norm_add_eq_iff_real, Complex.integral_comp_pi_polarCoord_symm, AnalyticAtWithin.compContinuousLinearMap, FormalMultilinearSeries.radius_pi_eq_iInf, ContinuousLinearMap.norm_inl_le_one, hasStrictFDerivAt_of_hasFDerivAt_of_continuousAt, iteratedFDeriv_sum_apply, MeasureTheory.norm_condExpL2_le, IsLocalMaxOn.hasFDerivWithinAt_nonpos, contDiffAt_norm_smul_iff, ProbabilityTheory.IsGaussian.integrable_dual, ZSpan.floor_eq_self_of_mem, ContinuousLinearEquiv.contDiff_comp_iff, AlternatingMap.continuous_of_bound, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, norm_iteratedFDerivWithin_smul_le, ContinuousLinearMap.opNorm_le_bound', ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan, MeasureTheory.weightedSMul_apply, ContinuousMultilinearMap.norm_map_snoc_le, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, ContinuousLinearMap.comp_condExp_comm, Differentiable.clm_comp, not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioi, ImplicitFunctionData.isInvertible_fderiv_prodFun, derivWithin_mul_const, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, iteratedFDerivWithin_eventually_congr_set, ApproximatesLinearOn.lipschitz, HasDerivWithinAt.cosh, Real.hasStrictDerivAt_rpow_const_of_ne, logDeriv_comp, Orientation.linearEquiv_det_rotation, mdifferentiableOn_iff, StrongDual.polarSubmodule_eq_setOf, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousLinearMap.isBigOWith_sub, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, EuclideanGeometry.Sphere.wbtw_secondInter, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, HasStrictDerivAt.pow, ContDiff.hasStrictFDerivAt, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, DifferentiableAt.div, hasDerivWithinAt_taylorWithinEval, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite, Differentiable.continuousMultilinear_apply_const, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, DifferentiableWithinAt.finCons, Meromorphic.deriv, norm_iteratedFDerivWithin_one, HasFTaylorSeriesUpTo.cont, ContDiffAt.clm_apply, ImplicitFunctionData.isCompl_ker, EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne, HasDerivAt.hasDerivWithinAt, ContinuousLinearMap.hasDerivAtFilter, fderivWithin_csinh, DoubleCentralizer.intCast_snd, Real.fourierIntegral_eq, PeriodPair.basis_one, mdifferentiableWithinAt_iff_of_mem_maximalAtlas, MeasureTheory.L1.norm_setToL1_le, HasDerivAtFilter.comp_hasFDerivAtFilter, StrictConvexOn.deriv_lt_slope, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, DoubleCentralizer.range_toProdMulOpposite, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, HasDerivWithinAt.fun_div, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, Submodule.re_inner_starProjection_eq_normSq, RCLike.conjCLE_norm, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, ProperCone.innerDual_univ, Affine.Simplex.circumcenter_mem_affineSpan, HasFPowerSeriesOnBall.add, differentiableWithinAt_pi'', HasDerivWithinAt.complexToReal_fderiv', Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude, Orientation.kahler_comp_rightAngleRotation', dist_sq_lineMap_lineMap_of_inner_eq_zero, circleIntegral_def_Icc, DifferentiableAt.fun_inv, Differentiable.cosh, VectorField.fderiv_apply_lieBracket, Differentiable.add_iff_right, MeasureTheory.inner_condExpL2_left_eq_right, MeasureTheory.integral_unique, HasFDerivWithinAt.of_local_left_inverse, Orientation.rotation_eq_self_iff, setIntegral_withDensity_eq_setIntegral_smul₀, ContinuousLinearMap.opNorm_ext, Complex.hasSum_taylorSeries_of_entire, Affine.Simplex.excenter_singleton_mem_affineSpan_range, OpenPartialHomeomorph.hasDerivAt_symm, ProbabilityTheory.hasSum_integral_poissonMeasure, AnalyticOnNhd.compContinuousLinearMap, AffineIsometryEquiv.linear_eq_linear_isometry, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, WeakDual.isClosed_image_polar_of_mem_nhds, intervalIntegral.intervalIntegral_eq_integral_uIoc, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, derivWithin_const, ZLattice.covolume_eq_det_inv, ContinuousLinearMap.integral_apply, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, differentiableWithinAt_neg_iff, HasDerivAt.fun_finset_prod, circleIntegrable_iff, ProbabilityTheory.covarianceBilinDual_apply, Submodule.reflection_orthogonal_apply, hasFDerivAt_stereoInvFunAux, OpenPartialHomeomorph.hasStrictFDerivAt_symm, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ContinuousLinearMap.comp_memLp, IsOpen.exists_subset_affineIndependent_span_eq_top, ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_toLinearEquiv, Real.fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.orthogonal_ker, SchauderBasis.tendsto_proj, ProbabilityTheory.isGaussian_multivariateGaussian, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearIsometryEquiv.comp_fderivWithin, EuclideanGeometry.orthogonalProjection_congr, LinearMap.IsPositive.re_inner_nonneg_right, Real.fourier_continuousLinearMap_apply, intervalIntegral.integral_deriv_of_contDiffOn_uIcc, Unitization.real_cfcₙ_eq_cfc_inr, norm_iteratedFDeriv_comp_le', real_inner_smul_self_left, banach_steinhaus_iSup_nnnorm, ProbabilityTheory.IndepFun.charFunDual_map_fun_add_eq_mul, norm_iteratedFDeriv_mul_le, fderivWithin_fun_pow', SchauderBasis.proj_zero, intervalIntegral.fderiv_integral_of_tendsto_ae, ContDiffAt.fderiv_right_succ, ImplicitFunctionData.hasStrictFDerivAt_leftFun, LipschitzWith.memLp_lineDeriv, Orientation.volumeForm_robust_neg, Submodule.starProjection_orthogonal', RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, isBounded_iff_subset_smul_ball, AffineIsometryEquiv.ofTop_apply, deriv_fun_finset_prod, deriv_eq, HasFDerivWithinAt.clm_apply, DoubleCentralizer.natCast_fst, hasFPowerSeriesOnBall_pi_iff, SmoothPartitionOfUnity.contMDiffAt_finsum, LinearMap.IsSymmetric.im_inner_self_apply, DifferentiableAt.prodMap, ContinuousLinearMap.IsPositive.toLinearMap, AnalyticOnNhd.iteratedFDeriv_of_isOpen, ContinuousLinearMap.norm_compLp_le, Submodule.toLinearEquiv_orthogonalDecomposition, HasFPowerSeriesOnBall.unshift, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, Affine.Simplex.dist_point_faceOppositeCentroid, differentiableWithinAt_abs_pos, continuousOn_dslope, ContinuousLinearEquiv.symm_toDiffeomorph, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, StrictConcaveOn.lt_slope_of_hasDerivAt, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, ContinuousAlternatingMap.opNNNorm_pi, HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', Module.Dual.extendRCLikeₗ_symm_apply, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, iteratedDerivWithin_vcomp_two, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Orientation.areaForm_le, ContinuousWithinAt.continuousLinearMapCoprod, isClosedEmbedding_cfcₙAux, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, setIntegral_withDensity_eq_setIntegral_toReal_smul, DifferentiableOn.sub_const, deriv_comp_const_sub, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, TensorProduct.enorm_comm, innerSL_apply_apply, Submodule.isOrtho_sup_right, fderiv_multiset_prod, HasFPowerSeriesWithinOnBall.restrictScalars, isVonNBounded_iff, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Orthonormal.codRestrict, ProbabilityTheory.covarianceBilin_multivariateGaussian, DifferentiableWithinAt.sqrt, aemeasurable_smul_const, LinearIsometry.rTensor_def, DifferentiableWithinAt.fun_const_smul, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, LinearIsometryEquiv.fderivWithin, Affine.Simplex.incenter_map, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerₛₗ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, Real.differentiable_sinh, HasFTaylorSeriesUpTo.hasFDerivAt, HasFDerivAtFilter.fun_sum, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, LinearMap.singularValues_zero, norm_iteratedFDerivWithin_clm_apply, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, MeasureTheory.Measure.toSphere_apply_aux, Orientation.neg_rotation, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, HasFDerivAtFilter.sub, Unitization.splitMul_apply, GaussianFourier.integral_cexp_neg_mul_sq_norm, tendsto_integral_peak_smul_of_integrable_of_tendsto, ContMDiffOn.clm_postcomp, inner_eq_norm_mul_iff, Bundle.Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, differentiable_fun_neg_iff, Measurable.apply_continuousLinearMap, ProbabilityTheory.covarianceBilin_apply_eq_cov, iteratedDerivWithin_comp_two, ProbabilityTheory.covarianceBilin_self, DoubleCentralizer.nnnorm_def', deriv_fun_sum, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, DifferentiableWithinAt.add, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, ClosedSubmodule.orthogonal_gc, LinearMap.isPositive_id, dist_left_midpoint, AffineSubspace.left_mem_perpBisector, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, dist_iteratedFDerivWithin_one, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, image_isVonNBounded_iff, nnnorm_cfcₙ_lt_iff, EuclideanGeometry.preimage_inversion_perpBisector_inversion, eqOn_dslope_sub_smul, deriv_mul_const_field, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, Submodule.orthogonalProjection_mem_subspace_eq_self, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, ContinuousLinearMap.nnnorm_def, ContinuousLinearMap.IsPositive.inner_nonneg_right, DifferentiableOn.deriv, Differentiable.fun_smul, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', StrictConcaveOn.slope_lt_rightDeriv, TemperedDistribution.fourierMultiplierCLM_smul, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, Orientation.eq_rotation_self_iff_angle_eq_zero, hasDerivAt_bernoulliFun, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, FormalMultilinearSeries.le_changeOriginSeries_radius, Orientation.volumeForm_neg_orientation, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, derivWithin_fderivWithin, HasFDerivWithinAt.prodMap, norm_iteratedFDerivWithin_comp_le_aux, derivWithin_natCast, intervalIntegral.integral_deriv_smul_comp', DifferentiableOn.cpow_const, deriv_fun_pow', CFC.nnnorm_sqrt, IsometryEquiv.toRealLinearIsometryEquiv_apply, MeasureTheory.condExpIndL1Fin_smul, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, MultilinearMap.mkContinuousMultilinear_apply, InnerProductSpace.span_gramSchmidtNormed_range, ImplicitFunctionData.implicitFunction_hasStrictFDerivAt, HasFDerivWithinAt.hasLineDerivWithinAt, ContinuousLinearMap.opNorm_comp_linearIsometryEquiv, ProbabilityTheory.uncenteredCovarianceBilin_apply, Submodule.orthogonal_disjoint, InnerProductGeometry.angle_smul_right_of_pos, HasFDerivWithinAt.complexOfReal, StrongDual.norm_extendRCLike_bound, TemperedDistribution.lineDerivOp_fourier_eq, WeakFEPair.symm_Λ₀_eq, ContDiffPointwiseHolderAt.isBigO, Real.deriv_log, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, ContDiff.differentiable_deriv_two, StrictConvexOn.rightDeriv_lt_slope, SchwartzMap.decay', Module.Basis.ofZLatticeBasis_apply, ContinuousAlternatingMap.map_insertNth, derivWithin_arctan, intervalIntegral.integral_comp_sub_div, FormalMultilinearSeries.derivSeries_coeff_one, VonNeumannAlgebra.ext_iff, Filter.EventuallyEq.lineDerivWithin_eq, Complex.ofRealCLM_norm, Submodule.starProjection_add_starProjection_orthogonal, ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le, HasStrictFDerivAt.add_const, Matrix.spectrum_toLpLin, HasDerivAt.comp_ofReal, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, tangentConeAt_nonempty_of_properSpace, instIsZLatticeComap, not_differentiableAt_norm_zero, ContinuousOn.cfcₙ', mdifferentiableOn_symm_coordChangeL, DifferentiableAt.csinh, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, intervalIntegral.integral_comp_mul_left, StarAlgebra.elemental.characterSpaceToSpectrum_coe, LipschitzWith.ae_exists_fderiv_of_countable, rotation_injective, Continuous.integral_hasStrictDerivAt, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, deriv_const_smul, fderiv_clm_comp, BoxIntegral.unitPartition.mem_smul_span_iff, intervalIntegral.integral_comp_mul_sub, ProbabilityTheory.measurePreserving_restrict₂_multivariateGaussian, SchwartzMap.bilinLeftCLM_apply, derivWithin_congr, HasDerivAt.comp_hasFDerivAt_of_eq, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, OrthogonalFamily.of_pairwise, GeneralSchauderBasis.tendsto_proj, deriv_mul_const, IsConformalMap.is_complex_or_conj_linear, fderiv_continuousAlternatingMap_apply_const, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, AkraBazziRecurrence.isBigO_apply_r_sub_b, HasStrictFDerivAt.finCons, HasGradientAt.hasDerivAt', MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, derivWithin_comp_const_sub, IsHilbertSum.linearIsometryEquiv_symm_apply, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, DifferentiableAt.sigmoid, Affine.Triangle.sbtw_touchpoint_singleton, Affine.Triangle.dist_point_faceOppositeCentroid, OrderedFinpartition.norm_applyOrderedFinpartition_le, ContinuousLinearMap.cpolynomialAt, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_same_orientation, differentiableOn_pi, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, HasFPowerSeriesAt.eventually_hasSum, HasDerivAt.clm_apply, LeftInvariantDerivation.left_invariant, ContinuousLinearMap.comp_condExp_add_const_comm, ContDiffMapSupportedIn.seminorm_fderivLM_le, RKHS.coe_smul, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContDiffMapSupportedIn.seminorm_fderivLM_top, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Affine.Simplex.mem_circumsphere, HasStrictDerivAt.of_local_left_inverse, hasStrictFDerivAt_snd, IsGreatest.nnnorm_cfcₙ, Complex.convexHull_reProdIm, toIsBoundedSMul, Complex.conjLIE_apply, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux, ContDiffWithinAt.clm_apply, CPolynomialOn.iterated_deriv, ContDiff.continuous_deriv_one, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, EuclideanGeometry.orthogonalProjection_contLinear, curveIntegralFun_smul, Bundle.Trivialization.localFrame_coeff_apply_of_notMem_baseSet, intervalIntegral.integral_deriv_eq_sub, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt, hasDerivAt_exp_zero_of_radius_pos, Module.Basis.exists_opNorm_le, ClosedSubmodule.mem_orthogonal', ContinuousLinearMap.ker_le_ker_iff_range_le_range, egauge_ball_le_of_one_lt_norm, fourierIntegral_gaussian_innerProductSpace', ContinuousAffineMap.differentiable, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, MeasureTheory.charFun_toDual_symm_eq_charFunDual, hasDerivWithinAt_iff_isLittleO, GeneralSchauderBasis.proj_apply, AnalyticOn.iteratedFDerivWithin, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, extDerivWithin_pullback, derivWithin_fun_const_smul_field, DifferentiableOn.clm_apply, ContMDiff.clm_apply, OrthogonalFamily.orthonormal_sigma_orthonormal, Differentiable.fun_inv, mdifferentiableWithinAt_iff_target_inter, differentiableWithinAt_fun_neg_iff, LinearMap.continuous_of_seq_closed_graph, InnerProductSpace.canonicalCovariantTensor_eq_sum, MeasureTheory.charFun_eq_fourierIntegral, ContinuousAlternatingMap.piLIE_apply_apply, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, combo_mem_ball_of_ne, UniqueMDiffOn.uniqueDiffOn, fderivWithin_fderivWithin, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, EuclideanGeometry.oangle_sign_eq_zero_iff_collinear, Set.OrdConnected.image_deriv, ContinuousLinearMap.isBigOWith_id, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, HasFDerivAt.of_isLittleO, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, curveIntegrable_fun_neg_iff, hasDerivWithinAt_zero, AlternatingMap.bound_of_shell_of_continuous, HasStrictDerivAt.pow', TestFunction.monoCLM_eq_zero, TopologicalGroup.IsSES.integral_inducedMeasure, LineDifferentiableWithinAt.lineDifferentiableAt, hasDerivAt_star_conj_iff, ContDiffAt.hasStrictDerivAt, ContinuousLinearEquiv.coe_toDiffeomorph_symm, Submodule.reflection_symm, Differentiable.fun_neg, OrthonormalBasis.det_eq_neg_det_of_opposite_orientation, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces, MeasureTheory.isAddHaarMeasure_hausdorffMeasure, TensorProduct.ext_iff_inner_right_threefold', tangentCoordChange_def, FormalMultilinearSeries.hasSum_of_finite, signedDist_right_congr, Filter.EventuallyEq.lineDeriv_eq, differentiableWithinAt_inv, CurveIntegrable.zero, fderiv_comp_deriv, ContinuousMultilinearMap.contDiffAt, hasDerivAtFilter_ofNat, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, VectorField.mlieBracket_smul_left, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, Complex.hasSum_taylorSeries_on_ball, TensorProduct.toLinearEquiv_lidIsometry, HasFPowerSeriesOnBall.restrictScalars, ContDiffOn.clm_apply, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, Real.differentiableOn_arcsin, HasFDerivAtFilter.const_add, ContinuousLinearMap.opNNNorm_le_iff, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, derivWithin_zero_of_frequently_const, ContinuousLinearMap.isometry_mul_flip, DiffContOnCl.differentiableAt', ZSpan.smul, DifferentiableOn.fun_mul, AnalyticOnNhd.eval_linearMap', HasStrictFDerivAt.mul', inner_gradientWithin_right, EuclideanGeometry.reflection_map, fderiv_fun_pow, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, Module.Basis.ofZLatticeComap_apply, AffineEquiv.continuous_of_finiteDimensional, conformal_const_smul, ProbabilityTheory.HasGaussianLaw.toLp_pi, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, HasStrictFDerivAt.comp_hasStrictDerivAt, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, HasFDerivAtFilter.const_sub, balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, NumberField.natAbs_discr_eq_natAbs_discr_pow_mul_natAbs_discr_pow, ContinuousLinearMap.isPositive_natCast, tendsto_birkhoffAverage_apply_sub_birkhoffAverage, ContinuousMultilinearMap.opNorm_zero_iff, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, hasStrictFDerivAt_exp_smul_const_of_mem_ball', MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, contDiffOn_iff_continuousOn_differentiableOn, DifferentiableWithinAt.inverse, Submodule.sub_mem_orthogonal_of_inner_left, hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, WithCStarModule.prod_norm_sq, Submodule.starProjection_comp_starProjection_eq_zero_iff, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, FDerivMeasurableAux.differentiable_set_subset_D, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, CStarModule.innerSL_apply, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt, MeromorphicOn.fun_smul, monomial_has_deriv_aux, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.smul_convolution, Bundle.ContinuousLinearMap.vectorBundle, Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff, Real.vector_fourierIntegral_eq_integral_exp_smul, StrictConvexOn.strictMonoOn_deriv, ContinuousLinearMap.isCompact_image_coe_of_bounded_of_closed_image, HasDerivWithinAt.sub, HasFDerivAt.le_of_lipschitzOn, DifferentiableAt.clog, DifferentiableAt.zpow, LinearMap.toMatrixOrthonormal_reindex, contDiff_one_iff_fderiv, MeasureTheory.ConvolutionExistsAt.integrable, LinearMap.ker_self_comp_adjoint, Complex.taylorSeries_eq_of_entire, nndist_midpoint_right, HasStrictFDerivAt.pow, Real.hasDerivAt_mul_log, IsBoundedLinearMap.differentiableWithinAt, Real.fourier_real_eq_integral_exp_smul, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, EuclideanGeometry.Sphere.mem_tangentsFrom_iff, derivWithin_cosh, ProbabilityTheory.covarianceOperator_apply, fderivWithin_sinh, InnerProductGeometry.angle_smul_left_of_neg, iter_deriv_zpow', derivWithin_fun_mul, differentiableWithinAt_abs, MeasureTheory.integral_tilted, ContDiffAt.laplacian_CLM_comp_left, CStarAlgebra.span_nonneg_inter_unitBall, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, Real.deriv_arccos, HasFDerivWithinAt.comp_of_tendsto, Complex.differentiableOn_dslope, hasDerivAt_of_hasDerivAt_of_ne, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, MeasureTheory.average_mem_openSegment_compl_self, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, HasFiniteFPowerSeriesOnBall.sum, HasStrictFDerivAt.const_mul, Distribution.IsVanishingOn.smulLeftCLM, LocallyBoundedVariationOn.ae_differentiableWithinAt, MeasureTheory.Measure.toSphere_real_apply_univ, ContinuousLinearMap.opNorm_mul_flip_apply, deriv_conj_conj, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, DifferentiableOn.smul_const, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum, ContinuousLinearMap.ebound, InnerProductSpace.inner_left_rankOne_apply, cfcₙHom_nnreal_eq_restrict, integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable, HasFDerivWithinAt.fst, norm_iteratedFDeriv_clm_apply, TestFunction.toBoundedContinuousFunctionCLM_apply, Conformal.const_smul, MeasureTheory.Lp.instFourierInvSMul, IsLocalFrameOn.coeff_apply_of_mem, hasFDerivWithinAt_sub_const_iff, ClosedSubmodule.orthogonal_injective, ContinuousAlternatingMap.norm_def, ContinuousLinearEquiv.hasTemperateGrowth, InnerProductSpace.gramSchmidtNormed_linearIndependent, stronglyMeasurable_derivWithin_Ioi, HasFDerivAt.finset_prod, ContinuousLinearMap.ofMemClosureImageCoeBounded_apply, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, ContinuousLinearMap.smul_compLp, difference_quotients_converge_uniformly, hasDerivWithinAt_abs_pos, HasDerivWithinAt.sub_const, Submodule.norm_starProjection_apply_le, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, Bundle.Trivialization.localFrame_coeff_congr, ContinuousLinearMap.contMDiff, ContinuousLinearMap.mdifferentiable, StrictConcaveOn.slope_lt_derivWithin, HasStrictFDerivAt.fun_sum, HasSum.hasSum_at_zero, HasFPowerSeriesAt.add, differentiableWithinAt_sub_const_iff, HasFDerivAt.norm_sq, differentiable_descPochhammer_eval, VectorBundleCore.coordChange_self, EuclideanGeometry.Sphere.mem_commonTangents_iff, differentiable_fst, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, FormalMultilinearSeries.taylorComp_sub_taylorComp_isBigO, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, LinearIsometry.map_starProjection', intervalIntegral.deriv_integral_right, Continuous.clm_comp, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, antideriv_bernoulliFun, DifferentiableAt.fderiv_prodMk, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerₛₗ_apply_apply, AddCircle.integral_haarAddCircle, WithCStarModule.inner_def, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, centerMass_mem_ball_of_strictConvexSpace, InnerProductSpace.HarmonicAt.const_smul, eventually_nhds_norm_smul_sub_lt, differentiableAt_sigmoid, LinearIsometryEquiv.coe_toAffineIsometryEquiv, exists_dist_slope_lt_pairwiseDisjoint_hasSum, DoubleCentralizer.pow_snd, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, Affine.Simplex.excenterWeightsUnnorm_reindex, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, OrthonormalBasis.repr_self, PointwiseConvergenceCLM.tendsto_nhds, ContMDiffAt.clm_postcomp, Submodule.symmetric_isOrtho, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, scalarSMulCLE_symm_apply, Real.fourier_deriv, ContMDiffWithinAt.clm_postcomp, iteratedDeriv_scomp_three, ContDiffAt.continuousAt_fderiv, fderiv_fun_pow', hasDerivWithinAt_pi, IsometryEquiv.midpoint_fixed, lineDifferentiableWithinAt_congr_set, DifferentiableAt.add_const, Real.integrable_prod_sub, Orientation.oangle_smul_left_of_neg, isVonNBounded_ball, HasFDerivWithinAt.csin, OrthogonalFamily.norm_sq_diff_sum, MDifferentiable.smul, deriv_const', norm_smul_inv_norm, ContinuousLinearEquiv.comp_hasFDerivAt_iff, ContinuousLinearMap.eq_adjoint_iff, deriv.star, Submodule.starProjection_tendsto_self, ContDiffAt.fderiv_succ, Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, MeasureTheory.Measure.addHaar_ball_of_pos, SchwartzMap.toLpCLM_apply, Differentiable.restrictScalars, LinearMap.IsSymmetric.directSum_decompose_apply, Differentiable.zpow, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_sum, ProbabilityTheory.iIndepFun.charFunDual_map_finset_sum_eq_prod, derivWithin.scomp, mem_posTangentConeAt_of_frequently_mem, deriv_abs_neg, DifferentiableOn.circleIntegral_sub_inv_smul, LinearMap.IsSymmetric.splits_charpoly, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Real.differentiableWithinAt_arccos_Ici, HasFPowerSeriesAt.comp, HasFDerivAt.continuousMultilinear_apply_const, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousLinearMap.IsPositive.smul_of_nonneg, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, fderiv_add_const, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, AnalyticOn.iteratedFDerivWithin_comp_perm, Unitary.coe_linearIsometryEquiv_apply, FormalMultilinearSeries.sum_of_finite, OrthonormalBasis.toBasis_adjustToOrientation, MeasureTheory.convolution_tendsto_right, gelfandStarTransform_apply_apply, Submodule.reflection_singleton_apply, DifferentiableWithinAt.abs_of_pos, RCLike.nonUnitalContinuousFunctionalCalculus, smul_unitClosedBall_of_nonneg, HasFTaylorSeriesUpToOn.zero_eq', fderiv_sum, deriv.log, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, AffineIsometryEquiv.pointReflection_midpoint_left, HarmonicAt.analyticAt_complex_partial, SchauderBasis.range_proj_eq_span, MeasureTheory.SimpleFunc.setToSimpleFunc_const, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, interior_convexHull_nonempty_iff_affineSpan_eq_top, DifferentiableWithinAt.fderivWithin_prodMk, ContDiff.continuous_deriv, isIntegralCurveAt_comp_mul_ne_zero, ContinuousMultilinearMap.fin0_apply_enorm, HasStrictDerivAt.clm_comp, Dual.toWeakDual_continuous, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', HasFiniteFPowerSeriesAt.finite, HasFDerivWithinAt.const_mul, isClosed_setOf_tendsto_birkhoffAverage, MeasureTheory.weightedSMul_nonneg, ConcaveOn.slope_le_of_hasDerivAt, signedDist_left_congr, deriv_fun_inv'', MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, exists_deriv_eq_zero, FormalMultilinearSeries.id_apply_one', ContDiffMapSupportedIn.monoLM_apply, HasDerivWithinAt.Iic_of_Iio, contDiffOn_nat_iff_continuousOn_differentiableOn_deriv, ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, AnalyticOnNhd.iteratedFDeriv, ContinuousLinearEquiv.contDiffAt_comp_iff, Affine.Simplex.ExcenterExists.touchpoint_map, WeakFEPair.h_feq, LipschitzWith.hasFDerivAt_of_hasLineDerivAt_of_closure, derivWithin_clm_comp, differentiableAt_smul_iff, ContinuousLinearMap.precompL_apply, cfcₙ_integral, DoubleCentralizer.nnnorm_snd, Orientation.inner_rightAngleRotation_swap', differentiableAt_comp_add_const, IsSelfAdjoint.adjoint_eq, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, Submodule.finrank_add_finrank_orthogonal', Bundle.Pretrivialization.continuousLinearMap_apply, ContinuousLinearEquiv.isBigO_comp, MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', HasStrictFDerivAt.star, LinearMap.isHermitian_toMatrix_iff, QuadraticForm.equivalent_signType_weighted_sum_squared, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, EuclideanGeometry.Cospherical.inclusion_iff, Module.Basis.parallelepiped_reindex, Submodule.reflection_apply, curveIntegralFun_segment, HasDerivWithinAt.clm_apply, SchwartzMap.integral_fourierInv_smul_eq, DifferentiableAt.hasDerivAt, Differentiable.fst, RKHS.kernel_apply, HasDerivAt.finCons, RCLike.reCLM_norm, Seminorm.bound_of_continuous_normedSpace, IsCoercive.unique_continuousLinearEquivOfBilin, Besicovitch.SatelliteConfig.exists_normalized_aux2, differentiable_finCons', signedDist_triangle, Submodule.orthogonal_eq_bot_iff, HasDerivWithinAt.sin, TensorProduct.adjoint_map, DifferentiableWithinAt.lineDifferentiableWithinAt, HasDerivAtFilter.add, Real.hasDerivAt_arcosh, curveIntegral_neg, cfcₙ_setIntegral, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, IsBoundedLinearMap.differentiable, HasFDerivAt.sub, VectorBundleCore.contMDiffOn_coordChange, FormalMultilinearSeries.radius_le_smul, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, MDifferentiable.clm_postcomp, InnerProductSpace.gramSchmidt_def, HasFDerivAt.star, ConvexOn.monotoneOn_rightDeriv, deriv_zero_of_not_differentiableAt, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, LinearMap.ker_adjoint_comp_self, ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin, CStarMatrix.toCLM_injective, EuclideanGeometry.Cospherical.inclusion, iteratedFDerivWithin_succ_const, enorm_fderiv_norm_rpow_le, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, Complex.integral_circleTransform, ContinuousLinearMap.isPositive_self_comp_adjoint, dslope_eventuallyEq_slope_nhdsNE, iteratedDeriv_scomp_eq_sum_orderedFinpartition, trivialization_linear, formalMultilinearSeries_geometric_apply_norm_le, ContinuousLinearMap.hasFPowerSeriesAt, convexOn_univ_dist, Bundle.Trivial.continuousLinearMapAt_trivialization, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, StrongFEPair.differentiable_Λ, fderivWithin_const_sub, hasDerivAt_iff_isLittleO, DifferentiableWithinAt.comp, DifferentiableAt.fun_finset_prod, Affine.Simplex.orthogonalProjectionSpan_eq_point, HasDerivAt.arctan, LocallyBoundedVariationOn.ae_differentiableAt, ProbabilityTheory.iIndepFun.charFunDual_map_fun_sum_eq_prod, Unitization.sqrt_inr, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, UniqueDiffWithinAt.smul, MonotoneOn.intervalIntegrable_deriv, Unitary.linearIsometryEquiv_coe_apply, isBounded_iff_subset_smul_closedBall, HasDerivAt.sqrt, LDL.lowerInv_eq_gramSchmidtBasis, ContDiffAt.differentiableAt, ContinuousLinearMap.coe_equivProdOfSurjectiveOfIsCompl, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, hasFPowerSeriesAt_const, hasStrictFDerivAt_pi', HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, HasFDerivAtFilter.neg, fderiv_eq_deriv_mul, Submodule.starProjection_inner_eq_zero, nndist_right_lineMap, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, HasFPowerSeriesOnBall.const_smul, Orientation.abs_volumeForm_apply_of_orthonormal, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, DifferentiableAt.fun_neg, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, ContinuousMultilinearMap.curry0_apply, HasFDerivWithinAt.fun_const_smul, hasFDerivAtFilter_sub_const_iff, Affine.Simplex.sSameSide_incenter_point, norm_iteratedFDerivWithin_zero, iteratedFDerivWithin_of_isOpen, HasStrictFDerivAt.const_smul, HasFPowerSeriesWithinOnBall.fderivWithin, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, FormalMultilinearSeries.radius_compNeg, isSymm_inner, EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq, HasFDerivAt.multilinear_comp, BoxIntegral.hasIntegral_GP_pderiv, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, Polynomial.differentiableOn_aeval, SchwartzMap.integral_bilin_fourierIntegral_eq, Bundle.Trivialization.localFrame_coeff_eq_coeff, TopologicalGroup.IsSES.pushforward_def, fourier_gaussian_innerProductSpace, SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM, Real.fourierIntegral_continuousMultilinearMap_apply, EuclideanGeometry.oangle_midpoint_right, ProbabilityTheory.HasGaussianLaw.smul, LinearPMap.adjointAux_unique, Affine.Simplex.ExcenterExists.excenter_map, HasStrictDerivAt.fun_sum, mdifferentiableAt_iff, LinearIsometryEquiv.adjoint_eq_symm, DifferentiableWithinAt.sum, NumberField.mixedEmbedding.negAt_apply_snd, extDeriv_fun_smul, fderivWithin_ccosh, TensorProduct.mapIsometry_id_id, StrictConvexOn.lt_slope_of_hasDerivAt, ContinuousAlternatingMap.toAlternatingMap_curryLeft, ProbabilityTheory.HasGaussianLaw.neg, Orientation.neg_rotation_neg_pi_div_two, Matrix.toEuclideanLin_apply, IsContDiffImplicitAt.hasFDerivAt, ContinuousMultilinearMap.uniformity_eq_seminorm, HasDerivAt.congr_of_eventuallyEq, iteratedDerivWithin_eq_iteratedFDerivWithin, HasFDerivWithinAt.mul, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, ContinuousLinearMap.sSup_sphere_eq_nnnorm, analyticOrderAt_smul_eq_top_of_left, isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousAlternatingMap.le_opNNNorm, LinearIsometryEquiv.trans_smul, MeasureTheory.charFunDual_eq_charFun_map_one, HasFPowerSeriesOnBall.tendsto_partialSum_prod, EuclideanGeometry.orthogonalProjection_map, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, hasFDerivWithinAt_pi', fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, IsHilbertSum.hasSum_linearIsometryEquiv_symm, ContinuousMultilinearMap.le_of_opNNNorm_le, ContinuousLinearMap.opNorm_mul, Submodule.IsOrtho.map_iff, DifferentiableOn.mul, DoubleCentralizer.smul_toProd, fderivWithin_pi, ModelWithCorners.isInvertible_fderivWithin_extendCoordChange, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, sameRay_iff_inv_norm_smul_eq_of_ne, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, AlternatingMap.bound_of_shell, norm_sum_lt_of_strictConvexSpace, DifferentiableOn.sub, iteratedDerivWithin_eq_iterate, UniformConvexOn.strictConvexOn, TemperedDistribution.smulLeftCLM_neg, Orthonormal.basisTensorProduct, Orientation.oangle_sign_sub_smul_left, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', MeasureTheory.SimpleFunc.integral_eq_sum_filter, HasFDerivAt.arctan, LinearEquiv.coe_isometryOfOrthonormal, fderivWithin_star, PiTensorProduct.mapL_one, Differentiable.fun_const_smul, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, Real.hasStrictDerivAt_arccos, DoubleCentralizer.toProdMulOpposite_injective, deriv_const_add', RCLike.conjCLE_apply, ContinuousLinearMap.norm_fst_le, HasStrictFDerivAt.eq_implicitFunctionOfComplemented, TestFunction.lineDerivOpCLM_eq_lineDerivCLM, MDifferentiable.cle_arrowCongr, Affine.Simplex.circumradius_restrict, not_differentiableWithinAt_of_deriv_tendsto_atBot_Ioi, MeasureTheory.Measure.quasiMeasurePreserving_smul, ContMDiffAt.mfderiv_apply, hasFDerivAt_snd, Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne, HasFTaylorSeriesUpTo.fderiv_eq, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Complex.reCLM_nnnorm, HasDerivAt.fun_pow', DoubleCentralizer.norm_fst_eq_snd, EuclideanGeometry.Sphere.isTangentAt_of_dist_sq_eq_power, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, Unitization.nnnorm_def, HasStrictFDerivAt.abs, ContinuousLinearMap.exists_lt_apply_of_lt_opNNNorm, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Orientation.rightAngleRotation_def, nndist_left_lineMap, Unitization.instStarOrderedRing, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, ContinuousLinearMap.le_opNorm, TestFunction.fderivCLM_ofSupportedIn, ImplicitFunctionData.range_leftDeriv, aemeasurable_lineDeriv_uncurry, HasFDerivAt.fun_smul, fderivWithin_fun_neg, Function.HasTemperateGrowth.toTemperedDistribution_apply, Euclidean.closedBall_eq_image, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, DifferentiableAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, IsIntegralCurveOn.comp_mul, Orthonormal.inner_left_fintype, NumberField.mixedEmbedding.negAt_preimage, LinearMap.IsSymmetricProjection.sub_of_range_le_range, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, LinearMap.IsSymmetric.conj_adjoint, HasLineDerivAt.tendsto_slope_zero_right, ContDiffPointwiseHolderAt.differentiableAt, ZLattice.comap_toAddSubgroup, fderiv_continuousAlternatingMapCompContinuousLinearMap, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, Complex.deriv_ofReal_cpow_const, ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_apply, Submodule.coe_orthogonalDecomposition_symm, Affine.Simplex.excenterExists_reindex, Convex.cthickening, PiTensorProduct.mapL_smul, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, MDifferentiableWithinAt.differentiableWithinAt_writtenInExtChartAt, MDifferentiableAt.differentiableAt, MeasureTheory.aestronglyMeasurable_condExpL2, MeasureTheory.L1.SimpleFunc.setToL1S_add_left, EuclideanGeometry.Sphere.secondInter_collinear, Submodule.orthogonalProjection_bot, Real.fderiv_fourier, DoubleCentralizer.norm_def', ApproximatesLinearOn.norm_fderiv_sub_le, MeasureTheory.charFunDual_pi', ContinuousLinearMap.adjointAux_norm, MeasureTheory.L1.setToL1_smul_left, differentiable_apply, CStarMatrix.norm_def', coe_basisOfOrthonormalOfCardEqFinrank, derivWithin_univ, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Submodule.range_starProjection, DifferentiableAt.fun_div, norm_sub_le_mul_volume_of_norm_lineDeriv_le, MeasureTheory.Measure.addHaar_ball_mul, fderiv_neg, Real.norm_deriv_mulExpNegMulSq_le_one, LinearIsometryEquiv.inner_map_eq_flip, MeasureTheory.convolution_smul, MeasureTheory.L1.setToL1_zero_left, Quaternion.linearIsometryEquivTuple_symm_apply, hasDerivAtFilter_natCast, EuclideanGeometry.angle_orthogonalProjection_self, Affine.Simplex.ninePointCircle_eq_circumsphere_medial, EuclideanGeometry.Sphere.inner_vsub_center_midpoint_vsub, EuclideanGeometry.orthogonalProjection_apply_mem, meromorphicOrderAt_ne_top_iff, ContinuousLinearMap.integrableAtFilter_comp, HasFPowerSeriesAt.differentiableAt, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, ProbabilityTheory.covarianceBilin_apply_basisFun_self, IsSelfAdjoint.isSymmetric, HasDerivAt.comp_hasFDerivWithinAt, LinearMap.toMatrixOrthonormal_apply_apply, MeasureTheory.condExpInd_nonneg, HasFDerivAt.restrictScalars, StrictConvex.extremePoints_eq_diff_interior, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, ContinuousLinearMap.fpowerSeries_apply_zero, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint, EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eq, StrictConcaveOn.deriv_lt_slope, Orientation.areaForm_to_volumeForm, stereoInvFunAux_apply, StrongFEPair.functional_equation, Submodule.finrank_add_inf_finrank_orthogonal, VectorPrebundle.mk_contMDiffCoordChange, deriv_fun_mul, norm_curveIntegral_segment_le, derivWithin.fun_neg, DifferentiableOn.const_cpow, Submodule.exists_add_mem_mem_orthogonal, PiTensorProduct.projectiveSeminorm_apply, extDerivWithin_constOfIsEmpty, VectorFourier.fourierIntegral_continuousLinearMap_apply, ContinuousAffineMap.norm_def, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, AffineSubspace.coe_subtypeₐᵢ, Real.not_continuousAt_deriv_mul_log_zero, iteratedDeriv_succ', ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, HasFDerivAtFilter.isThetaTVS_sub, HasStrictFDerivAt.arsinh, ContinuousLinearEquiv.coeFn_ofBijective, EuclideanGeometry.Sphere.IsTangentAt.mem_space, iteratedDerivWithin_one, ContinuousLinearMap.integral_comp_comm', Affine.Simplex.circumcenter_reindex, LinearMap.IsSymmetric.coe_re_inner_self_apply, AffineSubspace.isConnected_setOf_wOppSide, circleIntegral.integral_sub_inv_smul_sub_smul, HasFDerivWithinAt.exp, ContinuousLinearMap.comp_memLp', HasStrictFDerivAt.list_prod', SchwartzMap.fourier_lineDerivOp_eq, DifferentiableAt.smul, HasFDerivWithinAt.isThetaTVS_sub, Manifold.IsImmersionAtOfComplement.map_target_subset_target, ContinuousLinearMapWOT.inducingFn_apply, EuclideanGeometry.affineSpan_of_orthocentricSystem, TemperedDistribution.instLineDerivLeftSMulReal, norm_iteratedFDerivWithin_clm_apply_const, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, CStarMatrix.inner_toCLM_conjTranspose_left, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, Orientation.areaForm_neg_orientation, hasStrictDerivAt_exp_smul_const, MeasureTheory.iteratedFDeriv_charFun, AffineBasis.interior_convexHull, ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_sum, EuclideanGeometry.inversion_vsub_center, Filter.EventuallyEq.ftaylorSeries, isBoundedBilinearMap_comp, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, aestronglyMeasurable_lineDeriv, fderivWithin_sin, set_smul_sphere_zero, Orientation.rightAngleRotation_trans_rightAngleRotation, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, StrictConcaveOn.slope_lt_deriv, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, Module.Basis.mulOpposite_is_orthonormal_iff, ContMDiff.smul, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, CFC.continuousOn_sqrt, FormalMultilinearSeries.nnnorm_changeOrigin_le, Filter.EventuallyEq.deriv, Monotone.ae_differentiableAt, hasStrictDerivAt_add_const_iff, hasLineDerivWithinAt_smul_iff, ConvexOn.slope_le_deriv, inrNonUnitalStarAlgHom_comp_cfcₙHom_eq_cfcₙAux, Asymptotics.IsTheta.smul, TemperedDistribution.fourierInv_lineDerivOp_eq, MDifferentiable.const_smul, MeasureTheory.condExpL2_indicator_ae_eq_smul, Affine.Simplex.excenter_eq_affineCombination, ContinuousLinearMap.exists_lt_apply_of_lt_opNorm, Differentiable.abs, fderiv_fun_sub, conformalAt_const_smul, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, IsMIntegralCurveOn.hasDerivWithinAt, Bundle.Trivialization.coe_continuousLinearEquivAt_eq, DifferentiableOn.rpow, FormalMultilinearSeries.rightInv_removeZero, DifferentiableOn.cpow, isCompactOperator_iff_isCompact_closure_image_ball, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', HasDerivWithinAt.comp, hasStrictDerivAt_exp_smul_const', SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, LinearIsometry.toAffineIsometry_toAffineMap, MeromorphicAt.fun_smul, Real.fourier_iteratedFDeriv, Differentiable.ccos, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, HasDerivAt.add, RCLike.nonUnitalContinuousFunctionalCalculusIsClosedEmbedding, SchwartzMap.smulLeftCLM_real_smul, Real.dimH_univ_eq_finrank, InnerProductSpace.toDualMap_apply_apply, Differentiable.cexp, EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents, LinearMap.exists_map_addHaar_eq_smul_addHaar, Submodule.le_orthogonal_orthogonal, MeasureTheory.Measure.integral_comp_inv_mul_left, ContDiffBump.measure_closedBall_div_le_integral, HasMFDerivAt.smul, Orientation.kahler_eq_zero_iff, PositiveLinearMap.preGNS_norm_def, deriv_sub, LinearMap.eq_adjoint_iff_basis_left, contDiff_succ_iff_fderiv, HasStrictDerivAt.div, PositiveLinearMap.leftMulMapPreGNS_apply, ContinuousLinearMap.opNNNorm_prod, ContinuousLinearEquiv.comp_differentiableOn_iff, MeasureTheory.measure_smul_average, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', MDifferentiableOn.smul, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, MDifferentiableAt.clm_prodMap, InnerProductSpace.HarmonicOnNhd.comp_CLM, ZLattice.rank, Orientation.oangle_sign_sub_smul_right, hasDerivAtFilter_zero, HasMFDerivAt.neg, ProperCone.innerDual_sUnion, AffineSubspace.perpBisector_nonempty, Complex.integral_comp_polarCoord_symm, Seminorm.map_eq_zero_of_norm_zero, DifferentiableAt.rpow_const, smul_closedBall', signedDist_apply_apply, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, ZSpan.quotientEquiv_apply_mk, LinearMap.IsSymmetricProjection.isIdempotentElem, HasFDerivAt.fun_const_smul, Real.differentiableAt_rpow_const_of_ne, derivWithin_zpow, MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le, deriv.fun_neg', Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Orientation.oangle_smul_left_self_of_nonneg, PiTensorProduct.norm_def, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, ProbabilityTheory.gaussianReal_map_continuousLinearMap, WeakDual.toStrongDual_inj, DifferentiableOn.csinh, EuclideanSpace.volume_closedBall_fin_three, DifferentiableAt.neg, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, norm_lineDeriv_le_of_lipschitz, SchwartzMap.differentiable, Differentiable.pow, Differentiable.finCons, LinearIsometryEquiv.fderiv, Orientation.areaForm_swap, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, fromTangentSpace_mfderiv_smul_apply, Differentiable.const_smul, ContinuousLinearMap.holderₗ_apply_apply, hasFDerivAt_add_const_iff, taylor_tendsto, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, DifferentiableAt.const_cpow, dslope_sub_smul, hasDerivAt_id', rescale_to_shell_semi_normed_zpow, ContinuousMultilinearMap.unit_le_opNorm, HasDerivWithinAt.cos, ext_inner_map, Differentiable.sinh, ProbabilityTheory.covarianceOperator_zero, HasFDerivAt.curveIntegral_segment_source, Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, LinearIsometryEquiv.measurePreserving, deriv_fun_smul, Submodule.instHasOrthogonalProjectionOfCompleteSpace, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, iteratedFDeriv_comp_const_smul, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', InnerProductSpace.unique_continuousLinearMapOfBilin, fderiv.log, HasStrictDerivAt.arctan, AffineIsometryEquiv.pointReflection_toAffineEquiv, HasStrictDerivAt.mul, DifferentiableAt.const_add, FDerivMeasurableAux.norm_sub_le_of_mem_A, HasFDerivAt.add, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, Affine.Simplex.finrank_direction_altitude, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, Bundle.Trivialization.eq_sum_localFrame_coeff_smul, MeasureTheory.convolution_lsmul, MDifferentiableAt.clm_postcomp, TemperedDistribution.instFourierAdd, Submodule.orthogonal_orthogonal_monotone, Complex.sameRay_of_arg_eq, fderiv_continuousAlternatingMap_apply, hasFDerivAt_sub_const_iff, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, curveIntegral_fun_zero, ContDiffWithinAt.continuousWithinAt_iteratedFDerivWithin, ContDiffMapSupportedIn.monoLM_eq_of_scalars, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ModelWithCorners.uniqueDiffOn_preimage, LinearMap.nonneg_iff_isPositive, EuclideanGeometry.Sphere.IsDiameter.wbtw, iteratedFDeriv_zero, hasDerivAt_abs_neg, Affine.Simplex.mongePoint_mem_mongePlane, Orientation.kahler_swap, coe_innerSL_apply, fderivWithin_finset_prod, Orientation.det_rotation, strongConcaveOn_zero, HasFDerivWithinAt.const_sub, Orientation.rotation_pi_apply, integral_withDensity_eq_integral_smul, intervalIntegral.integral_comp_add_div, LinearMap.IsSymmetric.inner_map_self_eq_zero, ContinuousLinearMap.isCompact_image_coe_closedBall, HasDerivAt.pow, Real.deriv_sqrt_aux, OrthonormalBasis.prod_apply, iteratedFDeriv_add_apply, derivWithin_of_mem_nhdsWithin, deriv_fderiv, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, RegularNormedAlgebra.isometry_mul', Affine.Simplex.isTangentAt_insphere_touchpoint, Orientation.rotation_rotation, cauchyPowerSeries_apply, convexHull_diam, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, ContDiffWithinAt.hasFDerivWithinAt_nhds, Affine.Simplex.excenterWeightsUnnorm_map, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, HasFDerivAt.sum, HasStrictDerivAt.real_of_complex, DifferentiableAt.const_smul, ContinuousLinearMap.isClosed_image_coe_closedBall, DoubleCentralizer.central, Matrix.PosSemidef.det_sqrt, MeasureTheory.integral_condExpL2_eq, LinearPMap.adjoint_apply_eq, HasFPowerSeriesOnBall.coeff_zero, Orientation.rotation_map_complex, ContinuousLinearMap.instStarOrderedRing, BoxIntegral.HasIntegral.smul, Real.deriv_rpow_const, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, DifferentiableAt.add_iff_left, VectorBundleCore.localTriv_symm_fst, range_cfcₙHom, HasFPowerSeriesWithinOnBall.differentiableOn, fun_meromorphicOrderAt_smul, HasMFDerivWithinAt.prodMap, HasDerivAt.differentiableAt, SameRay.inv_norm_smul_eq, StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iio, DifferentiableWithinAt.dist, TestFunction.limitCLM_apply, VectorField.pullbackWithin_eq_of_fderivWithin_eq, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, hasFDerivAtFilter_iff_isLittleO, Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius, DifferentiableAt.fun_add, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, TensorProduct.lidIsometry_apply, HasFDerivAt.clm_apply, HasStrictDerivAt.const_mul, ContDiffMapSupportedIn.seminorm_le_iff, OrthogonalFamily.isInternal_iff_of_isComplete, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, ContinuousLinearMap.hasDerivAt, Affine.Simplex.ninePointCircle_restrict, hasDerivAt_of_tendstoUniformly, DifferentiableAt.star_conj, ContinuousLinearMap.antilipschitz_of_isEmbedding, Convex.exists_forall_hasFDerivAt_of_fderiv_symmetric, BoundedVariationOn.intervalIntegrable_deriv, Orientation.volumeForm_def, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, UniqueMDiffOn.uniqueDiffOn_target_inter, MeasureTheory.Measure.integral_comp_smul_of_nonneg, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, DiffContOnCl.circleIntegral_sub_inv_smul, extDerivWithin_add, CompletelyPositiveMap.instLinearMapClassComplex, Real.deriv_sinh, exists_ratio_deriv_eq_ratio_slope, ClosedSubmodule.inner_real_eq_re_inner, Module.Basis.coe_toOrthonormalBasis_repr, iteratedFDeriv_sum, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, norm_cfcₙ_lt, ContinuousMultilinearMap.opNorm_smul_le, EuclideanGeometry.oangle_pointReflection_left, contDiffAt_one_iff, Function.HasTemperateGrowth.fun_smul, HasFDerivAt.continuousAlternatingMap_apply, MeasureTheory.convolution_