Documentation Verification Report

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`	—	`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`	`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` `NormedSpace.toModule`	—	`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`	`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` `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.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.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.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	29 math math: `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`, `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	548 math math: `TemperedDistribution.lineDerivOpCLM_eq`, `HasStrictFDerivAt.fun_mul'`, `unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `HasMFDerivAt.mul`, `ContinuousLinearMap.mulLeftRight_isBoundedBilinear`, `IsSelfAdjoint.quasispectrumRestricts`, `IsStarNormal.spectralRadius_eq_nnnorm`, `Matrix.IsHermitian.isClosedEmbedding_cfcAux`, `IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `CStarAlgebra.mem_Icc_algebraMap_iff_norm_le`, `hasStrictFDerivAt_list_prod_finRange'`, `Subalgebra.spectrum_sUnion_connectedComponentIn`, `ContMDiffMap.coeFnAlgHom_apply`, `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`, `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'`, `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`, `RCLike.re_add_im_ax`, `Matrix.PosSemidef.sqrt_eq_zero_iff`, `FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal`, `NormedSpace.exp_series_hasSum_exp'`, `HasFPowerSeriesOnBall.restrictScalars`, `HasStrictFDerivAt.mul'`, `fderiv_fun_pow`, `Complex.hasStrictFDerivAt_exp_real`, `ModularForm.prod_slash`, `SchwartzMap.laplacianCLM_eq`, `fderiv_fun_smul`, `HasStrictFDerivAt.pow`, `isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts`, `HasStrictFDerivAt.const_mul`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars`, `HasFDerivAt.finset_prod`, `ContinuousLinearMap.norm_extendTo𝕜`, `fderiv_fun_pow'`, `RCLike.smul_re`, `