precompR_apply, Complex.differentiableOn_update_limUnder_of_isLittleO, MultilinearMap.norm_image_sub_le_of_bound', ContinuousLinearMap.instCStarRingId, WeakDual.coe_toStrongDual, eq_zero_iff_forall_dual_eq_zero, SchwartzMap.compSubConstCLM_apply, hasFDerivAt_finCons, LineDifferentiableWithinAt.congr_of_eventuallyEq, VectorFourier.fourierIntegral_iteratedFDeriv, HasMFDerivWithinAt.neg, ModularGroup.lcRow0Extend_symm_apply, TopologicalAddGroup.IsSES.pushforward_apply_apply, AffineIsometryEquiv.map_vsub, DifferentiableWithinAt.mul, hasFDerivWithinAt_finCons, dist_left_midpoint_eq_dist_right_midpoint, norm_injOn_ray_right, InformationTheory.hasDerivAt_klFun, UnconditionalSchauderBasis.enorm_proj_le_enormProjBound, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, AlternatingMap.coe_mkContinuous, contDiffOn_one_iff_derivWithin, stronglyMeasurable_lineDeriv, ContinuousMultilinearMap.norm_restr, StrictConvexOn.slope_lt_deriv, ContinuousMultilinearMap.norm_image_sub_le, ProbabilityTheory.isPosSemidef_covarianceBilin, fderiv_smul, BoundedContinuousFunction.mem_charPoly, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, OrthonormalBasis.orthogonalProjection_apply_eq_sum, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, Orientation.kahler_comp_rightAngleRotation, Seminorm.ball_smul, differentiable_snd, BoundedContinuousFunction.charAlgHom_apply, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, iteratedFDerivWithin_const_smul_apply, EuclideanGeometry.oangle_eq_pi_iff_sbtw, HasFDerivWithinAt.star, HasDerivAt.fun_pow, HasStrictFDerivAt.fst, ae_differentiableAt_norm, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, FormalMultilinearSeries.taylorComp_sub_taylorComp_isLittleO, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, FormalMultilinearSeries.continuousOn_of_finite, LinearMap.isSymmetric_self_comp_adjoint, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, AffineIsometryEquiv.toContinuousAffineEquiv_symm, ContinuousLinearMap.coe_equivRange, HasGradientWithinAt.differentiableWithinAt, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, VectorField.fderivWithin_pullbackWithin, ContinuousLinearMap.interior_preimage, TemperedDistribution.delta_apply, ContinuousAlternatingMap.curryLeft_apply_apply, isVonNBounded_closedBall, affinity_unitClosedBall, ContinuousLinearMap.flip_smul, ContinuousLinearMap.contDiffPointwiseHolderAt, ContDiffBump.normed_le_div_measure_closedBall_rOut, Bundle.Trivial.vectorBundle, HasDerivAtFilter.mono, Submodule.IsCompl.closedComplemented_of_isClosed, ContinuousLinearEquiv.isBigO_sub, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Submodule.norm_eq_iInf_iff_inner_eq_zero, HasDerivWithinAt.fun_pow', HasDerivAt.deriv, MeasureTheory.integral_singleton', LinearMap.exists_antilipschitzWith, HasCompactSupport.hasDerivAt_convolution_right, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, hasDerivWithinAt_neg, DifferentiableWithinAt.const_mul, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, HasDerivWithinAt.const_add, Complex.differentiableOn_update_limUnder_of_bddAbove, Orientation.volumeForm_zero_pos, RKHS.isHermitian_kernel, MeasureTheory.L1.setToL1_mono_left', differentiableWithinAt_pow, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, hasMFDerivAt_neg, HasFDerivWithinAt.const_smul, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, AnalyticAt.deriv, ContinuousLinearEquiv.hasMFDerivAt, MeasureTheory.ConvolutionExistsAt.integrable_swap, IsGreatest.norm_cfcₙ, DifferentiableWithinAt.fun_pow, ContinuousOn.clm_comp, SchwartzMap.laplacianCLM_eq', Polynomial.deriv_aeval, VectorBundleCore.trivializationAt_coordChange_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, MultilinearMap.coe_mkContinuous, norm_inner_eq_norm_iff, VectorField.DifferentiableWithinAt.pullbackWithin, Real.circleAverage_eq_circleIntegral, HasFiniteFPowerSeriesOnBall.eq_partialSum, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, DirectSum.IsInternal.subordinateOrthonormalBasis_subordinate, hasDerivAt_tsum_of_isPreconnected, Matrix.gram_eq_conjTranspose_mul, MeasureTheory.charFunDual_prod, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, DifferentiableAt.fderiv_norm_self, continuousOn_tangentCoordChange, EuclideanGeometry.Sphere.orthRadius_center, NumberField.Units.span_basisOfIsMaxRank, convexOn_dist, MultilinearMap.bound_of_shell_of_norm_map_coord_zero, LinearIsometryEquiv.smul_apply, nnnorm_cfcₙ_nnreal_lt, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, mem_posTangentConeAt_of_segment_subset, real_linearMap_map_smul_complex, LinearIsometryEquiv.contDiff, LinearMap.IsSymmetric.card_filter_eigenvalues_eq, HasFDerivAt.comp_hasFDerivWithinAt, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ContDiff.continuous_fderiv_apply, FiniteDimensional.RCLike.properSpace_submodule, AffineMap.hasDerivAt_lineMap, fderivWithin_continuousAlternatingMap_apply_const_apply, MeasureTheory.setToFun_smul_left', EuclideanGeometry.dist_orthogonalProjection_eq_of_two_zsmul_oangle_eq, Function.hasTemperateGrowth_iff_isBigO, range_stereographic_symm, FiniteDimensional.rclike_to_real, Complex.equivRealProdCLM_symm_apply, ContinuousLinearMap.norm_eq_iSup_rayleighQuotient, TemperedDistribution.instContinuousFourier, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left', mellinInv_eq_fourierIntegralInv, iteratedFDerivWithin_neg_apply, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, ProbabilityTheory.strong_law_ae, HasDerivWithinAt.fun_finset_prod, ContinuousAt.clm_apply, HasDerivWithinAt.norm_sq, smul_mem_polar, HasGradientAtFilter.hasDerivAtFilter', CFC.norm_star_mul_mul_self_of_nonneg, DifferentiableWithinAt.prodMk, Module.Basis.prod_addHaar, Orientation.volumeForm_robust, PiLp.volume_preserving_toLp, CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, HasStrictFDerivAt.to_implicitFunctionOfComplemented, IsLocalExtr.fderiv_eq_zero, derivWithin_congr_set', ZSpan.measureReal_fundamentalDomain, EuclideanGeometry.orthogonalProjection_apply', SmoothPartitionOfUnity.contDiffAt_finsum, WithSeminorms.continuous_normedSpace_dom, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, ContMDiffAt.smul, isOpenEmbedding_stereographic_symm, intervalIntegral.integral_hasDerivWithinAt_left, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, GeneralSchauderBasis.expansion, HasFPowerSeriesOnBall.fderiv_eq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, strictConvex_closedBall, NumberField.Units.basisOfIsMaxRank_apply, ContinuousLinearMap.opNorm_le_of_shell', Continuous.cfcₙ_of_mem_nhdsSet, toNormSMulClass, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, Real.differentiableOn_rpow_const, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, EuclideanGeometry.Sphere.coe_secondInter, MeromorphicOn.fun_deriv, ContinuousMultilinearMap.nnnorm_constOfIsEmpty, isBigO_rpow_top_log_smul, inclusionInDoubleDual_norm_eq, HasDerivAtFilter.fun_add, differentiableAt_star_iff, VectorBundle.trivialization_linear', SchwartzMap.smulLeftCLM_sum, PiTensorProduct.projectiveSeminorm_tprod_le, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', DifferentiableAt.inverse, AffineMap.hasDerivWithinAt_lineMap, PeriodPair.basis_zero, DifferentiableWithinAt.const_cpow, mfderiv_prod_eq_add_comp, ContinuousAffineMap.decompLinearIsometryEquiv_symm_apply, ContinuousLinearMap.fderiv_of_bilinear, has_fderiv_at_filter_real_equiv, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, aestronglyMeasurable_deriv, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, cfcₙHom_integral, EuclideanGeometry.orthogonalProjection_orthogonalProjection_of_le, unitary.linearIsometryEquiv_coe_symm_apply, PiTensorProduct.tprodL_toFun, MeasureTheory.setIntegral_condExpInd, ContinuousLinearMap.isPositive_def, LipschitzWith.ae_lineDifferentiableAt, Continuous.cfcₙ, DifferentiableWithinAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.nnnorm_toSpanSingleton, EuclideanGeometry.oangle_midpoint_rev_left, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_add, ContinuousLinearEquiv.hasMFDerivWithinAt, iteratedFDerivWithin_succ_apply_right, ContinuousAlternatingMap.alternatizeUncurryFin_smul, InformationTheory.leftDeriv_klFun, contDiffAt_map_inverse, fderiv_mul_const', MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, tendsto_integral_exp_smul_cocompact, RKHS.posSemidef_tfae, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Affine.Triangle.touchpoint_singleton_sbtw, SchwartzMap.toBoundedContinuousFunctionCLM_apply, extDeriv_apply_vectorField, ContDiffMapSupportedIn.monoCLM_eq_of_scalars, curveIntegral_segment, MultilinearMap.restr_norm_le, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, Bundle.Trivialization.continuousLinearEquivAt_apply', HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorphOfComplemented_target, deriv_id'', HasFTaylorSeriesUpToOn.hasFDerivWithinAt, ContinuousAlternatingMap.norm_restrictScalars, Real.fourierIntegral_continuousLinearMap_apply, OrthonormalBasis.coe_ofRepr, Submodule.starProjection_top', ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, aemeasurable_deriv_with_param, HasFDerivWithinAt.abs_of_neg, Orientation.rotation_symm, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, hasStrictFDerivAt_exp, Affine.Simplex.exradius_map, HasDerivAtFilter.sub, IsCoercive.range_eq_top, AnalyticOn.fderivWithin, LinearMap.isSymmetric_adjoint_mul_self, ProbabilityTheory.differentiableAt_mgf, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, FiniteDimensional.of_locallyCompact_manifold, deriv_const_mul_field', ContinuousLinearEquiv.uniqueDiffOn_image, inclusionInDoubleDualWeak_apply_apply, Orientation.oangle_eq_zero_iff_sameRay, RCLike.conjLIE_apply, Submodule.reflection_orthogonalComplement_singleton_eq_neg, deriv_fun_div, ContinuousLinearEquiv.comp_fderiv, convexOn_univ_norm, derivWithin.neg, Differentiable.sub_iff_right, LinearIsometryEquiv.reflections_generate_dim_aux, HasFDerivWithinAt.fun_smul, Complex.orthonormalBasisOneI_repr_apply, ContinuousLinearMap.isBigO_id, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, MeasureTheory.L1.setToL1_eq_setToL1SCLM, intervalIntegral.integral_deriv_comp_smul_deriv', MeasureTheory.integral2_divergence_prod_of_hasFDerivAt_off_countable, ContDiffAt.fderiv_right, Complex.differentiable_exp, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, Affine.Triangle.dist_circumcenter_reflection_orthocenter, HasStrictFDerivAt.prodMk, MeasureTheory.norm_condExpL2_coe_le, ContMDiffFiberwiseLinear.locality_aux₂, ContinuousMultilinearMap.curryLeft_norm, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, HasDerivAtFilter.iterate, InnerProductSpace.trace_rankOne, HasFPowerSeriesOnBall.differentiableOn, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MeasureTheory.Submartingale.smul_nonneg, MDifferentiableWithinAt.cle_arrowCongr, RCLike.imLm_coe, EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_finrank_eq_one, deriv.neg, ContinuousLinearMap.exists_approx_preimage_norm_le, ContinuousMultilinearMap.uncurry0_norm, MeasureTheory.L1.setToL1_nonneg, ContDiffOn.continuousOn_iteratedFDerivWithin, FDerivMeasurableAux.D_subset_differentiable_set, openSegment_subset_ball_of_ne, HasFPowerSeriesWithinOnBall.prod, LinearMap.IsSymmetric.isSelfAdjoint, normalize_smul, MDifferentiableWithinAt.clm_precomp, IsBoundedBilinearMap.differentiableOn, HasDerivAt.fun_add, SchwartzMap.fourierMultiplierCLM_sum, MeasureTheory.integrable_withDensity_iff_integrable_smul', HasDerivAt.neg, FDerivMeasurableAux.differentiable_set_eq_D, ContinuousLinearMap.isClosed_image_coe_of_bounded_of_weak_closed, ContMDiffVectorBundle.continuousLinearMap, Real.differentiable_cos, Orientation.angle_eq_iff_oangle_eq_or_sameRay, eq_iff_forall_dual_eq, ContinuousLinearEquiv.integral_comp_comm, Real.fourierIntegralInv_comp_linearIsometry, HasDerivAt.star, IsBoundedBilinearMap.fderivWithin, deriv_zero, ContinuousMultilinearMap.le_opNorm, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, Bundle.Trivial.linearMapAt_trivialization, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, continuousOn_cfcₙ, HasFDerivWithinAt.neg, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, SchwartzMap.delta_apply, InnerProductGeometry.angle_eq_zero_iff, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, AffineIsometry.toContinuousAffineMap_id, isBoundedBilinearMap_compMultilinear, ContinuousLinearEquiv.comp_right_fderiv, hasLineDerivAt_smul_iff, Submodule.isIdempotentElem_starProjection, norm_cauchyPowerSeries_le, differentiableOn_finCons', VectorField.lieBracket_const_smul_left, Orientation.rotation_map, sum_mul_eq_sub_integral_mul', LinearEquiv.isometryOfOrthonormal_toLinearEquiv, HasDerivWithinAt.const_rpow, Orientation.oangle_rotation_left, hasFDerivAt_norm_rpow, derivWithin_ofNat, dist_birkhoffAverage_apply_birkhoffAverage, IsSelfAdjoint.isClosed, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, mellinInv_eq_fourierInv, ZSpan.repr_ceil_apply, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, HasFPowerSeriesOnBall.uniform_geometric_approx, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_monotoneOn, ProperCone.innerDual_zero, LinearIsometry.inner_map_map, DoubleCentralizer.neg_snd, Set.Nonempty.intrinsicInterior, Affine.Simplex.excenterWeights_reindex, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, ZLattice.comap_equiv_apply, norm_sub_le_mul_volume_of_norm_deriv_le_of_le, EuclideanGeometry.collinear_of_angle_eq_zero, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, IsBoundedLinearMap.differentiableOn, sameRay_iff_of_norm_eq, ContinuousLinearMap.analyticAt, iteratedFDeriv_succ_const, ClosedSubmodule.orthogonal_le, HasDerivAtFilter.const_smul, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, toLinearMap_inclusionInDoubleDualWeak, Submodule.orthogonalProjection_mem_subspace_orthogonalComplement_eq_zero, fourier_gaussian_innerProductSpace', norm_smul_of_nonneg, ContDiffAt.iteratedFDeriv_right, dist_affineCombination_lt_of_strictConvexSpace, VectorFourier.fourierIntegral_const_smul, HasFPowerSeriesWithinAt.fderivWithin_eq, ContDiffBump.convolution_tendsto_right, RKHS.kerFun_apply, Matrix.linfty_opNNNorm_toMatrix, HasFTaylorSeriesUpToOn.cont, dist_lineMap_left, inCoordinates_apply_eq₂, measurable_deriv, extDeriv_extDeriv, ContDiffAt.contDiffAt_norm_smul, Real.fourier_real_eq, AnalyticOnNhd.fderiv_of_isOpen, ContinuousAlternatingMap.le_opNorm, Bundle.Trivialization.comp_continuousLinearEquivAt_eq_coord_change, FormalMultilinearSeries.id_comp', LinearIndependent.eventually, Affine.Simplex.ExcenterExists.isTangentAt_touchpoint, Asymptotics.IsEquivalent.smul, differentiableAt_apply, MeasureTheory.L1.integral_def, MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_poles, contDiffOn_infty_iff_fderivWithin, Affine.Simplex.inradius_reindex, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, hasFDerivAt_iff_isLittleO, derivWithin_fun_div, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, derivWithin_inv, Matrix.toEuclideanCLM_toLp, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_add, HasDerivAt.comp, WeakDual.CharacterSpace.homeoEval_naturality, Submodule.IsCompl.projection_isSymmetricProjection_of_isOrtho, signedDist_eq_zero_of_orthogonal, EuclideanGeometry.preimage_inversion_perpBisector, DifferentiableWithinAt.hasDerivWithinAt, CPolynomialOn.iteratedFDeriv, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, realPart.norm_le, ContinuousLinearMap.isPositive_id, ZSpan.volume_fundamentalDomain, StrictMonoOn.exists_slope_lt_deriv_aux, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, FormalMultilinearSeries.coeff_eq_zero, ProbabilityTheory.covarianceBilin_zero, differentiableAt_pi'', RCLike.conjCLE_coe, Ioo_smul_sphere_zero, HasFPowerSeriesOnBall.sum, Real.tendsto_integral_gaussian_smul', HasFDerivAt.comp_hasDerivAt, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, VectorFourier.differentiable_fourierIntegral, Affine.Simplex.incenter_mem_interior, HasDerivWithinAt.mul, SchauderBasis.finrank_range_proj, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, Real.finrank_eq_int_finrank_of_discrete, DifferentiableOn.ccos, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, HasDerivAt.log, LeftInvariantDerivation.evalAt_coe, derivWithin_const_add, Unitary.coe_symm_linearIsometryEquiv_apply, fderiv_inverse, DifferentiableAt.ccosh, Affine.Simplex.altitudeFoot_map, smul_sphere', hasStrictFDerivAt_exp_smul_const', derivWithin_subset, SchwartzMap.smulLeftCLM_fun_neg, ClosedSubmodule.mulI_sup, deriv_pow, HasFPowerSeriesOnBall.fderiv, LinearMap.adjoint_rTensor, ZSpan.measure_fundamentalDomain, MeasureTheory.setIntegral_countable, lineDerivWithin_of_isOpen, ContMDiffOn.clm_precomp, dist_midpoint_midpoint_le, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, contDiffOn_nat_iff_continuousOn_differentiableOn, Differentiable.sin, LinearMap.IsPositive.add, ProbabilityTheory.HasGaussianLaw.add, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, measurableSet_of_differentiableAt_of_isComplete, Real.deriv_Gamma_nat, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, ContinuousLinearMap.isUnit_of_forall_le_norm_inner_map, LinearMap.adjoint_inner_right, HasStrictFDerivAt.of_local_left_inverse, MeasureTheory.mem_lpMeas_indicatorConstLp, iteratedFDeriv_const_smul_apply', InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, Convex.interior_nonempty_iff_affineSpan_eq_top, PiLp.hasFDerivAt_toLp, stereoInvFun_apply, DifferentiableWithinAt.snd, PiTensorProduct.mapL_coe, Isometry.mapsTo_perpBisector, EuclideanGeometry.Cospherical.affineIndependent_of_ne, Filter.EventuallyEq.hasDerivAt_iff, Manifold.IsImmersionAt.writtenInCharts, fderiv_pow, InnerProductSpace.rankOne_eq_zero, ContinuousLinearMap.lipschitz, Polynomial.differentiable_aeval, ProbabilityTheory.isGaussian_map_equiv_iff, DoubleCentralizer.range_toProd, Distribution.delta_eq_zero_of_notMem, Affine.Simplex.circumcenter_eq_point, Real.fourierIntegral_convergent_iff', fderivWithin_continuousMultilinear_apply_const_apply, hasDerivAt_deriv_iff, Unitization.splitMul_injective_of_clm_mul_injective, RCLike.mul_wInner_left, TensorProduct.ext_iff_inner_left_threefold', Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, ClosedSubmodule.bot_orthogonal_eq_top, LinearIsometry.norm_compContinuousMultilinearMap, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, fun_iteratedFDerivWithin_add_apply, MeasureTheory.integral_indicatorConstLp, MeasureTheory.Measure.toSphere_apply_univ, HasStrictDerivAt.sin, Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, AffineIsometry.linear_eq_linearIsometry, inner_map_polarization', HasStrictDerivAt.clog_real, UniqueDiffOn.of_real, Bundle.ContMDiffRiemannianMetric.symm, ContMDiffOn.coordChangeL, hasDerivAt_of_hasDerivAt_of_ne', intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, MeasureTheory.charFunDual_eq_prod_iff, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, VectorField.fderiv_pullback, ContDiff.differentiable_iteratedFDeriv, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, HasFDerivAt.pow, Real.fourier_comp_linearIsometry, HasDerivWithinAt.sqrt, MeasureTheory.Measure.integral_comp_smul, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, IsSelfAdjoint.hasEigenvector_of_isMaxOn, Asymptotics.isBigOTVS_iff_isBigO, ContinuousMultilinearMap.isLeast_opNorm, fderivWithin_comp_derivWithin, ContDiff.continuous_fderiv, mdifferentiableAt_hom_bundle, HasFPowerSeriesWithinOnBall.unshift, setIntegral_withDensity_eq_setIntegral_smul₀', Real.hasDerivAt_qaryEntropy, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, continuousAt_dslope_same, PositiveLinearMap.preGNS_inner_def, MeasureTheory.condExpIndSMul_smul, fderivWithin_inv', AffineIsometryEquiv.vaddConst_toAffineEquiv, StandardSubspace.IsSeparating, hasDerivAt_add_const_iff, hasDerivWithinAt_pow, CStarAlgebra.instNonnegSpectrumClassComplexNonUnital, Orthonormal.equiv_symm, MultilinearMap.exists_bound_of_continuous, MeasureTheory.ae_ae_add_linearMap_mem_iff, differentiableAt_star_conj_iff, real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivWithinAt.cpow, Affine.Simplex.altitude_restrict_eq_comap_subtype, TensorProduct.ext_iff_inner_left_threefold, MDifferentiableAt.differentiableWithinAt_writtenInExtChartAt, MeasureTheory.lintegral_nnnorm_condExpL2_le, LinearMap.IsSymmetric.toLinearMap_symm, EuclideanGeometry.oangle_eq_zero_iff_wbtw, Monotone.ae_hasDerivAt, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, StrongDual.toLp_of_not_memLp, ContinuousLinearMap.fderivWithin_of_bilinear, AffineSubspace.isometryEquivMap.toAffineMap_eq, HasFPowerSeriesOnBall.compContinuousLinearMap, DoubleCentralizer.add_fst, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonpos, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', AffineSubspace.signedInfDist_eq_signedDist_of_mem, HasStrictFDerivAt.const_cpow, MeasureTheory.L1.setToFun_eq_setToL1, deriv_pi, differentiableWithinAt_of_derivWithin_ne_zero, LinearMap.IsSymmetric.coe_toSelfAdjoint, one_mem_posTangentConeAt_iff_mem_closure, ContinuousLinearEquiv.iteratedFDerivWithin_comp_right, HasFDerivWithinAt.csinh, quasispectrum.isCompact, ContinuousWithinAt.clm_comp, HasFPowerSeriesWithinAt.coeff_zero, RealRMK.rieszMeasure_le_of_eq_one, TensorProduct.inner_lid_lid, DiffContOnCl.deriv_eq_smul_circleIntegral, EuclideanSpace.volume_closedBall_fin_two, OrthonormalBasis.toBasis_map, DifferentiableOn.deriv_eq_smul_circleIntegral, ContDiffMapSupportedIn.uniformSpace_eq_iInf, extDerivWithin_extDerivWithin_eqOn, DifferentiableOn.add_const, DifferentiableAt.log, GeneralSchauderBasis.proj_apply_basis_mem, hasFDerivAt_apply, derivWithin_div_const, Matrix.piLp_ofLp_toEuclideanLin, iteratedFDerivWithin_smul_const_apply, cfcₙAux_id, Bundle.Trivialization.continuousLinearEquivAt_prod, LinearMap.IsSymmetric.diagonalization_symm_apply, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, maximal_orthonormal_iff_basis_of_finiteDimensional, HasFDerivAt.abs_of_pos, TensorProduct.norm_comm, contDiffWithinAt_iff_of_ne_infty, inclusionInDoubleDual_norm_le, AnalyticOnNhd.eval_linearMap, Set.OrdConnected.image_derivWithin, LinearIsometryEquiv.coe_toMeasurableEquiv, LinearIsometry.re_apply_eq_re_of_add_conj_eq, hasFTaylorSeriesUpToOn_pi', RCLike.rank_le_two, curveIntegral_segment_const, Differentiable.sum, hasDerivWithinAt_one, deriv_comp_add_const, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, VectorBundleCore.localTriv_symm_apply, Bundle.Trivialization.eventually_eq_localFrame_sum_coeff_smul, HasFDerivAt.abs, ConcaveOn.slope_le_of_hasDerivWithinAt_Ioi, WeakDual.isCompact_closedBall, MeasureTheory.L1.integral_eq_setToL1, Convex.second_derivative_within_at_symmetric, Bundle.Trivialization.prod_apply', ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, ContinuousLinearMap.isPositive_toLinearMap_iff, Affine.Simplex.signedInfDist_apply_self, BoxIntegral.BoxAdditiveMap.volume_apply, ProbabilityTheory.HasGaussianLaw.fun_smul, TangentBundle.trivializationAt_apply, PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm, ConvexOn.sSup_of_countable_affine_eq, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, Real.differentiableAt_rpow_of_ne, Convex.uniformContinuous_gauge, HasStrictFDerivAt.abs_of_neg, RCLike.reCLM_coe, HasFDerivWithinAt.abs, ContDiffBump.normed_convolution_eq_right, ProbabilityTheory.gaussianReal_map_linearMap, ProbabilityTheory.iIndepFun.hasGaussianLaw_add, LinearMap.norm_mkContinuous₂_aux, PiTensorProduct.bddBelow_projectiveSemiNormAux, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, CStarAlgebra.norm_posPart_le, OrthonormalBasis.tensorProduct_repr_tmul_apply', HasLineDerivAt.tendsto_slope_zero, HasStrictDerivAt.to_local_left_inverse, ContinuousLinearMap.norm_map_of_mem_unitary, HasDerivWithinAt.inner, ContinuousLinearMap.derivWithin, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, DifferentiableAt.inner, ContinuousLinearMap.holder_smul_left, exists_mem_interior_convexHull_affineBasis, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, ContinuousAffineMap.norm_eq, HarmonicAt.differentiableAt_complex_partial, AffineIsometry.image_intrinsicInterior, Real.differentiable_fourierIntegral, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, dist_right_midpoint, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, isSymmSndFDerivAt_iff_iteratedFDeriv, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, Seminorm.comp_smul, IsGreatest.nnnorm_cfcₙ_nnreal, HasFDerivWithinAt.mul_const, hasFDerivWithinAt_iff_isLittleO, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Real.fourierIntegral_iteratedDeriv, intervalIntegral.smul_integral_comp_mul_sub, Real.fourierInv_comp_linearIsometry, DifferentiableOn.inv, MeasureTheory.hasFDerivAt_convolution_right_with_param, ContinuousLinearEquiv.differentiableAt, CStarAlgebra.span_nonneg_inter_unitClosedBall, ProbabilityTheory.IsGaussian.charFun_eq', InnerProductSpace.exists_of_rankOne_eq_rankOne, deriv_neg_left_of_sign_deriv, Real.deriv_inv_log, fderiv_pow', ProbabilityTheory.covarianceBilinDual_eq_covariance, ContMDiffAt.mfderiv_const, AnalyticOn.domDomCongr_iteratedFDeriv, fderiv_mul, signedDist_zero, MeasureTheory.condExpL1CLM_indicatorConstLp, Asymptotics.IsLittleO.isLittleOTVS, hasDerivAt_ofNat, SchwartzMap.postcompCLM_apply, LinearIsometry.isConformalMap, LinearIsometryEquiv.reflections_generate, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, ContinuousLinearMap.ratio_le_opNorm, fderivWithin_sub_const, Submodule.map_orthogonal_equiv, iteratedFDerivWithin_eq_equiv_comp, dist_center_homothety, CompactlySupportedContinuousMap.toRealLinearMap_apply, EuclideanSpace.coe_proj, IsLocalExtr.deriv_eq_zero, IsLocalMax.deriv_eq_zero, Matrix.l2_opNNNorm_mulVec, aestronglyMeasurable_derivWithin_Ioi, Differentiable.fun_add, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, hasFDerivAt_prodMk_left, AffineIsometryEquiv.toContinuousAffineEquiv_refl, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, HasStrictFDerivAt.isLittleO, AlternatingMap.mkContinuousAlternating_norm_le, MeromorphicOn.fun_iterated_deriv, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ClosedSubmodule.top_orthogonal_eq_bot, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, differentiableAt_inv_iff, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, SchwartzMap.norm_iteratedFDeriv_le_seminorm, ProbabilityTheory.covarianceBilinDual_zero, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, EuclideanGeometry.wbtw_of_collinear_of_dist_center_le_radius, MeasureTheory.L1.setToL1_add_left', Submodule.norm_orthogonalProjection_apply_le, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, HasStrictDerivAt.exp, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, Affine.Simplex.incenter_notMem_affineSpan_face, RealRMK.integral_rieszMeasure, LinearMap.deriv, VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas, HasStrictFDerivAt.map_implicitFunction_eq, uniqueDiffWithinAt_convex_of_isRCLikeNormedField, Continuous.fderiv, CFC.continuous_abs, contDiff_iff_iteratedDeriv, HasFDerivWithinAt.inner, polar_ball_subset_closedBall_div, TensorProduct.norm_assoc, TensorProduct.nnnorm_tmul, Affine.Triangle.affineSpan_pair_eq_orthRadius, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, MeasureTheory.SimpleFunc.integral_eq_sum, DoubleCentralizer.smul_fst, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, fderivWithin.snd, norm_fderiv_le_of_lipschitz, DifferentiableWithinAt.fun_sum, InnerProductSpace.toDualMap_apply, LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute, Bundle.Pretrivialization.continuousLinearMap.isLinear, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonneg, LinearMap.IsSymmetric.adjoint_conj, DifferentiableWithinAt.abs, hasFDerivWithinAt_finCons', HasDerivAt.cosh, DifferentiableAt.conj_conj, AffineIsometryEquiv.ofTop_symm_apply_coe, MeasureTheory.L1.setToL1_mono_left, Real.differentiable_exp, TangentBundle.coordChange_model_space, fun_iteratedFDeriv_add, normalize_smul_of_pos, ContinuousLinearMap.adjoint_inner_left, MeasureTheory.condExpInd_disjoint_union, fderivWithin_cos, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, PointwiseConvergenceCLM.isInducing_inducingFn, ImplicitFunctionData.hasStrictFDerivAt_implicitFunction_fderiv, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, TensorProduct.inner_mapIncl_mapIncl, Orientation.oangle_rotation_oangle_right, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, ProbabilityTheory.differentiableOn_mgf, fun_iteratedFDeriv_sub, AlternatingMap.mkContinuous_norm_le, ContDiffMapSupportedIn.seminorm_monoLM_le, intervalIntegral.integral_comp_smul_deriv'', Polynomial.derivWithin, ContinuousLinearMap.isBoundedBilinearMap, WeakFEPair.Λ₀_eq, fdifferential_apply, ContinuousMultilinearMap.opNorm_nonneg, FiberwiseLinear.trans_openPartialHomeomorph_apply, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, InnerProductSpace.AlgebraOfCoalgebra.mul_def, fderivWithin_const_add, Real.hasStrictDerivAt_arcosh, Filter.EventuallyEq.iteratedFDerivWithin, HasDerivAt.sub, intervalIntegral.integral_comp_smul_deriv, HasStrictFDerivAt.implicitToOpenPartialHomeomorphOfComplemented_apply_ker, Filter.EventuallyEq.lineDerivWithin_eq_nhds, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, HasLineDerivWithinAt.smul, Affine.Simplex.orthogonalProjectionSpan_congr, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, Real.differentiableAt_cos, HasStrictDerivAt.sum, FormalMultilinearSeries.apply_eq_pow_smul_coeff, EuclideanGeometry.image_inversion_perpBisector, hasDerivAtFilter_id, innerₗ_apply, fderivWithin_continuousMultilinear_apply_const, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, MeasureTheory.setIntegral_condExpIndSMul, MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_of_le, ContinuousLinearEquiv.integrable_comp_iff, Orientation.rightAngleRotation_symm, MeasureTheory.weightedSMul_empty, ContDiffAt.hasStrictFDerivAt', MeasureTheory.integrable_withDensity_iff_integrable_smul₀, inv_norm_smul_mem_unitClosedBall, Affine.Simplex.mongePlane_def, Affine.Triangle.acuteAngled_iff_angle_lt, Differentiable.fun_pow, fderivWithin_ccos, ContinuousLinearMap.coe_ofSeqClosedGraph, ModularGroup.lcRow0Extend_apply, Matrix.isSymmetric_toEuclideanLin_iff, MDifferentiableOn.coordChangeL, Real.deriv_log', VectorField.lieBracketWithin_smul_left, Submodule.norm_eq_iInf_iff_real_inner_eq_zero, ProbabilityTheory.map_pi_eq_stdGaussian, hasDerivAt_update, ContinuousLinearMap.IsPositive.isSymmetric, ContinuousAlternatingMap.ofSubsingletonLIE_apply, HasStrictFDerivAt.clog, nnnorm_apply_le_nnnorm_cfcₙ, fderiv_fun_add, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, AlternatingMap.exists_bound_of_continuous, OrthonormalBasis.equiv_apply, TemperedDistribution.fourierMultiplierCLM_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, Seminorm.bound_of_continuous, ContinuousLinearMap.lipschitz_apply, ContDiff.euclidean_dist, DifferentiableOn.log, HasStrictDerivAt.smul, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, AnalyticWithinAt.differentiableWithinAt, intervalIntegral.integral_comp_add_mul, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, ContinuousLinearMap.closed_complemented_range_of_isCompl_of_ker_eq_bot, fderiv_pow_ring, constFormalMultilinearSeries_apply_zero, LinearMap.IsSymmetric.restrict_invariant, hasDerivAt_tsum, DifferentiableAt.fderiv_restrictScalars, hasFTaylorSeriesUpToOn_top_iff', MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable_of_equiv, ContinuousLinearMap.lsmul_apply, MeasureTheory.setIntegral_rnDeriv_smul, inTangentCoordinates_eq, extDerivWithin_apply_vectorField_of_pairwise_commute, StrictMonoOn.exists_deriv_lt_slope_aux, LinearMap.isometryOfInner_toLinearMap, ContinuousLinearMap.rayleighQuotient_zero_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, FormalMultilinearSeries.radius_smul_eq, DifferentiableAt.comp_ringHom, selfAdjoint.unitarySelfAddISMul_coe, Bundle.ContMDiffRiemannianMetric.pos, AffineIsometryEquiv.ofEq_symm, HasStrictFDerivAt.sqrt, Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, HasDerivWithinAt.complexToReal_fderiv, signedDist_triangle_left, ContinuousLinearMap.equivRange_symm_apply, Affine.Simplex.altitudeFoot_eq_point_rev, ContinuousLinearMap.bilinearComp_zero_right, ContinuousLinearMap.opNNNorm_le_bound, Complex.IsExactOn.differentiableOn, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, LinearMap.adjoint_comp_self_injective_iff, LinearMap.IsSymmetric.continuous, WeakDual.isBounded_closure, IsContMDiffRiemannianBundle.exists_contMDiff, Affine.Simplex.excenterExists_map, ContDiffWithinAt.fderivWithin'', DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul, deriv_const_mul_field, ProbabilityTheory.IsGaussianProcess.restrict, hasDerivAtFilter_add_const_iff, HasDerivWithinAt.arsinh, isBounded_iff_asymptoticCone_subset_singleton, LinearIsometry.extend_apply, ProbabilityTheory.instIsGaussianMapHSub, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, ContinuousLinearMap.iteratedFDerivWithin_comp_left, Real.deriv2_binEntropy, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, LinearMap.isSymmetric_sum, HasDerivWithinAt.scomp_of_eq, Module.Basis.coe_toOrthonormalBasis_repr_symm, MDifferentiableAt.const_smul, LinearMap.toSeminorm_comp, HasDerivAt.exp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, Submodule.isOrtho_top_left, gauge_closure_zero, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, Differentiable.inverse, IsometricContinuousFunctionalCalculus.toNonUnital, Convex.taylor_approx_two_segment, MDifferentiableOn.clm_prodMap, contMDiffAt_coordChangeL, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, DifferentiableAt.sqrt, DifferentiableOn.div_const, HasFDerivWithinAt.fun_sub, HasStrictFDerivAt.rpow, VectorFourier.fourierIntegral_convergent_iff, InnerProductSpace.toDual_apply_apply, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, AlgHom.instContinuousLinearMapClassOfAlgHomClass, iteratedFDeriv_tsum, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.nonneg_iff_isPositive, Real.hasDerivAt_arcsin, OrthogonalFamily.isInternal_iff, Orientation.inner_rotation_pi_div_two_right, integral_comp_polarCoord_symm, Affine.Simplex.exsphere_reindex, fderivWithin_fun_sub, coe_lpBCFₗᵢ, ContinuousAffineMap.norm_contLinear_le, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, gauge_ball, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Submodule.linearEquiv_det_reflection, IsCompactOperator.hasEigenvalue_or_mem_resolventSet, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, fderivWithin_fun_mul', ProbabilityTheory.IsGaussianProcess.comp_left, ProperCone.innerDual_singleton, VonNeumannAlgebra.coe_mk, Submodule.IsOrtho.map, EuclideanGeometry.reflection_eq_self_iff, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, LinearIsometryEquiv.comp_differentiableOn_iff, LinearIsometryEquiv.comp_differentiableAt_iff, differentiable_inner, HasFPowerSeriesWithinOnBall.sub, TemperedDistribution.fourierMultiplierCLM_const, HasLineDerivAt.tendsto_slope_zero_left, ContDiffWithinAt.continuousLinearMap_comp, Continuous.clm_apply, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, derivWithin_const_smul_field, HasFDerivWithinAt.prodMk, OrthonormalBasis.volume_parallelepiped, ContinuousAlternatingMap.norm_ofSubsingleton, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', hasFDerivAt_integral_of_dominated_loc_of_lip', Submodule.toLinearMap_starProjection_eq_isComplProjection, DifferentiableOn.fun_const_smul, RKHS.kerFun_dense, hasStrictFDerivAt_finCons, Affine.Simplex.altitudeFoot_mem_affineSpan, InnerProductSpace.rankOne_def, Affine.Simplex.ExcenterExists.touchpointWeights_restrict, MDifferentiableWithinAt.coordChangeL, HasDerivAt.smul_const, TensorProduct.nnnorm_map, Module.Basis.ofZLatticeBasis_span, IsLocalMinOn.hasFDerivWithinAt_nonneg, HasDerivAtFilter.sub_const, Orientation.oangle_rotation, Real.deriv_tan_sub_id, LinearMap.singularValues_eq_zero_iff, DifferentiableOn.inversion, ContinuousLinearMap.coe_flipₗᵢ', mul_gauge_le_norm, EuclideanGeometry.Sphere.ncard_inter_orthRadius_eq_two_of_dist_lt_radius, Real.leftDeriv_mul_log, WeakFEPair.h_feq', PiTensorProduct.norm_eval_le_injectiveSeminorm, MeasureTheory.weightedSMul_null, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, deriv_inv, Submodule.sub_starProjection_mem_orthogonal, ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, Real.differentiableAt_Gamma, HasDerivAt.cos, Polynomial.fderiv_aeval, Real.pow_mul_norm_iteratedFDeriv_fourier_le, fderivWithin_fderivWithin_eq_of_mem_nhds, Module.Basis.addHaar_reindex, orthogonalBilin_innerₗ, ContinuousLinearMap.norm_smulRight_apply, Real.hasStrictDerivAt_cosh, differentiable_add_const_iff, ConvexOn.real_univ_sSup_of_countable_affine_eq, contDiff_iff_continuous_differentiable, HasFTaylorSeriesUpTo.tsupport_mono, norm_deriv_le_of_lipschitzOn, dist_birkhoffAverage_birkhoffAverage, NumberField.mixedEmbedding.mem_span_latticeBasis, hasDerivAt_const, dslope_sub_smul_of_ne, HasFDerivWithinAt.of_isLittleO, deriv_add_const', ProbabilityTheory.IsGaussian.charFunDual_eq_of_forall_strongDual_eq_zero, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, iteratedDerivWithin_comp_three, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, AffineIsometry.coe_toAffineMap, fderiv_const_add, IsometryEquiv.map_midpoint, fderiv_mul', LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, hasFDerivWithinAt_const_add_iff, iteratedDerivWithin_of_isOpen_eq_iterate, Filter.EventuallyEq.ftaylorSeriesWithin, UniformSpace.Completion.norm_toComplL, ContDiffOn.differentiableOn, fderivWithin_const_smul_of_field, ProbabilityTheory.covarianceBilin_comm, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, Orientation.inner_rotation_pi_div_two_left, HasStrictDerivAt.cosh, HasStrictFDerivAt.ccos, LinearEquiv.extendOfIsometry_symm_eq, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, VectorField.lieBracket_fmul_left, ContinuousLinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_range, integrable_cfcₙ, HasFDerivAtFilter.sum, SchwartzMap.integral_bilin_fourier_eq, gradient_eq_deriv', Orientation.oangle_rotation_self_left, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, ContinuousLinearEquiv.contDiffPointwiseHolderAt, ContinuousMultilinearMap.analyticAt, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, DifferentiableOn.clm_comp, MDifferentiable.differentiable, ContDiffMapSupportedIn.monoCLM_apply, ClosedSubmodule.orthogonal_eq_inter, ftaylorSeriesWithin_zero, DifferentiableWithinAt.arctan, PositiveLinearMap.toPreGNS_ofPreGNS, EuclideanGeometry.Sphere.orthogonalProjection_orthRadius_center, ContinuousMultilinearMap.prodL_apply, Orientation.kahler_neg_orientation, EuclideanGeometry.exists_of_range_subset_orthocentricSystem, FormalMultilinearSeries.radius_inv_eq_limsup, Real.hasStrictDerivAt_log, HasFDerivWithinAt.cexp, HasStrictDerivAt.mul_const, hasFDerivWithinAt_iff_hasDerivWithinAt, InnerProductSpace.HarmonicContOnCl.const_smul, mdifferentiableWithinAt_iff_image, affinity_unitBall, MonotoneOn.intervalIntegrable_slope, convex_eball, nndist_left_midpoint, hasFTaylorSeriesUpToOn_succ_iff_right, fderiv_comp_fderivWithin, ContinuousLinearMap.coe_flipMultilinearEquiv, DifferentiableWithinAt.fst, EuclideanGeometry.image_inversion_affineSubspace_of_mem, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, ContinuousMultilinearMap.norm_map_init_le, ContinuousLinearMap.iteratedFDerivWithin_comp_right, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', HasStrictFDerivAt.hasStrictFDerivAt_implicitFunctionOfProdDomain, SchwartzMap.compCLMOfAntilipschitz_apply, ContinuousAlternatingMap.hasStrictFDerivAt, ContinuousAffineMap.hasStrictFDerivAt, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, HasDerivWithinAt.fun_neg, Real.differentiableOn_Gamma_Ioi, Real.differentiableOn_mul_log, LinearIsometryEquiv.conjStarAlgEquiv_refl, CurveIntegrable.fun_zero, Complex.conjCLE_toLinearEquiv, HasDerivAt.tendsto_slope_zero_left, InnerProductSpace.laplacian_smul, MeasureTheory.setToFun_smul_left, HasDerivAt.complexToReal_fderiv', hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, derivWithin_fun_const_smul, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', contDiff_nat_iff_iteratedDeriv, DifferentiableAt.continuousAlternatingMap_apply, eventually_singleton_add_smul_subset, MeasureTheory.L1.setToL1_smul_left', ConvexOn.slope_le_leftDeriv, LinearMap.IsSymmetric.toSelfAdjoint_apply, EuclideanGeometry.image_inversion_sphere_dist_center, Submodule.coe_continuous_linearProjOfClosedCompl, ContDiffWithinAt.continuousWithinAt_fderivWithin, InnerProductSpace.volume_ball, EuclideanGeometry.orthogonalProjection_subtype, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, DifferentiableAt.const_mul, iteratedFDeriv_neg_apply, HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorphOfComplemented_source, MeasureTheory.aemeasurable_fderivWithin, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, Submodule.coe_orthogonalDecomposition, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, VectorField.lieBracket_eq, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, DifferentiableAt.fun_sub, HasDerivAt.complexToReal_fderiv, differentiableAt_fst, ContinuousLinearMapWOT.isInducing_inducingFn, fderivWithin_fderivWithin_eq_of_eventuallyEq, integrableOn_Ioi_deriv_ofReal_cpow, EuclideanGeometry.Sphere.sbtw_secondInter, StandardSubspace.IsCyclic, PositiveLinearMap.exists_norm_apply_le, DoubleCentralizer.star_fst, Real.fourierIntegral_real_eq_integral_exp_smul, differentiableOn_pi'', InnerProductSpace.laplacianWithin_smul, Real.deriv_mulExpNegMulSq, StrongDual.polarSubmodule_eq_polar, HasDerivWithinAt.Ici_of_Ioi, Submodule.finrank_orthogonal_span_singleton, Real.deriv_fourierIntegral, PiTensorProduct.liftEquiv_symm_apply, HasFDerivWithinAt.uniqueDiffWithinAt, norm_cfcₙ_lt_iff, ContinuousLinearMap.fpowerSeries_apply_add_two, TestFunction.coe_ofSupportedInLM, HasStrictDerivAt.cexp, Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, extDerivWithin_fun_smul, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, LinearMap.isPositive_natCast, DifferentiableWithinAt.fun_mul, inner_smul_real_right, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, AffineSubspace.isConnected_setOf_wSameSide, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, TensorProduct.toLinearEquiv_congrIsometry, ContMDiffOn.clm_comp, ftaylorSeries_fun_zero, SchauderBasis.proj_apply, LinearMap.injective_iff_forall_lt_finrank_singularValues_pos, AnalyticAt.analyticOrderAt_deriv_add_one, HasDerivAt.add_const, ContinuousMultilinearMap.opNorm_zero, hasFDerivAt_exp_smul_const', Bundle.Trivialization.continuousLinearMapAt_symmL, iteratedFDerivWithin_one_apply, dense_differentiableAt_norm, MeromorphicAt.iterated_deriv, EuclideanGeometry.Sphere.dist_sq_eq_iff_mem_orthRadius, ContDiffWithinAt.domDomCongr_iteratedFDerivWithin, MeasureTheory.SignedMeasure.re_toComplexMeasure, TemperedDistribution.smulLeftCLM_sub, fromTangentSpace_mfderiv_smul', CStarAlgebra.instNonnegSpectrumClass, HasDerivAt.of_isLittleO, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, Submodule.isOrtho_iSup_left, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, UniqueDiffOn.image, SchwartzMap.postcompCLM_postcompCLM, Affine.Simplex.ExcenterExists.excenter_restrict, iteratedDerivWithin_scomp_eq_sum_orderedFinpartition, Submodule.norm_subtypeL, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, AffineSubspace.closed_of_finiteDimensional, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, fourierCoeff.const_smul, MonotoneOn.intervalIntegral_deriv_mem_uIcc, Submodule.mem_orthogonal', NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, instPolynormableSpace, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', HasDerivAt.sub_const, hasFDerivAt_finCons', Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, HasDerivWithinAt.derivWithin, LinearMap.toMatrixOrthonormal_symm_apply, Real.deriv_qaryEntropy, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, contDiffPointwiseHolderAt_iff, ContinuousLinearMap.IsStarNormal.orthogonal_range, Real.deriv_arctan, hasSum_cauchyPowerSeries_integral, LinearMap.coe_complexOfReal, AffineSubspace.isPreconnected_setOf_wOppSide, ContinuousLinearMap.aestronglyMeasurable_comp₂, differentiableWithinAt_comp_sub, DirectSum.IsInternal.collectedBasis_orthonormal, Matrix.posDef_gram_iff_linearIndependent, monotoneOn_deriv_descPochhammer_eval, MeasureTheory.Lp.instFourierSMul, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, SchwartzMap.smulLeftCLM_const, hasStrictFDerivAt_piLp, MeasureTheory.integral_fintype, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, HasDerivWithinAt.rpow, IsLocalMinOn.hasFDerivWithinAt_eq_zero, Differentiable.arctan, MeasureTheory.setToFun_indicator_const, LinearMap.toMatrix_innerₛₗ_apply, HasFDerivAt.finCons, deriv_fun_add, strictConvexSpace_iff, intervalIntegral.smul_integral_comp_sub_mul, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, PointwiseConvergenceCLM.equivWeakDual_symm_apply, hasDerivAt_of_tendstoUniformlyOn, ContinuousLinearMap.IsIdempotentElem.TFAE, Orientation.rightAngleRotation_map', ConvexOn.le_slope_of_hasDerivWithinAt_Ioi, TensorProduct.toLinearEquiv_commIsometry, ContinuousLinearMap.opNorm_le_of_ball, EuclideanGeometry.oangle_midpoint_left, fderiv_fun_sum, ContinuousAffineMap.decompLinearIsometryEquiv_symm_contLinear, NumberField.mixedEmbedding.negAt_apply_isComplex, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, ProbabilityTheory.isGaussian_iff_charFun_eq, Orientation.inner_rotation_pi_div_two_left_smul, LinearEquiv.extendOfIsometry_symm_apply, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Submodule.norm_sq_eq_add_norm_sq_projection, ContinuousAffineMap.contDiff, smul_sphere, HasCompactSupport.integral_Iic_deriv_eq, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, tangentCoordChange_comp, Complex.differentiableAt_exp, HasFDerivWithinAt.fun_neg, MeasureTheory.setToFun_zero_left, LinearIsometry.norm_iteratedFDeriv_comp_left, HasStrictDerivAt.scomp_of_eq, MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul, DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap, HasStrictDerivAt.fun_finset_prod, fourierIntegral_eq_half_sub_half_period_translate, LineDifferentiableAt.congr_of_eventuallyEq, ContinuousLinearMap.equivRange_symm_toLinearEquiv, Affine.Simplex.circumsphere_unique_dist_eq, Submodule.orthogonal_gc, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, fderiv_const_smul_of_invertible, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux2, Matrix.inner_toEuclideanCLM, IsLocalMax.hasFDerivAt_eq_zero, ContinuousLinearEquiv.dimH_image, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, EuclideanGeometry.orthogonalProjection_vadd_eq_self, dist_lineMap_right, hasFDerivWithinAt_pow', HasFTaylorSeriesUpToOn.continuousLinearMap_comp, SchauderBasis.bddAbove_range_nnnorm_proj, AffineMap.differentiableAt, hasStrictDerivAt_finCons', hasDerivWithinAt_taylorWithinEval_at_Icc, ProbabilityTheory.instIsGaussianDirac, ClosedSubmodule.orthogonal_orthogonal_monotone, dist_iteratedFDerivWithin_zero, curveIntegral_restrictScalars, HasFPowerSeriesOnBall.hasSum, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, HasFDerivAt.iterate, Submodule.starProjection_apply, Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, MeasureTheory.Measure.addHaar_parallelepiped, isVonNBounded_iff', Polynomial.rootSet_derivative_subset_convexHull_rootSet, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', VonNeumannAlgebra.mem_carrier, ContinuousLinearMap.opNorm_le_bound, DifferentiableWithinAt.inversion, WeakDual.isSeqCompact_closedBall, TestFunction.lineDerivCLM_add, differentiableOn_fun_neg_iff, hasStrictDerivAt_finCons, enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc, PiTensorProduct.liftEquiv_apply, HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorph_target, HasFDerivAt.cexp, extDerivFun_zero, DoubleCentralizer.add_snd, intervalIntegral.integral_deriv_comp_smul_deriv, WeakDual.isBounded_iff_isVonNBounded, HasDerivWithinAt.congr_of_eventuallyEq_of_mem, EuclideanGeometry.preimage_inversion_sphere_dist_center, HasFDerivAt.ccos, MeasureTheory.norm_condExpInd_apply_le, has_antideriv_at_fourier_neg, Real.differentiableAt_log_iff, hasFTaylorSeriesUpTo_top_iff', MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, hasStrictDerivAt_zpow, norm_iteratedFDerivWithin_prod_le, fderivWithin_iteratedFDerivWithin, fromTangentSpace_mfderiv_smul_apply', ContDiffWithinAt.clm_comp, Convex.isLittleO_alternate_sum_square, CStarModule.norm_inner_le, Orientation.rotation_neg_orientation_eq_neg, rescale_to_shell, ContinuousLinearMap.rayleighQuotient_add, ContinuousMultilinearMap.contDiff, Matrix.instNonnegSpectrumClass, HasStrictFDerivAt.implicitToOpenPartialHomeomorphOfComplemented_self, MultilinearMap.mkContinuousLinear_norm_le, LinearIsometry.toSpanSingleton_apply, hasFDerivAt_iff_tendsto, Orientation.eq_rotation_self_iff, VonNeumannAlgebra.centralizer_centralizer, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, mdifferentiable_iff, DifferentiableAt.norm_sq, DifferentiableWithinAt.sin, LinearMap.isSelfAdjoint_iff', FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, ContinuousLinearMap.deriv_of_bilinear, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, HasFDerivWithinAt.log, Orientation.areaForm'_apply, Affine.Triangle.two_zsmul_oangle_excenter_eq, HasStrictDerivAt.comp_of_eq, VectorBundleCore.coe_coordChange, hasFDerivAtFilter_iff_hasDerivAtFilter, MeasureTheory.hausdorffMeasure_lineMap_image, HasFDerivAt.clog, innerSLFlip_apply_apply, Continuous.cfcₙ_nnreal, ContinuousLinearEquiv.mdifferentiableOn, ContinuousLinearMap.nnnorm_holder_apply_apply_le, HasFDerivAt.of_local_left_inverse, AffineMap.lipschitzWith_of_finiteDimensional, mdifferentiableWithinAt_iff_differentiableWithinAt, Affine.Triangle.dist_orthocenter_reflection_circumcenter, ContinuousLinearMap.isClosed_range_iff_antilipschitz_of_injective, OrthogonalFamily.hasSum_linearIsometry, Polynomial.hasFDerivAt, Asymptotics.isTheta_const_smul_left, intervalIntegral.integral_smul_measure, StrictConcaveOn.slope_lt_of_hasDerivAt, isOpen_setOf_affineIndependent, signedDist_smul_of_pos, Distribution.mapCLM_apply, finrank_euclideanSpace, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange, HasDerivAtFilter.star, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, EuclideanGeometry.oangle_orthogonalProjection_self, LinearMap.IsPositive.isSelfAdjoint, Affine.Simplex.map_altitude_restrict, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, UpperHalfPlane.smulFDeriv_J_mul, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, Filter.EventuallyEq.hasLineDerivWithinAt_iff_of_mem, VectorBundle.continuousLinearEquivAt_apply, differentiableOn_add_const_iff, DoubleCentralizer.norm_snd, Submodule.top_orthogonal_eq_bot, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, Orthonormal.equiv_trans, Submodule.fst_orthogonalDecomposition_apply, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, HasDerivAt.sinh, Bundle.Trivialization.symmL_continuousLinearMapAt, HasDerivAtFilter.scomp, ContinuousLinearMap.antilipschitz_antiLipschitzConstant_of_injective_of_isClosed_range, Submodule.orthogonal_orthogonal_eq_closure, ContinuousLinearEquiv.nhds, ContDiffAt.derivWithin, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, Affine.Simplex.exradius_reindex, Submodule.smul_starProjection_singleton, Affine.Simplex.ninePointCircle_reindex, eqOn_dslope_slope, ContinuousLinearMap.opNorm_comp_le, contMDiff_smul, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonpos, MeasureTheory.dist_convolution_le, nndist_midpoint_left, DoubleCentralizer.nnnorm_fst, ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, MeasureTheory.Measure.addHaar_real_closedBall', Orientation.inner_comp_rightAngleRotation, intervalIntegral.integral_hasStrictFDerivAt, TensorProduct.ext_iff_inner_right, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, fderivWithin_mul_const', ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right, HasDerivWithinAt.fun_smul, DifferentiableAt.lineDifferentiableAt, ContDiffOn.derivWithin, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, TestFunction.lineDerivOp_eq_lineDerivCLM, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, LinearEquiv.isPositive_symm_iff, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, Module.Basis.exists_opNNNorm_le, aestronglyMeasurable_smul_const_iff, Orthonormal.inner_finsupp_eq_sum_right, HasStrictDerivAt.fun_div, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, Convex.exists_forall_hasDerivWithinAt, PiTensorProduct.mapL_mul, cfcHom_real_eq_restrict, intervalIntegral.inv_smul_integral_comp_sub_div, hasDerivWithinAt_taylor_coeff_within, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left, ContinuousLinearMap.toLinearMap_innerSL_apply, WithLp.volume_preserving_toLp, UniformConvexOn.convexOn, differentiableAt_comp_const_sub, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, HasFPowerSeriesAt.hasStrictDerivAt, derivWithin_comp_of_eq, Submodule.orthogonalFamily_self, SchwartzMap.fourierMultiplierCLM_apply, EuclideanGeometry.dist_orthogonalProjection_eq_dist_iff_eq_of_mem, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, NumberField.Units.regOfFamily_of_isMaxRank, Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable, Module.Basis.equivFunL_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, ClosedSubmodule.mem_symplComp_iff, ContinuousAt.cfcₙ_nnreal, inner_map_complex, IsBoundedBilinearMap.differentiableAt, hasFDerivAt_list_prod_finRange', ContDiffOn.differentiableOn_one, ContDiff.smulRight, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, LinearMap.IsSymmetric.adjoint_eq, BoundedContinuousFunction.probCharDual_zero, IsSelfAdjoint.dense_domain, LinearMap.isPositive_sum, ContinuousMultilinearMap.flipLinear_apply_apply, derivWithin_cos, Submodule.starProjection_norm_le, HasStrictFDerivAt.neg, ContinuousAlternatingMap.norm_toContinuousMultilinearMap, HasGradientAt.hasFDerivAt, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, LinearMap.hasDerivWithinAt, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, RKHS.inner_kerFun, CStarMatrix.toCLM_apply_single, PiLp.volume_preserving_ofLp, Affine.Simplex.exradius_restrict, Differentiable.const_add, DifferentiableOn.add_iff_right, hasSum_two_pi_I_cauchyPowerSeries_integral, Real.fourier_fderiv, rescale_to_shell_semi_normed, DifferentiableWithinAt.restrictScalars, ContinuousLinearMap.lipschitzWith_of_opNorm_le, FormalMultilinearSeries.comp_id, differentiableWithinAt_star_iff, ContinuousMultilinearMap.hasStrictFDerivAt, Submodule.inner_orthogonalProjection_eq_of_mem_right, hasFDerivAt_of_tendsto_locally_uniformly_on', Submodule.reflection_reflection, ContDiffOn.differentiableOn_iteratedDerivWithin, fderivWithin_comp_smul_eq_fderivWithin_smul, Continuous.continuousLinearMapCoprod, ContinuousLinearMap.isLeast_opNNNorm, sameRay_iff_norm_add, 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, Submodule.isOrtho_iff_le, FormalMultilinearSeries.cpolynomialAt_changeOrigin_of_finite, MeasureTheory.condExp_smul, imaginaryPart.norm_le, Seminorm.const_isBounded, hasFTaylorSeriesUpTo_succ_nat_iff_right, IsCovariantDerivativeOn.leibniz, SchwartzMap.compSubConstCLM_zero, ContDiffMapSupportedIn.seminorm_top_le_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, iteratedFDeriv_add, ProbabilityTheory.IsGaussianProcess.shift, LinearPMap.adjoint_apply_of_not_dense, ConvexOn.monotoneOn_deriv, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, HasFDerivWithinAt.norm_sq, hasFDerivWithinAt_piLp, MeasureTheory.norm_weightedSMul_le, Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, TendstoLocallyUniformlyOn.deriv, differentiableOn_piLp, Differentiable.comp_differentiableOn, differentiableAt_abs_neg, ClosedSubmodule.iInf_orthogonal, LinearMap.tracePositiveLinearMap_apply, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, hasDerivAt_fourier_neg, MDifferentiableAt.clm_comp, Orientation.rotation_zero, DifferentiableWithinAt.div_const, ProbabilityTheory.isGaussian_gaussianReal, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity', HasFiniteFPowerSeriesOnBall.differentiableOn, HasDerivAt.clm_comp, derivWithin_const_rpow, ProbabilityTheory.HasGaussianLaw.map, EuclideanGeometry.reflection_apply_of_mem, norm_fderiv_norm_rpow_le, DifferentiableWithinAt.sub, HasFPowerSeriesOnBall.neg, deriv_abs_zero, VectorFourier.fderiv_fourierIntegral, iteratedDerivWithin_scomp_three, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, range_cfcₙHom_le, VectorBundle.continuousOn_coordChange', StrongDual.extendRCLikeₗ_apply, LinearMap.bound_of_ball_bound', LinearMap.isPositive_linearIsometryEquiv_conj_iff, HasDerivWithinAt.differentiableWithinAt, ContinuousLinearMap.rayleighQuotient_le_of_norm_mem_resolventSet, ZSpan.coe_floor_self, HasCompactSupport.enorm_le_lintegral_Ici_deriv, HasFDerivWithinAt.smul_const, ContinuousLinearMap.mfderiv_eq, MeasureTheory.integral_posConvolution, hasStrictDerivAt_abs, Orthonormal.linearIsometryEquiv_symm_apply_single_one, nndist_midpoint_midpoint_le', hasFDerivAt_const_add_iff, OrthonormalBasis.equiv_self_rfl, InnerProductSpace.volume_ball_of_dim_odd, ContinuousAlternatingMap.isLeast_opNorm, EuclideanGeometry.OrthocentricSystem.affineIndependent, SchwartzMap.fourierInv_lineDerivOp_eq, Affine.Simplex.touchpointWeights_reindex, VectorFourier.integral_fourierIntegral_swap, RCLike.finrank_le_two, IsOpen.smul_sphere, EuclideanGeometry.Sphere.secondInter_smul, inclusionInDoubleDualWeak_apply, InnerProductSpace.harmonicAt_comp_CLE_iff, InnerProductSpace.coe_gramSchmidtBasis, Bundle.RiemannianMetric.symm, dist_homothety_self, LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, isVonNBounded_of_isBounded, HasStrictFDerivAt.add, strongConcaveOn_iff_convex, iteratedFDeriv_eq_equiv_comp, Affine.Simplex.height_map, Submodule.reflection_inv, linear_isometry_complex, sum_mul_eq_sub_integral_mul₀', MeasureTheory.condExpIndL1_smul, deriv_rpow_const, Differentiable.continuousMultilinearMapCompContinuousLinearMap, Unitization.norm_eq_sup, IsBoundedBilinearMap.hasFDerivWithinAt, ContinuousWithinAt.clm_apply, ProbabilityTheory.isGaussian_map, instIsZLatticeRealSpan, Affine.Simplex.orthogonalProjection_circumcenter, instFiniteDimensionalRealComplex, Real.hasDerivAt_cos, ContinuousMap.toLp_norm_eq_toLp_norm_coe, DifferentiableAt.inv, Differentiable.sigmoid, Matrix.ofLp_toEuclideanCLM, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Fourier.fourierIntegral_const_smul, HasDerivWithinAt.comp_hasDerivAt_of_eq, AffineSubspace.signedInfDist_eq_const_of_mem, HasFDerivWithinAt.finCons, hasDerivAtFilter_iff_isLittleO, HasDerivAt.fun_const_smul, HasDerivAt.fun_sub, CStarMatrix.toCLM_apply_eq_sum, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_increments, HasStrictFDerivAt.restrictScalars, DifferentiableWithinAt.inv, ContinuousLinearMap.coe_linearMap_equivRange, Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line, ContinuousLinearMap.le_of_opNorm_le, deriv_comp, AffineIsometry.map_vsub, PiTensorProduct.mapL_comp, derivWithin_cexp, Differentiable.neg, HasFDerivAt.ccosh, Submodule.norm_starProjection, differentiableOn_pow, isCompactOperator_iff_image_closedBall_subset_compact, StrictConvexOn.strictMonoOn_derivWithin, fderiv_cos, Filter.Tendsto.cfcₙ, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, FormalMultilinearSeries.isLittleO_one_of_lt_radius, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', hasDerivAt_exp_smul_const, ClosedSubmodule.sub_mem_orthogonal_of_inner_left, LinearPMap.adjoint_isClosed, HasDerivAtFilter.add_const, Meromorphic.fun_smul, MeasureTheory.weightedSMul_add_measure, Unitary.linearIsometryEquiv_coe_symm_apply, MeasureTheory.Measure.NullMeasurableSet.const_smul, mdifferentiableOn_iff_of_subset_source, Submodule.eq_starProjection_of_mem_of_inner_eq_zero, WithCStarModule.pi_norm, Filter.EventuallyEq.derivWithin_eq, ContDiff.comp_continuousLinearMap, exists_dual_vector, nndist_center_homothety, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, HasFDerivAt.abs_of_neg, DifferentiableOn.norm_sq, Orthonormal.map_equiv, Affine.Triangle.orthocenter_replace_orthocenter_eq_point, ContDiffMapSupportedIn.locallyConvexSpace, hasFDerivWithinAt_comp_smul_smul_iff, banach_steinhaus, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, LinearMap.IsSymmetric.hasEigenvalue_eigenvalues, Orientation.oangle_rotation_oangle_left, ContinuousLinearMap.rayleighQuotient_le_norm, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, OrthonormalBasis.det_to_matrix_orthonormalBasis, smul_unitBall_of_pos, differentiableAt_const_add_iff, DifferentiableAt.fun_pow, MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst, HasStrictDerivAt.congr_deriv, Differentiable.norm_rpow, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, AffineIsometryEquiv.symm_constVSub, stronglyMeasurable_lineDeriv_uncurry, fderiv.snd, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, ContinuousLinearMap.norm_def, OrthogonalFamily.summable_of_lp, ProbabilityTheory.IsGaussian.charFunDual_eq, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, LinearIsometryEquiv.analyticWithinAt, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', HasFPowerSeriesAt.apply_eq_zero, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', derivWithin_mul_const_field, Real.differentiableWithinAt_arcsin_Ici, logDeriv_apply, ContinuousLinearMap.le_opNorm_of_le, iteratedDeriv_comp_const_smul, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, norm_inner_eq_norm_tfae, Real.circleAverage_def, DifferentiableWithinAt.fun_div, derivWithin_zero_of_notMem_closure, ContinuousMultilinearMap.opNorm_pi, curveIntegral_fun_add, ContDiffWithinAt.derivWithin, FormalMultilinearSeries.changeOrigin_eval_of_finite, ContinuousLinearEquiv.lipschitz, iteratedDeriv_vcomp_three, VectorField.fderivWithin_apply_lieBracket_of_isSymmSndFDerivWithinAt, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_eval, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, Seminorm.map_eq_zero_of_norm_eq_zero, fderivWithin_fun_pow, RCLike.sqrt_map, derivWithin_exp, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, Submodule.reflection_mul_reflection, iteratedFDerivWithin_two_apply', HasDerivAt.const_smul, Real.hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, UniqueDiffWithinAt.smul_iff, HasStrictFDerivAt.arctan, curveIntegral_fun_neg, InnerProductSpace.instIsContPerfPairRealInnerₗOfCompleteSpace, RCLike.inner_tmul_eq, LinearPMap.IsFormalAdjoint.le_adjoint, deriv.scomp, HasStrictDerivAt.add, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, HasStrictFDerivAt.to_implicitFunction, inr_comp_cfcₙHom_eq_cfcₙAux, rotationOf_rotation, not_sameRay_iff_of_norm_eq, differentiableAt_finCons, InnerProductSpace.gramSchmidt_triangular, DifferentiableOn.const_sub, ContinuousLinearMap.opNNNorm_le_bound', equicontinuous_TFAE, hasDerivAt_taylorWithinEval_succ, Submodule.starProjection_map_apply, CFC.monotoneOn_one_sub_one_add_inv_real, AlternatingMap.norm_image_sub_le_of_bound, IsMIntegralCurveAt.hasMFDerivAt, Bornology.IsBounded.smul₀, HasFDerivAt.multiset_prod, Differentiable.cpow, extDerivFun_add, LinearMap.star_eq_adjoint, deriv_neg_right_of_sign_deriv, DifferentiableOn.const_add, PMF.integral_eq_tsum, SpectrumRestricts.real_iff, dist_self_homothety, HasFTaylorSeriesUpTo.tsupport_subset, contDiffWithinAt_succ_iff_hasFDerivWithinAt', DiffContOnCl.circleAverage_smul_div, deriv_fun_sub, IsLocalFrameOn.eventually_eq_sum_coeff_smul, hasFDerivAt_of_restrictScalars, Filter.EventuallyEq.iteratedFDerivWithin', Differentiable.mul_const, contDiffOn_succ_iff_hasFDerivWithinAt, HasFDerivAt.mul_const, fderivWithin_add_const, Bundle.Pretrivialization.continuousLinearMap_symm_apply, Filter.EventuallyEq.extDerivWithin', intervalIntegral.deriv_integral_left, differentiableWithinAt_euclidean, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', intervalIntegral.integral_comp_div, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, DifferentiableAt.fun_sub_iff_right, ContinuousLinearMap.opNorm_add_le, HasSum.exists_hasSum_smul_of_apply_eq_zero, ContinuousLinearMap.sSup_sphere_eq_norm, DoubleCentralizer.neg_toProd, FormalMultilinearSeries.radius_unshift, aestronglyMeasurable_derivWithin_Ici, HasFPowerSeriesAt.fderiv_eq, LinearPMap.adjointDomainMkCLM_apply, Orientation.oangle_sign_smul_left, deriv_abs_pos, CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg, Matrix.isPositive_toEuclideanLin_iff, ContDiffPointwiseHolderAt.continuousLinearMap_comp, derivWithin_rpow_const, HasDerivAtFilter.scomp_of_eq, ContinuousWithinAt.cfcₙ_nnreal, HasDerivWithinAt.deriv_eq_zero, ContinuousLinearMap.coe_restrictScalarsIsometry, HasLineDerivWithinAt.hasLineDerivAt, TensorProduct.enorm_tmul, ContinuousLinearMap.memLp_of_bilin, EuclideanGeometry.oangle_pointReflection_right, HasFPowerSeriesOnBall.tendstoUniformlyOn, HasDerivAt.scomp_hasDerivWithinAt_of_eq, SchauderBasis.exists_norm_proj_le, ContinuousLinearMap.norm_inr, DifferentiableOn.sinh, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior_faceOpposite, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, Submodule.starProjection_bot, MeasureTheory.convolution_mono_right_of_nonneg, ConvexBody.isBounded, VectorField.mlieBracketWithin_smul_left, ContinuousLinearMap.isometry_iff_adjoint_comp_self, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, VectorBundle.continuousLinearEquivAt_symm_apply, ZSpan.isAddFundamentalDomain', continuousMultilinearCurryFin0_apply, CStarMatrix.ofMatrix_eq_ofMatrixL, Affine.Simplex.touchpoint_mem_affineSpan, HasFDerivWithinAt.const_add, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, HasGradientAt.differentiableAt, ContDiffAt.hasStrictFDerivAt, PiTensorProduct.dualSeminorms_bounded, Conformal.differentiable, FormalMultilinearSeries.radius_neg, VectorPrebundle.pretrivialization_linear', Real.differentiableAt_cosh, HasFDerivWithinAt.mul_const', InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, HasDerivAt.comp_hasFDerivWithinAt_of_eq, extDeriv_smul, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, homeomorphUnitSphereProd_symm_apply_coe, ProbabilityTheory.iIndepFun.charFunDual_map_sum_eq_prod, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, ProbabilityTheory.covarianceBilin_self_nonneg, HasStrictFDerivAt.iterate, ContinuousLinearMap.opNNNorm_le_of_unit_nnnorm, Orientation.rightAngleRotation_rightAngleRotation, DifferentiableOn.abs, HasDerivAt.comp_const_sub, taylorWithinEval_succ, HasDerivAt.norm_sq, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, ProbabilityTheory.integral_linearMap_gaussianReal, HasDerivWithinAt.add, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, IsSelfAdjoint.conj_adjoint, TensorProduct.inner_assoc_assoc, ContinuousMultilinearMap.curryMidEquiv_apply, conformalAt_iff_isConformalMap_fderiv, complexOfReal_deriv, StrictConvexSpace.strictConvex_closedBall, fderiv_const_mul, Real.fourier_eq, ApproximatesLinearOn.lipschitz_sub, ContinuousMultilinearMap.iteratedFDeriv_eq, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eq, HasStrictFDerivAt.continuousMultilinear_apply_const, ContDiffMapSupportedIn.monoLM_eq_zero, Real.dimH_of_nonempty_interior, fderiv_sub_const, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, Polynomial.hermite_eq_deriv_gaussian', MDifferentiableAt.mfderiv, EuclideanGeometry.Sphere.ncard_inter_orthRadius_le_two, ContinuousLinearMap.reApplyInnerSelf_apply, hasFDerivAt_pi'', ZSpan.fundamentalDomain_reindex, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable', Orientation.oangle_sign_smul_add_smul_smul_add_smul, ProbabilityTheory.indepFun_iff_charFunDual_prod', fderiv_exp, Affine.Simplex.direction_mongePlane, DoubleCentralizer.algebraMap_snd, Differentiable.log, intervalIntegral.derivWithin_integral_right, WeakDual.polar_def, UnconditionalSchauderBasis.norm_proj_le_nnnormProjBound, MeasureTheory.Measure.integral_comp_mul_left, ContinuousOn.continuousOn_iteratedFDerivWithin, AnalyticAt.analyticOrderNatAt_eq_iff, fderiv_arctan, ProbabilityTheory.covarianceBilinDual_self_eq_variance, LinearMap.IsIdempotentElem.isSymmetric_iff_isOrtho_range_ker, MonotoneOn.derivWithin_nonneg, LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply, ProperCone.innerDual_union, MeasureTheory.integrable_smul_const, SchauderBasis.RankOneDecomposition.basisCoeff_spec, hasFiniteFPowerSeriesOnBall_const, LinearMap.le_def, Affine.Simplex.dist_point_centroid, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, iteratedFDerivWithin_succ_apply_left, Differentiable.sub, Orientation.areaForm_comp_linearIsometryEquiv, HasFDerivAtFilter.fun_const_smul, iteratedFDerivWithin_add_apply, hasStrictFDerivAt_norm_sq, Submodule.starProjection_unit_singleton, Affine.Simplex.altitudeFoot_reindex, fderiv_tsum, SchwartzMap.fourier_evalCLM_eq, LinearIsometryEquiv.comp_differentiableWithinAt_iff, support_deriv_subset, LinearMap.adjoint_toSpanSingleton, DoubleCentralizer.one_snd, ContinuousWithinAt.integral_sub_linear_isLittleO_ae, OrthonormalBasis.coe_toBasis, DifferentiableOn.continuousMultilinear_apply_const, ContDiff.differentiable_iteratedDeriv, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, Differentiable.add_iff_left, Affine.Simplex.affineCombination_eq_touchpoint_iff, WeakDual.withSeminorms, DifferentiableAt.fun_const_smul, contDiffOn_infty_iff_fderiv_of_isOpen, hasDerivWithinAt_natCast, Real.deriv_exp, ContinuousLinearEquiv.comp_right_fderivWithin, fderivWithin_comp_of_eq, hasFDerivWithinAt_tangentCoordChange, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, Orientation.oangle_sign_smul_sub_left, ContinuousLinearEquiv.analyticOn, SchwartzMap.hasFDerivAt, DifferentiableWithinAt.csin, ContinuousMultilinearMap.opNorm_add_le, fderiv_pow_ring', QuasispectrumRestricts.real_iff, MeasureTheory.memL1_smul_of_L1_withDensity, ContinuousLinearMap.bilinearComp_apply, ProbabilityTheory.HasGaussianLaw.fun_add, ContinuousMultilinearMap.instContinuousEval, differentiableAt_piLp, derivWithin_pow_field, Submodule.reflection_sub, differentiableWithinAtProp_self_source, MeasureTheory.Measure.toSphere_apply', TemperedDistribution.instLineDerivSMulReal, deriv_sinh, EuclideanGeometry.Sphere.mem_inter_orthRadius_iff_radius_nonneg_and_vsub_mem_and_norm_sq, iteratedDeriv_comp_neg, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOn, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, LinearEquiv.extendOfIsometry_apply, SchwartzMap.evalCLM_apply_apply, StrictConcaveOn.derivWithin_lt_slope, Affine.Simplex.altitudeFoot_mem_altitude, MDifferentiableWithinAt.mfderivWithin, HasStrictDerivAt.log, iteratedFDerivWithin_zero, LinearMap.IsSymmetric.natCast, Orientation.rotation_eq_self_iff_angle_eq_zero, HasFDerivAtFilter.fun_sub, upperHemicontinuous_quasispectrum, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ClosedSubmodule.mem_orthogonal, ContinuousMultilinearMap.norm_restrictScalars, analyticOn_taylorComp, LinearEquiv.coe_isometryOfInner, DiffContOnCl.smul_const, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior, MeasureTheory.condExpIndL1_smul', Polynomial.differentiableAt_aeval, DifferentiableAt.cosh, isBounded_convexHull, MeasureTheory.Measure.toTemperedDistribution_apply, Filter.Tendsto.cfcₙ_nnreal, Filter.EventuallyEq.lineDifferentiableWithinAt_iff_of_mem, TopologicalGroup.IsSES.integrate_apply, Complex.analyticOn_iff_differentiableOn, WeakDual.CharacterSpace.compContinuousMap_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, fderivWithin_snd, HasDerivAt.fun_div, Affine.Simplex.circumcenter_restrict, ContinuousOn.prod_mapL, iteratedFDerivWithin_prodMk, LinearMap.re_inner_adjoint_mul_self_nonneg, hasDerivAt_id, differentiable_pi, StrictConvexOn.slope_lt_derivWithin, MeasureTheory.integral_biUnion_eq_sum_powerset, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, CStarMatrix.toCLM_apply, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent, ContinuousLinearEquiv.hasFDerivWithinAt, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, ContinuousMultilinearMap.isLeast_opNNNorm, Orientation.oangle_rotation_right, Affine.Simplex.height_restrict, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, RKHS.coeCLM_injective, DoubleCentralizer.algebraMap_toProd, Affine.Triangle.affineSpan_orthocenter_point_le_altitude, continuousMultilinearCurryFin0_symm_apply_apply, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, HasDerivWithinAt.fun_const_smul, LinearMap.isPositive_self_comp_adjoint, deriv_cexp, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ConvexOn.slope_le_of_hasDerivWithinAt, ContinuousLinearMap.ker_self_comp_adjoint, differentiableAt_norm_smul, FormalMultilinearSeries.id_comp, fderivWithin.log, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, aestronglyMeasurable_lineDeriv_uncurry, ProbabilityTheory.HasGaussianLaw.fun_sub, deriv_update, Real.circleAverage_eq_integral_add, HasFPowerSeriesAt.restrictScalars, Real.iter_deriv_exp, contMDiffOn_symm_coordChangeL, DifferentiableWithinAt.finset_prod, hasDerivAt_integral_of_dominated_loc_of_deriv_le, HasFDerivWithinAt.sinh, tangentBundleCore_coordChange_model_space, intervalIntegral.inv_smul_integral_comp_div_sub, Module.Basis.prod_parallelepiped, DifferentiableWithinAt.fun_neg, ContinuousLinearMap.instStarModuleId, Real.differentiable_iteratedDeriv_cos, nndist_lineMap_right, EuclideanGeometry.Cospherical.affineIndependent, Polynomial.hasFDerivAt_aeval, contMDiffAt_hom_bundle, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right, ContinuousAt.continuousLinearMapCoprod, VectorField.mlieBracketWithin_smul_right, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, LinearIsometryEquiv.toLinearEquiv_lTensor, Differentiable.norm_sq, DoubleCentralizer.instIsCentralScalar, HasDerivWithinAt.const_mul, polar_closure, Matrix.linearIndependent_of_posDef_gram, ContDiffAt.restrictScalars_iteratedFDeriv, exists_dual_vector'', HasFDerivAt.continuousAlternatingMap_apply_const, LinearIsometry.adjoint_comp_self', deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, LinearIsometryEquiv.toLinearEquiv_smul, MeasureTheory.MemLp.continuousLinearMap_comp, ProbabilityTheory.IsGaussian.memLp_dual, LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re, norm_fderiv_iteratedFDeriv, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, Module.Dual.extendRCLikeₗ_apply, isConnected_setOf_sameRay_and_ne_zero, curveIntegralFun_neg, TestFunction.lineDerivCLM_eq_fderivCLM, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, TopologicalAddGroup.IsSES.integrate_mono, HasDerivWithinAt.div, MeasureTheory.Lp.norm_constL_le, meromorphicOrderAt_smul, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, conformalFactorAt_inner_eq_mul_inner', NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, hasFDerivAtFilter_snd, StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iio, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, HasFDerivAt.log, LinearIsometryEquiv.analyticOn, HasDerivWithinAt.arctan, TemperedDistribution.fourier_lineDerivOp_eq, LinearIsometryEquiv.analyticAt, convexHull_sphere_eq_closedBall, ContDiffPointwiseHolderAt.clm_apply, DifferentiableWithinAt.cpow_const, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', Matrix.l2_opNNNorm_def, ContinuousMultilinearMap.instIsBoundedSMul, MeasureTheory.charFunDual_map_const_add, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, VonNeumannAlgebra.IsIdempotentElem.mem_iff, hasDerivAtFilter_sub_const_iff, EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two, MeasureTheory.L1.SimpleFunc.setToL1S_const, SmoothPartitionOfUnity.finsum_smul_mem_convex, MeasureTheory.charFunDual_map_add_const, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.integrable_comp, ContinuousLinearMap.adjointAux_adjointAux, ImplicitFunctionData.differentiableAt_implicitFunction, HasStrictFDerivAt.const_sub, Submodule.coe_inner, GeneralSchauderBasis.proj_empty, HasFDerivAt.sub_const, fderiv_sub, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, HasStrictDerivAt.const_add, Complex.conjCLE_coe_toLinearMap, Orientation.rotation_trans, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, dslope_same, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, ZSpan.span_top, Complex.differentiableOn_compl_singleton_and_continuousAt_iff, contDiffOn_succ_iff_deriv_of_isOpen, ContDiffOn.clm_comp, hasFDerivAt_single, DifferentiableOn.cos, signedDist_lineMap_left, ContMDiffAt.clm_precomp, selfAdjoint.realPart_unitarySelfAddISMul, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, TestFunction.lineDerivCLM_apply, ProbabilityTheory.covarianceBilin_real_self, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, LinearMap.eq_adjoint_iff, SchauderBasis.RankOneDecomposition.finrank_range, Differentiable.iterate, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, deriv_smul, nnnorm_cfcₙ_nnreal_lt_iff, Real.tendsto_rightDeriv_mul_log_atTop, Real.hasStrictDerivAt_arsinh, PositiveLinearMap.gnsStarAlgHom_apply, ContDiffOn.continuousOn_fderivWithin_apply, Orthonormal.equiv_toLinearEquiv, Real.fourier_iteratedDeriv, DifferentiableOn.fun_add_iff_right, iter_deriv_pow', MeasureTheory.integral_comp_rpow_Ioi, HasFDerivWithinAt.iterate, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, convex_closedEBall, hasDerivAt_iff_tendsto_slope_zero, MeasureTheory.condExp_ae_eq_condExpL1CLM, EuclideanGeometry.Sphere.dist_center_midpoint_lt_radius, HasMFDerivWithinAt.sum, Orthonormal.inner_right_finsupp, AffineIsometry.norm_map, DifferentiableOn.fun_comp, Asymptotics.isLittleOTVS_iff_isLittleO, OrthonormalBasis.tensorProduct_apply', EuclideanSpace.basisFun_repr, ImplicitFunctionData.hasStrictFDerivAt, NumberField.mixedEmbedding.span_latticeBasis, ContinuousLinearMap.integral_comp_id_comm', UniqueMDiffWithinAt.uniqueDiffWithinAt, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, inner_product_apply_eigenvector, HasFTaylorSeriesUpToOn.hasFDerivAt, WeakFEPair.hf_zero, RCLike.realLinearIsometryEquiv_symm_apply, Convex.exists_subset_interior_convexHull_finset_of_isCompact, LinearIsometry.norm_toContinuousLinearMap_comp, convex_ball, hasStrictFDerivAt_inv, AlternatingMap.norm_image_sub_le_of_bound', real_inner_smul_right, ContinuousLinearMap.isBigOWith_comp, EuclideanGeometry.Sphere.mem_of_mem_tangentsFrom, scalarSMulCLE_apply, ContinuousLinearMap.flip_add, hasFiniteFPowerSeriesAt_const, MDifferentiable.clm_prodMap, continuous_clm_apply, ContinuousLinearMap.hasTemperateGrowth, InnerProductSpace.gramSchmidtOrthonormalBasis_det, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, AffineSubspace.isometryEquivMap.coe_apply, not_differentiableWithinAt_of_deriv_tendsto_atTop_Iio, Orientation.oangle_sub_right_smul_rotation_pi_div_two, LinearIsometry.coe_toSpanSingleton, ConcaveOn.le_slope_of_hasDerivWithinAt, LinearMap.isPositive_iff_complex, VectorFourier.fourierSMulRight_apply, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, ContinuousLinearEquiv.isBigO_sub_rev, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, HasFDerivWithinAt.restrictScalars, DoubleCentralizer.pow_toProd, OrthonormalBasis.equiv_apply_euclideanSpace, measurable_fderiv_apply_const, MeasureTheory.euclideanHausdorffMeasure_homothety_image, stereographic_neg_apply, StrongConcaveOn.strictConcaveOn, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, MeasureTheory.Measure.addHaar_image_linearMap, IsLocalFrameOn.coeff_apply_of_notMem, isSelfAdjoint_starProjection, Affine.Simplex.sOppSide_excenter_singleton_point, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, VectorBundleCore.localTriv_coordChange_eq, ContinuousMultilinearMap.uncurryRight_apply, Seminorm.closedBall_smul, HasDerivAt.comp_const_add, MeasureTheory.L1.tendsto_setToL1, eventually_norm_symmL_trivializationAt_self_comp_lt, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', OrthonormalBasis.det_adjustToOrientation, MeasureTheory.condExpL1CLM_indicatorConst, SchwartzMap.fourierMultiplierCLM_ofReal, DifferentiableAt.sub_iff_left, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, fderiv_inv, MeromorphicAt.fun_deriv, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, differentiableWithinAt_iff_restrictScalars, DifferentiableOn.continuousAlternatingMap_apply, Differentiable.prodMk, normalize_smul_of_neg, ContDiffWithinAt.comp_continuousLinearMap, Complex.orthonormalBasisOneI_repr_symm_apply, MeasureTheory.euclideanHausdorffMeasure_homothety_preimage, tangentBundleCore_coordChange, derivWithin_comp_mul_left, MeasureTheory.L1.nnnorm_Integral_le_one, HasFDerivAt.exp, ContDiffWithinAt.laplacianWithin_CLM_comp_left, HasFDerivAtFilter.prodMk, hasDerivAt_circleMap, ContinuousLinearMap.orthogonalComplement_iSup_eigenspaces_eq_bot, LinearIsometry.norm_iteratedFDerivWithin_comp_left, HasFDerivAtFilter.isLittleO, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, derivWithin_zero_of_not_uniqueDiffWithinAt, curveIntegralFun_fun_zero, hasFDerivWithinAt_closure_of_tendsto_fderiv, EuclideanGeometry.oangle_homothety, ClosedSubmodule.mulI_inf, derivWithin_fun_smul, ContinuousLinearMap.bilinearComp_zero, MeasureTheory.integral_fun_norm_addHaar, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, HasFDerivAt.fun_pow', tendsto_sum_mul_atTop_nhds_one_sub_integral₀, MeasureTheory.setIntegral_ge_of_const_le, HasDerivWithinAt.scomp_hasDerivAt_of_eq, signedDist_anticomm, dslope_of_ne, ZSpan.map, DifferentiableAt.prodMk, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, MeasureTheory.weightedSMul_smul, HasMFDerivWithinAt.mul', ContinuousLinearEquiv.norm_symm_pos, MeasureTheory.integral_continuousLinearMap_prod, Submodule.sInf_orthogonal, norm_deriv_le_of_lipschitz, intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, LinearMap.IsSymmetric.directSum_isInternal_of_commute, segment_subset_closedBall_left, fderivWithin_comp', ContinuousMultilinearMap.cpolynomialAt, MultilinearMap.mkContinuousLinear_norm_le', ContinuousLinearMap.NonlinearRightInverse.right_inv, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, TemperedDistribution.laplacian_eq_sum, Affine.Simplex.dist_circumcenter_eq_circumradius, curveIntegralFun_def', NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, WithCStarModule.pi_inner, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, Orientation.areaForm_comp_rightAngleRotation, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, Submodule.isOrtho_span, contDiffOn_fderiv_coord_change, HasFPowerSeriesWithinAt.differentiableWithinAt, Bundle.Trivialization.coordChangeL_prod, ZSpan.exist_unique_vadd_mem_fundamentalDomain, ContinuousMultilinearMap.ratio_le_opNorm, ContDiff.iterate_deriv, HasFDerivAtFilter.fun_add, ZSpan.fundamentalDomain_subset_parallelepiped, HasDerivWithinAt.neg, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos, ContinuousLinearMap.norm_extendTo𝕜'_bound, sum_mem_ball_of_strictConvexSpace, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, extDeriv_add, MeasureTheory.hausdorffMeasure_homothety_image, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, HasFDerivWithinAt.hasDerivWithinAt, Real.differentiableAt_arctan, ContinuousMultilinearMap.integral_apply, HasFTaylorSeriesUpToOn.differentiableAt, eq_lineMap_of_dist_eq_mul_of_dist_eq_mul, HasStrictDerivAt.smul_const, MultilinearMap.continuous_of_bound, ProbabilityTheory.IsGaussianProcess.comp_right, ProbabilityTheory.HasGaussianLaw.fun_neg, HasStrictDerivAt.sub, ContDiff.deriv', MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, DifferentiableOn.add_iff_left, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, HasFiniteFPowerSeriesOnBall.neg, derivWithin_intCast, HasGradientWithinAt.fderivWithin_apply, ContMDiffOn.clm_apply, differentiableWithinAt_abs_neg, sum_mul_eq_sub_integral_mul₁, MeasureTheory.integral_comp, TemperedDistribution.instContinuousLineDeriv, HasDerivWithinAt.Ioo_of_Ioi, HasFDerivAtFilter.comp, MeasureTheory.L1.setToL1_unique, SchauderBasis.finrank_range_succSub_eq_one, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, MeasureTheory.average_union_mem_segment, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, WithCStarModule.prod_norm, norm_derivWithin_eq_norm_fderivWithin, differentiableWithinAt_dslope_of_ne, ApproximatesLinearOn.antilipschitz, iteratedFDeriv_zero_apply, DifferentiableWithinAt.smul_const, ContinuousLinearMap.le_def, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, AffineMap.derivWithin, contDiff_succ_iff_fderiv_apply, HasDerivAt.arsinh, hasDerivAt_fourier, coe_lpPiLpₗᵢ, complexOfReal_fderivWithin, DiffContOnCl.circleAverage_poissonKernel_smul, VectorBundleCore.localTriv_apply, LinearIsometry.inr_apply, fderiv_ccos, LinearMap.isPositive_zero, DoubleCentralizer.zero_fst, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, fderiv_update, RKHS.coeCLM_apply, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, StrongDual.extendRCLikeₗᵢ_symm_apply, ContDiffOn.continuousOn_derivWithin, Real.rightDeriv_mul_log, dist_add_dist_eq_iff, extDerivWithin_apply_vectorField, Real.fourier_bilin_convolution_eq, BoxIntegral.BoxAdditiveMap.toSMul_apply, ProbabilityTheory.IsGaussian.map_rotation_eq_self, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, fdifferential_comp, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, CStarMatrix.mul_entry_mul_eq_inner_toCLM, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, LinearIsometry.orthonormal_comp_iff, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, homeomorphSphereProd_symm_apply_coe, hom_trivializationAt, ContinuousLinearMap.IsStarProjection.ext_iff, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Diffeomorph.uniqueDiffOn_image, FormalMultilinearSeries.le_comp_radius_of_summable, ContinuousLinearMap.le_opNorm₂, DifferentiableOn.fun_sum, ContinuousLinearMap.lpPairing_eq_integral, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero, HasFDerivAt.smul_const, MeasureTheory.integrable_tilted_iff, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, TopologicalGroup.IsSES.pushforward_apply_apply, isIntegralCurveOn_comp_mul_ne_zero, ProbabilityTheory.covarianceOperator_inner, DifferentiableWithinAt.neg, ProbabilityTheory.HasGaussianLaw.sub, InnerProductSpace.rankOne_def', ContDiff.clm_comp, ContDiff.fderiv_apply, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, ContinuousLinearMap.opNorm_mul_le, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, Affine.Simplex.incenter_restrict, ContinuousLinearMap.uncurryLeft_norm, hasFDerivAtFilter_fst, Submodule.isClosed_orthogonal, ContDiffWithinAt.fderivWithin', differentiableWithinAt_comp_add_right, EuclideanGeometry.Sphere.IsDiameter.sbtw, ContinuousLinearMap.opNorm_subsingleton, TestFunction.instLineDerivLeftSMulRealTopENat, mellin_eq_fourierIntegral, hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, MeasureTheory.AEStronglyMeasurable.fourierPowSMulRight, HasFDerivAt.comp_hasDerivWithinAt, ContinuousLinearMap.holder_smul_right, HasFDerivWithinAt.multilinear_comp, HasFPowerSeriesOnBall.tendstoUniformlyOn', AffineSubspace.mem_perpBisector_iff_inner_eq_inner, extremePoints_closedBall_subset_sphere, HasFPowerSeriesWithinOnBall.const_smul, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, InnerProductGeometry.angle_eq_angle_add_angle_iff, intervalIntegral.deriv_integral_of_tendsto_ae_right, fderiv_apply_one_eq_deriv, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, DifferentiableWithinAt.abs_of_neg, HasFTaylorSeriesUpToOn.compContinuousLinearMap, ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero, Affine.Triangle.oangle_excenter_singleton_eq, DifferentiableWithinAt.cosh, SchwartzMap.fourierMultiplierCLM_const, ContDiffOn.continuousOn_fderivWithin, HasFPowerSeriesOnBall.sub, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, SchwartzMap.integral_sesq_fourierIntegral_eq, Submodule.norm_orthogonalProjection_apply, Distribution.IsVanishingOn.iteratedLineDerivOp, contDiffAt_succ_iff_hasFDerivAt, fderivWithin_const_smul_of_invertible, ContinuousLinearMap.IsPositive.inner_nonneg_left, Real.fourierIntegral_eq', ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, TestFunction.monoCLM_eq_of_scalars, HasFDerivAt.inner, LinearMap.adjoint_lTensor, HasDerivAt.rpow, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', intervalIntegral.integral_comp_smul_deriv', EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Complex.hasSum_taylorSeries_on_emetric_ball, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, HasStrictDerivAt.of_notMem_tsupport, fderiv_continuousMultilinear_apply_const_apply, MeasureTheory.integrable_withDensity_iff_integrable_smul, CStarModule.norm_sq_eq, LinearMap.singularValues_pos_iff_lt_finrank_range, MeasureTheory.Integrable.convolution_integrand, HasFDerivAtFilter.star, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, OrthonormalBasis.map_apply, derivWithin_fun_sub, LinearMap.toMatrixOrthonormal_apply, hasFPowerSeriesOn_cauchy_integral, MeasureTheory.condExpL1CLM_lpMeas, measurableSet_of_differentiableAt, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, Module.Basis.coe_parallelepiped, fderivWithin_exp, Submodule.isSymmetricProjection_starProjection, ProbabilityTheory.HasGaussianLaw.map_fun, Submodule.eq_starProjection_of_mem_orthogonal, DifferentiableWithinAt.csinh, Differentiable.clm_apply, deriv_inv'', ContinuousLinearMap.mdifferentiableWithinAt, SeparatingDual.completeSpace_continuousLinearMap_iff, DifferentiableAt.mul_const, OrthogonalFamily.inner_sum, EuclideanGeometry.inversion_def, deriv_circleMap, LinearMap.IsPositive.smul_of_nonneg, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, vonNBornology_eq, ProbabilityTheory.covarianceBilin_apply_pi, cfcₙAux_injective, HasStrictFDerivAt.fun_sub, ProbabilityTheory.deriv_mgf, SchwartzMap.integral_bilinear_laplacian_right_eq_left, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, IsBoundedLinearMap.hasFDerivAtFilter, ZLattice.covolume_eq_det_mul_measureReal, hasDerivWithinAt_const, LinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_range, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', intervalIntegral.integral_comp_sub_mul, ContinuousLinearMap.antilipschitz_of_injective_of_isClosed_range, ProbabilityTheory.integral_strongDual_stdGaussian, ContinuousLinearMap.isOpen_injective, mdifferentiableWithinAt_iff', NonUnitalCommCStarAlgebra.toStarModule, ContDiff.continuous_iteratedFDeriv', OrthonormalBasis.sum_repr_symm, HasFDerivAt.const_mul, homeomorphUnitSphereProd_apply_fst_coe, DifferentiableOn.snd, LipschitzWith.ae_differentiableAt, StrongDual.toLpₗ_apply, Orientation.kahler_apply_self, MeasureTheory.L1.setToL1_apply_coeToLp, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, DifferentiableWithinAt.restrictScalars_fderivWithin, Affine.Simplex.dist_circumcenter_eq_circumradius', Real.differentiableWithinAt_arcsin_Iic, SchwartzMap.norm_toBoundedContinuousFunction_le, EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, HasStrictFDerivAt.isEquivalent_sub, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, HasStrictFDerivAt.continuousAlternatingMap_apply, Orthonormal.inner_left_sum, Orientation.inner_smul_rotation_pi_div_two_right, HasLineDerivAt.congr_of_eventuallyEq, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, ZSpan.instDiscreteTopologySubtypeMemSubmoduleIntSpanRangeCoeBasisRealOfFinite, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, ContinuousLinearMap.continuous_uncurry_of_multilinear, Complex.analyticOn_univ_iff_differentiable, UniformConcaveOn.concaveOn, Complex.conjCLE_nnorm, differentiable_const_add_iff, Polynomial.differentiableOn, hasFDerivAt_of_tendstoLocallyUniformlyOn, StrongDual.extendRCLikeₗ_symm_apply, Pi.orthonormalBasis.toBasis, HasDerivAtFilter.congr_of_eventuallyEq, HasStrictDerivAt.complexToReal_fderiv', LinearIsometry.map_starProjection, Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric, StrictConcaveOn.strictAntiOn_deriv, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, hasFDerivAt_polarCoord_symm, EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter, fourierIntegral_gaussian_innerProductSpace, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', ConcaveOn.slope_le_derivWithin, DifferentiableAt.of_dslope, EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius, DifferentiableOn.fun_inv, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero, HasFDerivWithinAt.rpow_const, differentiableOn_neg, fderivWithin_multiset_prod, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ZSpan.isAddFundamentalDomain, HasFDerivAt.mul, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, VectorField.lieBracket_const_smul_right, LinearMap.singularValues_fin, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, Asymptotics.IsBigO.hasFDerivWithinAt, LinearMap.opNorm_extendOfNorm_le, dist_homothety_center, LinearMap.continuous_of_nonzero_on_open, Submodule.inf_orthogonal, LinearMap.sq_singularValues_of_lt, Continuous.prod_map_equivL, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_zero, MeasureTheory.integral_continuousLinearMap_prod', ConvexOn.real_univ_sSup_affine_eq, DifferentiableWithinAt.clm_comp, MeasureTheory.weightedSMul_union, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, abs_signedDist_eq_dist_iff_vsub_mem_span, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, EuclideanGeometry.measurePreserving_vaddConst, MeasureTheory.uniformIntegrable_average, hasFDerivAt_exp_zero, differentiableAt_fun_neg_iff, LinearIsometryEquiv.strictConvex_image, fderiv_add, SchauderBasis.proj_comp, MultilinearMap.mkContinuousMultilinear_norm_le', SchwartzMap.le_seminorm, DoubleCentralizer.nnnorm_fst_eq_snd, WithCStarModule.inner_single_right, ConvexOn.monotoneOn_leftDeriv, Unitization.norm_def, Submodule.IsOrtho.le, Submodule.reflection_map, differentiableOn_neg_iff, Real.iteratedDeriv_fourier, EuclideanGeometry.Concyclic.Coplanar, VonNeumannAlgebra.IsStarProjection.mem_iff, MeasureTheory.L1.setToL1_congr_left', EuclideanGeometry.Sphere.mem_tangentSet_of_mem_tangentsFrom, Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint, InnerProductSpace.span_gramSchmidt_Iic, MDifferentiableAt.smul, LinearMap.IsSymmetric.direct_sum_isInternal, Submodule.det_reflection, linear_isometry_complex_aux, HasStrictDerivAt.const_smul, ContinuousLinearMap.measurable_apply, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, selfAdjoint.star_coe_unitarySelfAddISMul, deriv_neg', HasDerivAt.fun_sum, deriv_zero_of_frequently_const, Orientation.kahler_rotation_left', fderivWithin_neg, MeasureTheory.Measure.addHaar_affineSubspace, Real.differentiable_sin, MeasureTheory.setIntegral_rnDeriv_smul', IsBoundedBilinearMap.fderiv, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, derivWithin_zero_of_not_accPt, second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonneg, ContinuousMultilinearMap.curryRight_apply, TensorProduct.inner_comm_comm, HasFDerivAtFilter.fst, ContDiff.fourierPowSMulRight, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Distribution.dsupport_smulLeftCLM_subset, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContMDiffWithinAt.mfderivWithin, Affine.Simplex.pointsWithCircumcenter_point, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, differentiableWithinAt_pi, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, Bundle.Trivialization.baseSet_continuousLinearMap, intervalIntegral.smul_integral_comp_mul_left, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul, IsCompactOperator.image_subset_compact_of_bounded, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, derivWithin_sin, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, HasFDerivAt.sinh, rotation_trans, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, Filter.EventuallyEq.derivWithin_eq_of_mem, Real.eulerMascheroniConstant_eq_neg_deriv, MeasureTheory.SimpleFunc.setToSimpleFunc_indicator, not_sameRay_iff_abs_lt_norm_sub, HasFDerivAt.comp_hasDerivWithinAt_of_eq, CPolynomialOn.deriv, deriv_const_rpow, EuclideanSpace.volume_ball_fin_three, Real.not_differentiableAt_inv_log_zero, Affine.Simplex.inradius_restrict, ProbabilityTheory.IsGaussian.integral_dual, Affine.Simplex.mongePoint_reindex, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', uniformConcaveOn_zero, Filter.EventuallyEq.deriv_eq, Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, CurveIntegrable.fun_neg, enorm_sub_le_lintegral_deriv_of_contDiffOn_Icc, Orientation.abs_areaForm_le, EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq, AffineSubspace.subtypeₐᵢ_linear, Real.deriv_mul_log, ContDiffWithinAt.laplacianWithin_CLM_comp_left_nhds, fderivWithin_comp₃, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, AnalyticAt.iterated_deriv, hasStrictFDerivAt_pow', EuclideanGeometry.angle_homothety, Polynomial.hasStrictDerivAt_aeval, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, AnalyticOn.iteratedFDeriv_comp_perm, ContinuousLinearMap.norm_single, VectorPrebundle.exists_coordChange, HasFDerivWithinAt.snd, DoubleCentralizer.one_fst, ContinuousLinearMap.norm_extendTo𝕜', InnerProductGeometry.angle_smul_smul, MDifferentiableOn.clm_apply, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, DifferentiableWithinAt.pow, AnalyticOnNhd.deriv_of_isOpen, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, Convex.image_derivWithin, HasDerivAtFilter.const_add, HasDerivWithinAt.of_notMem_tsupport, LinearIsometry.coe_toAffineIsometry, differentiableAt_iff_comp_const_sub, Affine.Simplex.altitude_reindex, linearIndependent_of_ne_zero_of_inner_eq_zero, MDifferentiableAt.clm_precomp, ModelWithCorners.convex_range, ContDiffMapSupportedIn.postcompCLM_apply, LinearPMap.isSelfAdjoint_def, DirectSum.IsInternal.subordinateOrthonormalBasis_def, SchwartzMap.compSubConstCLM_comp, HasFDerivAt.complexOfReal_hasFDerivAt, HasDerivWithinAt.mono_of_mem_nhdsWithin, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, ContinuousAlternatingMap.curryLeft_zero, signedDist_neg, IsContDiffImplicitAt.bijective, norm_lineDeriv_le_of_lipschitzOn, Submodule.eq_starProjection_of_mem_orthogonal', ProbabilityTheory.covarianceBilin_apply_basisFun, ContDiffBump.integral_normed_smul, dslope_eventuallyEq_slope_of_ne, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ProbabilityTheory.instIsGaussianMapHAdd_1, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, Orientation.oangle_sign_smul_right, DifferentiableWithinAt.sub_const, Orientation.normSq_kahler, Differentiable.fun_sub_iff_left, ContinuousMultilinearMap.opNNNorm_prod, MDifferentiableWithinAt.differentiableWithinAt, ContinuousLinearEquiv.comp_right_differentiableOn_iff, ContinuousLinearMap.opENorm_comp_le, HasFDerivWithinAt.clog, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, LinearMap.IsSymmetric.invariant_orthogonalComplement_eigenspace, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, curveIntegrable_neg_iff, LinearMap.finrank_range_adjoint, ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, ModelWithCorners.uniqueDiffOn_extendCoordChange_source, maximal_orthonormal_iff_orthogonalComplement_eq_bot, iteratedFDeriv_fun_sum_apply, SmoothBumpFunction.contMDiff_smul, HasDerivWithinAt.Ioi_of_Ioo, iteratedFDeriv_one_apply, ContinuousLinearEquiv.iteratedFDeriv_comp_left, MultilinearMap.norm_image_sub_le_of_bound, HasDerivWithinAt.fun_mul, DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap, gauge_unit_ball, Filter.Tendsto.zero_smul_isBoundedUnder_le, Submodule.reflection_orthogonal, fderivWithin_comp_of_eq', hasFDerivAt_exp_smul_const_of_mem_ball, intervalIntegral.derivWithin_integral_of_tendsto_ae_right, fderiv_fun_mul', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFPowerSeriesOnBall.factorial_smul, HasFDerivAt.const_smul, HasFDerivAt.hasLineDerivAt, Real.differentiableAt_tan, LinearEquiv.isometryOfInner_toLinearEquiv, derivWithin_pi, ContinuousAlternatingMap.norm_image_sub_le', Real.differentiable_cosh, NumberField.mixedEmbedding.negAt_symm, HasFPowerSeriesWithinAt.prod, LinearMap.sq_singularValues_fin, HasDerivWithinAt.pow', EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius, DifferentiableAt.rpow, VectorFourier.contDiff_fourierIntegral, MeasureTheory.L1.setToL1_congr_left, ContMDiffMap.coe_smul, ContinuousLinearMap.adjoint_comp_self_injective_iff, iteratedFDeriv_succ_apply_right, ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_add, Submodule.isOrtho_top_right, FormalMultilinearSeries.leftInv_coeff_one, LinearMap.IsSymmetric.smul, ConcaveOn.leftDeriv_le_slope, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul', HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ContinuousLinearMap.hasMFDerivAt, TensorProduct.assocIsometry_apply, NumberField.finite_of_discr_bdd, sameRay_iff_inv_norm_smul_eq, Matrix.toLin_conjTranspose, ProbabilityTheory.variance_dual_stdGaussian, Real.Convex.dimH_eq_finrank_vectorSpan, mdifferentiableOn_continuousLinearMapCoordChange, derivWithin_one, hasDerivAtFilter_intCast, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, Orthonormal.inner_finsupp_eq_sum_left, HasDerivWithinAt.sinh, cfcHom_nnreal_eq_restrict, Bundle.Trivialization.continuousLinearEquivAt_apply, fderiv_deriv, BoxIntegral.integral_smul, LinearMap.range_adjoint_comp_self, ContDiffAt.hasStrictFDerivAt_implicitFunction, WithLp.unitizationAlgEquiv_symm_apply_ofLp, DifferentiableOn.finset_prod, MeasureTheory.L1.setToL1_smul, integrableOn_cfcₙ, hasFPowerSeriesAt_pi_iff, mfderivWithin_eq_fderivWithin, norm_cfcₙ_le, ProbabilityTheory.integral_tilted_mul_eq_mgf, DifferentiableOn.fst, ConcaveOn.derivWithin_le_slope, MeasureTheory.integral_simpleFunc_larger_space, hasDerivWithinAt_univ, LinearIsometryEquiv.hasFDerivAt, ContDiffBump.apply, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, Orientation.oangle_sign_add_smul_left, HasFDerivAtFilter.add, HasFDerivAt.lim_real, differentiableAt_add_const_iff, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, uniqueMDiffWithinAt_iff, continuous_barycentric_coord, signedDist_vsub_self_rev, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, LinearIsometryEquiv.rTensor_apply, LinearIsometryEquiv.inner_map_map, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, Orientation.neg_rotation_pi_div_two, HasFDerivAt.rpow_const, InnerProductSpace.isStarProjection_rankOne_self, deriv_sub_const, coord_norm', ProperCone.relative_hyperplane_separation, HasFDerivWithinAt.comp, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, DirectSum.IsInternal.collectedOrthonormalBasis_mem, ContinuousAlternatingMap.piLIE_symm_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, DifferentiableOn.neg, LinearIsometry.integral_comp_comm, contDiff_clm_apply_iff, HasFPowerSeriesAt.hasFDerivAt, StrictConvex.linearIsometry_preimage, OrthonormalBasis.measurePreserving_repr_symm, Orientation.linearIsometryEquiv_comp_rightAngleRotation, Seminorm.cont_withSeminorms_normedSpace, CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg', WeakDual.isClosed_polar, hasStrictFDerivAt_finCons', spec_cfcₙAux, norm_fderiv_norm, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, DifferentiableOn.inner, ClosedSubmodule.orthogonal_eq_top_iff, fderiv_comp, StrongDual.extendRCLikeₗᵢ_apply, UniformConcaveOn.strictConcaveOn, DifferentiableOn.fun_finset_prod, QuadraticMap.lineDifferentiableAt, EuclideanSpace.piLpCongrLeft_single, HasDerivAt.ofReal_comp, Submodule.sup_orthogonal_inf_of_hasOrthogonalProjection, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, ContinuousOn.cfcₙ_nnreal', hasFDerivAt_exp_smul_const, Differentiable.inner, DifferentiableAt.iterate, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, HasFPowerSeriesOnBall.eventually_hasSum, LinearMap.IsPositive.trace_nonneg, LinearMap.mkContinuous₂_norm_le, DifferentiableWithinAtProp_self, VectorBundle.finrank_eq, DifferentiableAt.sin, DifferentiableAt.ofReal_cpow_const, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, ProbabilityTheory.IsGaussianProcess.of_isGaussianProcess, Orientation.rotation_eq_matrix_toLin, MeasureTheory.AEStronglyMeasurable.fourierSMulRight, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, smul_unitBall, intervalIntegral.integral_const_of_cdf, DifferentiableWithinAt.const_smul, IsSymmSndFDerivAt.iteratedFDeriv_cons, HasStrictFDerivAt.const_rpow, Orientation.inner_rightAngleRotation_swap, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, intervalIntegral.integral_const', MeasureTheory.condExp_smul_of_aestronglyMeasurable_left, Bundle.Trivialization.apply_eq_prod_continuousLinearEquivAt, Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral, ContinuousLinearMap.comp_analyticOn, hasStrictDerivAt_const, integrable_cfcₙ', fderiv_finset_prod, intervalIntegral.integral_smul_deriv_eq_deriv_smul, ConcaveOn.deriv_le_slope, ContinuousLinearMap.self_comp_adjoint_injective_iff, Bundle.Trivialization.continuousLinearMapAt_apply, Bundle.Trivial.trivialization.isLinear, DifferentiableAt.fun_sum, ContinuousLinearMap.coeFn_compLpL, hasStrictFDerivAt_list_prod_attach', rotationOf_coe, MDifferentiableOn.differentiableOn, Real.Lp.fourierTransformCLM_apply, NumberField.mixedEmbedding.volume_negAt_plusPart, HasFDerivAt.snd, deriv_single, stronglyMeasurable_deriv, StrongDual.norm_toLpₗ_le, HasStrictDerivAt.scomp, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, hasFDerivWithinAt_euclidean, Bundle.Trivialization.continuousLinearEquivAt_symm_apply, ClosedSubmodule.mem_orthogonal_iff, Orientation.oangle_sub_left_smul_rotation_pi_div_two, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, HasFPowerSeriesWithinAt.restrictScalars, DoubleCentralizer.sub_fst, tangentConeAt_real_subset_isRCLikeNormedField, HasFDerivWithinAt.abs_of_pos, ProperCone.innerDual_insert, DifferentiableWithinAt.ccosh, range_deriv_subset_closure_span_image, Module.Basis.parallelepiped_eq_map, WeakDual.isBounded_toWeakDual_preimage_iff_isBounded, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, ContDiffMapSupportedIn.norm_apply_le_seminorm, integral_withDensity_eq_integral_toReal_smul, contDiffOn_clm_apply, measurable_lineDeriv_uncurry, ZLattice.covolume.tendsto_card_div_pow', ContinuousLinearMap.le_opNNNorm, Bundle.Trivialization.symmL_apply, fderiv_continuousAlternatingMap_apply_apply, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, DifferentiableAt.differentiableAt_norm_of_smul, FormalMultilinearSeries.id_apply_zero, SchwartzMap.hasDerivAt, HasDerivWithinAt.fun_sub, Submodule.starProjection_orthogonal, EuclideanGeometry.Sphere.inter_orthRadius_eq_singleton_iff, PiTensorProduct.mapLMultilinear_apply_apply, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, ContinuousLinearMap.instNonnegSpectrumClassRealId, iteratedDeriv_comp_two, HasStrictFDerivAt.cos, Affine.Simplex.incenter_eq_affineCombination, ContinuousLinearMap.IsIdempotentElem.isPositive_iff_isSelfAdjoint, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, HasFDerivWithinAt.clm_comp, ContinuousLinearMap.uncurryMid_apply, hasFDerivAt_update, signedDist_self, iteratedDeriv_eq_iterate, isBoundedBilinearMap_apply, PiTensorProduct.projectiveSeminorm_zero, AEMeasurable.apply_continuousLinearMap, HasFPowerSeriesWithinOnBall.coeff_zero, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', FormalMultilinearSeries.analyticOnNhd, fderiv_comp_add_right, Unitization.nnreal_cfcₙ_eq_cfc_inr, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_prodMk, hasDerivAtFilter_iff_tendsto, ProperCone.dual_flip_dual, ContinuousLinearMap.integral_comp_commSL, RCLike.ofRealCLM_norm, HasFPowerSeriesAt.eventually_differentiableAt, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse, Matrix.IsHermitian.eigenvectorUnitary_coe, Submodule.ClosedComplemented.of_finiteDimensional, HasStrictDerivAt.comp, Complex.sqrt_map, InnerProductSpace.HarmonicOnNhd.const_smul, deriv_cos, ContinuousAffineMap.hasFDerivAtFilter, hasStrictFDerivAt_ringInverse, Continuous.const_clm_comp, MeasureTheory.setIntegral_indicatorConstLp, InnerProductSpace.HarmonicContOnCl.fun_const_smul, ContDiffOn.continuousOn_fderiv_of_isOpen, signedDist_vsub_self, DifferentiableAt.arsinh, ContinuousLinearMap.mul_apply', EuclideanGeometry.inversion_mul, fromTangentSpace_mfderiv_smul, ContDiffOn.continuousLinearMap_comp, HasFDerivAt.fun_sum, stereographic_target, MeasureTheory.SignedMeasure.rnDeriv_smul, Unitary.norm_map, ProbabilityTheory.iIndepFun.hasGaussianLaw, ProbabilityTheory.isGaussian_conv, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, LinearMap.instStarModuleId, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, MeasureTheory.hausdorffMeasure_smul_right_image, signedDist_smul, StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquiv, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_pos, ContinuousAlternatingMap.le_of_opNorm_le, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, HasDerivAt.tendsto_slope, DifferentiableOn.fun_pow, HasFDerivWithinAt.arsinh, InnerProductSpace.rankOne_comp_rankOne, TemperedDistribution.fourierTransform_apply, ContinuousLinearMap.opNorm_zero, MeasureTheory.convolution_lsmul_swap, Orientation.oangle_add_right_smul_rotation_pi_div_two, HasStrictDerivAt.comp_hasStrictFDerivAt, EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq, HasDerivWithinAt.comp_hasFDerivWithinAt, not_sameRay_iff_norm_add_lt, TestFunction.mkCLM_apply, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem, Real.hasStrictDerivAt_arctan, HasFTaylorSeriesUpToOn.prodMk, SchauderBasis.proj_apply_basis_mem, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ContDiffAt.domDomCongr_iteratedFDeriv, HasDerivAtFilter.comp_of_eq, isSeparable_range_deriv, Orientation.inner_smul_rotation_pi_div_two_left, HasFDerivAt.add_const, BoxIntegral.hasIntegral_const, ZLattice.volume_image_eq_volume_div_covolume, StrictConcaveOn.strictAntiOn_derivWithin, hasDerivAtFilter_finCons', MeasureTheory.Supermartingale.smul_nonpos, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, deriv_tsum, LinearIsometry.toLinearMap_rTensor, Real.map_linearMap_volume_pi_eq_smul_volume_pi, PiLp.hasStrictFDerivAt_apply, CStarModule.norm_eq_csSup, hasStrictFDerivAt_fst, TestFunction.fderivCLM_eq_of_scalars, DifferentiableAt.comp_semilinear₁, Matrix.toEuclideanLin_eq_toLin, LinearMap.mkContinuous_norm_le', setIntegral_withDensity_eq_setIntegral_smul, UniqueMDiffOn.uniqueDiffOn_inter_preimage, Affine.Simplex.sOppSide_point_excenter_singleton, DoubleCentralizer.pow_fst, mdifferentiableWithinAt_iff_target_inter', DifferentiableOn.sub_iff_right, StrongDual.toLpₗ_of_not_memLp, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, PiTensorProduct.mapL_apply, hasDerivWithinAt_finCons', Euclidean.closedBall_eq_preimage, mellin_comp_rpow, Matrix.isHermitian_iff_isSymmetric, ProbabilityTheory.integral_poissonMeasure, MeasureTheory.integrable_continuousLinearMap_prod', ContinuousAffineMap.hasFDerivAt, MeasureTheory.Submartingale.sum_smul_sub', NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, deriv.fun_neg, AffineSubspace.mem_perpBisector_iff_dist_eq', DifferentiableAt.fun_comp', Matrix.PosSemidef.inv_sqrt, ContinuousMultilinearMap.norm_iteratedFDeriv_le', support_iteratedFDeriv_subset, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, hasStrictFDerivAt_finset_prod, DifferentiableAt.continuousMultilinear_apply_const, TestFunction.lineDerivCLM_eq_of_scalars, AffineSubspace.isPreconnected_setOf_wSameSide, AnalyticOnNhd.deriv, Submodule.le_orthogonal_iff_le_orthogonal, fderiv_fun_neg, Differentiable.sub_iff_left, intervalIntegral.differentiable_integral_of_continuous, intervalIntegral.smul_integral_comp_mul_add, curveIntegral_zero, IsIntegralCurveAt.comp_mul_ne_zero, deriv_zpow, SchauderBasis.nnnorm_proj_le_nnnormProjBound, hasFDerivAt_comp_sub, LipschitzWith.locallyIntegrable_lineDeriv, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, Affine.Simplex.ninePointCircle_center_mem_affineSpan, DifferentiableWithinAt.fun_sub, Submodule.IsOrtho.comap_iff, InnerProductSpace.rankOne_comp, Convex.exists_forall_hasFDerivWithinAt_of_fderivWithin_symmetric, HasDerivWithinAt.comp_hasFDerivAt, Submodule.mem_orthogonal, ContinuousAffineMap.norm_image_zero_le, StrongDual.mem_polarSubmodule, exists_dual_vector', derivWithin_inv', MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Asymptotics.IsTheta.const_smul_left, LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute, DifferentiableWithinAt.fun_smul, Orientation.kahler_rightAngleRotation_left, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, HasDerivWithinAt.scomp, ConcaveOn.slope_le_of_hasDerivWithinAt, hasFPowerSeriesWithinAt_pi_iff, isCompactOperator_iff_isCompact_closure_image_closedBall, DifferentiableWithinAt.div, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, hasDerivAt_iff_isLittleO_nhds_zero, HasFDerivAt.le_of_lip', inner_smul_right, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, Real.fourierIntegral_fderiv, HasMFDerivAt.sub, InnerProductSpace.toMatrix_rankOne, MDifferentiableWithinAt.clm_comp, HasFDerivWithinAt.continuousMultilinear_apply_const, derivWithin_fun_sum, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, eventually_norm_symmL_trivializationAt_lt, differentiableAt_comp_add_left, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, cfcₙHom_real_eq_restrict, deriv_const, differentiableAt_euclidean, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, hasFDerivAtFilter_finCons, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, AffineSubspace.perpBisector_eq_top, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, iteratedFDeriv_smul_const_apply, MDifferentiableOn.clm_comp, HasStrictDerivAt.fun_const_smul, MeasureTheory.Measure.addHaar_smul_of_nonneg, OrthonormalBasis.reindex_toBasis, HasDerivWithinAt.congr_deriv, ContinuousLinearMap.opNorm_le_iff, EuclideanGeometry.orthogonalProjection_mem, mdifferentiableOn_iff_of_mem_maximalAtlas', InnerProductSpace.isSymmetric_rankOne_self, Real.differentiableOn_arccos, Orientation.oangle_smul_right_of_neg, deriv_eqOn, analyticOrderAt_deriv_of_pos, Real.fourierIntegral_convergent_iff, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, fun_iteratedFDerivWithin_sub_apply, IsLocalMin.deriv_eq_zero, Real.hasDerivAt_cosh, ConcaveOn.le_slope_of_hasDerivWithinAt_Iio, MultilinearMap.bound_of_shell_of_continuous, Real.tendsto_deriv_mul_log_atTop, HasFDerivAt.sin, fderiv_const_sub, continuousMultilinearCurryLeftEquiv_apply, ProbabilityTheory.HasGaussianLaw.map_equiv, Orientation.abs_areaForm_of_orthogonal, ProbabilityTheory.stdGaussian_map, LipschitzOnWith.ae_differentiableWithinAt_real, HasFPowerSeriesAt.deriv, SchauderBasis.RankOneDecomposition.proj_zero, upperHemicontinuous_quasispectrum_nnreal, DifferentiableAt.const_sub, IsBoundedBilinearMap.hasStrictFDerivAt, FDerivMeasurableAux.mem_A_of_differentiable, LinearIsometryEquiv.symm_rTensor, LinearMap.isSymmetricProjection_iff, innerₗ_apply_apply, ProbabilityTheory.HasGaussianLaw.prodMk, differentiable_pow, IsIntegralCurveAt.hasDerivAt, Affine.Simplex.orthogonalProjectionSpan_restrict, DifferentiableOn.div, uniqueMDiffWithinAt_iff_inter_range, HasMFDerivWithinAt.add, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, SchwartzMap.norm_toLp_top_le, HasCompactSupport.iteratedFDeriv, HasFDerivAt.csin, TensorProduct.commIsometry_symm, isStarProjection_starProjection, MeasureTheory.integral_rnDeriv_smul, StrictConvexOn.lt_slope_of_hasDerivWithinAt, ContMDiffAt.clm_prodMap, unitary.norm_map, Set.EqOn.iteratedFDerivWithin, ContinuousLinearEquiv.fderiv, fourierCoeff_eq_intervalIntegral, CStarAlgebra.conjugate_le_norm_smul', ContMDiffWithinAt.mfderivWithin_apply, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, measurableSet_lineDifferentiableAt_uncurry, ContinuousLinearEquiv.mdifferentiableWithinAt, hfdifferential_apply, ContinuousLinearMap.NonlinearRightInverse.right_inv', ContinuousLinearEquiv.mdifferentiable, AffineSubspace.midpoint_mem_perpBisector, AnalyticAt.exists_eq_sum_add_pow_mul, inner_sum_smul_sum_smul_of_sum_eq_zero, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, iteratedDerivWithin_comp_const_smul, ContinuousLinearMap.integral_comp_L1_comm, curveIntegralFun_add, StrictConvexSpace.extremePoints_closedBall_eq_sphere, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Matrix.isSymmetric_toLin_iff, CompactlySupportedContinuousMap.toNNRealLinear_apply, ContinuousLinearMap.opNorm_zero_iff, Affine.Simplex.touchpoint_reindex, LinearEquiv.isSymmetric_symm_iff, Complex.taylorSeries_eq_on_eball, MeasureTheory.Measure.map_addHaar_smul, aemeasurable_lineDeriv, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, OrthonormalBasis.equiv_symm, HasFDerivAtFilter.snd, AnalyticOnNhd.fderiv, Filter.EventuallyEq.extDeriv, WStarAlgebra.exists_predual, Differentiable.const_mul, HasFDerivWithinAt.comp_hasDerivWithinAt, PMF.integral_eq_sum, HasFDerivWithinAt.add_const, HasFDerivWithinAt.isEquivalent_sub, MeasureTheory.average_add_measure, hasDerivAt_intCast, EuclideanGeometry.inner_weightedVSub, nndist_midpoint_midpoint_le, Orientation.kahler_rotation_left, HasFDerivWithinAt.sub, HasDerivWithinAt.inv, HasFDerivAtFilter.fun_neg, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcₙHom, fderivWithin_continuousAlternatingMap_apply_apply, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, EuclideanGeometry.Sphere.center_mem_orthRadius_iff, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, differentiableOn_inverse, Complex.conjCLE_enorm, ContinuousLinearEquiv.comp_differentiableAt_iff, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonpos, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, Real.differentiableWithinAt_arccos_Iic, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, MeasureTheory.charFunDual_eq_pi_iff, FormalMultilinearSeries.leftInv_comp, EuclideanGeometry.collinear_of_sin_eq_zero, deriv_one, OrthonormalBasis.orthonormal_adjustToOrientation, spectrum.differentiableOn_inverse_one_sub_smul, MeasureTheory.aestronglyMeasurable_condExpL1CLM, Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, HasFPowerSeriesAt.const_smul, intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Icc, Filter.EventuallyEq.lineDifferentiableWithinAt_iff, iteratedFDeriv_succ_eq_comp_right, ContinuousOn.cfcₙ, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, derivWithin_comp, ContinuousMultilinearMap.changeOriginSeries_support, ContinuousLinearEquiv.comp_hasFDerivAt_iff', WeakFEPair.functional_equation₀, CFC.nnrpow_le_nnrpow, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, Real.tendsto_integral_cexp_sq_smul, Differentiable.csinh, curveIntegralFun_sub, ContDiffMapSupportedIn.seminorm_apply, inner_map_self_eq_zero, FormalMultilinearSeries.isLittleO_of_lt_radius, tsupport_iteratedFDeriv_subset, OrthogonalFamily.eq_ite, ProbabilityTheory.iIndepFun.hasGaussianLaw_sub, ContinuousAffineMap.snd_decompLinearIsometryEquiv, convexHull_ediam, DifferentiableOn.fun_add_iff_left, HasDerivWithinAt.limsup_slope_le', deriv_of_notMem_tsupport, aemeasurable_withDensity_iff, derivWithin_const_smul, HasFDerivAt.isThetaTVS_sub, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, DifferentiableAt.clm_comp, GeneralSchauderBasis.ortho, Orientation.inner_sq_add_areaForm_sq, ContinuousMultilinearMap.hasFDerivAt, ODE.hasDerivWithinAt_picard_Icc, signedDist_smul_of_neg, DifferentiableAt.sub, VectorField.lieBracket_smul_left, ContinuousLinearMap.rotation_apply, Real.iteratedFDeriv_fourier, PiTensorProduct.projectiveSeminorm_add_le, MultilinearMap.bound_of_shell, circleAverage_sub_sub_inv_smul_of_differentiable_on, TopologicalAddGroup.IsSES.pushforward_def, DoubleCentralizer.algebraMap_fst, differentiableOn_euclidean, RCLike.reLm_coe, mdifferentiableWithinAt_iff_of_mem_source', hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, nnnorm_fderiv_norm_rpow_le, differentiableAt_abs_pos, Differentiable.exp, deriv_clm_comp, HasStrictFDerivAt.approximates_deriv_on_open_nhds, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, hasStrictFDerivAt_exp_zero_of_radius_pos, ContinuousLinearMap.toBilinForm_injective, DifferentiableOn.fun_sub_iff_left, DifferentiableAt.fun_smul, circleIntegral.integral_smul_const, ContDiffMapSupportedIn.structureMapCLM_top_apply, InnerProductSpace.mem_span_gramSchmidt, ContinuousLinearMap.mfderivWithin_eq, ContinuousMultilinearMap.nnnorm_ofSubsingleton, norm_iteratedFDerivWithin_comp_le, inner_smul_real_left, aemeasurable_deriv, DifferentiableWithinAt.cpow, Complex.isConservativeOn_and_continuousOn_iff_isDifferentiableOn, ContDiffOn.fderivWithin, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, ContDiff.continuous_iteratedFDeriv, WeakDual.metrizable_of_isCompact, mdifferentiableOn_iff_differentiableOn, TangentBundle.symmL_model_space, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, EuclideanGeometry.cospherical_iff_exists_mem_of_complete, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Affine.Triangle.orthocenter_mem_altitude, MeasureTheory.integrable_condExpL2_indicator, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, ImplicitFunctionData.range_rightDeriv, HasStrictDerivAt.arsinh, tangentCoordChange_self, CStarAlgebra.span_nonneg_inter_closedBall, toSpanSingleton_derivWithin, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, fderiv_norm_smul, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, Affine.Simplex.excenterWeights_restrict, ContinuousAlternatingMap.isLeast_opNNNorm, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, WithLp.volume_preserving_symm_measurableEquiv_toLp_prod, spectrum.hasFDerivAt_resolvent, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, ContinuousLinearMap.exists_mul_lt_apply_of_lt_opNNNorm, HasFDerivAt.hasFDerivAt_norm_smul, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, Submodule.sub_mem_orthogonal_of_inner_right, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, deriv_comp_of_eq, LineDifferentiableWithinAt.mono_of_mem_nhdsWithin, HasFiniteFPowerSeriesOnBall.eq_partialSum', EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, mdifferentiableWithinAt_iff, LinearIsometry.enorm_toContinuousLinearMap, fderivWithin_fun_add, Unitization.instCStarRing, coe_lpBCFₗᵢ_symm, FiniteDimensional.of_isCompactOperator_id, range_mfderiv_coe_sphere, HasDerivAt.comp_hasDerivWithinAt, RKHS.kerFun_inner, Complex.wedgeIntegral_add_wedgeIntegral_eq, uniqueMDiffOn_iff_uniqueDiffOn, coe_lpPiLpₗᵢ_symm, Bundle.Trivialization.continuousLinearMap_apply, IsBoundedBilinearMap.toContinuousLinearMap_apply, LinearEquiv.continuous_symm, Differentiable.continuousAlternatingMap_apply_const, HasFDerivWithinAt.curveIntegral_segment_source, differentiable_piLp, ClosedSubmodule.inf_orthogonal_eq_bot, HasFPowerSeriesOnBall.pi, Affine.Triangle.eulerPoint_eq_midpoint, isCompact_closure_of_isBounded, StrictConcaveOn.slope_lt_of_hasDerivWithinAt, Submodule.reflection_eq_self_iff, HasFPowerSeriesWithinOnBall.fderivWithin_eq, MeasureTheory.weightedSMul_union', MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, Orthonormal.equiv_refl, stereographic_source, ProbabilityTheory.charFunDual_map_sum_pi_eq_prod, ContinuousMultilinearMap.piₗᵢ_symm_apply, hom_trivializationAt_source, HasStrictFDerivAt.implicitToOpenPartialHomeomorph_self, AlgHom.coe_toContinuousLinearMap, hahnEmbedding_isOrderedModule_rat, ContDiff.iteratedFDeriv_right', Differentiable.add_const, ConvexOn.derivWithin_le_slope, HasDerivAt.scomp, HasFDerivWithinAt.sqrt, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Affine.Simplex.sign_signedInfDist_touchpoint_empty, ContinuousLinearMap.norm_id_le, HasFDerivAt.le_of_lipschitz, ContDiffMapSupportedIn.structureMapLM_top_apply, DifferentiableAt.derivWithin, deriv.neg', ContinuousLinearMap.ker_adjoint_comp_self, AnalyticAt.analyticOrderAt_ne_top, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, MultilinearMap.mkContinuous_norm_le, Matrix.ofLp_toEuclideanLin_apply, signedDist_vadd_right_swap, ContinuousOn.cfcₙ_of_mem_nhdsSet, Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable, DifferentiableAt.restrictScalars, ContinuousAffineMap.fderivWithin, HasDerivAt.const_mul, Real.hasFDerivAt_fourierIntegral, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, HasDerivWithinAt.congr, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, Real.differentiable_mulExpNegMulSq, EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, hasDerivAt_one, HasDerivAtFilter.fun_neg, LinearMap.IsSymmetric.apply_eigenvectorBasis, HasStrictFDerivAt.hasStrictDerivAt, FormalMultilinearSeries.radius_shift, EuclideanSpace.volume_ball_fin_two, DirectSum.IsInternal.card_filter_subordinateOrthonormalBasisIndex_eq, ContinuousLinearEquiv.comp_right_differentiableAt_iff, Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, fderivWithin_sqrt, Submodule.finrank_add_inf_finrank_orthogonal', Complex.conjCLE_apply, polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, IsZLattice.span_top, Real.not_DifferentiableAt_log_mul_zero, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, innerSLFlip_apply, ContinuousLinearEquiv.differentiableOn, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousLinearEquiv.hasStrictFDerivAt, LinearMap.mkContinuous_norm_le, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_right, AffineSubspace.linear_equivMapOfInjective, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, fderivWithin_derivWithin, Submodule.ker_starProjection, IsOpen.exists_between_affineIndependent_span_eq_top, ContinuousLinearEquiv.mfderiv_eq, hasDerivAt_const_mul, hasLineDerivAt_iff_tendsto_slope_zero, differentiableAt_comp_add_right, norm_iteratedFDeriv_comp_le, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', ProbabilityTheory.strong_law_Lp, fderivWithin_const_smul_field, fderiv_continuousMultilinearMapCompContinuousLinearMap, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, deriv_fun_const_smul, ContinuousMultilinearMap.opNorm_neg, MeasureTheory.integral_const, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, ContinuousLinearMap.measurable_coe, HasDerivWithinAt.smul_const, Euclidean.ball_eq_preimage, HasFDerivAt.fun_neg, ContinuousLinearMap.analyticOn, Polynomial.fderivWithin_aeval, fderiv_sinh, ContinuousLinearMap.nndist_le_opNNNorm, CStarAlgebra.star_left_conjugate_le_norm_smul, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, norm_iteratedFDeriv_prod_le, DifferentiableOn.smul, contDiff_nat_iff_continuous_differentiable, MeasureTheory.L1.SimpleFunc.setToL1S_zero_left, hasFDerivAt_pow', absorbent_ball, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, OrderedFinpartition.compAlongOrderFinpartition_apply, Submodule.topologicalClosure_eq_top_iff, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, mdifferentiableOn_coordChangeL, Polynomial.fderivWithin, HasFDerivWithinAt.const_cpow, HasFiniteFPowerSeriesOnBall.add, Filter.EventuallyEq.extDerivWithin, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, iteratedDeriv_comp_const_sub, SummableLocallyUniformlyOn.differentiableOn, ContDiffAt.iteratedFDeriv_comp_perm, Polynomial.hasDerivAt, DifferentiableAt.sub_iff_right, HasFDerivAt.fun_add, HasFDerivAt.fst, VectorPrebundle.mk_coordChange, ContinuousLinearMap.opNorm_lsmul_le, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, EuclideanSpace.volume_ball, LinearMap.IsSymmetric.zero, TensorProduct.enorm_assoc, hasFDerivWithinAt_comp_add_right, LinearMap.coe_isometryOfInner, OrthonormalBasis.repr_symm_single, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, MultilinearMap.mkContinuousMultilinear_norm_le, iteratedFDerivWithin_fun_sum_apply, WeakDual.CharacterSpace.norm_le_norm_one, ContDiffMapSupportedIn.monoCLM_eq_zero, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, HasFPowerSeriesAt.eventually_hasSum_of_comp, hasDerivAt_natCast, HasDerivAtFilter.fun_sub, MeasureTheory.L1.norm_setToL1_le_mul_norm', HasDerivWithinAt.union, Submodule.reflection_bot, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, ContinuousMultilinearMap.opNNNorm_pi, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, StrictConcaveOn.slope_lt_of_hasDerivWithinAt_Ioi, InnerProductSpace.toDual_apply_eq_toDualMap_apply, AffineSubspace.perpBisector_self, Real.fourier_bilin_convolution_eq_integral, AffineIsometryEquiv.toAffineEquiv_injective, closedBall_normSeminorm, Real.hasStrictDerivAt_cos, SchauderBasis.RankOneDecomposition.exists_coeff, IntervalIntegrable.intervalIntegrable_slope, HasStrictFDerivAt.implicitToOpenPartialHomeomorph_fst, ContinuousLinearMap.isPositive_def', LinearMap.adjoint_inner_left, HasDerivWithinAt.add_const, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, iter_deriv_inv, exists_deriv_eq_zero', AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, ProperCone.innerDual_empty, Matrix.star_dotProduct_gram_mulVec, OpenPartialHomeomorph.univUnitBall_apply, hasStrictFDerivAt_exp_zero, ContinuousLinearMap.norm_compL_le, AnalyticAt.differentiableAt, DifferentiableWithinAt.iterate, Differentiable.dist, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, Convex.lipschitz_gauge, Asymptotics.IsBigO.continuousMultilinearMap_apply_eq_zero, Orientation.oangle_map, ContMDiffVectorBundle.contMDiffOn_coordChangeL, MeasureTheory.Measure.addHaar_preimage_linearMap, EulerSine.antideriv_cos_comp_const_mul, deriv_natCast, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, curveIntegral_eq_intervalIntegral_deriv, fderivWithin_clm_comp, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, ContinuousLinearMap.inCoordinates_eq, meromorphicOrderAt_smul_of_ne_zero, HasDerivWithinAt.congr_set, lineDerivWithin_congr_set, Differentiable.sqrt, hasFDerivAt_of_tendstoUniformlyOnFilter, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, HasFPowerSeriesAt.sub, RightDerivMeasurableAux.differentiable_set_eq_D, ProbabilityTheory.HasGaussianLaw.fun_sum, ContDiffAt.continuousLinearMap_comp, BoxIntegral.integralSum_smul, taylor_integral_remainder_aux, ContinuousMultilinearMap.norm_domDomCongr, ProbabilityTheory.variance_dual_prod', HasStrictFDerivAt.fun_neg, hasDerivWithinAt_zpow, HasFDerivWithinAt.arctan, ZSpan.quotientEquiv.symm_apply, OrthogonalFamily.range_linearIsometry, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, isIntegralCurve_comp_mul_ne_zero, Real.tendsto_integral_exp_smul_cocompact, HasStrictFDerivAt.sum, mellin_convergent_iff_norm, Monotone.deriv_nonneg, MeasureTheory.setIntegral_tilted', EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, HasStrictFDerivAt.implicitToOpenPartialHomeomorph_apply_ker, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, fderivWithin_inv, Submodule.ker_orthogonalProjection, EuclideanGeometry.oangle_midpoint_rev_right, fderiv_continuousMultilinear_apply_const, Orientation.kahler_mul, SchauderBasis.succSub_ortho, derivWithin_fun_finset_prod, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, HasDerivWithinAt.smul, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', lineDerivWithin_of_mem_nhds, Submodule.reflection_map_apply, sameRay_iff_norm_sub, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, HasStrictFDerivAt.to_localInverse, TensorProduct.dist_tmul_le, affineSpan_eq_top_of_nonempty_interior, ProbabilityTheory.isGaussian_iff_charFunDual_eq, ProbabilityTheory.iteratedDeriv_two_cgf, ContinuousOn.integral_sub_linear_isLittleO_ae, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, DifferentiableWithinAt.rpow_const, AffineIsometry.map_vadd, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one, DifferentiableOn.pow, isEmbedding_inclusionInDoubleDualWeak, ContinuousMultilinearMap.curry0_norm, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, Submodule.sup_orthogonal_of_hasOrthogonalProjection, measurableSet_of_differentiableWithinAt_Ioi, HasDerivWithinAt.fun_pow, WeakDual.isBounded_polar, TensorProduct.norm_lid, HasDerivWithinAt.finset_prod, MeasureTheory.lpTrimToLpMeas_ae_eq, ContinuousLinearMap.norm_fst, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, HasFDerivWithinAt.rpow, Real.differentiable_iteratedDeriv_sin, OrderedFinpartition.applyOrderedFinpartition_apply, ProbabilityTheory.deriv_mgf_zero, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, AffineIsometry.toContinuousAffineMap_injective, EuclideanGeometry.OrthocentricSystem.eq_insert_orthocenter, SchwartzMap.instLocallyConvexSpace, differentiableAt_neg_iff, ContinuousLinearMap.opNNNorm_comp_le, Affine.Simplex.incenter_mem_affineSpan_range, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, HasDerivWithinAt.mono, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, ContinuousMultilinearMap.analyticOn, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, Orientation.oangle_smul_smul_self_of_nonneg, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, HasMFDerivAt.prod, MeromorphicNFAt.smul_analytic, fderivWithin_csin, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, ProbabilityTheory.isGaussian_of_charFunDual_eq, Real.deriv_sigmoid, Submodule.IsOrtho.disjoint, exists_ratio_deriv_eq_ratio_slope', ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, LinearEquiv.coeFn_toContinuousLinearEquivOfContinuous, derivWithin_sum, ZLattice.volume_image_eq_volume_div_covolume', ProperCone.dual_dual_flip, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, PiTensorProduct.mapL_opNorm, Differentiable.fun_comp, flip_innerₗ, HasFDerivWithinAt.comp_hasDerivAt, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, SchwartzMap.compCLM_apply, EuclideanGeometry.orthogonalProjection_orthogonalProjection, iter_deriv_inv', toMatrix_innerSL_apply, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le, OrthonormalBasis.equiv_apply_basis, TemperedDistribution.fourierMultiplierCLM_apply_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, intervalIntegral.fderivWithin_integral_of_tendsto_ae, Affine.Simplex.eulerPoint_reindex, HasDerivAt.mul, Function.HasTemperateGrowth.smul, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, DoubleCentralizer.mul_fst, rescale_to_shell_zpow, MeasureTheory.Measure.addHaar_ball_mul_of_pos, Orientation.rightAngleRotation_trans_neg_orientation, ContMDiff.clm_postcomp, Orientation.volumeForm_robust', EuclideanGeometry.orthogonalProjection_vsub_mem_direction, ProbabilityTheory.HasGaussianLaw.map_equiv_fun, balanced_closedBall_zero, integrableOn_peak_smul_of_integrableOn_of_tendsto, iteratedFDeriv_zero_fun, Submodule.HasOrthogonalProjection.exists_orthogonal, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, HasFDerivAt.prodMk, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure, ContinuousLinearEquiv.comp_contDiffOn_iff, fun_iteratedFDeriv_sub_apply, ModelWithCorners.convex_range', Dual.dual_norm_topology_le_weak_dual_topology, MDifferentiableAt.coordChangeL, fderivWithin_continuousAlternatingMap_apply_const, extDeriv_fun_add, dist_left_lineMap, Manifold.IsImmersionAt.target_subset_preimage_target, Complex.norm_deriv_le_one_of_mapsTo_ball, Submodule.starProjection_top, toLocallyConvexSpace, Affine.Simplex.excenterWeights_map, ContDiffAt.clm_comp, EulerSine.antideriv_sin_comp_const_mul, hasFDerivAt_sub_const, DifferentiableOn.arctan, Submodule.iInf_orthogonal, ContinuousLinearMap.norm_restrictScalars, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, coe_normSeminorm, ApproximatesLinearOn.closedBall_subset_target, NumberField.mixedEmbedding.fundamentalCone.logMap_expMap, signedDist_vadd_left, ModularGroup.tendsto_lcRow0, Differentiable.fun_finset_prod, AffineSpace.asymptoticNhds_le_cobounded, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpace, MDifferentiableWithinAt.clm_postcomp, derivWithin_sub_const_fun, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, HasDerivWithinAt.const_sub, sInter_polar_eq_closedBall, ContDiffBump.convolution_eq_right, TemperedDistribution.instFourierInvSMul, hasFDerivWithinAt_fst, ExistsContDiffBumpBase.w_def, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, measurable_derivWithin_Ioi, HasDerivWithinAt.const_smul, ProbabilityTheory.deriv_cgf, MeasureTheory.Measure.setIntegral_comp_smul, PositiveLinearMap.ofPreGNS_toPreGNS, ContMDiff.clm_prodMap, Complex.imCLM_coe, ModelWithCorners.transContinuousLinearEquiv_range, isBoundedBilinearMap_inner, TensorProduct.nnnorm_assoc, DifferentiableOn.cosh, WeakFEPair.hf_modif_FE, IsSelfAdjoint.conj_starProjection, FormalMultilinearSeries.analyticAt_changeOrigin, HasDerivWithinAt.hasDerivAt, ContinuousLinearMap.opNorm_mul_apply_le, deriv_smul_const, Affine.Simplex.incenter_notMem_affineSpan_pair, PiTensorProduct.tprodL_apply, CStarMatrix.normedSpaceCore, intervalIntegral.integral_hasFDerivWithinAt, HasFPowerSeriesAt.tendsto_partialSum, DifferentiableAt.cpow_const, Diffeomorph.uniqueDiffOn_preimage, deriv_pow_field, TopologicalGroup.IsSES.pushforward_mono, ZSpan.repr_fract_apply, ContinuousLinearMap.orthogonal_range, contDiff_one_iff_hasFDerivAt, MeasureTheory.charFunDual_prod', HasFiniteFPowerSeriesAt.add, Submodule.lipschitzWith_starProjection, HasFPowerSeriesAt.hasDerivAt, ContinuousLinearMap.isPositive_iff_complex, LinearIsometryEquiv.toMeasurableEquiv_symm, hasDerivWithinAt_congr_set', HasFDerivWithinAt.comp_hasFDerivAt_of_eq, norm_smul_le, HasFPowerSeriesAt.eventually_hasSum_sub, HasDerivWithinAt.rpow_const, deriv_comp_neg, ProbabilityTheory.covarianceBilin_apply, Affine.Simplex.mongePoint_restrict, DifferentiableAt.star_star, DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul, fourierIntegral_half_period_translate, BoxIntegral.integralSum_sub_partitions, Polynomial.hasDerivAt_aeval, ContinuousLinearMap.comp_cpolynomialOn, HasFDerivAt.cos, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, DifferentiableWithinAt.arsinh, ContinuousLinearMap.opNorm_smul_le, StrictConvexSpace.sphere_subset_extremePoints_closedBall, InnerProductSpace.span_gramSchmidt, MeasureTheory.L1.norm_setToL1_le', TestFunction.fderivCLM_apply_of_gt, MeasureTheory.withDensitySMulLI_apply, IsBoundedBilinearMap.deriv_apply, Orthonormal.inner_finsupp_eq_zero, HasStrictFDerivAt.isThetaTVS_sub, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, MeasureTheory.Measure.addHaar_nnreal_smul, deriv_finset_prod, Affine.Simplex.touchpoint_eq_point_rev, ContinuousLinearMap.range_eq_map_coprodSubtypeLEquivOfIsCompl, ContinuousLinearMap.spectralRadius_eq_nnnorm, Distribution.dsupport_iteratedLineDerivOp_subset, Complex.taylorSeries_eq_on_emetric_ball, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, fderiv_comp', isBigO_deriv_ofReal_cpow_const_atTop, MeasureTheory.convolutionExistsAt_iff_integrable_swap, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, PiLp.hasFDerivAt_ofLp, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, TemperedDistribution.instFourierInvAdd, PiTensorProduct.projectiveSeminorm_smul_le, dist_div_norm_sq_smul, deriv_div, torusIntegral_smul, ZLattice.comap_comp, stronglyMeasurable_derivWithin_Ici, exists_deriv_eq_slope', norm_iteratedFDeriv_one, Continuous.cfcₙ', posTangentConeAt_mono, hasDerivAt_ofReal_cpow_const, LinearMap.coe_isometryOfOrthonormal, LinearIsometryEquiv.comp_differentiable_iff, CFC.norm_abs, Affine.Simplex.eulerPoint_restrict, hasDerivAt_norm_rpow, hasFDerivAt_tsum, Affine.Simplex.signedInfDist_reindex, ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite, ContinuousLinearMap.spectrum_eq, HasStrictFDerivAt.fun_const_smul, OrthonormalBasis.span_apply, isConformalMap_id, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, iteratedFDerivWithin_eventually_congr_set', ContinuousMultilinearMap.analyticOnNhd, AffineSubspace.isPreconnected_setOf_sOppSide, NumberField.mixedEmbedding.latticeBasis_apply, EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_radius_lt_dist, StronglyMeasurable.apply_continuousLinearMap, ClosedSubmodule.orthogonal_toSubmodule_eq, HasFDerivAt.hasDerivAt, EuclideanGeometry.vsub_orthogonalProjection_mem_direction, fderivWithin_const_smul, extDerivWithin_extDerivWithin_apply, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, HasStrictDerivAt.fun_sub, differentiableAt_finCons', ContinuousLinearMap.isPositive_iff, MeasureTheory.Measure.addHaar_submodule, HasDerivWithinAt.star, TensorProduct.mapIsometry_apply, differentiableWithinAt_inverse, AnalyticAt.analyticAt_localInverse, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, VectorBundleCore.inCoordinates_eq, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, HasStrictFDerivAt.prodMap, TemperedDistribution.fourierInv_apply, MeromorphicOn.extract_zeros_poles, VectorField.pullbackWithin_eq, ProbabilityTheory.IsGaussianProcess.smul, HasDerivAtFilter.prodMk, cfcₙAux_mem_range_inr, ContinuousLinearMap.norm_bilinearRestrictScalars, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin, PiTensorProduct.liftIsometry_apply_apply, DifferentiableOn.inverse, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, DifferentiableWithinAt.clog, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, derivWithin_fun_const, Affine.Simplex.ExcenterExists.touchpointWeights_map, ContinuousLinearMap.norm_inl, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, IsSelfAdjoint.hasEigenvector_of_isMinOn, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, LinearMap.IsSymmetric.sub, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HasDerivAt.sum, EuclideanGeometry.collinear_of_angle_eq_pi, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, Affine.Simplex.mongePoint_map, ContinuousLinearEquiv.comp_differentiable_iff, Affine.Simplex.eulerPoint_map, SchwartzMap.instFourierSMul, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, HasFPowerSeriesOnBall.prod, Affine.Simplex.ExcenterExists.touchpoint_restrict, Unitization.nnnorm_eq_sup, Orientation.two_zsmul_oangle_smul_right_self, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, TendstoLocallyUniformlyOn.differentiableOn, SchwartzMap.fourierTransformCLM_apply, HasFDerivAt.curveIntegral_segment_source', AffineSubspace.signedInfDist_singleton, HasFPowerSeriesWithinOnBall.neg, norm_deriv_eq_norm_fderiv, Seminorm.bound_of_shell_sup, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, deriv_tsum_apply, EuclideanGeometry.angle_midpoint_eq_pi, intervalIntegral.integral_deriv_smul_deriv_comp, DoubleCentralizer.zero_toProd, Differentiable.inversion, Orientation.coe_basisRightAngleRotation, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, PointwiseConvergenceCLM.tendsto_nhds_atTop, AkraBazziRecurrence.differentiableAt_smoothingFn, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, HasFDerivAt.const_rpow, ContinuousLinearMap.bilinearComp_zero_left, HasStrictDerivAt.finCons, ContinuousLinearMap.nnnorm_smulRight_apply, deriv_id, hasFPowerSeriesWithinOnBall_pi_iff, HasDerivAt.fun_smul, hasDerivAt_zero, LinearIsometryEquiv.smul_trans, SchwartzMap.fderivCLM_fourier_eq, Complex.norm_deriv_le_div_of_mapsTo_ball, intrinsicInterior_nonempty, CStarModule.inner_mul_inner_swap_le, Bundle.ContinuousRiemannianMetric.pos, ContinuousLinearEquiv.contDiffOn_comp_iff, mellin_const_smul, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, TemperedDistribution.instLineDerivAdd, SchwartzMap.derivCLM_apply, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, HasFPowerSeriesOnBall.eventually_hasSum_sub, EuclideanGeometry.Sphere.orthRadius_map, TensorProduct.toLinearMap_mapIsometry, RCLike.map_nonneg_iff, ContinuousMultilinearMap.opNNNorm_le_iff, IsCompactOperator.image_closedBall_subset_compact, Convex.image_deriv, StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioi, Real.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, Real.deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, VectorBundleCore.continuousOn_coordChange, Affine.Simplex.excenterWeightsUnnorm_restrict, LinearMap.singularValues_finrank_range_self, Affine.Simplex.affineCombination_touchpointWeights, MeasureTheory.integral_fun_fst, Orientation.volumeForm_zero_neg, SmoothPartitionOfUnity.contMDiff_finsum_smul, hasDerivWithinAt_inter', MeasureTheory.pdf.integrable_pdf_smul_iff, ContinuousLinearEquiv.fderivWithin, Real.differentiableAt_binEntropy, HasDerivWithinAt.scomp_hasDerivAt, AffineSubspace.subtypeₐᵢ_linearIsometry, Unitary.inner_map_map, ContDiffBump.dist_normed_convolution_le, MDifferentiableOn.clm_precomp, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, HasFDerivWithinAt.fun_sum, VectorField.lieBracketWithin_smul_right, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, isCompactOperator_of_tendsto, mellin_differentiableAt_of_isBigO_rpow_exp, fderiv_fun_const_smul, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', TensorProduct.enorm_map, Orientation.areaForm_map, ContDiff.iterate_deriv', uniformEquicontinuous_birkhoffAverage, Affine.Triangle.orthocenter_mem_affineSpan, LinearMap.IsSymmetric.det_eq_prod_eigenvalues, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear, differentiable_neg, deriv_comp_mul_left, hasDerivAt_neg, LinearMap.derivWithin, LinearMap.IsSymmetric.id, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, inner_gradientWithin_left, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, deriv_bernoulliFun, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, HasStrictDerivAt.prodMk, intervalIntegral.integral_hasDerivAt_right, det_fderivPiPolarCoordSymm, isConformalMap_iff, hasFTaylorSeriesUpToOn_succ_iff_left, HasDerivWithinAt.mul_const, HasCompactSupport.hasDerivAt_convolution_left, iteratedFDeriv_sub, measurableSet_lineDifferentiableAt, Polynomial.hasStrictDerivAt, deriv_const_mul, ContDiff.clm_apply, HasDerivWithinAt.cexp, IsConformalMap.comp, IsConvexMetricSpace.of_convex, Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle, WithLp.volume_preserving_ofLp, Real.deriv2_qaryEntropy, ContinuousLinearEquiv.isBigO_comp_rev, VectorFourier.integral_bilin_fourierIntegral_eq_flip, Real.differentiableAt_exp, Affine.Simplex.mongePoint_mem_affineSpan, deriv_clm_apply, MDifferentiableWithinAt.differentiableWithinAt_comp_extChartAt_symm, Real.hasStrictDerivAt_arcsin, ConvexOn.slope_le_of_hasDerivAt, hasStrictFDerivAt_sub_const_iff, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, norm_withSeminorms, CFC.monotone_sqrt, HasFPowerSeriesWithinOnBall.add, ContinuousLinearMap.add_compLp, curveIntegralFun_restrictScalars, contDiffOn_succ_iff_fderivWithin, NumberField.mixedEmbedding.commMap_apply_of_isReal, ProbabilityTheory.charFunDual_map_add_prod_eq_mul, ImplicitFunctionData.hasStrictFDerivAt_implicitFunction, derivWithin_fun_pow, EuclideanGeometry.Sphere.IsTangent.isTangentAt, FormalMultilinearSeries.changeOrigin_finite_of_finite, AffineMap.hasStrictDerivAt, ConvexBody.iInter_smul_eq_self, LipschitzWith.ae_differentiableAt_of_real, ProperCone.mem_innerDual, InnerProductSpace.toLinearMap_rankOne, instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, HasDerivWithinAt.Ioi_of_Ici, EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff, ContinuousLinearMap.adjointAux_inner_right, IsClosed.diffContOnCl_iff, ContinuousLinearMap.isCompact_closure_image_coe_of_bounded, HasDerivWithinAt.Ioi_iff_Ioo, VectorField.mpullback_mfderivWithin_apply_smul, MeromorphicOn.smul, Seminorm.finset_sup_smul, Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real, quasispectrum.isCompact_nnreal, Complex.taylorSeries_eq_on_ball, HasMFDerivWithinAt.mul, Bundle.RiemannianMetric.pos, ContDiffWithinAt.iteratedFDerivWithin_right, TemperedDistribution.instLineDerivSMulComplex, ContinuousLinearEquiv.isOpen, HilbertBasis.repr_self, CStarAlgebra.instNonnegSpectrumClass', CStarAlgebra.conjugate_le_norm_smul, HasStrictFDerivAt.clm_apply, AnalyticAt.differentiableWithinAt, fderiv.fst, TensorProduct.commIsometry_apply, ContinuousLinearEquiv.coe_toDiffeomorph, ContDiffMapSupportedIn.fderivLM_apply, deriv_intCast, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Seminorm.isBounded_sup, fderivWithin_sub, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, norm_midpoint_lt_iff, Module.Basis.coe_toOrthonormalBasis, continuousMultilinearCurryRightEquiv_symm_apply', MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', ContinuousLinearMap.isBigO_sub, HasFDerivAt.arsinh, ContinuousAt.cfcₙ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, AffineSubspace.isConnected_setOf_sOppSide, DoubleCentralizer.norm_fst, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, measurable_smul_const, MeasureTheory.L1.setToL1_add_left, ContDiffWithinAt.fderivWithin, WeakFEPair.functional_equation, WeakDual.isCompact_of_bounded_of_closed, ContinuousLinearMap.opNNNorm_eq_of_bounds, MeasureTheory.Submartingale.sum_smul_sub, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, iteratedFDerivWithin_sub_apply, TensorProduct.congrIsometry_symm, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, DifferentiableAt.abs, sub_mem_posTangentConeAt_of_segment_subset, EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi, ContinuousAlternatingMap.norm_ofSubsingleton_id, LinearIsometry.contDiff, Complex.equivRealProdCLM_symm_apply_re, intervalIntegral.integral_comp_smul_deriv''', DifferentiableOn.cexp, Affine.Simplex.incenter_reindex, HasDerivWithinAt.fun_add, LinearMap.isStarProjection_toContinuousLinearMap_iff, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, Bundle.Trivialization.prod.isLinear, MeromorphicOn.divisor_smul, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, AffineSubspace.mem_perpBisector_iff_dist_eq, LinearMap.IsSymmetric.orthogonal_range, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, isCompactOperator_id_iff_finiteDimensional, iteratedDerivWithin_eq_equiv_comp, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, HasFDerivAt.const_sub, Polynomial.differentiableAt, MeasureTheory.charFunDual_eq_pi_iff', LinearPMap.adjointDomainMkCLMExtend_apply, nnnorm_cfcₙ_le_iff, Besicovitch.card_le_of_separated, HasDerivAt.const_add, ProbabilityTheory.HasGaussianLaw.snd, dimH_orthogonalProjection_le, BoundedContinuousFunction.toLp_norm_le, DifferentiableAt.cos, iteratedFDerivWithin_two_apply, extDerivWithin_smul, fderiv_ccosh, instDiscreteTopologySubtypeMemSubmoduleIntComap, ContDiffMapSupportedIn.seminorm_postcompLM_le, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.bound, LinearIsometry.im_apply_eq_im, MeasureTheory.integral_countable, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_sum, DoubleCentralizer.coe_fst, HasDerivAt.prodMk, HasStrictFDerivAt.fun_smul, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, EuclideanGeometry.Sphere.mem_inter_orthRadius_iff_vsub_mem_and_norm_sq, HasStrictFDerivAt.cpow, iteratedFDeriv_fun_zero, ContDiffPointwiseHolderAt.fderiv, CompactlySupportedContinuousMap.toReal_smul, fderiv_fun_mul, Orientation.inner_rightAngleRotationAux₁_right, hasFDerivAt_pi_polarCoord_symm, curveIntegral_fun_sub, HasFiniteFPowerSeriesOnBall.finite, Meromorphic.iterated_deriv, Submodule.re_inner_starProjection_nonneg, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, Convex.lipschitzWith_gauge, norm_cfcₙ_one_sub_one_add_inv_lt_one, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, derivWithin_sqrt, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, HasFDerivAt.pow', continuousOn_cfcₙ_nnreal, DifferentiableWithinAt.norm_sq, HasStrictFDerivAt.pow', EuclideanGeometry.reflection_apply', OrthogonalFamily.sum_projection_of_mem_iSup, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, hasFDerivWithinAt_iff_hasGradientWithinAt, Real.fourierIntegral_continuousLinearMap_apply', iteratedDerivWithin_succ, CurveIntegrable.smul, AffineIsometryEquiv.ofEq_rfl, BoxIntegral.Integrable.smul, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, ConvexOn.deriv_le_slope, ContinuousAffineMap.differentiableOn, ContinuousLinearMap.hasFDerivAt_of_bilinear, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, Submodule.isOrtho_bot_right, LinearMap.adjoint_comp, FormalMultilinearSeries.min_radius_le_radius_add, ContinuousAlternatingMap.opNorm_le_iff, contDiffOn_succ_iff_fderiv_apply, hasStrictDerivAt_one, EuclideanGeometry.oangle_self_orthogonalProjection, HasDerivWithinAt.of_isLittleO, ContinuousAffineMap.norm_comp_le, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, signedDist_right_lineMap, IsCompactOperator.image_ball_subset_compact, ContinuousLinearMap.closed_range_of_antilipschitz, ConvexOn.rightDeriv_le_slope, ProbabilityTheory.uncenteredCovarianceBilin_zero, HasStrictFDerivAt.multiset_prod, tendsto_integral_comp_smul_smul_of_integrable, DifferentiableAt.star, LinearMap.IsPositive.inner_nonneg_right, HasDerivAt.div_const, HasDerivAt.scomp_of_eq, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, ContDiffMapSupportedIn.continuous_iff_comp_order_le, Real.differentiable_fourierChar, iteratedFDerivWithin_fun_zero, InnerProductSpace.span_gramSchmidt_Iio, mdifferentiableAt_iff_of_mem_source, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, derivWithin_tsum, TopologicalAddGroup.IsSES.integral_inducedMeasure, HasFPowerSeriesAt.pi, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, hasFDerivAt_comp_add_left, iteratedDerivWithin_succ', EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_iff, smul_ball, LinearIsometryEquiv.lTensor_def, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', EuclideanGeometry.Sphere.mem_tangentSet_iff, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, LinearIsometry.strictConvexSpace_range_iff, Submodule.starProjection_orthogonal_apply_eq_zero, VectorFourier.fourierPowSMulRight_apply, HasFDerivWithinAt.smul, extDeriv_apply_vectorField_of_pairwise_commute, OrthonormalBasis.norm_dual, DifferentiableOn.sin, inner_eq_norm_mul_iff_real, HasDerivAt.cexp, Affine.Simplex.altitude_map, ContinuousAlternatingMap.prodLIE_apply, ContMDiffWithinAt.clm_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, MeasureTheory.Submartingale.smul_nonpos, Manifold.IsImmersionAtOfComplement.writtenInCharts, Real.deriv_cos', LinearIsometry.inl_apply, isBigO_deriv_rpow_const_atTop, Bundle.Trivial.contMDiffVectorBundle, hasDerivAt_pow, SchwartzMap.decay, contDiff_succ_iff_deriv, ModelWithCorners.uniqueDiffWithinAt_image, WithCStarModule.inner_single_left, LinearIsometryEquiv.comp_hasFDerivAt_iff', Submodule.mem_adjoint_iff, Continuous.deriv_integral, FormalMultilinearSeries.summable_nnnorm_mul_pow, norm_fderiv_le_of_lipschitzOn, ContinuousLinearMap.isBoundedLinearMap, HasStrictFDerivAt.of_isLittleO, DifferentiableOn.dist, MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable, LinearMap.isSymmetric_iff_isSelfAdjoint, Real.deriv_rpow_const', ContinuousLinearMap.opNorm_le_iff_lipschitz, CPolynomialOn.fderiv, StrictConcaveOn.lt_slope_of_hasDerivWithinAt, ftaylorSeries_zero, DifferentiableOn.ccosh, ContinuousLinearMap.opNNNorm_le_of_lipschitz, NumberField.mixedEmbedding.normAtPlace_negAt, Submodule.reflection_involutive, ContinuousLinearMap.norm_pi_le_of_le, SchwartzMap.convolution_flip, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, Real.differentiableAt_arcosh, HasDerivWithinAt.isLittleO, Distribution.dsupport_lineDerivOp_subset, MeasureTheory.L1.norm_setToL1_le_mul_norm, ContinuousLinearMap.opNorm_le_of_nhds_zero, StrictConvexOn.derivWithin_lt_slope, HasDerivAt.rpow_const, AffineIsometry.toAffineMap_injective, ContinuousLinearMap.opNorm_flip, contDiffOn_succ_iff_derivWithin, Module.Basis.parallelepiped_map, IsLocalMaxOn.fderivWithin_eq_zero, AffineIsometryEquiv.toAffineEquiv_refl, AlternatingMap.measure_def, Seminorm.bound_of_shell_smul, ContDiffAt.differentiableAt_one, HasDerivWithinAt.prodMk, MeasureTheory.charFunDual_dirac, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, WeakDual.isBounded_toStrongDual_preimage_iff_isBounded, VectorPrebundle.continuousOn_coordChange, Filter.Tendsto.integral_sub_linear_isLittleO_ae, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, DifferentiableAt.fst, hasDerivAt_sub_const_iff, hasStrictDerivAt_exp, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, measurable_fderiv_with_param, LinearIsometryEquiv.reflections_generate_dim, HasDerivAt.div, Convex.exists_forall_hasFDerivWithinAt_of_hasFDerivWithinAt_symmetric, Submodule.orthogonal_le, Complex.isometryOfOrthonormal_apply, IsConformalMap.smul, DifferentiableOn.iterate, iteratedFDeriv_prodMk, nndist_lineMap_lineMap, ProbabilityTheory.IndepFun.hasGaussianLaw, intervalIntegral.smul_integral_comp_mul_right, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left', LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, HasDerivWithinAt.pow, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity, Complex.sameRay_iff, SchwartzMap.lineDerivOp_apply_eq_fderiv, deriv_add_const, LinearMap.bound_of_sphere_bound, intervalIntegral.integral_comp_div_add, ContinuousLinearMap.abs_rayleighQuotient_le_of_norm_mem_resolventSet, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, Real.hasStrictDerivAt_sqrt, mdifferentiableAt_iff_differentiableAt, EuclideanGeometry.Sphere.isTangentAt_center_iff, ContinuousLinearMap.tendsto_of_tendsto_pointwise_of_cauchySeq, conformalFactorAt_inner_eq_mul_inner, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, TemperedDistribution.fourierMultiplierCLM_sum, ContMDiffCovariantDerivativeOn.contMDiff, RKHS.kernel_inner, Orientation.areaForm_map_complex, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, hasFDerivWithinAt_pi, BoxIntegral.integral_const, intervalIntegral.integral_smul_const, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, DifferentiableOn.rpow_const, Polynomial.deriv, FormalMultilinearSeries.derivSeries_eq_zero, InnerProductSpace.laplacianWithin_smul_nhds, ContinuousMultilinearMap.uncurry0_apply, differentiableWithinAt_apply, TestFunction.lineDerivCLM_smul, DifferentiableWithinAt.continuousAlternatingMap_apply, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_invariant, ContinuousLinearMap.isPositive_iff', ContDiffWithinAt.smulRight, HasDerivWithinAt.congr_of_eventuallyEq, LinearIsometryEquiv.comp_hasFDerivAt_iff, derivWithin_const_add_fun, HasDerivAtFilter.isEquivalent_sub, Differentiable.fun_add_iff_right, Real.hasDerivAt_tan_of_mem_Ioo, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, Submodule.finrank_add_finrank_orthogonal, NumberField.mixedEmbedding.finrank, ContinuousMultilinearMap.le_of_opNorm_le, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ContinuousLinearMap.star_eq_adjoint, SchwartzMap.integral_fourier_smul_eq, Real.dimH_segment, UnconditionalSchauderBasis.bddAbove_range_nnnorm_proj, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, FormalMultilinearSeries.comp_rightInv, IsBoundedLinearMap.fderivWithin, Submodule.orthogonal_eq_top_iff, Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable, ContinuousMultilinearMap.curryLeft_apply, ContinuousAlternatingMap.hasFDerivWithinAt, differentiableAt_pow, AlgHom.toContinuousLinearMap_norm, ContDiffAt.laplacian_CLM_comp_left_nhds, ContDiff.differentiable, iteratedDeriv_comp_three, PiLp.hasFDerivAt_apply, Submodule.lipschitzWith_orthogonalProjection, HasStrictDerivAt.fun_neg, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, measurableSet_of_differentiableAt_of_isComplete_with_param, HasFPowerSeriesWithinAt.neg, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, Orientation.inner_rightAngleRotation_right, HasFDerivAt.hasFDerivAt_norm_smul_neg, ContinuousLinearMap.opNorm_le_of_shell, continuousOn_cfcₙ_setProd, Real.hasDerivAt_exp, Differentiable.div_const, fderiv_sqrt, volume_euclideanSpace_eq_dirac, MeasureTheory.Integrable.apply_continuousLinearMap, derivWithin_comp_add_const, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, LinearMap.isSymmetric_adjoint_comp_self, derivWithin.star, hasStrictDerivAt_inv, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_sub, EuclideanGeometry.Sphere.orthRadius_injective, fderivWithin_list_prod', AlternatingMap.mkContinuousLinear_norm_le, asymptoticCone_subset_singleton_of_bounded, ProperCone.hyperplane_separation_of_notMem, OrderedFinpartition.applyOrderedFinpartition_update_left, Module.End.mem_invtSubmodule_adjoint_iff, LinearMap.continuous_of_isClosed_ker, Unitization.complex_cfcₙ_eq_cfc_inr, orthogonalFamily_iff_pairwise, ZSpan.map_fundamentalDomain, MeasureTheory.charFun_map_smul_comp, DifferentiableWithinAt.continuousMultilinear_apply_const, fderiv_clm_apply, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, derivWithin_zero, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, FormalMultilinearSeries.radius_le_radius_derivSeries, Orientation.volumeForm_apply_le, ContinuousAlternatingMap.curryLeftLI_apply, deriv_comp_const_add, ContinuousLinearMap.norm_single_le_one, HasDerivAt.iterate, ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasis, deriv_const_add, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, LinearMap.IsSymmetric.im_inner_apply_self, Submodule.inf_orthogonal_eq_bot, differentiableAt_iff_comp_add_const, HasFDerivWithinAt.fun_mul', ContinuousLinearEquiv.ofBijective_symm_apply_apply, uniqueDiffOn_convex_of_isRCLikeNormedField, ContinuousLinearMap.norm_compSL_le, MeasureTheory.norm_condExpInd_le, TestFunction.monoCLM_apply, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, fderivWithin_smul_const, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, ProbabilityTheory.iIndepFun.hasGaussianLaw_sum, ContDiffMapSupportedIn.withSeminorms, differentiableWithinAt_snd, ContMDiffFiberwiseLinear.locality_aux₁, Submodule.isOrtho_sSup_left, Bundle.Trivial.trivialization.coordChangeL, MeasureTheory.withDensityᵥ_smul, ContDiffAt.exists_eventually_eq_hasDerivAt, CStarAlgebra.norm_negPart_le, LinearMap.range_self_comp_adjoint, ContinuousMultilinearMap.analyticWithinAt, TopologicalAddGroup.IsSES.pushforward_mono, NumberField.mixedEmbedding.negAt_apply_norm_isReal, fderiv_star, MeasureTheory.integrable_comp_smul_iff, derivWithin_fun_const_smul', HasFPowerSeriesWithinAt.unshift, MeasureTheory.Measure.addHaar_preimage_linearEquiv, SchauderBasis.enorm_proj_le_enormProjBound, innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, DifferentiableAt.add_iff_right, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, deriv_inner_apply, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, Affine.Simplex.orthogonalProjectionSpan_reindex, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, riesz_lemma_of_lt_one, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, ContinuousLinearEquiv.hasFDerivAt, hasStrictFDerivAt_list_prod, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, ContinuousLinearMap.tendsto_birkhoffAverage_orthogonalProjection, InnerProductSpace.isIdempotentElem_rankOne_self_iff, HasDerivAt.tendsto_slope_zero, Submodule.norm_starProjection_apply, Filter.EventuallyEq.iteratedFDeriv, fderivWithin_continuousLinearEquiv_comp, ContinuousLinearMap.opNorm_nonneg, MeasureTheory.hausdorffMeasure_affineSegment, HasFDerivAtFilter.of_isLittleO, IsSelfAdjoint.hasEigenvector_of_isLocalExtrOn, div_le_egauge_ball, hasDerivAtFilter_pi, stereographic_apply, Affine.Triangle.sbtw_touchpoint_empty, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, OrthogonalFamily.norm_sum, Orientation.rotation_apply, derivWithin_fun_add, ContinuousLinearMap.coe_flipₗᵢ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, SameRay.norm_smul_eq, IsLocalMin.hasFDerivAt_eq_zero, inner_map_polarization, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, DifferentiableAt.fun_add_iff_right, HasFDerivAtFilter.iterate, Submodule.inner_starProjection_left_eq_right, ContinuousLinearMap.normOneClass, DifferentiableWithinAt.fun_finset_prod, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.opNNNorm_subsingleton, ContMDiffAt.mfderiv, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, ContinuousLinearMap.IsPositive.spectrumRestricts, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Submodule.reflection_mem_subspace_eq_self, Real.iteratedFDeriv_fourierIntegral, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonneg, HasStrictDerivAt.sinh, Orthonormal.mapLinearIsometryEquiv, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, differentiableAt_snd, DifferentiableAt.comp, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, IsCoercive.ker_eq_bot, dist_lt_dist_add_dist_iff, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, WithSeminorms.continuous_normedSpace_rng, ContinuousLinearEquiv.analyticOnNhd, StieltjesFunction.ae_hasDerivAt, IsConformalMap.injective, InnerProductSpaceable.innerProp, LinearIsometry.strictConvexSpace_range, contDiff_infty_iff_deriv, MeasureTheory.withDensityᵥ_rnDeriv_smul, ContinuousLinearMap.opNorm_neg, PositiveLinearMap.norm_apply_le_of_nonneg, OrthogonalFamily.independent, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero_symm, differentiableWithinAt_smul_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry, Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne, MeasureTheory.condExpInd_disjoint_union_apply, fderivWithin_pow_ring', ContinuousLinearMap.analyticOn_uncurry_of_multilinear, iteratedDeriv_one, norm_sub_le_mul_volume_of_norm_fderiv_le, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, FormalMultilinearSeries.changeOrigin_eval, ZLattice.covolume_comap, LinearMap.toSeminorm_ball_zero, differentiableWithinAt_add_const_iff, Real.differentiableAt_negMulLog, continuousAt_hom_bundle, LinearIsometryEquiv.hasFDerivWithinAt, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, DifferentiableAt.cexp, Submodule.fstL_comp_coe_orthogonalDecomposition, StrongConvexOn.strictConvexOn, iter_deriv_inv_linear_sub, DifferentiableOn.const_smul, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Module.Basis.ofZLatticeBasis_comap, isStarProjection_iff_eq_starProjection_range, ContinuousLinearMap.reApplyInnerSelf_smul, ContinuousLinearMap.add_compLpL, NonUnitalCStarAlgebra.toIsScalarTower, Orientation.inner_rightAngleRotationAux₁_left, MeasureTheory.integral_indicator_const, MeasureTheory.L1.setToL1_simpleFunc_indicatorConst, not_differentiableWithinAt_of_deriv_tendsto_atBot_Iio, LinearIsometryEquiv.symm_units_smul, LinearMap.IsSymmetric.roots_charpoly_eq_eigenvalues, IsHilbertSum.linearIsometryEquiv_symm_apply_single, IsSelfAdjoint.adjoint_conj, DifferentiableOn.const_mul, AffineIsometryEquiv.map_vadd, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, VonNeumannAlgebra.mem_commutant_iff, Complex.norm_fderiv_le_one_of_mapsTo_ball, UnitAddTorus.mFourierBasis_repr, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, ProbabilityTheory.iIndepFun.charFunDual_map_fun_finset_sum_eq_prod, ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zero, HasDerivAt.inner, HasFPowerSeriesAt.prod, DifferentiableWithinAt.zpow, LinearMap.toSeminorm_apply, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, LinearIsometryEquiv.toLinearIsometry_rTensor, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image₀, VectorPrebundle.contMDiffOn_contMDiffCoordChange, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonneg, CFC.sqrt_le_sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, ContinuousAlternatingMap.opNorm_le_bound, Submodule.starProjection_minimal, DiffContOnCl.differentiableAt, EuclideanGeometry.orthogonalProjection_linear, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ContinuousLinearMap.contMDiffWithinAt, StrictConvexOn.slope_lt_of_hasDerivWithinAt, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, lineDeriv_smul, MeasureTheory.integrable_rnDeriv_smul_iff, AlternatingMap.mkContinuousAlternating_norm_le_max, PiTensorProduct.mapL_pow, Complex.analyticOnNhd_iff_differentiableOn, LinearMap.continuous_of_isClosed_graph, DoubleCentralizer.natCast_toProd, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, ProbabilityTheory.strong_law_ae_simpleFunc_comp, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, Complex.conjCLE_norm, ContinuousLinearMap.dslope_comp, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, Affine.Simplex.sSameSide_point_excenter_singleton, mdifferentiableAt_coordChangeL, hasDerivAt_finCons', ProbabilityTheory.variance_linearMap_gaussianReal, HasStrictDerivAt.hasDerivAt, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, Submodule.orthogonalProjection_orthogonal_apply_eq_zero, ConvexOn.monotoneOn_derivWithin, AffineSubspace.signedInfDist_def, MeasureTheory.Measure.addHaar_closedBall, ContinuousLinearMap.unit_le_opNorm, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, HasFPowerSeriesWithinAt.add, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le', Submodule.starProjection_mem_subspace_eq_self, Affine.Simplex.acuteAngled_reindex_iff, ConcaveOn.slope_le_rightDeriv, MeasureTheory.L1.setToL1_zero_left', Complex.norm_deriv_le_of_forall_mem_sphere_norm_le, ContDiffMapSupportedIn.fderivCLM_apply_of_le, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, DifferentiableOn.add, Submodule.angle_coe, exists_extension_norm_eq, InnerProductSpace.gramSchmidt_linearIndependent, Real.tendsto_integral_gaussian_smul, DifferentiableWithinAt.clm_apply, HasStrictFDerivAt.to_local_left_inverse, CStarModule.continuous_inner, EuclideanGeometry.Sphere.inter_orthRadius_eq_singleton_of_dist_eq_radius, DifferentiableAt.comp_differentiableWithinAt, ContinuousLinearMap.norm_id, FormalMultilinearSeries.id_apply_of_one_lt, hasFDerivAt_integral_of_dominated_of_fderiv_le'', ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, HasFDerivWithinAt.fun_pow', ConcaveOn.antitoneOn_derivWithin, DifferentiableAt.sinh, differentiable_pi'', HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, TensorProduct.norm_tmul, ContDiff.contDiff_fderiv_apply, hasStrictDerivAt_exp_zero_of_radius_pos, deriv_star_conj, LinearMap.isPositive_iff, MeasureTheory.L1.norm_Integral_le_one, ContinuousLinearMap.measurable_apply', differentiableAt_conj_conj_iff, HasStrictFDerivAt.continuousAlternatingMap_apply_const, VectorFourier.fourierIntegral_comp_add_right, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, closedBall_inv_subset_polar_closedBall, MeasureTheory.integral2_divergence_prod_of_hasFDerivAt, ContDiffMapSupportedIn.postcompLM_apply, Affine.Simplex.mem_altitude, Affine.Simplex.isDiameter_ninePointCircle, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, MeasureTheory.convolution_mono_right, DifferentiableAt.clm_apply, ContDiff.dimH_range_le, signedDist_lineMap_right, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, DifferentiableOn.finCons, TemperedDistribution.laplacian_apply_apply, derivWithin_neg, DoubleCentralizer.one_toProd, MeasureTheory.withDensityᵥ_smul', Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, differentiableAt_iff_restrictScalars, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, HasFDerivAt.comp_semilinear, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, intervalIntegral.integral_deriv_smul_comp''', Filter.Tendsto.cesaro_smul, extDeriv_extDeriv_apply, ContinuousAffineMap.fst_decompLinearIsometryEquiv, VectorField.pullback_eq_of_fderiv_eq, hasDerivAt_single, deriv_fun_const_smul_field, tendsto_integral_exp_inner_smul_cocompact, OrthonormalBasis.coe_toBasis_repr_apply, Affine.Simplex.mongePlane_reindex, det_rotation, MeasureTheory.integrable_continuousLinearMap_prod, extDeriv_pullback, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, Continuous.fourierPowSMulRight, differentiableOn_apply, TemperedDistribution.isVanishingOn_delta, ProbabilityTheory.HasGaussianLaw.fst, iteratedFDerivWithin_sum_apply, LinearIsometryEquiv.star_eq_symm, ContinuousLinearEquiv.dimH_preimage, ContDiffWithinAt.fderivWithin_right_apply, hasStrictFDerivAt_add_const_iff, SchwartzMap.integral_smul_laplacian_right_eq_left, differentiableAt_pi, MeasureTheory.setToFun_const, HasFDerivWithinAt.fun_add, hasStrictDerivAt_exp_of_mem_ball, FormalMultilinearSeries.radius_prod_eq_min, Bundle.Pretrivialization.continuousLinearMap_symm_apply', OrthonormalBasis.coe_equiv_euclideanSpace, complexOfReal_fderiv, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, fderivWithin_mul_const, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, Affine.Simplex.height_eq_dist, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, Orientation.rightAngleRotation_map, VectorFourier.norm_fourierSMulRight_le, continuous_cfcₙAux, continuousWithinAt_hom_bundle, AlternatingMap.measure_parallelepiped, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, ConvexOn.le_slope_of_hasDerivWithinAt, ConvexOn.slope_le_derivWithin, Differentiable.snd, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, derivWithin_finset_prod, UnconditionalSchauderBasis.nnnorm_proj_le_nnnormProjBound, derivWithin_div, ContinuousAffineMap.hasFDerivWithinAt, fderivWithin.fst, NonUnitalCommCStarAlgebra.toSMulCommClass, IsCompactOperator.isCompact_closure_image_of_bounded, HasFDerivAt.mul_const', ContinuousAlternatingMap.nnnorm_ofSubsingleton, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, MeasureTheory.charFunDual_map, hasFDerivWithinAt_add_const_iff, HasFiniteFPowerSeriesOnBall.fderiv', Orientation.two_zsmul_oangle_smul_left_self, ContinuousLinearMap.le_of_opNorm₂_le_of_le, ContinuousLinearMap.ofTendstoOfBoundedRange_apply, Bundle.Trivialization.pullback_linear, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Submodule.orthogonalProjectionFn_eq, DifferentiableOn.mul_const, Fourier.fourierIntegral_def, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, Complex.IsExactOn.with_val_at, iteratedFDerivWithin_clm_apply_const_apply, ContinuousMultilinearMap.currySum_apply, isOpenMap_barycentric_coord, TensorProduct.nnnorm_comm, Submodule.IsOrtho.ge, not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero, Affine.Simplex.signedInfDist_affineCombination, tendsto_sum_mul_atTop_nhds_one_sub_integral, TemperedDistribution.lineDerivOp_apply_apply, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, WeakDual.isBounded_closedBall, Polynomial.differentiableWithinAt_aeval, Submodule.bot_orthogonal_eq_top, signedDist_apply, HasDerivAt.pow', Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Set.EqOn.deriv, ContinuousLinearMap.IsPositive.conj_starProjection, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', EuclideanGeometry.angle_self_orthogonalProjection, measurable_fderiv, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, le_egauge_ball_one, LinearMap.IsSymmetric.charpoly_eq, GeneralSchauderBasis.range_proj_eq_span, ZLattice.covolume.tendsto_card_le_div'', TestFunction.instLineDerivSMulTopENat, Orthonormal.comp_linearIsometryEquiv, TemperedDistribution.lineDerivOp_fourierInv_eq, Submodule.map_orthogonal, fourierCoeffOn_eq_integral, HasStrictFDerivAt.comp, Differentiable.clog, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, AnalyticAt.compContinuousLinearMap, DoubleCentralizer.natCast_snd, VonNeumannAlgebra.coe_commutant, ContDiffMapSupportedIn.bounded_iteratedFDeriv, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, HasFTaylorSeriesUpToOn.differentiableOn, MeasureTheory.SimpleFunc.integral_const, MeromorphicAt.deriv, mfderiv_smul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, ProbabilityTheory.variance_dual_prod, ProbabilityTheory.isGaussian_map_equiv, differentiableWithinAt_const_sub_iff, isSymmSndFDerivWithinAt_iff_iteratedFDerivWithin, HasFDerivAt.hasGradientAt, EuclideanGeometry.dist_affineCombination, hasStrictDerivAt_zero, Differentiable.sub_const, HasStrictFDerivAt.sin, VectorBundleCore.coordChange_linear_comp, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Real.differentiableAt_sinh, ContinuousAlternatingMap.alternatizeUncurryFin_add, Orientation.oangle_sign_smul_add_smul_right, Module.Basis.ofZLatticeComap_repr_apply, signedDist_eq_dist_iff_vsub_mem_span, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, Filter.EventuallyEq.lineDifferentiableAt_iff, Real.differentiable_iteratedDeriv_sinh, HasDerivAtFilter.finCons, AffineSubspace.direction_perpBisector, MeasureTheory.integral_deriv_smul_comp_Ioi, Besicovitch.multiplicity_le, LinearIsometryEquiv.toMatrix_mem_unitaryGroup, FormalMultilinearSeries.coeff_iterate_fslope, AffineSubspace.angle_coe, LinearMap.IsSymmetric.conj_inner_sym, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.coeFn_compLp, HasFDerivWithinAt.const_rpow, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, ContMDiffWithinAt.clm_prodMap, deriv_const_smul', ContinuousAt.clm_comp, ContinuousLinearMap.isOpenMap, ContDiffMapSupportedIn.fderivCLM_apply, intervalIntegral.integral_comp_mul_right, ContDiffWithinAt.iteratedFDerivWithin_comp_perm, LinearMap.IsSymmetric.LinearMap.IsSymmetric.directSum_isInternal_of_pairwise_commute, hasStrictDerivAt_exp_smul_const_of_mem_ball', Differentiable.fun_mul, rotation_symm, OrthonormalBasis.same_orientation_iff_det_eq_det, MeasureTheory.L1.setToL1_mono, hasFDerivWithinAt_comp_sub, derivWithin_comp_sub_const, TestFunction.fderivCLM_apply, ClosedSubmodule.orthogonal_disjoint, CompletelyPositiveMap.map_cstarMatrix_nonneg', fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, Differentiable.fun_add_iff_left, ContDiff.differentiable_iteratedDeriv', Affine.Simplex.ninePointCircle_map, iteratedFDerivWithin_const_of_ne, ContinuousMultilinearMap.norm_ofSubsingleton, MeasureTheory.integral_concaveOn_of_integrand_ae, ContinuousLinearMap.isAdjointPair_inner, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, VectorFourier.norm_fourierPowSMulRight_le, TensorProduct.norm_map, EuclideanGeometry.dist_smul_vadd_eq_dist, deriv_pos_left_of_sign_deriv, derivWithin_Ioi_eq_Ici, dist_birkhoffAverage_birkhoffAverage_le, Complex.equivRealProdCLM_symm_apply_im, ContinuousLinearMap.coe_le_coe_iff, AddChar.linearIndependent, MeasureTheory.integral_singleton, riesz_lemma, intervalIntegral.integral_comp_div_sub, SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply, hasFDerivAtFilter_finCons', ContinuousLinearEquiv.analyticWithinAt, nndist_homothety_center, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, complexOfReal_hasDerivAt, ConvexBody.hausdorffDist_coe, Real.hasFDerivAt_fourierChar_neg_bilinear_right, MeasureTheory.integral_comp_smul_deriv_Ioi, EuclideanGeometry.orthogonalProjection_eq_self_iff, ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormal, DifferentiableAt.smul_const, LinearIsometryEquiv.differentiableAt, DifferentiableWithinAt.cexp, Real.fourier_continuousMultilinearMap_apply, LinearIsometryEquiv.differentiable, Unitization.splitMul_injective, Antitone.deriv_nonpos, AffineSubspace.mem_perpBisector_iff_inner_eq, WeakFEPair.f_modif_aux1, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, Asymptotics.IsTheta.const_smul_right, EuclideanGeometry.reflection_subtype, differentiable_tsum', HasFPowerSeriesAt.coeff_zero, Submodule.orthogonal_le_orthogonal_iff, DoubleCentralizer.sub_snd, DifferentiableOn.continuousAlternatingMap_apply_const, Differentiable.fun_sub, ModelWithCorners.coe_transContinuousLinearEquiv, SeparatingDual.completeSpace_continuousMultilinearMap_iff, Submodule.orthogonal_le_iff_orthogonal_le, Orientation.finOrthonormalBasis_orientation, ContDiffOn.comp_continuousLinearMap, norm_iteratedFDerivWithin_mul_le, VectorFourier.norm_fourierSMulRight, Complex.differentiableOn_update_limUnder_insert_of_isLittleO, HasStrictDerivAt.div_const, DifferentiableAt.inversion, HasStrictDerivAt.fun_mul, Polynomial.differentiable, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, InnerProductSpace.volume_closedBall, ContinuousLinearEquiv.coord_norm', DifferentiableOn.star, deriv_fun_pow, HasFPowerSeriesOnBall.hasSum_sub, ContinuousLinearMap.nnnorm_id, fderivWithin_continuousAlternatingMap_apply, HasDerivAt.fun_inv, DifferentiableAt.div_const, differentiableOn_abs, ContinuousLinearMap.IsStarProjection.isSymmetricProjection, Bundle.Trivial.symmₗ_trivialization, WithCStarModule.pi_norm_sq, ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, HasFPowerSeriesAt.eq_zero_of_eventually, norm_smul_normalize, hom_chart, ContinuousLinearMap.isPositive_zero, cfcₙ_setIntegral', div_le_egauge_closedBall, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, hasStrictFDerivAt_inv', AffineIsometryEquiv.coe_vaddConst', LinearMap.support_singularValues, ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_sub, LinearMap.mem_span_iff_bound, homeomorphSphereProd_apply_fst_coe, ContinuousOn.cfcₙ_nnreal, uniqueMDiffWithinAt_iff_uniqueDiffWithinAt, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_sub, hasFDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_mul_const, HasDerivAt.scomp_hasDerivWithinAt, MeasureTheory.Lp.toTemperedDistribution_apply, SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', MDifferentiable.clm_apply, deriv_descPochhammer_eval_eq_sum_prod_range_erase, strongConvexOn_iff_convex, HasStrictDerivAt.add_const, Module.Basis.ofZLatticeBasis_repr_apply, DifferentiableOn.clog, derivWithin_id, HasMFDerivAt.sum, Differentiable.mul, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, intervalIntegral.integral_hasStrictDerivAt_right, Orientation.oangle_eq_pi_iff_sameRay_neg, MeasureTheory.charFunDual_pi, strongConvexOn_zero, dist_midpoint_midpoint_le', LinearEquiv.extendOfIsometry_eq, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, ConvexBody.hausdorffEDist_coe, exists_deriv_eq_slope, ContinuousLinearMap.integral_comp_id_comm, hasStrictFDerivAt_exp_smul_const, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MeasureTheory.SimpleFunc.integral_eq, integral_withDensity_eq_integral_toReal_smul₀, EuclideanGeometry.angle_pointReflection_right, SchwartzMap.fourier_convolution_apply, Complex.hasStrictFDerivAt_log_real, MeasureTheory.SimpleFunc.setToSimpleFunc_const', Real.iteratedDeriv_fourierIntegral, derivWithin_mul, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, AffineSubspace.isometryEquivMap.apply_symm_apply, MeasureTheory.setIntegral_finset, Submodule.starProjection_le_starProjection_iff, iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition, iteratedFDerivWithin_zero_fun, InnerProductSpace.volume_closedBall_of_dim_odd, real_inner_smul_left, WeakDual.isSeqCompact_of_isBounded_of_isClosed, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, TemperedDistribution.smulLeftCLM_sum, HasStrictFDerivAt.mul, intervalIntegral.integral_hasStrictDerivAt_left, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ContinuousLinearMap.analyticOnNhd, fderiv_fst, iter_deriv_inv_linear, ProbabilityTheory.deriv_cgf_zero, DifferentiableOn.exp, sum_mul_eq_sub_sub_integral_mul', AffineMap.differentiable, IsLocalMaxOn.hasFDerivWithinAt_eq_zero, ContMDiffAt.clm_apply, ContDiffOn.continuousOn_deriv_of_isOpen, Orientation.oangle_rotation_self_right, ContinuousAlternatingMap.differentiable, Differentiable.fun_sum, hasFDerivAt_of_tendstoUniformly, WeakDual.toStrongDual_apply, FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2, DifferentiableAt.finset_prod, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, hom_trivializationAt_apply, AffineEquiv.coe_toHomeomorphOfFiniteDimensional, ContinuousLinearEquiv.uniqueDiffOn_image_iff, NumberField.mixedEmbedding.euclidean.finrank, ProbabilityTheory.multivariateGaussian_zero_one, LinearMap.eq_adjoint_iff_basis_right, DifferentiableAt.norm, MDifferentiable.clm_precomp, ContinuousLinearMap.hasMFDerivWithinAt, ContinuousLinearEquiv.nnnorm_symm_pos, InnerProductSpace.laplacian_smul_nhds, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, MDifferentiable.clm_comp, Real.differentiable_fourierChar_neg_bilinear_left, Submodule.instOrthogonalCompleteSpace, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, ConvexBody.hausdorffEdist_coe, ContDiffMapSupportedIn.fderivLM_apply_of_le, AffineBasis.centroid_mem_interior_convexHull, ProbabilityTheory.HasGaussianLaw.toLp_prodMk, DifferentiableOn.fun_div, ContMDiff.clm_comp, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, fderiv_norm_smul_pos, EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq, FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, continuousMultilinearCurryLeftEquiv_symm_apply, WithLp.unitization_mul, UnitAddTorus.mFourierCoeff_eq_integral, MeasureTheory.Measure.addHaar_closedBall_mul, hasDerivAt_exp_smul_const', dist_right_lineMap, hasFDerivAtFilter_const_add_iff, DoubleCentralizer.instStarModule, fderivWithin_add, WeakDual.CharacterSpace.compContinuousMap_comp, HasStrictDerivAt.finset_prod, VectorBundleCore.localTriv.isLinear, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, ContinuousLinearMap.contDiff, TemperedDistribution.instContinuousFourierInv, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, differentiable_star_iff, ContinuousLinearMap.instBorelSpace, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, CStarAlgebra.star_right_conjugate_le_norm_smul, Convex.second_derivative_within_at_symmetric_of_mem_interior, norm_apply_le_norm_cfcₙ, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, innerₛₗ_apply_coe, iteratedDerivWithin_scomp_two, AnalyticOn.differentiableOn, fderiv_csinh, ContinuousLinearMap.exists_mul_lt_of_lt_opNorm, mellin_differentiableAt_of_isBigO_rpow, DifferentiableAt.fun_sub_iff_left, TestFunction.instContinuousSMulReal, MeasureTheory.integral_comp_mul_left_Ioi, HasStrictFDerivAt.fun_add, IsLocalMinOn.fderivWithin_nonneg, IsBoundedLinearMap.hasFDerivAt, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, ContinuousLinearMap.norm_snd_le, LinearMap.orthogonal_range, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, Submodule.isOrtho_self, LinearIsometryEquiv.toLinearIsometry_lTensor, analyticOrderAt_iterated_deriv, ContinuousMapZero.toNNReal_neg_smul, ContinuousLinearMap.smul_compLpL, DifferentiableOn.prodMk, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, MeasureTheory.SimpleFunc.map_integral, IsContDiffImplicitAt.implicitFunction_def, LinearMap.singularValues_of_lt, InnerProductSpace.euclideanHausdorffMeasure_eq_volume, differentiableAt_of_deriv_ne_zero, FormalMultilinearSeries.summable_norm_mul_pow, ContinuousLinearMap.contMDiffOn, ProbabilityTheory.instIsGaussianMapHAdd, VonNeumannAlgebra.instStarMemClass, AntilipschitzWith.completeSpace_range_clm, AlternatingMap.bound_of_shell_of_norm_map_coord_zero, ContDiffMapSupportedIn.fderivLM_apply_of_gt, EuclideanSpace.restrict₂_apply, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, Convex.norm_image_sub_le_of_norm_fderiv_le', HasDerivAt.hasDerivAtFilter, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, ext_iff, IsBoundedLinearMap.hasFDerivWithinAt, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousLinearMap.nnbound, stronglyMeasurable_deriv_with_param, HasDerivAt.comp_hasDerivWithinAt_of_eq, ContinuousLinearMap.opNorm_mulLeftRight_le, DoubleCentralizer.intCast_fst, EuclideanGeometry.Cospherical.subtype_val, HasFDerivAt.sqrt, MeasureTheory.measure_smul_setAverage, ClosedSubmodule.orthogonal_closure, ContDiffPointwiseHolderAt.iteratedFDeriv, ContinuousLinearMap.norm_compLpL_le, MeasureTheory.Integrable.comp_smul, ZSpan.vadd_mem_fundamentalDomain, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, mfderiv_eq_fderiv, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, sum_mul_eq_sub_integral_mul, derivWithin_add_const, TemperedDistribution.fourier_apply, fderiv_comp_add_left, HasFDerivWithinAt.curveIntegral_segment_source', deriv_sin, ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, Module.Basis.opNNNorm_le, Orientation.areaForm_rightAngleRotation_right, MeasureTheory.setIntegral_condExpL1CLM, SchwartzMap.lineDerivOp_apply, OrthonormalBasis.orientation_adjustToOrientation, ContDiffAt.continuousAt_iteratedFDeriv, ContMDiffWithinAt.clm_precomp, ZSpan.fract_apply, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, IsLocalMin.fderiv_eq_zero, norm_iteratedFDerivWithin_fderivWithin, Module.Basis.map_addHaar, HasDerivAtFilter.comp, AffineIsometryEquiv.norm_map, ContinuousLinearMap.cpolynomialOn, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, ContinuousLinearMap.coe_complexOfReal, MeasureTheory.Integrable.fourier_smul, fderiv_comp_sub, HasFDerivWithinAt.finset_prod, ContinuousAlternatingMap.nnnorm_constOfIsEmpty, hasStrictFDerivAt_list_prod', Real.differentiableAt_qaryEntropy, ContinuousLinearMap.le_opENorm, continuousMultilinearCurryFin1_symm_apply, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, HasStrictDerivAt.fun_add, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, differentiableWithinAt_comp_add_left, ContinuousMultilinearMap.opNorm_le_iff, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, ModelWithCorners.uniqueDiffOn_extendCoordChange_target, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, intervalIntegral.integral_comp_mul_add, FormalMultilinearSeries.radius_pi_le, DifferentiableAt.exp, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, hom_trivializationAt_baseSet, HasDerivAt.comp_of_eq, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, VectorFourier.integral_fourierIntegral_smul_eq_flip, ContinuousLinearMap.mdifferentiableOn, BoundedContinuousFunction.charMonoidHom_apply, MeasureTheory.eLpNorm_condExpL2_le, Complex.integral_boundary_rect_of_differentiableOn_real, Affine.Simplex.touchpoint_mem_affineSpan_simplex, ContinuousLinearMap.lsmul_flip_apply, aemeasurable_derivWithin_Ici, Differentiable.finset_prod, Orientation.inner_smul_rotation_pi_div_two_smul_left, iteratedFDeriv_sub_apply, closure_diff_intrinsicInterior, ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, HasStrictFDerivAt.smul_const, SchwartzMap.coe_apply, MeasureTheory.Measure.addHaar_ball, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, ContinuousLinearEquiv.coord_self, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, sub_smul_dslope, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, LinearMap.antilipschitz_of_comap_nhds_le, MeasureTheory.condExp_bot', ContinuousAlternatingMap.unit_le_opNorm, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, extDerivWithin_apply, Orientation.oangle_smul_right_of_pos, norm_iteratedFDeriv_smul_le, ContDiffAt.differentiableAt_iteratedFDeriv, LinearMap.IsPositive.adjoint_eq, abs_real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivAt.hasFDerivAt_norm_smul_pos, Orientation.oangle_map_complex, Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn, ContinuousLinearEquiv.comp_fderivWithin, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, HasFDerivAtFilter.finCons, iteratedDeriv_vcomp_two, ContinuousLinearEquiv.coord_norm, ContinuousAlternatingMap.opNNNorm_le_iff, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, ContinuousOn.continuousOn_iteratedFDeriv, ProbabilityTheory.instIsGaussianProdProdOfSecondCountableTopologyEither, HasDerivAt.finset_prod, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, HasStrictFDerivAt.cosh, Matrix.toEuclideanLin_eq_toLin_orthonormal, ContDiffOn.smulRight, IsBoundedBilinearMap.differentiable, LinearMap.isometryOfOrthonormal_toLinearMap, isTheta_deriv_ofReal_cpow_const_atTop, ContinuousLinearMap.opNorm_eq_of_bounds, MeasureTheory.lpMeasToLpTrim_smul, Real.hasStrictDerivAt_const_rpow, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, HasStrictDerivAt.cos, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, MeasureTheory.integral_finset, Affine.Simplex.circumsphere_reindex, intervalIntegral.integral_deriv_eq_sub_uIoo, isStarProjection_iff_eq_starProjection, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, spectrum.hasDerivAt_resolvent_const_right, Orientation.inner_smul_rotation_pi_div_two_smul_right, LinearMap.IsSymmetricProjection.le_iff_range_le_range, derivWithin_congr_set, SchauderBasis.RankOneDecomposition.proj_comp, hasDerivWithinAt_intCast, MeasureTheory.integral_bilinear_hasDerivAt_eq_sub, differentiableWithinAt_zpow, ContinuousAt.integral_sub_linear_isLittleO_ae, CircleIntegrable.out, ContMDiff.clm_precomp, VonNeumannAlgebra.instSubringClass, contDiffOn_infty_iff_deriv_of_isOpen, VectorField.fderivWithin_apply_lieBracket, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, fderivWithin_pow, HasFPowerSeriesWithinAt.compContinuousLinearMap, VectorPrebundle.coordChange_apply, ContinuousMultilinearMap.norm_map_cons_le, ContinuousMultilinearMap.norm_smulRight, EuclideanGeometry.orthogonalProjection_apply, hasFDerivAt_exp_zero_of_radius_pos, CStarAlgebra.span_nonneg_inter_ball, EuclideanGeometry.Sphere.direction_orthRadius, Real.hasDerivAt_fourierIntegral, fderivWithin_fun_const_smul, mdifferentiableWithinAt_iff_of_mem_source, Bundle.ContinuousLinearMap.memTrivializationAtlas, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, ContinuousMapZero.elemental_eq_top, ContMDiffOn.clm_prodMap, ContinuousMapZero.adjoin_id_dense, HasStrictDerivAt.iterate, Complex.rightAngleRotation, Affine.Simplex.Equilateral.angle_eq_pi_div_three, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono, derivWithin_sub, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, StrictMonoOn.exists_slope_lt_deriv, EuclideanGeometry.cospherical_iff_exists_mem_of_finiteDimensional, ContinuousAlternatingMap.bound, EuclideanGeometry.existsUnique_dist_eq_of_insert, Affine.Simplex.circumradius_reindex, ContinuousLinearMap.hasDerivWithinAt, differentiableWithinAt_piLp, AffineIndependent.existsUnique_dist_eq, LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, HasDerivWithinAt.comp_of_eq, IsCompactOperator.isCompact_closure_image_ball, FormalMultilinearSeries.derivSeries_apply_diag, ContMDiffWithinAt.clm_comp, polar_closedBall, derivWithin_comp_const_add, Submodule.norm_orthogonalProjection, AnalyticAt.fderiv, HasDerivAt.conj_conj, ContinuousLinearEquiv.differentiableWithinAt, ClosedSubmodule.symplComp_sup, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, Submodule.instHasOrthogonalProjectionTop, iteratedFDeriv_clm_apply_const_apply, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, ContinuousLinearMap.opNorm_lsmul, LinearIsometry.toLinearMap_lTensor, deriv_pos_right_of_sign_deriv, EuclideanGeometry.orthogonalProjection_mem_orthogonal, HasFPowerSeriesWithinOnBall.hasSum, coe_innerₛₗ_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp, FormalMultilinearSeries.norm_changeOriginSeriesTerm, PiLp.hasStrictFDerivAt_ofLp, fderivWithin_arctan, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, VectorField.lieBracketWithin_const_smul_right, curveIntegral_add, StrictMonoOn.exists_deriv_lt_slope, EuclideanSpace.euclideanHausdorffMeasure_eq_volume, DifferentiableOn.fun_sub_iff_right, HasGradientAt.hasDerivAt, TensorProduct.nndist_tmul_le, ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, ModularGroup.lcRow0_apply, hasDerivAt_exp_zero, ContinuousMultilinearMap.opNorm_le_bound, HasFTaylorSeriesUpTo.zero_eq', deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, Complex.exists_cthickening_tendstoUniformlyOn, ContinuousLinearEquiv.analyticAt, Differentiable.continuousAlternatingMap_apply, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, DifferentiableAt.pow, Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, HasCompactSupport.deriv, instIsConvexMetricSpace, ContinuousMultilinearMap.norm_def, double_dual_bound, HasDerivAt.comp_ringHom, fourierCoeffOn.const_smul, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, PeriodPair.indep, MeasureTheory.convolution_eq_swap, Real.fourierInv_eq, Module.Basis.opNorm_le, ModelWithCorners.coe_transContinuousLinearEquiv_symm, Real.differentiable_rpow_const, AffineIsometryEquiv.toAffineEquiv_symm, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, differentiable_finCons, ContDiff.fderiv_right, hasDerivAt_const_add_iff, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonpos, ProperCone.innerDual_iUnion, HasFDerivAt.prodMap, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContinuousAlternatingMap.opNorm_pi, norm_injOn_ray_left, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ContDiffOn.deriv_of_isOpen, FormalMultilinearSeries.id_apply_one, ContinuousLinearEquiv.comp_contDiff_iff, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, fderiv_csin, ContinuousLinearMap.norm_snd, ZSpan.repr_floor_apply, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, WeakDual.isSeqCompact_polar, WeakDual.seminormFamily_apply, MeasureTheory.condExpIndSMul_ae_eq_smul, HasFTaylorSeriesUpTo.fderiv, ContinuousLinearMap.iteratedFDeriv_comp_right, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, Quaternion.linearIsometryEquivTuple_apply, norm_fderiv_le_of_lip', DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, MeasureTheory.isAddHaarMeasure_euclideanHausdorffMeasure, DiffContOnCl.differentiableOn, ContinuousLinearMap.rayleighQuotient_neg_apply, HasFDerivAtFilter.isEquivalent_sub, ContinuousMultilinearMap.apply_zero_uncurry0, fderiv_cosh, PiTensorProduct.injectiveSeminorm_tprod_le, DifferentiableWithinAt.fun_inv, IsOpen.affineSpan_eq_top, lipschitzWith_lineMap, HasStrictFDerivAt.fun_mul, Filter.EventuallyEq.hasLineDerivAt_iff, ContDiff.continuousLinearMap_comp, ContinuousLinearMap.norm_holderL_le, LinearEquiv.coeFn_toContinuousLinearEquivOfContinuous_symm, SmoothPartitionOfUnity.contMDiff_smul, hasFDerivWithinAt_pow, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, contDiff_infty_iff_fderiv, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, interval_average_eq, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, MeasureTheory.lpMeas.ae_fin_strongly_measurable', hasStrictDerivAt_id, curveIntegral_sub, ProbabilityTheory.HasGaussianLaw.eval, cfcₙL_integrable, HasFDerivWithinAt.mul', HasFPowerSeriesWithinOnBall.fderivWithin_of_mem_of_analyticOn, instNonemptySeedRatReal, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, ContinuousAlternatingMap.instContinuousEval, differentiableWithinAt_complex_iff_differentiableWithinAt_real, ContinuousLinearMap.comp_analyticOnNhd, Differentiable.rpow_const, TemperedDistribution.derivCLM_apply_apply, OrthonormalBasis.tensorProduct_apply, TorusIntegrable.function_integrable, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, hasStrictFDerivAt_pi'', MeasureTheory.L1.setToL1'_eq_setToL1SCLM, LinearIsometryEquiv.integrable_comp_iff, deriv_neg, intervalIntegral.derivWithin_integral_left, range_derivWithin_subset_closure_span_image, AffineIsometryEquiv.toContinuousAffineEquiv_injective, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, OpenPartialHomeomorph.hasStrictDerivAt_symm, HasStrictFDerivAt.sinh, DifferentiableAt.fun_mul, ContinuousLinearMap.finite_dimensional_eigenspace, ContinuousLinearMap.locallyIntegrableOn_comp, DifferentiableAt.sub_const, ContDiffWithinAt.differentiableWithinAt', MeasureTheory.Supermartingale.smul_nonneg, abs_signedDist_le_dist, EuclideanGeometry.Sphere.instNonemptySubtypeMemAffineSubspaceRealOrthRadius, norm_iteratedFDeriv_zero, Orientation.norm_kahler, dist_midpoint_left, NumberField.mixedEmbedding.disjoint_span_commMap_ker, HasFDerivAt.cpow, LinearPMap.mem_adjoint_domain_of_exists, deriv_sum, hasDerivWithinAt_Ici_of_tendsto_deriv, spectrum.hasDerivAt_resolvent_const_left, ContinuousLinearMap.exists_nnnorm_eq_one_lt_apply_of_lt_opNNNorm, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, CFC.norm_mul_mul_star_self_of_nonneg, norm_iteratedFDeriv_eq_norm_iteratedDeriv, MDifferentiableWithinAt.smul, intervalIntegral.deriv_integral_of_tendsto_ae_left, Complex.isometryOfOrthonormal_symm_apply, WithLp.unitizationAlgEquiv_apply, Real.hasStrictDerivAt_rpow_const, deriv_mul, HasStrictFDerivAt.implicitFunctionOfComplemented_apply_image, MeasureTheory.weightedSMul_smul_measure, VectorField.lieBracket_smul_right, HasFDerivAtFilter.restrictScalars, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, ContinuousLinearMap.coeFn_ofSeqClosedGraph, intervalIntegral.integral_hasFDerivAt, ProperCone.innerDual_toSubmodule, LinearMap.self_comp_adjoint_injective_iff, CurveIntegrable.sub, InnerProductSpace.HarmonicAt.comp_CLM, differentiableAt_inv, deriv_pow', Orientation.inner_rightAngleRotation_self, HasFiniteFPowerSeriesOnBall.fderiv_eq, smul_closedBall, ContMDiffOn.smul, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, ProbabilityTheory.instIsGaussianMapHSub_1, derivWithin_add, MeasureTheory.hausdorffMeasure_homothety_preimage, ContinuousLinearEquiv.comp_contDiffAt_iff, TestFunction.lineDerivCLM_apply_of_gt, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real, ContinuousAlternatingMap.hasFDerivAt, DifferentiableAt.arctan, DifferentiableOn.comp, FormalMultilinearSeries.summable, HasFPowerSeriesAt.locally_zero_iff, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, InnerProductSpace.laplacian_CLE_comp_left, hasDerivAt_iff_tendsto_slope, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, PiTensorProduct.mapL_add, Differentiable.comp, intervalIntegral.integral_unitInterval_deriv_eq_sub, ContinuousLinearMap.analyticAt_bilinear, inner_gradient_left, DifferentiableWithinAt.mul_const, EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq, eventually_norm_trivializationAt_lt, TensorProduct.congrIsometry_apply, integral_withDensity_eq_integral_smul₀, Submodule.starProjection_comp_starProjection_of_le, ZMod.dft_eq_fourier, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', HasFDerivWithinAt.comp_hasDerivAt_of_eq, HasFPowerSeriesAt.hasStrictFDerivAt, contDiffOn_fderivWithin_apply, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, HasDerivWithinAt.comp_hasDerivAt, ModelWithCorners.uniqueDiffOn_preimage_source, isConnected_setOf_sameRay, MeasureTheory.integral_prod_smul, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, RealRMK.le_rieszMeasure_tsupport_subset, innerSL_apply_coe, differentiableOn_finCons, Differentiable.add, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, AffineSubspace.signedInfDist_apply_of_mem, hasDerivAt_exp_of_mem_ball, fderivWithin_mul', ContinuousLinearMap.bound, hasStrictDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, IsBoundedLinearMap.fderiv, ContinuousLinearMap.isPositive_one, HasDerivWithinAt.fun_sum, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousLinearMap.isPositive_sum, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, Real.hasDerivAt_Gamma_nat, AffineSubspace.equivMapOfInjective_toFun, MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg, Orientation.oangle_smul_right_self_of_nonneg, HasStrictFDerivAt.inner, TopologicalGroup.IsSES.integrate_mono, CStarAlgebra.instNonnegSpectrumClassComplexUnital, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, ZSpan.fract_eq_fract, hasDerivAt_pi, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, differentiableAt_abs, LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commute, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, HasDerivAt.of_notMem_tsupport, le_gauge_of_subset_closedBall, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, derivWithin_fun_inv', ConvexOn.real_sSup_of_nat_affine_eq, MeasureTheory.integrable_fun_norm_addHaar, integral_bilinear_fderiv_right_eq_neg_left_of_integrable, EuclideanGeometry.orthogonalProjection_sup_of_orthogonalProjection_eq, hasFDerivAt_inv', ProbabilityTheory.isGaussian_stdGaussian, LinearMap.toMatrix_adjoint, ProbabilityTheory.isPositive_covarianceOperator, MeasureTheory.dominatedFinMeasAdditive_weightedSMul, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, HasDerivAt.fun_mul, HasStrictDerivAt.const_sub, hasDerivWithinAt_finCons, Affine.Simplex.height_reindex, WeakDual.CharacterSpace.exists_apply_eq_zero, HasFDerivAt.cosh, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, DifferentiableAt.comp_semilinear₂, derivWithin_sinh, exists_continuousLinearEquiv_fderiv_symm_eq, HasDerivAt.smul, FormalMultilinearSeries.rightInv_coeff, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, DifferentiableOn.norm, hasFDerivAt_of_tendstoUniformlyOn, Affine.Simplex.inradius_map, Complex.map_isometryOfOrthonormal, DifferentiableAt.ccos, Meromorphic.smul, OpenPartialHomeomorph.unitBallBall_symm_apply, quasispectrum.instCompactSpaceNNReal, hasDerivAt_zpow, TemperedDistribution.fourierTransformInv_apply, HasDerivAt.sin, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Orientation.oangle_neg_orientation_eq_neg, FormalMultilinearSeries.summable_norm_apply, Orientation.oangle_sign_smul_add_smul_left, ContinuousMultilinearMap.norm_constOfIsEmpty, tendsto_integral_comp_smul_smul_of_integrable', uniqueDiffOn_extChartAt_target, DifferentiableWithinAt.fun_add, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, LinearMap.isSymmetric_iff_inner_map_self_real, MeromorphicOn.iterated_deriv, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, WeakDual.CharacterSpace.compContinuousMap_id, derivWithin_of_isOpen, EuclideanGeometry.Sphere.secondInter_eq_lineMap, sum_mul_eq_sub_integral_mul₀, measurable_derivWithin_Ici, HasDerivWithinAt.exp, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContinuousLinearMap.integral_comp_comm, hasFDerivWithinAt_iff_tendsto, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, ContDiffOn.differentiableOn_iteratedFDerivWithin, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, differentiableAt_iff_comp_const_add, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, MeasureTheory.average_union_mem_openSegment, fderiv_pi, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', differentiableAt_inverse, Matrix.l2_opNorm_def, fderivWithin_comp_add_right, Real.fourierInv_eq', Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div', signedDist_apply_linear, EuclideanGeometry.Sphere.secondInter_map, Real.differentiableAt_sin, OrthogonalFamily.linearIsometry_apply, ContinuousMultilinearMap.le_opNNNorm, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, StrictConcaveOn.leftDeriv_lt_slope, nnnorm_cfcₙ_le, OrthogonalFamily.pairwise, Complex.tendstoUniformlyOn_deriv_of_cthickening_subset, HasStrictFDerivAt.const_add, LinearMap.IsSymmetric.toMatrix_eigenvectorBasis, continuous_stereoInvFun, HasStrictDerivAt.neg, MellinConvergent.cpow_smul, parallelepiped_orthonormalBasis_one_dim, ContinuousLinearMap.iteratedFDeriv_comp_left, Real.fourierIntegral_deriv, ContinuousLinearMap.isCompact_image_coe_of_bounded_of_weak_closed, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, Submodule.orthogonalProjection_eq_zero_iff, ContinuousLinearMap.holderL_apply_apply, differentiableAt_comp_sub, FormalMultilinearSeries.comp_rightInv_aux2, derivWithin_sub_const, HasFDerivAt.isEquivalent_sub, Complex.reCLM_enorm, MeasureTheory.integral_fun_snd, ContinuousMultilinearMap.opNorm_prod, AffineMap.antilipschitzWith_of_finiteDimensional, MeasureTheory.condExpInd_empty, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, ZLattice.covolume.tendsto_card_div_pow'', Real.hasDerivAt_sinh, MeasureTheory.condExpL1CLM_smul, Real.deriv_log_comp_eq_logDeriv, isConformalMap_const_smul, real_inner_smul_self_right, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, dist_smul_add_one_sub_smul_le, Complex.norm_fderiv_le_div_of_mapsTo_ball, norm_innerSL_le, MeromorphicAt.smul, DifferentiableAt.add, AffineSubspace.subtypeₐᵢ_toAffineMap, VectorFourier.hasFDerivAt_fourierChar_smul, Differentiable.const_cpow, ContinuousLinearMap.HasLeftInverse.of_injective_of_isClosed_range_of_closedComplement_range, HasStrictFDerivAt.sub, OrthonormalBasis.measurePreserving_measurableEquiv, Orientation.rotation_pi, Real.fourierIntegral_real_eq, HasStrictFDerivAt.csinh, ContMDiffWithinAt.cle_arrowCongr, ContinuousLinearMap.isLeast_opNorm, InformationTheory.not_differentiableAt_klFun_zero, fderiv_const_smul_of_field, ContinuousLinearEquiv.coe_ofBijective, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, HasFDerivWithinAt.cos, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, ContinuousLinearMap.IsPositive.isSelfAdjoint, MeasureTheory.measure_unitBall_eq_integral_div_gamma, HasLineDerivAt.smul, Submodule.orthogonalProjection_starProjection_of_le, GeneralSchauderBasis.proj_comp, Real.exists_extension_norm_eq, OrthonormalBasis.sum_repr', WeakDual.isClosed_image_coe_of_bounded_of_closed, continuousMultilinearCurryRightEquiv_apply, antilipschitzWith_lineMap, ContinuousLinearMap.integrableOn_comp, Submodule.coe_orthogonalProjection_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, HasDerivAt.comp_add_const, Submodule.starProjection_coe_eq_isCompl_projection, HasFDerivAt.neg, EuclideanGeometry.Sphere.instHasOrthogonalProjectionRealDirectionOrthRadius, ContDiffMapSupportedIn.structureMapLM_zero_apply, SchwartzMap.differentiableAt, nnnorm_cfcₙ_nnreal_le, hasFDerivAtFilter_add_const_iff, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, MeasureTheory.average_union, LinearMap.injective_iff_antilipschitz, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, gauge_closedBall, OpenPartialHomeomorph.univUnitBall_symm_apply, ContinuousLinearEquiv.iteratedFDerivWithin_comp_left, ContinuousLinearMap.IsIdempotentElem.hasOrthogonalProjection_range, deriv.star', Real.deriv_sin, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, AffineMap.deriv, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countable, Submodule.ClosedComplemented.of_quotient_finiteDimensional, fderiv_comp_deriv_of_eq, DifferentiableOn.hasDerivAt, DifferentiableWithinAt.sinh, DifferentiableOn.arsinh, contDiffOn_infty_iff_derivWithin, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcₙ_nnreal, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, ProbabilityTheory.covarianceBilinDual_of_not_memLp', LinearMap.posSemidef_toMatrix_iff, UnconditionalSchauderBasis.exists_norm_proj_le, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left', intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, MontelSpace.finiteDimensional_of_normedSpace, Orientation.two_zsmul_oangle_smul_smul_self, ContDiff.fderiv, Submodule.starProjection_apply_eq_zero_iff, fderiv_list_prod', SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, ContDiff.differentiable_one, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', intervalIntegral.integral_deriv_smul_comp'', SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, norm_lineDeriv_le_of_lip', fderivWithin_comp_smul, Orientation.rotation_symm_apply, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, AnalyticOnNhd.iterated_deriv, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, ContinuousLinearMap.orthogonal_mem_invtSubmodule, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, VectorFourier.integrable_fourierPowSMulRight, Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Orthonormal.inner_right_fintype, contDiffOn_iff_continuousOn_differentiableOn_deriv, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, HasFPowerSeriesAt.compContinuousLinearMap, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, EuclideanGeometry.mapsTo_inversion_affineSubspace_of_mem, DifferentiableWithinAt.exp, expNegInvGlue.differentiable_polynomial_eval_inv_mul, WeakFEPair.f_modif_aux2, Asymptotics.isTheta_const_smul_right, HasFDerivAt.star_star, continuousOn_cfcₙ_nnreal_setProd, fderivWithin_clm_apply, fderivWithin_fst, exists_continuousLinearEquiv_fderivWithin_symm_eq, ContinuousLinearMap.instLocallyBoundedMapClass, HasStrictFDerivAt.implicitFunction_apply_image, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', posTangentConeAt_univ, OrthonormalBasis.abs_det_adjustToOrientation, mellin_cpow_smul, HasGradientWithinAt.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le_max, ContinuousLinearMap.dist_le_opNorm, DifferentiableWithinAt.rpow, FormalMultilinearSeries.rightInv_coeff_one, hasFDerivAt_exp, Differentiable.rpow, ContinuousAlternatingMap.opNNNorm_prod, Orientation.volumeForm_comp_linearIsometryEquiv, ContDiffWithinAt.differentiableWithinAt, Pi.orthonormalBasis_repr, deriv_mul_const_field', fderiv_continuousAlternatingMap_apply_const_apply, Differentiable.smul_const, DifferentiableAt.cpow, EuclideanGeometry.inversion_eq_lineMap, Polynomial.hasDerivWithinAt, ZSpan.mem_fundamentalDomain, Collinear.sbtw_of_dist_eq_of_dist_lt, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, differentiableAt_iff_comp_sub_const, InnerProductGeometry.IsConformalMap.preserves_angle, uniqueDiffWithinAt_extChartAt_target, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, complexOfReal_derivWithin, ApproximatesLinearOn.lipschitzOnWith, CFC.norm_sqrt, LipschitzOnWith.ae_differentiableWithinAt, Orthonormal.tmul, norm_fderiv_norm_id_rpow, Submodule.IsCompl.projection_isSymmetric_iff, MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero, NumberField.Units.basisOfIsMaxRank_fundSystem, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum, LinearMap.isAdjointPair_inner, MeasureTheory.condExpIndL1Fin_smul', LinearMap.IsPositive.adjoint_conj, LinearMap.tendsto_birkhoffAverage_of_ker_subset_closure, ContinuousLinearMap.norm_holder_apply_apply_le, HasDerivWithinAt.log, DifferentiableOn.csin, ClosedSubmodule.involutive_mulI, LinearMap.isPositive_one, ClosedSubmodule.symplComp_inf, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, intervalIntegral.integral_deriv_smul_comp, differentiable_tsum, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, ContinuousLinearMap.homothety_norm, hasDerivAt_conj_conj_iff, fderivWithin_sum, RKHS.posSemidef_kernel, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, Orientation.rotation_oangle_eq_iff_norm_eq, Affine.Simplex.signedInfDist_apply_of_ne, Submodule.norm_subtypeL_le, ContinuousLinearMap.hasStrictDerivAt, sum_mul_eq_sub_sub_integral_mul, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, AffineIsometry.coe_toContinuousAffineMap, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, fderivWithin_pow_ring, dist_sq_lineMap_of_inner_eq_zero, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, hasFDerivAtFilter_pi', measurable_fderiv_apply_const_with_param, constFormalMultilinearSeries_apply_succ, ImplicitFunctionData.hasStrictFDerivAt_rightFun, aestronglyMeasurable_deriv_with_param, fderivWithin_comp, signedDist_left_lineMap, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, FormalMultilinearSeries.continuousOn, hasFDerivAt_inv, HasStrictFDerivAt.clm_comp, iteratedFDeriv_tsum_apply, Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, Real.deriv_mul_log_zero, ContinuousLinearMap.coe_ofIsClosedGraph, ProbabilityTheory.Kernel.integral_withDensity, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, Orientation.oangle_sign_smul_sub_right, DoubleCentralizer.toProdHom_apply, HasFDerivWithinAt.of_restrictScalars, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, Submodule.isOrtho_bot_left, Differentiable.inv, HasStrictFDerivAt.sub_const, DoubleCentralizer.mul_snd, HasFDerivWithinAt.comp_hasFDerivAt, MonotoneOn.nnnorm_cfcₙ, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.fpowerSeries_apply_one, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, MeasureTheory.L1.integral_eq, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, continuousOn_clm_apply, Real.hasDerivAt_sqrt, WeakFEPair.Λ_residue_zero, SchwartzMap.one_add_le_sup_seminorm_apply, Submodule.exists_norm_eq_iInf_of_complete_subspace, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, derivWithin_pow, MDifferentiableWithinAt.clm_prodMap, HasFDerivAt.fun_mul', derivWithin_inter, ContMDiffAt.clm_comp, constFormalMultilinearSeries_zero, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, OpenPartialHomeomorph.unitBallBall_apply, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, Affine.Simplex.circumcenter_eq_centroid, Real.fourierIntegralInv_eq, Convex.thickening, HasStrictFDerivAt.continuousMultilinearMap_apply, MeasureTheory.weightedSMul_zero_measure, Asymptotics.IsBigO.isBigOTVS, taylor_within_apply, Bundle.Trivialization.localFrame_coeff_apply_of_mem_baseSet, LinearPMap.adjointAux_inner, HasStrictFDerivAt.mul_const, Real.hasDerivWithinAt_arccos_Iic, ContDiffBump.convolution_tendsto_right_of_continuous, ConcaveOn.slope_le_deriv, Affine.Simplex.excenter_reindex, WithCStarModule.prod_inner, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top, measurableSet_of_differentiableWithinAt_Ici, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ConvexOn.slope_le_of_hasDerivWithinAt_Iio, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, AffineIsometry.image_intrinsicFrontier, ProbabilityTheory.HasGaussianLaw.sum, ContinuousMultilinearMap.curryFinFinset_apply, deriv_zero_of_frequently_mem, EuclideanGeometry.orthogonalProjection_eq_iff_mem, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, ContDiffAt.smulRight, HasLineDerivWithinAt.congr_of_eventuallyEq, Affine.Simplex.ninePointCircle_center, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, nndist_self_homothety, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, OrderedFinpartition.applyOrderedFinpartition_update_right, derivWithin_smul_const, FormalMultilinearSeries.changeOriginSeriesTerm_bound, eq_midpoint_of_dist_eq_half, MultilinearMap.mkContinuous_norm_le', HasDerivWithinAt.sum, MeasureTheory.integral_smul_measure, deriv_sqrt_mul_log', Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, LinearMap.IsSymmetric.hasEigenvector_eigenvectorBasis, VectorBundleCore.coordChange_comp, MeasureTheory.L1.setToL1'_apply_coeToLp, derivWithin_const_sub, SchwartzMap.denseRange_toLpCLM, ConformalAt.const_smul, Orientation.linearIsometryEquiv_comp_rightAngleRotation', LinearIsometry.re_apply_eq_re, hasFDerivAt_fst, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Real.differentiableAt_binEntropy_iff_ne_zero_one, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, derivWithin_const_mul_field, mdifferentiableWithinAt_hom_bundle, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, CFC.nnnorm_nnrpow, SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, Real.deriv_tan, Module.Basis.addHaar_self, HasFTaylorSeriesUpToOn.restrictScalars, ConcaveOn.antitoneOn_deriv, Differentiable.smul, isConformalMap_iff_is_complex_or_conj_linear, AnalyticAt.hasStrictFDerivAt, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, ProbabilityTheory.integral_poissonMeasure', HasDerivAtFilter.neg, ContinuousLinearMap.apply_apply, MeasureTheory.L1.setToL1_const, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, intrinsicClosure_eq_closure, RCLike.span_one_I, Asymptotics.isThetaTVS_iff_isTheta, hasFDerivAt_pi', AffineSubspace.euclideanHausdorffMeasure_coe_image, HasFDerivWithinAt.sub_const, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, iteratedFDeriv_neg, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, DifferentiableOn.sub_iff_left, CurveIntegrable.add, PiTensorProduct.mapLMultilinear_opNorm, hasDerivWithinAt_inter, fderivWithin_restrictScalars_comp, OpenPartialHomeomorph.hasFDerivAt_symm, IsLocalExtr.hasFDerivAt_eq_zero, ContinuousMultilinearMap.norm_image_sub_le', Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, hasFPowerSeriesAt_iff', hasFDerivAt_tsum_of_isPreconnected, LinearIsometryEquiv.differentiableOn, Real.fourier_eq', Real.differentiable_fourier, fderivWithin_fun_sum, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, MeasureTheory.charFunDual_eq_prod_iff', UpperHalfPlane.hasStrictFDerivAt_smul, inner_gradient_right, hasDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, InnerProductSpace.laplacianWithin_CLE_comp_left, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Orthonormal.equiv_apply, deriv_const_smul_field, NonUnitalCStarAlgebra.toSMulCommClass, UpperHalfPlane.det_smulFDeriv, Submodule.orthogonalProjection_norm_le, Bundle.Trivialization.coe_continuousLinearEquivAt_eq', HasFDerivAt.mul', DoubleCentralizer.intCast_toProd, ContinuousAffineMap.differentiableAt, Matrix.PosDef.posDef_sqrt, WeakFEPair.Λ_residue_k, DifferentiableAt.sum, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, Function.HasTemperateGrowth.isBigO_uniform, InnerProductSpace.volume_ball_of_dim_even, differentiableOn_snd, Differentiable.cos, norm_cfcₙ_le_iff, LinearMap.ker_le_ker_of_range, Complex.analyticAt_iff_eventually_differentiableAt, differentiableAt_comp_sub_const, iteratedFDerivWithin_zero_apply, EuclideanSpace.volume_closedBall, Orientation.rightAngleRotation_neg_orientation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, Orientation.rotationAux_apply, Fourier.fourierIntegral_comp_add_right, derivWithin_clm_apply, GeneralSchauderBasis.linearIndependent, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, fderiv_single, hom_trivializationAt_target, SchwartzMap.fourierMultiplierCLM_smul, finrank_euclideanSpace_fin, ZLattice.comap_span_top, mdifferentiable_iff_differentiable, Submodule.orthogonalProjection_orthogonal, ConcaveOn.le_slope_of_hasDerivAt, Real.hasStrictDerivAt_exp, MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar, CFC.norm_nnrpow, differentiableWithinAt_const_add_iff, DifferentiableWithinAt.const_add, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, HasStrictDerivAt.congr_of_eventuallyEq, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_div, Complex.conjLIE_toCLE, InformationTheory.deriv_klFun, mdifferentiableOn_iff_of_mem_maximalAtlas, MeasureTheory.L1.setToL1_lipschitz, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, LinearIsometryEquiv.rTensor_def, MeasureTheory.norm_condExpL2_le_one, ContinuousLinearEquiv.mdifferentiableAt, MDifferentiableWithinAt.clm_apply, HasCompactSupport.convolution_integrand_bound_right, differentiable_sigmoid, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, RightDerivMeasurableAux.mem_A_of_differentiable, integral_comp_pi_polarCoord_symm, UniqueMDiffOn.uniqueDiffWithinAt_range_inter, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, Affine.Simplex.incenter_notMem_affineSpan_faceOpposite, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, deriv_add, SchauderBasis.RankOneDecomposition.e_mem_range, MeasureTheory.setToFun_eq, DifferentiableAt.lineDeriv_eq_fderiv, OrthonormalBasis.repr_reindex, HasDerivAt.comp_semilinear, DifferentiableAt.abs_of_pos, Differentiable.star, MeasureTheory.condExpL2_comp_continuousLinearMap, hasLineDerivWithinAt_congr_set, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, HasDerivAt.clog_real, HasDerivAt.comp_sub_const, MeasureTheory.charFun_map_smul, isOpen_setOf_linearIndependent, ZSpan.setFinite_inter, LinearIsometryEquiv.differentiableWithinAt, convex_closedBall, intervalIntegral.integral_deriv_smul_deriv_comp', ContinuousOn.continuousLinearMapCoprod, AffineIsometry.id_toAffineMap, ContMDiffAt.cle_arrowCongr, differentiableOn_const_add_iff, AnalyticOnNhd.eval_continuousLinearMap, hasStrictFDerivAt_pi, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_sup_left, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, HasDerivWithinAt.comp_hasFDerivAt_of_eq, HasFDerivAt.clm_comp, ContinuousLinearMap.adjoint_innerSL_apply, HasFDerivAt.rpow, ZLattice.coe_comap, HasDerivAt.of_local_left_inverse, EuclideanGeometry.reflection_mem_of_le_of_mem, sameRay_iff_norm_smul_eq, DifferentiableOn.fun_sub, Submodule.IsOrtho.comap, hasFDerivAt_iff_isLittleO_nhds_zero, fderivWithin_comp_sub, Distribution.IsVanishingOn.lineDerivOp, OrthogonalFamily.inner_right_fintype, ContinuousLinearMap.isQuotientMap, ProbabilityTheory.integral_tilted_mul_self, Bundle.Pretrivialization.continuousLinearMapCoordChange_apply, DifferentiableWithinAt.smul, integrableOn_Ioi_deriv_norm_ofReal_cpow, ContDiffMapSupportedIn.structureMapLM_apply, CStarAlgebra.span_unitary, AffineSubspace.right_mem_perpBisector, ContinuousLinearMap.circleAverage_comp_comm, fderiv_tsum_apply, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, DifferentiableOn.of_dslope, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, HasDerivWithinAt.iterate, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, derivWithin_const_smul', VectorPrebundle.contMDiffCoordChange_apply, isBoundedLinearMap_prod_multilinear, nndist_homothety_self, DifferentiableAt.abs_of_neg, fderivWithin_fun_mul, Differentiable.div, ContinuousOn.prod_map_equivL, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, differentiableWithinAt_fst, EuclideanGeometry.reflection_apply, continuousOn_coordChange, HasCompactSupport.convolution_integrand_bound_right_of_subset, deriv_const_sub, derivWithin_of_mem_nhds, LinearIsometryEquiv.comp_fderiv', LinearPMap.adjoint_apply_of_dense, tsupport_deriv_subset, hasStrictDerivAt_of_hasDerivAt_of_continuousAt, HasStrictDerivAt_ofNat, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, le_iff_norm_sqrt_mul_rpow, Real.fourier_smul_convolution_eq, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, DoubleCentralizer.smul_snd, deriv_div_const, HasFiniteFPowerSeriesAt.comp, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, Complex.det_conjLIE, not_differentiableAt_abs_zero, ContinuousLinearMap.integral_id_map, second_derivative_symmetric_of_eventually_of_real, MonotoneOn.ae_differentiableWithinAt, hasDerivWithinAt_iff_tendsto, DifferentiableAt.fun_add_iff_left, MeasureTheory.condExpL2_const_inner, ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero, curveIntegrable_restrictScalars_iff, ContDiffAt.hasStrictDerivAt', LinearMap.IsSymmetric.intCast, WeakFEPair.differentiable_Λ₀, MeasureTheory.integral_countable', IsCoercive.isClosed_range, RCLike.realLinearIsometryEquiv_apply, TemperedDistribution.laplacianCLM_apply, derivWithin.log, isBigO_rpow_zero_log_smul, DifferentiableWithinAt.ccos, ZSpan.ceil_eq_self_of_mem, contMDiffWithinAt_hom_bundle, HasDerivAt.star_conj, mdifferentiableOn_iff_of_subset_source', ProperCone.innerDual_innerDual, LinearMap.bound_of_ball_bound, Orientation.rightAngleRotation_map_complex, TensorProduct.ext_iff_inner_right_threefold, mem_contMDiffFiberwiseLinear_iff, intervalIntegral.integral_deriv_of_contDiffOn_Icc, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, Submodule.coe_prodEquivOfClosedCompl, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, ftaylorSeriesWithin_fun_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, ContinuousLinearMap.intervalIntegral_comp_comm, hasDerivAt_finCons, Orientation.areaForm_rightAngleRotation_left, HasFDerivAt.smul, Differentiable.ccosh, isPosSemidef_inner, ContinuousLinearMap.contMDiffAt, Differentiable.norm, Real.deriv_fourier, CStarAlgebra.exists_sum_four_nonneg, IsCompactOperator.finiteDimensional, isOpen_setOf_nat_le_rank, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, HasFDerivWithinAt.sin, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, differentiableAt_iff_comp_neg, isClosed_setOf_isCompactOperator, SchauderBasis.sum_succSub, DoubleCentralizer.coe_snd, ContinuousMultilinearMap.fin0_apply_norm, LinearIsometry.angle_map, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, ContinuousLinearMap.opNorm_le_bound₂, hasFPowerSeriesAt_iff, HasStrictFDerivAt.exp, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NumberField.mixedEmbedding.disjoint_negAt_plusPart, DifferentiableWithinAt.of_dslope, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorph_source, MeasureTheory.integral_convolution, ContinuousLinearMap.le_opNorm_enorm, DifferentiableAt.dist, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, Filter.EventuallyEq.nhdsNE_deriv, HasStrictFDerivAt.eq_implicitFunction, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, DifferentiableWithinAt.comp', fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, fderiv_sin, hasStrictDerivAt_pow, RightDerivMeasurableAux.le_of_mem_A, LinearMap.IsSymmetric.sort_roots_charpoly_eq_eigenvalues, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, derivWithin_mem_iff, DifferentiableOn.fun_neg, EuclideanGeometry.Sphere.finrank_orthRadius, AffineSubspace.isConnected_setOf_sSameSide, PositiveLinearMap.preGNS_norm_sq, ContinuousMultilinearMap.norm_curryMid, AlternatingMap.mkContinuous_norm_le', ConvexOn.univ_sSup_of_nat_affine_eq, differentiableOn_inv, ContinuousLinearEquiv.comp_right_differentiable_iff, TopologicalAddGroup.IsSES.integrate_apply, aestronglyMeasurable_withDensity_iff, ConvexOn.slope_le_leftDeriv_of_mem_interior, InnerProductGeometry.ConformalAt.preserves_angle, ContinuousAlternatingMap.ratio_le_opNorm, diffContOnCl_univ, Affine.Simplex.points_vsub_eulerPoint, hasDerivAt_of_tendstoUniformlyOnFilter, TensorProduct.assocIsometry_symm_apply, Submodule.starProjection_tendsto_closure_iSup, hasFDerivAt_exp_of_mem_ball, InnerProductGeometry.angle_smul_left_of_pos, LinearMap.exists_map_addHaar_eq_smul_addHaar', InnerProductSpace.gramSchmidt_mem_span, iteratedFDerivWithin_add_apply', domain_mvt, MeasureTheory.Measure.euclideanHausdorffMeasure_def, ModelWithCorners.uniqueDiffOn, norm_iteratedFDeriv_fderiv, MeasureTheory.Lp.toTemperedDistribution_smul_eq, Complex.differentiableOn_tsum_of_summable_norm, Submodule.reflection_mem_subspace_orthogonalComplement_eq_neg, dual_def, SchwartzMap.laplacian_eq_fourierMultiplierCLM, LinearMap.IsSymmetric.add, HasFDerivAtFilter.hasDerivAtFilter, HasDerivAt.inv, AffineMap.isOpenMap, TensorProduct.inner_map_map, Orientation.measure_orthonormalBasis, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, const_smul_mfderiv, ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_sub, fderiv_norm_sq, ContinuousLinearMap.opNorm_le_of_lipschitz, Filter.EventuallyEq.hasDerivAtFilter_iff, Seminorm.smul_le_smul, instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, AlternatingMap.norm_map_coord_zero, differentiableWithinAtProp_self_target, MeasureTheory.Measure.toSphere_apply_univ', HasMFDerivAt.const_smul, WeakDual.CharacterSpace.instStarHomClass, LinearMap.IsPositive.toLinearMap_symm, HasDerivAtFilter.fun_sum, Submodule.ClosedComplemented.of_isCompl_isClosed, TensorProduct.toLinearMap_mapInclIsometry, NonUnitalCommCStarAlgebra.toIsScalarTower, AnalyticOnNhd.differentiableOn, MeasureTheory.condExp_bot_ae_eq, HasStrictDerivAt.sqrt, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Function.HasTemperateGrowth.isBigO, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulₗᵢ, deriv_fun_const_smul', OrthogonalFamily.inner_right_dfinsupp, ContinuousLinearMap.isUnit_iff_bijective, LinearPMap.adjoint_graph_eq_graph_adjoint, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', EuclideanGeometry.angle_eq_pi_iff_sbtw, MeasureTheory.condExpL1_eq, norm_deriv_le_of_lip', UniqueDiffWithinAt.of_real, orthonormal_span, ModularGroup.smul_eq_lcRow0_add, deriv_cosh, OrthogonalFamily.projection_directSum_coeAddHom, HasFDerivWithinAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.innerSL_apply_comp, ApproximatesLinearOn.to_inv, conformalAt_iff', TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, ContinuousLinearMap.mdifferentiableAt, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, DifferentiableOn.sum, hasDerivAt_abs_pos, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, deriv_ofNat, ContDiffMapSupportedIn.structureMapLM_eq, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Orientation.oangle_smul_left_of_pos, HilbertBasis.hasSum_repr_symm, CStarMatrix.norm_def, ContinuousAlternatingMap.norm_image_sub_le, ProbabilityTheory.instIsGaussianMapNeg, ContMDiff.cle_arrowCongr, hasStrictFDerivAt_sub_const, ContinuousLinearMap.coe_deriv₂, IsMIntegralCurveAt.eventually_hasDerivAt, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, hasFDerivAt_stereoInvFunAux_comp_coe, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, differentiableWithinAt_Ioi_iff_Ici, LinearMap.adjoint_id, DifferentiableWithinAt.star, inner_smul_left, LipschitzWith.integral_lineDeriv_mul_eq, contDiff_succ_iff_hasFDerivAt, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', dist_lineMap_lineMap, MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, Affine.Triangle.dist_point_centroid, derivWithin_fun_pow', hasFDerivWithinAt_comp_add_left, extDeriv_apply, DifferentiableAt.csin, MeasureTheory.condExpL2_indicator_nonneg, DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, Affine.Triangle.orthocenter_reindex, HasCompactSupport.hasFDerivAt_convolution_left, ProbabilityTheory.charFunDual_stdGaussian, differentiableOn_zpow, Seminorm.cont_normedSpace_to_withSeminorms, Submodule.coe_prodEquivOfClosedCompl_symm, Affine.Simplex.circumradius_map, fderivWithin_mul, DoubleCentralizer.add_toProd, HasDerivWithinAt.fun_inv, Continuous.prod_mapL, MeasureTheory.ae_comp_linearMap_mem_iff, CFC.abs_eq_zero_iff, Bundle.ContinuousRiemannianMetric.isVonNBounded, HasDerivWithinAt.finCons, HasStrictDerivAt.clm_apply, HasFDerivWithinAt.sum, TemperedDistribution.smulLeftCLM_apply_apply, HasDerivAt.congr_deriv, DifferentiableAt.snd, IsCompactOperator.isCompact_closure_image_closedBall, HasDerivAt.tendsto_slope_zero_right, HasFDerivWithinAt.isLittleO, ContinuousLinearMap.closure_preimage, deriv_sqrt, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, IsSymmSndFDerivWithinAt.iteratedFDerivWithin_cons, nndist_lineMap_left, MeasureTheory.SimpleFunc.map_setToSimpleFunc, hasFDerivAt_pi, Orientation.inner_mul_areaForm_sub, ContinuousLinearMap.is_weak_closed_closedBall, ContinuousLinearMap.opNorm_le_of_re_inner_le, fderiv_inner_apply, differentiableOn_fst, contDiff_one_iff_deriv, ContinuousLinearMap.hasDerivAt_of_bilinear, Circle.norm_smul, ProbabilityTheory.covarianceOperator_of_not_memLp, AffineIsometryEquiv.pointReflection_midpoint_right, DirectSum.IsInternal.subordinateOrthonormalBasisIndex_def, hasFDerivWithinAt_snd, MeasureTheory.Measure.addHaar_closedBall', second_derivative_symmetric_of_eventually, uniformConvexOn_zero, HasFDerivAt.comp_hasDerivAt_of_eq, IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap, ContMDiff.coordChangeL, deriv2_sqrt_mul_log, GeneralSchauderBasis.finrank_range_proj, VectorField.lieBracketWithin_const_smul_left, mellin_comp_mul_left, DifferentiableOn.fun_smul, differentiableWithinAt_finCons, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, Real.hasStrictDerivAt_log_of_pos, derivWithin_comp_neg, ContinuousMultilinearMap.norm_ofSubsingleton_id, Affine.Simplex.altitude_def, HasFDerivWithinAt.fun_mul, hasFTaylorSeriesUpToOn_pi, derivWithin_pow', ZSpan.fundamentalDomain_ae_parallelepiped, IsBoundedBilinearMap.differentiableWithinAt, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', MeasureTheory.SignedMeasure.im_toComplexMeasure, HasDerivAtFilter.const_sub, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ContDiffWithinAt.fderivWithin_right, ContinuousLinearMap.LinearMap.IsSymmetricProjection.isStarProjection, Complex.rotation, AnalyticAt.hasStrictDerivAt, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, RCLike.complexLinearIsometryEquiv_apply, iter_deriv_pow, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, parallelepiped_single, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, HasStrictFDerivAt.finset_prod, Continuous.cfcₙ_nnreal', contDiffWithinAt_succ_iff_hasFDerivWithinAt, Filter.EventuallyEq.hasDerivWithinAt_iff, HasDerivWithinAt.limsup_slope_le, Filter.EventuallyEq.hasLineDerivWithinAt_iff, Asymptotics.IsBigO.hasFDerivAt, ContinuousAlternatingMap.le_of_opNNNorm_le, BoundedContinuousFunction.probCharDual_apply, hasFDerivWithinAt_apply, DifferentiableWithinAt.cos, Real.deriv2_negMulLog, intervalIntegral.inv_smul_integral_comp_add_div, InnerProductSpace.norm_rankOne, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Urysohns.CU.lim_eq_midpoint, HasFDerivAt.fun_sub, HasFDerivAt.const_cpow, hasFDerivAt_integral_of_dominated_loc_of_lip, DifferentiableWithinAt.add_const, measurableSet_of_differentiableAt_with_param, ContMDiffMap.coeFnLinearMap_apply, Submodule.isHilbertSumOrthogonal, ProbabilityTheory.IsGaussian.map_rotation_eq_self_of_forall_strongDual_eq_zero, DoubleCentralizer.neg_fst, EuclideanGeometry.Sphere.self_mem_orthRadius, PiTensorProduct.mapLMultilinear_toFun_apply, VectorField.mlieBracket_smul_right, CStarMatrix.inner_toCLM_conjTranspose_right, HasFDerivWithinAt.cosh, HasDerivAtFilter.fun_const_smul, LinearMap.singularValues_eq_zero_iff_le_finrank_range, Affine.Simplex.insphere_reindex, HasFiniteFPowerSeriesOnBall.fderiv, ContinuousLinearEquiv.norm_pos, MeasureTheory.integral_sum_dirac, HasFDerivAt.comp, Affine.Simplex.excenterExists_restrict, real_inner_I_smul_self, LinearIsometry.lTensor_def, iteratedDerivWithin_vcomp_three, HasFDerivAtFilter.add_const, HasFDerivWithinAt.uniqueDiffWithinAt_of_continuousLinearEquiv, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Orthonormal.inner_right_sum, mellin_comp_mul_right, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, GaussianFourier.integral_rexp_neg_mul_sq_norm, ContinuousLinearMap.antilipschitz_of_forall_le_inner_map, MDifferentiableAt.clm_apply, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, HasFDerivAt.isLittleO, convexOn_norm, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, ampleSet_univ, TensorProduct.edist_tmul_le, quasispectrum.instCompactSpace, fderiv_eq_smul_deriv, unitary.inner_map_map, CStarMatrix.toCLM_apply_single_apply, LinearMap.IsPositive.conj_adjoint, BoundedContinuousFunction.char_apply, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, MeasureTheory.Measure.addHaar_real_closedBall, tangentBundleCore_coordChange_achart, MeasureTheory.integral_sum_dirac_eq_tsum, HasStrictFDerivAt.rpow_const, ZLattice.comap_refl, intervalIntegral.differentiableOn_integral_of_continuous, hasStrictFDerivAt_exp_smul_const_of_mem_ball, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, differentiable_circleMap, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, LinearMap.IsSymmetric.pow, hasFDerivAt_prodMk_right, DoubleCentralizer.toProdMulOppositeHom_apply, HasDerivAt.mul_const, HasStrictDerivAt.fun_smul, ContinuousLinearMap.coeFn_compLp', derivWithin_const_mul, MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap, Unitization.cfcₙ_eq_cfc_inr, MeasureTheory.average_eq, ContinuousLinearEquiv.mfderivWithin_eq, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, LinearMap.IsSymmetric.orthogonalComplement_mem_invtSubmodule, EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, curveIntegralFun_zero, LinearMap.IsSymmetric.eigenvalues_eq_eigenvalues_iff, HasStrictFDerivAt.implicitToOpenPartialHomeomorphOfComplemented_apply, deriv_comp_sub_const, Affine.Simplex.sSameSide_point_incenter, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, iteratedFDeriv_add_apply', AffineMap.continuous_of_finiteDimensional, ProbabilityTheory.indepFun_iff_charFunDual_prod, iteratedFDeriv_succ_apply_left, ContDiffWithinAt.fderivWithin_apply, IsSymmSndFDerivAt.eq, le_iff_norm_sqrt_mul_sqrt_inv, Submodule.orthogonalProjectionFn_mem, MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOn, LinearMap.IsPositive.re_inner_nonneg_left, iteratedFDeriv_const_of_ne, hasDerivWithinAt_sub_const_iff, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, intervalIntegral.smul_integral_comp_add_mul, Complex.restrictScalars_toSpanSingleton', HasFDerivWithinAt.list_prod', Real.differentiableAt_negMulLog_iff, HasFDerivAt.continuousMultilinearMap_apply, Complex.hasSum_taylorSeries_on_eball, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, QuadraticMap.hasLineDerivAt, HasStrictFDerivAt.snd, fderiv_inv', MeasureTheory.Measure.integral_comp_inv_mul_right, MultilinearMap.norm_map_coord_zero, ContinuousLinearEquiv.contDiff, ContinuousLinearMapWOT.ext_inner_iff, Besicovitch.SatelliteConfig.exists_normalized_aux3, ContinuousLinearMap.coeFn_ofIsClosedGraph, cfcₙ_integral', ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, AffineSubspace.isPreconnected_setOf_sSameSide, Complex.rectangle_eq_convexHull, Continuous.fderiv_one, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, norm_inner_div_norm_mul_norm_eq_one_iff, MeasureTheory.lpMeas.aestronglyMeasurable, IsLocalMinOn.fderivWithin_eq_zero, HasStrictDerivAt.star, ProbabilityTheory.integral_tilted_mul_eq_cgf, Real.deriv2_mul_log, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, AffineIsometryEquiv.coe_toAffineEquiv, FormalMultilinearSeries.comp_assoc, Affine.Triangle.dist_orthogonalProjectionSpan_faceOpposite_eq_iff_two_zsmul_oangle_eq, PiTensorProduct.tprodL_coe, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, MeasureTheory.Measure.addHaar_smul, HasFPowerSeriesWithinAt.comp, Submodule.mem_iff_norm_starProjection, differentiable_neg_iff, MeasureTheory.hasSum_integral_sum_dirac, Complex.reCLM_apply, fderivWithin_pow', Real.hasDerivAt_negMulLog, AffineIsometryEquiv.coe_toContinuousAffineEquiv, HasFDerivAtFilter.sub_const, ContinuousLinearEquiv.ofBijective_apply_symm_apply, Orientation.abs_volumeForm_apply_le, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, continuousMultilinearCurryFin1_apply, LinearMap.IsSymmetric.eigenvectorBasis_def, IsCoercive.antilipschitz, PiLp.hasStrictFDerivAt_toLp, Complex.conjLIE_symm, LinearMap.card_support_singularValues, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, StrictConvexOn.slope_lt_of_hasDerivAt, LinearMap.IsSymmetric.apply_clm, deriv_id', Orthonormal.comp_linearIsometry, hasStrictFDerivAt_euclidean, hasFDerivAt_finset_prod, unitary.linearIsometryEquiv_coe_apply, Affine.Simplex.signedInfDist_incenter, HilbertBasis.finite_spans_dense, nnnorm_cfcₙ_lt, aemeasurable_derivWithin_Ioi, MeasureTheory.Measure.addHaar_image_homothety, LinearMap.IsSymmetric.mul_of_commute, MeasureTheory.setIntegral_const, HasStrictDerivAt.fun_pow, norm_combo_lt_of_ne, InnerProductSpace.HarmonicContOnCl.differentiableAt, norm_iteratedFDeriv_clm_apply_const, LinearIsometry.adjoint_comp_self, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq bridge: BoxIntegral.hasIntegralIndicatorConst

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cobounded_neBot 📖	mathematical	—	Filter.NeBot Bornology.cobounded PseudoMetricSpace.toBornology SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup	—	Filter.neBot_iff Bornology.cobounded_eq_bot_iff Bornology.isBounded_univ unbounded_univ
discreteTopology_zmultiples 📖	mathematical	—	DiscreteTopology AddSubgroup NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SetLike.instMembership AddSubgroup.instSetLike AddSubgroup.zmultiples instTopologicalSpaceSubtype UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup	—	IsAddTorsionFree.of_module_rat eq_or_ne AddSubgroup.zmultiples_zero_eq_bot Subsingleton.discreteTopology Unique.instSubsingleton discreteTopology_iff_isOpen_singleton_zero instSeparatelyContinuousAddOfContinuousAdd IsTopologicalAddGroup.toContinuousAdd AddSubgroup.instIsTopologicalAddGroupSubtypeMem SeminormedAddCommGroup.toIsTopologicalAddGroup isOpen_induced_iff Metric.isOpen_ball Set.ext AddSubgroup.mem_zmultiples_iff Set.mem_preimage mem_ball_zero_iff Set.mem_singleton_iff AddSubgroup.coe_zero norm_zsmul Int.norm_cast_rat Int.norm_eq_abs mul_lt_iff_lt_one_left IsStrictOrderedRing.toMulPosStrictMono Real.instIsStrictOrderedRing MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE norm_pos_iff Int.cast_one Int.cast_abs Int.cast_lt IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid Real.instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero Int.abs_lt_one_iff smul_eq_zero instIsTorsionFreeIntOfIsAddTorsionFree Int.instIsCancelMulZero
exists_lt_norm 📖	mathematical	—	Real Real.instLT Norm.norm NormedAddCommGroup.toNorm	—	exists_ne NormedField.exists_lt_norm norm_smul toNormSMulClass div_lt_iff₀ MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE IsStrictOrderedRing.toMulPosStrictMono Real.instIsStrictOrderedRing norm_pos_iff
ext 📖	—	SemigroupAction.toSMul Monoid.toSemigroup MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField MulAction.toSemigroupAction DistribMulAction.toMulAction AddCommMonoid.toAddMonoid AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup Module.toDistribMulAction toModule	—	—	—
ext_iff 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField MulAction.toSemigroupAction DistribMulAction.toMulAction AddCommMonoid.toAddMonoid AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup Module.toDistribMulAction toModule	—	ext
noncompactSpace 📖	mathematical	—	NoncompactSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup	—	unbounded_univ IsCompact.isBounded exists_ne Metric.isClosedEmbedding_of_pairwise_le_dist instDiscreteTopologyNat norm_pos_iff dist_eq_norm norm_smul toNormSMulClass Mathlib.Tactic.Push.not_and_eq sub_ne_zero Function.Embedding.injective one_mul le_refl Topology.IsClosedEmbedding.noncompactSpace Nat.instNoncompactSpace
norm_smul_le 📖	mathematical	—	Real Real.instLE Norm.norm SeminormedAddCommGroup.toNorm SemigroupAction.toSMul Monoid.toSemigroup MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField MulAction.toSemigroupAction DistribMulAction.toMulAction AddCommMonoid.toAddMonoid AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup Module.toDistribMulAction toModule Real.instMul NormedField.toNorm	—	—
restrictScalars_eq 📖	mathematical	—	restrictScalars	—	ext algebraMap_smul
toIsBoundedSMul 📖	mathematical	—	IsBoundedSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SeminormedAddCommGroup.toPseudoMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid SeminormedAddCommGroup.toAddCommGroup SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid toModule	—	NormSMulClass.toIsBoundedSMul toNormSMulClass
toNormSMulClass 📖	mathematical	—	NormSMulClass NormedField.toNorm SeminormedAddCommGroup.toNorm SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup toModule	—	NormedDivisionRing.toNormSMulClass IsBoundedSMul.of_norm_smul_le norm_smul_le
unbounded_univ 📖	mathematical	—	Bornology.IsBounded PseudoMetricSpace.toBornology SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup Set.univ	—	isBounded_iff_forall_norm_le exists_lt_norm LT.lt.not_ge

NormedSpace.Core

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
norm_eq_zero_iff 📖	mathematical	NormedSpace.Core	Norm.norm Real Real.instZero NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	—
toCore 📖	mathematical	NormedSpace.Core	SeminormedSpace.Core	—	—

PUnit

Definitions

Name	Category	Theorems
normedAlgebra 📖	CompOp	5 math math: Manifold.IsImmersionAtOfComplement.ofOpen, Manifold.IsImmersionOfComplement.ofOpen, Manifold.IsImmersionAtOfComplement.of_opens, Manifold.IsImmersionOfComplement.id, Manifold.IsImmersionOfComplement.of_opens

Pi

Definitions

Name	Category	Theorems
normedAlgebra 📖	CompOp	—
normedSpace 📖	CompOp	124 math math: NumberField.mixedEmbedding.fundamentalDomain_integerLattice, MeasureTheory.eval_integral, PiLp.contDiff_toLp, ContinuousMultilinearMap.cpolynomialOn, ZSpan.volume_real_fundamentalDomain, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, FormalMultilinearSeries.radius_pi_eq_iInf, ZLattice.covolume_eq_det_inv, hasFPowerSeriesOnBall_pi_iff, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContinuousAlternatingMap.opNNNorm_pi, analyticWithinAt_pi_iff, ContinuousAlternatingMap.piLIE_apply_apply, ContinuousMultilinearMap.contDiffAt, Module.Basis.parallelepiped_basisFun, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, analyticOnNhd_pi_iff, contDiffAt_pi', ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, contDiff_apply, Matrix.linfty_opNNNorm_eq_opNNNorm, NumberField.Units.instZLattice_unitLattice, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, contMDiffWithinAt_pi_space, contDiff_update, Matrix.linfty_opNNNorm_toMatrix, ZSpan.volume_fundamentalDomain, hasFTaylorSeriesUpToOn_pi', ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, contMDiffOn_pi_space, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, AnalyticOn.pi, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, ContinuousMultilinearMap.analyticAt, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, contDiff_pi', HasFPowerSeriesWithinAt.pi, ContinuousMultilinearMap.contDiff, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, ContinuousMultilinearMap.opNorm_pi, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, contDiff_apply_apply, ContinuousMultilinearMap.iteratedFDeriv_eq, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, AnalyticWithinAt.pi, contDiffAt_apply, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, ContinuousMultilinearMap.cpolynomialAt, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, ContinuousLinearMap.norm_single, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, hasFPowerSeriesAt_pi_iff, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, ContinuousAlternatingMap.piLIE_symm_apply_apply, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, PiLp.analyticOn_ofLp, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ZLattice.volume_image_eq_volume_div_covolume, PiLp.analyticOn_toLp, ContinuousMultilinearMap.norm_iteratedFDeriv_le', SmoothBumpCovering.embeddingPiTangent_injOn, hasFPowerSeriesWithinAt_pi_iff, MeasureTheory.charFunDual_eq_pi_iff, ContinuousMultilinearMap.changeOriginSeries_support, HasFPowerSeriesOnBall.pi, ContinuousMultilinearMap.piₗᵢ_symm_apply, analyticOn_pi_iff, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, Matrix.linfty_opNorm_toMatrix, ContinuousMultilinearMap.opNNNorm_pi, ContinuousMultilinearMap.analyticOn, contDiff_single, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, SmoothBumpCovering.embeddingPiTangent_injective, PiLp.contDiff_ofLp, ContinuousMultilinearMap.analyticOnNhd, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, hasFPowerSeriesWithinOnBall_pi_iff, ZSpan.fundamentalDomain_pi_basisFun, contDiffWithinAt_pi, AnalyticOnNhd.pi, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, HasFPowerSeriesAt.pi, Matrix.linfty_opNorm_eq_opNorm, ContinuousLinearMap.norm_pi_le_of_le, contDiffOn_pi, ContinuousLinearMap.norm_single_le_one, ContinuousMultilinearMap.analyticWithinAt, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, AnalyticAt.pi, contMDiff_pi_space, MeasureTheory.charFunDual_pi, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, FormalMultilinearSeries.le_radius_pi, contDiffAt_pi, ContinuousMultilinearMap.piₗᵢ_apply, Module.Basis.opNNNorm_le, FormalMultilinearSeries.radius_pi_le, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, Module.Basis.opNorm_le, HasFPowerSeriesWithinOnBall.pi, ContinuousAlternatingMap.opNorm_pi, contMDiffAt_pi_space, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, NumberField.Units.basisOfIsMaxRank_fundSystem, AnalyticOnNhd.eval_mvPolynomial, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, contDiff_pi, analyticAt_pi_iff, contDiffOn_apply, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, hasFTaylorSeriesUpToOn_pi, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, contDiffOn_pi'

Prod

Definitions

Name	Category	Theorems
normedAlgebra 📖	CompOp	—
normedSpace 📖	CompOp	525 math math: contDiffAt_snd, TangentBundle.tangentMap_tangentBundle_pure, contMDiff_prod_assoc, mfderiv_prod_eq_add, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, instLieGroup, Bundle.ContMDiffRiemannianMetric.contMDiff, Bundle.mdifferentiableAt_proj, contDiff_fst, ContinuousAlternatingMap.opNorm_prod, mdifferentiableAt_sub_section, ContinuousLinearMap.analyticWithinAt_bilinear, ContMDiffMul.prod, ContinuousLinearMap.opNorm_prod, ContinuousLinearMap.norm_inr_le_one, contDiff_prod_iff, MDifferentiableOn.finsum_section_of_locallyFinite, ModelWithCorners.range_prod, Bundle.contMDiffOn_zeroSection, MDifferentiableAt.clm_bundle_apply, ContDiffAt.implicitFunction_def, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, MDifferentiableAt.mfderiv_prod, MeasureTheory.contDiffOn_convolution_left_with_param, mdifferentiableWithinAt_totalSpace, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, ContMDiffOn.prodMk, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, norm_jacobiTheta₂_term_fderiv_ge, ContinuousLinearMap.norm_inl_le_one, analyticWithinAt_snd, contDiff_prodAssoc_symm, tangentMapWithin_prodSnd, ContMDiffOn.mlieBracketWithin_vectorField, ContMDiffWithinAt.mlieBracketWithin_vectorField, mdifferentiableAt_iff_localFrame_coeff, Bundle.Trivialization.contMDiffOn_section_baseSet_iff, ContDiffBumpBase.smooth, MDifferentiableOn.prodMk_space, MDifferentiableOn.smul_const_section, ContMDiffWithinAt.sub_section, Manifold.IsImmersionOfComplement.prodMap, contMDiff_addInvariantVectorField, HasStrictFDerivAt.rightFun_implicitFunctionDataOfProdDomain, mdifferentiableWithinAt_smul_const_section, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, mdifferentiableAt_add_section, HasMFDerivWithinAt.prodMk, ContMDiffAt.finsum_section_of_locallyFinite, contDiffWithinAt_fst, ContMDiffAdd.prod, ContMDiffMul.contMDiff_mul, Bundle.contMDiffWithinAt_zeroSection, mdifferentiableOn_snd, contMDiff_mul, contMDiff_mulInvariantVectorField, contMDiffWithinAt_snd, Bundle.Trivialization.contMDiffOn, contMDiffWithinAt_prod_iff, UniqueMDiffOn.prod, MDifferentiableWithinAt.finsum_section_of_locallyFinite, IsLocalFrameOn.contMDiffAt_of_coeff, contMDiff_equivTangentBundleProd_symm, contDiff_prodAssoc, mdifferentiableWithinAt_section, MDifferentiableWithinAt.prodMk_space, contMDiffOn_baseSet_iff_localFrame_coeff, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, ContMDiffWithinAt.add_section, ContDiffAt.prodMap, ContMDiffAt.add_section, ContinuousLinearMap.norm_fst_le, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, ContMDiffAdd.contMDiff_add, Manifold.IsSmoothEmbedding.prodMap, MDifferentiable.clm_bundle_apply₂, ContDiffAt.fst'', Manifold.IsImmersionAtOfComplement.prodMap, Diffeomorph.coe_prodCongr, hasMFDerivAt_fst, writtenInExtChart_prod, Bundle.contMDiffAt_zeroSection, ModelWithCorners.prod_target, ContinuousLinearMap.opNNNorm_prod, contMDiffAt_mulInvariantVectorField, MDifferentiableAt.clm_prodMap, MDifferentiable.prodMap, equivTangentBundleProd_apply, contMDiffWithinAt_prod_module_iff, ContinuousLinearMap.analyticOn_bilinear, MDifferentiable.clm_bundle_apply, MDifferentiableWithinAt.clm_bundle_apply₂, HasMFDerivWithinAt.prodMap, mdifferentiableAt_addInvariantVectorField, ContDiff.prodMk, ContMDiff.sum_section_of_locallyFinite, ContMDiff.contMDiff_tangentMap, MDifferentiableAt.mpullback_vectorField, ContMDiffWithinAt.sum_section, MeasureTheory.charFunDual_prod, MeasureTheory.contDiffOn_convolution_right_with_param, MDifferentiableAt.sum_section, Module.Basis.prod_addHaar, mdifferentiableAt_fst, Bundle.Trivialization.mdifferentiableAt_section_iff, analyticOnNhd_snd, MDifferentiableOn.prodMk, mfderiv_prod_eq_add_comp, MDifferentiableAt.prodMap', NumberField.mixedEmbedding.fundamentalDomain_idealLattice, AnalyticWithinAt.prod, ContMDiffAt.prodMap, HasFPowerSeriesWithinOnBall.prod, ImplicitFunctionData.implicitFunction_def, mdifferentiableAt_totalSpace, mdifferentiableOn_fst, mdifferentiable_mulInvariantVectorField, contDiff_prodMk_right, contDiffOn_fst, mdifferentiableOn_prod_module_iff, ContDiff.prodMap, ContMDiffOn.finsum_section_of_locallyFinite, MDifferentiableOn.sum_section_of_locallyFinite, ContDiffWithinAt.prodMap, MDifferentiableAt.prodMk, ContMDiffWithinAt.neg_section, analyticAt_smul, Diffeomorph.prodCongr_symm, MeasureTheory.charFunDual_eq_prod_iff, ContMDiffWithinAt.mpullbackWithin_vectorField_inter, ContDiff.fst', mdifferentiableAt_hom_bundle, IsLocalFrameOn.mdifferentiableAt_of_coeff_aux, mdifferentiable_fst, ContDiffPointwiseHolderAt.snd, Bundle.Trivialization.continuousLinearEquivAt_prod, mdifferentiableWithinAt_neg_section, modelWithCorners_prod_coe, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, Bundle.TotalSpace.isManifold, ContMDiffAt.const_smul_section, IsBoundedBilinearMap.contDiff, MeasureTheory.hasFDerivAt_convolution_right_with_param, contMDiff_vectorSpace_iff_contDiff, mdifferentiableAt_snd, ContMDiffOn.mpullbackWithin_vectorField_inter, mfderiv_prodMap, ContMDiffAt.clm_apply_of_inCoordinates, ContMDiffWithinAt.prodMk_space, Bundle.Trivialization.mdifferentiableWithinAt_totalSpace_iff, MDifferentiable.mpullback_vectorField, mdifferentiable_smul_const_section, Bundle.Trivialization.mdifferentiableOn_section_baseSet_iff, UniqueMDiffWithinAt.bundle_preimage', FiberBundle.exists_contMDiffOn_extend, AnalyticAt.prod, MDifferentiableAt.finsum_section_of_locallyFinite, IsContMDiffRiemannianBundle.exists_contMDiff, ModelWithCorners.prod_symm_apply, contMDiff_snd, ContMDiffAt.clm_bundle_apply, contMDiffAt_prod_iff, MDifferentiableOn.clm_prodMap, tangentMap_prodSnd, mdifferentiableAt_neg_section, Bundle.Trivialization.contMDiffOn_localFrame_baseSet, ContMDiffAt.prodMk_space, HasMFDerivAt.prodMap, MDifferentiableAt.clm_bundle_apply₂, ContMDiffWithinAt.mpullback_vectorField_of_mem_nhdsWithin_of_eq, FiberBundle.writtenInExtChartAt_trivializationAt, IsLocalFrameOn.mdifferentiableOn_of_coeff, ModelWithCorners.prod_source, ContMDiffWithinAt.mpullback_vectorField_preimage, ContinuousMultilinearMap.prodL_apply, hasMFDerivWithinAt_fst, MDifferentiableWithinAt.mpullbackWithin_vectorField_inter_of_eq, WithLp.contDiff_toLp, snd_integral, MDifferentiableOn.prodMap, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, MDifferentiableAt.smul_section, mdifferentiableAt_prod_module_iff, ContMDiffWithinAt.mpullback_vectorField_preimage_of_eq, FiberBundle.mdifferentiableAt_extend, swap_integral, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, ContDiffPointwiseHolderAt.prodMk, ContDiffWithinAt.prodMap', IsBoundedBilinearMap.isBoundedLinearMap_deriv, modelWithCorners_prod_coe_symm, MDifferentiable.prodMk_space, contMDiff_smul, MDifferentiableWithinAt.clm_apply_of_inCoordinates, Bundle.mdifferentiableWithinAt_proj, IsLocalFrameOn.contMDiffOn, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, MDifferentiableOn.clm_bundle_apply, MDifferentiableWithinAt.prodMk, Bundle.Trivialization.mdifferentiableOn_section_iff, tangentMapWithin_prodFst, ContMDiffWithinAt.finsum_section_of_locallyFinite, Bundle.contMDiffWithinAt_totalSpace, Diffeomorph.coe_prodComm, Bundle.Trivialization.contMDiffWithinAt_iff, mdifferentiableWithinAt_sub_section, Bundle.mdifferentiableOn_proj, contDiffOn_prod_iff, ContMDiffOn.prodMk_space, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, ContinuousLinearMap.norm_inr, mdifferentiableWithinAt_add_section, ContMDiffWithinAt.mpullbackWithin_vectorField', ContinuousLinearMap.analyticOnNhd_bilinear, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, equivTangentBundleProd_symm_apply_snd, MDifferentiable.sum_section, ContMDiffWithinAt.clm_bundle_apply₂, WithLp.contDiff_ofLp, iteratedFDerivWithin_prodMk, HasStrictFDerivAt.leftFun_implicitFunctionDataOfProdDomain, Module.Basis.prod_parallelepiped, IsLocalFrameOn.contMDiffAt, contMDiffAt_hom_bundle, ContMDiffOn.prodMap, MDifferentiable.sum_section_of_locallyFinite, ContMDiffRing.contMDiff_mul, contMDiff_prod_iff, FiberBundle.extChartAt, MDifferentiableWithinAt.sum_section_of_locallyFinite, ContMDiffAt.mlieBracket_vectorField, ContMDiffOn.add_section, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, mfderiv_prod_right, MDifferentiable.clm_prodMap, writtenInExtChartAt_prod, ContMDiff.finsum_section_of_locallyFinite, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, analyticAt_fst, Bundle.contMDiffWithinAt_proj, ModelWithCorners.boundary_of_boundaryless_left, modelWithCornersSelf_prod, Bundle.contMDiffAt_totalSpace, analyticWithinAt_fst, MDifferentiableAt.clm_apply_of_inCoordinates, MDifferentiableAt.prodMk_space, WithLp.analyticOn_toLp, ContDiffAt.snd', ContMDiffWithinAt.clm_bundle_apply, ContMDiff.clm_bundle_apply, contDiff_add, UniqueMDiffOn.tangentBundle_proj_preimage, MeasureTheory.average_pair, ContMDiff.clm_bundle_apply₂, mdifferentiable_snd, MDifferentiableOn.sum_section, mdifferentiableAt_prod_iff, MDifferentiable.prodMk, OpenPartialHomeomorph.extend_prod, FiberBundle.contMDiffAt_extend', contMDiffWithinAt_fst, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, Bundle.contMDiffOn_proj, ContinuousMultilinearMap.opNNNorm_prod, ContMDiffWithinAt.prodMk, Bundle.contMDiff_proj, HasFPowerSeriesWithinAt.prod, contMDiffOn_fst, ImplicitFunctionData.contDiffAt_implicitFunction, MDifferentiableAt.sum_section_of_locallyFinite, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, contDiffAt_inner, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, MDifferentiableOn.mpullback_vectorField_preimage, contMDiffOn_prod_iff, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, ContMDiffWithinAt.mpullbackWithin_vectorField_of_mem_of_eq, Manifold.IsImmersionAt.prodMap, IsManifold.prod, HasFTaylorSeriesUpToOn.prodMk, mfderivWithin_prodMap, integral_pair, SmoothBumpCovering.embeddingPiTangent_injOn, UniqueMDiffWithinAt.bundle_preimage, contMDiffAt_vectorSpace_iff_contDiffAt, ContMDiff.neg_section, Manifold.IsImmersion.prodMap, Bundle.mdifferentiableWithinAt_zeroSection, mfderiv_snd, ContMDiffAt.clm_prodMap, mdifferentiable_addInvariantVectorField, ContDiffAt.prodMap', VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm, modelWithCorners_prod_toPartialEquiv, fst_integral, Bundle.Trivialization.contMDiff_iff, ContMDiffWithinAt.sum_section_of_locallyFinite, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, ExistsContDiffBumpBase.y_smooth, Bundle.contMDiff_zeroSection, contDiff_inner, ContDiff.mlieBracket_vectorField, FiberBundle.extChartAt_target, IsContDiffImplicitAt.contDiffAt, contMDiffAt_localFrame_of_mem, mdifferentiableWithinAt_snd, mfderiv_prodMk, hasMFDerivWithinAt_snd, contMDiff_prod_module_iff, mdifferentiableAt_section, Bundle.Trivialization.contMDiffAt_section_iff, ContinuousLinearMap.norm_fst, Bundle.mdifferentiable_proj, ContMDiffWithinAt.clm_apply_of_inCoordinates, FiberBundle.writtenInExtChartAt_trivializationAt_symm, ModelWithCorners.boundary_of_boundaryless_right, ContMDiffAt.sub_section, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, ModelWithCorners.range_eq_univ_prod, ModelWithCorners.prod_apply, ContMDiff.clm_prodMap, SmoothBumpCovering.embeddingPiTangent_injective, MDifferentiableWithinAt.mpullback_vectorField_preimage, MDifferentiableWithinAt.clm_bundle_apply, ContMDiffSection.contMDiff, contDiff_mul, IsManifold.mem_maximalAtlas_prod, analyticOnNhd_fst, ContDiffAt.fst', contMDiff_equivTangentBundleProd, ContinuousMultilinearMap.prodL_symm_apply, ContinuousLinearMap.norm_inl, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HasFPowerSeriesOnBall.prod, UniqueMDiffOn.bundle_preimage, Bundle.Trivialization.contMDiffAt_iff, ContMDiffOn.const_smul_section, Bundle.contMDiffAt_section, Bundle.Trivialization.contMDiffWithinAt_section, ModelWithCorners.boundary_prod, ContinuousLinearMap.fpowerSeriesBilinear_radius, contDiff_smul, MDifferentiableOn.mpullbackWithin_vectorField_inter, ContMDiffAt.clm_bundle_apply₂, ContMDiffWithinAt.mpullbackWithin_vectorField_inter_of_eq, mDifferentiableOn_sub_section, equivTangentBundleProd_eq_tangentMap_prod_tangentMap, contDiffOn_snd, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, mdifferentiable_prod_iff, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, mdifferentiableOn_prod_iff, Bundle.Trivialization.contMDiffOn_symm, mdifferentiableAt_mulInvariantVectorField, mfderivWithin_prodMk, contMDiffAt_iff_localFrame_coeff, contMDiffAt_prod_module_iff, ContMDiffOn.sum_section_of_locallyFinite, ContinuousAlternatingMap.prodLIE_apply, ContMDiffAt.prodMap', contDiffAt_prod_iff, iteratedFDeriv_prodMk, tangentMap_prodFst, ContMDiffCovariantDerivativeOn.contMDiff, MDifferentiableWithinAt.mpullbackWithin_vectorField_inter, ContMDiffOn.contMDiffOn_tangentMapWithin, mdifferentiable_sub_section, ContMDiffWithinAt.const_smul_section, mdifferentiable_neg_section, ContMDiffWithinAt.prodMap', ContMDiffAt.sum_section_of_locallyFinite, mdifferentiableWithinAt_fst, MDifferentiable.finsum_section_of_locallyFinite, ContMDiffOn.mpullback_vectorField_preimage, IsLocalFrameOn.contMDiffOn_of_coeff, ModelWithCorners.BoundarylessManifold.prod, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, contMDiff_add, HasFPowerSeriesAt.prod, FiberBundle.exists_mdifferentiableOn_extend, Diffeomorph.prodComm_symm, instLieAddGroup, HasMFDerivAt.prodMk, ContDiff.contDiff_fderiv_apply, ContMDiff.sub_section, MDifferentiableWithinAt.mpullback_vectorField_preimage_of_eq, FormalMultilinearSeries.radius_prod_eq_min, analyticAt_mul, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, ContMDiffWithinAt.mpullbackWithin_vectorField, ContMDiffAt.prodMk, Bundle.contMDiffAt_proj, contMDiffAt_addInvariantVectorField, contMDiff_tangentBundleModelSpaceHomeomorph, ContMDiffWithinAt.clm_prodMap, MDifferentiableAt.smul_const_section, ContMDiffAt.mpullback_vectorField_preimage, ContMDiffOn.smul_section_of_tsupport, mdifferentiableWithinAt_prod_module_iff, ContMDiffWithinAt.smul_section, mdifferentiable_add_section, hasMFDerivAt_snd, ContDiff.snd', MDifferentiableOn.smul_section, MDifferentiableWithinAt.prodMap, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, Bundle.contMDiffWithinAt_section, Bundle.mdifferentiableOn_zeroSection, ContMDiffSection.mdifferentiable', ContinuousLinearMap.norm_snd_le, contMDiff_tangentBundleModelSpaceHomeomorph_symm, IsContDiffImplicitAt.implicitFunction_def, mfderiv_fst, mfderivWithin_fst, ContMDiffWithinAt.mpullbackWithin_vectorField_of_eq, ContMDiffOn.sub_section, ContDiffOn.prodMk, ContMDiffSection.mdifferentiableAt, contDiffWithinAt_snd, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, MDifferentiableOn.smul_section_of_tsupport, ContMDiff.add_section, ContMDiffOn.clm_prodMap, contDiffWithinAt_prod_iff, Bundle.Prod.contMDiffVectorBundle, ContMDiffOn.sum_section, AnalyticOn.prod, ContMDiffOn.neg_section, UniqueMDiffWithinAt.prod, mdifferentiable_prod_module_iff, equivTangentBundleProd_symm_apply_proj, ContMDiffSection.mdifferentiable, ContinuousLinearMap.norm_snd, HasStrictFDerivAt.pt_implicitFunctionDataOfProdDomain, contDiff_snd, Bundle.Trivialization.contMDiffOn_iff, ContMDiff.prodMk_space, ContMDiffWithinAt.prodMap, mdifferentiable_smul_section, ContDiffWithinAt.prodMk, Bundle.mdifferentiable_zeroSection, Bundle.Trivialization.mdifferentiableWithinAt_section_iff, contMDiffAt_fst, mdifferentiableWithinAt_prod_iff, ContMDiffWithinAt.mpullbackWithin_vectorField_of_mem, VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm, IsLocalFrameOn.mdifferentiableAt_of_coeff, ContinuousLinearMap.analyticAt_bilinear, contDiffOn_fderivWithin_apply, ContMDiffAt.sum_section, ContMDiff.const_smul_section, ContDiffAt.prodMk, tangentMap_prod_right, contMDiffOn_vectorSpace_iff_contDiffOn, ContDiffOn.prodMap, contDiffAt_fst, ContinuousMultilinearMap.opNorm_prod, ContMDiffOn.clm_bundle_apply, Bundle.Trivialization.contMDiffOn_section_iff, tangentMap_prod_left, mdifferentiableOn_add_section, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, ContMDiffSection.contMDiff_toFun, ContMDiffAt.smul_section, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, contDiffGroupoid_prod, ContinuousAlternatingMap.opNNNorm_prod, ModelWithCorners.interior_prod, contMDiffOn_snd, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, mfderiv_prod_left, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, MeasureTheory.contDiffOn_convolution_right_with_param_aux, MDifferentiableWithinAt.clm_prodMap, contMDiffOn_prod_module_iff, ContMDiffAt.neg_section, ContDiffPointwiseHolderAt.fst, MDifferentiableWithinAt.prodMap', mdifferentiableWithinAt_hom_bundle, IsLocalFrameOn.contMDiffAt_of_coeff_aux, ContDiffAt.snd'', Bundle.Trivialization.contMDiffOn_symm_trans, Real.contDiffAt_rpow_of_ne, contMDiff_fst, Bundle.mdifferentiableAt_zeroSection, boundary_product, contDiff_prodMk_left, MDifferentiableAt.prodMap, ContMDiff.sum_section, VectorBundle.prod, mdifferentiableOn_neg_section, Bundle.Trivialization.mdifferentiableAt_totalSpace_iff, isBoundedLinearMap_prod_multilinear, ContMDiff.prodMap, contMDiff_snd_tangentBundle_modelSpace, ContMDiffWithinAt.mpullbackWithin_vectorField_of_eq', contMDiffWithinAt_hom_bundle, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, mfderivWithin_snd, analyticOn_snd, MDifferentiableOn.clm_bundle_apply₂, contMDiffAt_snd, ContMDiffOn.clm_bundle_apply₂, mfderiv_prod_eq_add_apply, extChartAt_prod, ContMDiff.mpullback_vectorField, analyticOn_fst, Bundle.Trivialization.Bundle.Trivialization.mdifferentiable, MDifferentiableWithinAt.sum_section, WithLp.analyticOn_ofLp, ContMDiff.smul_section, HasStrictFDerivAt.implicitFunctionOfProdDomain_def, norm_jacobiTheta₂_term_fderiv_le, analyticAt_snd, ContMDiffWithinAt.mpullback_vectorField_of_mem_nhdsWithin, Manifold.LiftSourceTargetPropertyAt.prodMap, MDifferentiableWithinAt.smul_section, ContMDiffOn.smul_section, contMDiffOn_iff_localFrame_coeff, ProbabilityTheory.indepFun_iff_charFunDual_prod, AnalyticOnNhd.prod, ContMDiff.prodMk

PseudoEMetricSpace

Definitions

Name	Category	Theorems
ofSeminormedSpaceCore 📖	CompOp	—

PseudoMetricSpace

Definitions

Name	Category	Theorems
ofSeminormedSpaceCore 📖	CompOp	—
ofSeminormedSpaceCoreReplaceAll 📖	CompOp	—
ofSeminormedSpaceCoreReplaceTopology 📖	CompOp	—
ofSeminormedSpaceCoreReplaceUniformity 📖	CompOp	—

RealNormedSpace

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cobounded_neBot 📖	mathematical	—	Filter.NeBot Bornology.cobounded PseudoMetricSpace.toBornology SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup	—	NormedSpace.cobounded_neBot
noncompactSpace 📖	mathematical	—	NoncompactSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup	—	NormedSpace.noncompactSpace NontriviallyNormedField.infinite

RestrictScalars

Definitions

Name	Category	Theorems
normedAlgebra 📖	CompOp	—
normedSpace 📖	CompOp	—

SeminormedAddCommGroup

Definitions

Name	Category	Theorems
ofCore 📖	CompOp	—
ofCoreReplaceAll 📖	CompOp	—
ofCoreReplaceTopology 📖	CompOp	—
ofCoreReplaceUniformity 📖	CompOp	—

SeminormedSpace.Core

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
norm_nonneg 📖	mathematical	SeminormedSpace.Core	Real Real.instLE Real.instZero Norm.norm	—	—
norm_smul 📖	mathematical	SeminormedSpace.Core	Norm.norm SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid Real Real.instMul NormedField.toNorm	—	—
norm_triangle 📖	mathematical	SeminormedSpace.Core	Real Real.instLE Norm.norm AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup AddCommGroup.toAddCommMonoid Real.instAdd	—	—

SeparationQuotient

Definitions

Name	Category	Theorems
instNormedAlgebra 📖	CompOp	—
instNormedSpace 📖	CompOp	—

Subalgebra

Definitions

Name	Category	Theorems
toNormedAlgebra 📖	CompOp	—

SubalgebraClass

Definitions

Name	Category	Theorems
toNormedAlgebra 📖	CompOp	4 math math: Subalgebra.spectrum_sUnion_connectedComponentIn, Subalgebra.spectrum_eq_of_isPreconnected_compl, Subalgebra.frontier_subset_frontier, Subalgebra.frontier_spectrum

Submodule

Definitions

Name	Category	Theorems
normedSpace 📖	CompOp	28 math math: instStrictConvexSpace, AffineIsometryEquiv.ofTop_apply, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, AffineSubspace.coe_subtypeₐᵢ, contDiffOn_stereoToFun, AffineIsometryEquiv.coe_ofEq_apply, AffineSubspace.isometryEquivMap.toAffineMap_eq, AffineIsometryEquiv.ofTop_symm_apply_coe, AffineIsometryEquiv.ofEq_symm, norm_subtypeL, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, AffineSubspace.isometryEquivMap.coe_apply, AffineSubspace.subtypeₐᵢ_linear, coord_norm', AffineSubspace.subtypeₐᵢ_linearIsometry, AffineIsometryEquiv.ofEq_rfl, LinearIsometry.strictConvexSpace_range_iff, LinearIsometry.strictConvexSpace_range, exists_extension_norm_eq, ContinuousLinearEquiv.coord_norm', AffineSubspace.isometryEquivMap.apply_symm_apply, ContinuousLinearEquiv.coord_norm, norm_orthogonalProjection, AffineSubspace.subtypeₐᵢ_toAffineMap, Real.exists_extension_norm_eq, norm_subtypeL_le, orthogonalProjection_norm_le, MeasureTheory.norm_condExpL2_le_one

SubmoduleClass

Definitions

Name	Category	Theorems
toNormedSpace 📖	CompOp	—

ULift

Definitions

Name	Category	Theorems
normedSpace 📖	CompOp	—

(root)

Definitions

Name	Category	Theorems
NormedAlgebra 📖	CompData	—
instNonUnitalNormedCommRingRestrictScalars 📖	CompOp	—
instNonUnitalNormedRingRestrictScalars 📖	CompOp	—
instNonUnitalSeminormedCommRingRestrictScalars 📖	CompOp	—
instNonUnitalSeminormedRingRestrictScalars 📖	CompOp	—
instNormedAddCommGroupRestrictScalars 📖	CompOp	—
instNormedAlgebraULift 📖	CompOp	—
instNormedCommRingRestrictScalars 📖	CompOp	—
instNormedRingRestrictScalars 📖	CompOp	—
instSeminormedAddCommGroupRestrictScalars 📖	CompOp	—
instSeminormedCommRingRestrictScalars 📖	CompOp	—
instSeminormedRingRestrictScalars 📖	CompOp	—
normedAlgebraRat 📖	CompOp	6 math math: NormedSpace.exp_continuousMap_eq, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, hahnEmbedding_isOrderedModule_rat, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, instNonemptySeedRatReal, NumberField.mixedEmbedding.mem_rat_span_latticeBasis

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
algebraMap_cobounded_le_cobounded 📖	mathematical	—	Filter.Tendsto DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra Bornology.cobounded PseudoMetricSpace.toBornology SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	—	tendsto_algebraMap_cobounded
algebraMap_isometry 📖	mathematical	—	Isometry EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedField.toMetricSpace PseudoMetricSpace.toPseudoEMetricSpace SeminormedRing.toPseudoMetricSpace DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra	—	Isometry.of_dist_eq dist_eq_norm map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass norm_algebraMap'
dist_algebraMap 📖	mathematical	—	Dist.dist PseudoMetricSpace.toDist SeminormedRing.toPseudoMetricSpace DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra Real Real.instMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing Norm.norm SeminormedRing.toNorm AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne	—	dist_eq_norm RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass norm_algebraMap
dist_algebraMap' 📖	mathematical	—	Dist.dist PseudoMetricSpace.toDist SeminormedRing.toPseudoMetricSpace DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	—	dist_eq_norm RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass norm_algebraMap'
eventually_nhds_norm_smul_sub_lt 📖	mathematical	Real Real.instLT Real.instZero	Filter.Eventually Real Real.instLT Norm.norm SeminormedAddCommGroup.toNorm SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup NormedSpace.toModule SubNegMonoid.toSub nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	—	Continuous.tendsto' Continuous.norm Continuous.const_smul UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul Continuous.sub IsTopologicalAddGroup.to_continuousSub SeminormedAddCommGroup.toIsTopologicalAddGroup continuous_id' continuous_const sub_self smul_zero norm_zero Filter.Tendsto.eventually gt_mem_nhds instOrderTopologyReal
nnnorm_algebraMap 📖	mathematical	—	NNNorm.nnnorm SeminormedAddGroup.toNNNorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup SeminormedRing.toNonUnitalSeminormedRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra NNReal Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring NNReal.instSemiring NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne	—	norm_algebraMap
nnnorm_algebraMap' 📖	mathematical	—	NNNorm.nnnorm SeminormedAddGroup.toNNNorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup SeminormedRing.toNonUnitalSeminormedRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	—	norm_algebraMap'
nnnorm_algebraMap_nnreal 📖	mathematical	—	NNNorm.nnnorm SeminormedAddGroup.toNNNorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup SeminormedRing.toNonUnitalSeminormedRing DFunLike.coe RingHom NNReal Semiring.toNonAssocSemiring CommSemiring.toSemiring NNReal.instCommSemiring Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NNReal.instAlgebraOfReal NormedAlgebra.toAlgebra Real Real.normedField	—	norm_algebraMap_nnreal
norm_algebraMap 📖	mathematical	—	Norm.norm SeminormedRing.toNorm DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra Real Real.instMul NormedField.toNorm AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne	—	Algebra.algebraMap_eq_smul_one norm_smul NormedSpace.toNormSMulClass
norm_algebraMap' 📖	mathematical	—	Norm.norm SeminormedRing.toNorm DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra NormedField.toNorm	—	norm_algebraMap NormOneClass.norm_one mul_one
norm_algebraMap_nnreal 📖	mathematical	—	Norm.norm SeminormedRing.toNorm DFunLike.coe RingHom NNReal Semiring.toNonAssocSemiring CommSemiring.toSemiring NNReal.instCommSemiring Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NNReal.instAlgebraOfReal NormedAlgebra.toAlgebra Real Real.normedField NNReal.toReal	—	Real.norm_of_nonneg Subtype.prop norm_algebraMap'
norm_intCast_eq_abs_mul_norm_one 📖	mathematical	—	Norm.norm SeminormedRing.toNorm AddGroupWithOne.toIntCast Ring.toAddGroupWithOne SeminormedRing.toRing Real Real.instMul Real.instIntCast abs instLatticeInt Int.instAddGroup AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne	—	zsmul_one norm_smul Int.norm_eq_abs Int.cast_abs Real.instIsStrictOrderedRing
norm_natCast 📖	mathematical	—	Norm.norm SeminormedRing.toNorm AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne SeminormedRing.toRing Real Real.instNatCast	—	NormOneClass.norm_one mul_one norm_natCast_eq_mul_norm_one
norm_natCast_eq_mul_norm_one 📖	mathematical	—	Norm.norm SeminormedRing.toNorm AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne SeminormedRing.toRing Real Real.instMul Real.instNatCast AddMonoidWithOne.toOne	—	Int.cast_natCast Nat.abs_cast IsStrictOrderedRing.toIsOrderedRing Int.instIsStrictOrderedRing norm_intCast_eq_abs_mul_norm_one
norm_zsmul 📖	mathematical	—	Norm.norm SeminormedAddCommGroup.toNorm SubNegMonoid.toZSMul AddGroup.toSubNegMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup Real Real.instMul NormedField.toNorm AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing	—	norm_smul NormedSpace.toNormSMulClass Int.smul_one_eq_cast smul_assoc AddCommGroup.intIsScalarTower one_smul
tendsto_algebraMap_cobounded 📖	mathematical	—	Filter.Tendsto DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField Ring.toSemiring SeminormedRing.toRing RingHom.instFunLike algebraMap NormedAlgebra.toAlgebra Bornology.cobounded PseudoMetricSpace.toBornology SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing	—	Filter.mem_map Bornology.isCobounded_def Bornology.isBounded_compl_iff isBounded_iff_forall_norm_le norm_algebraMap'

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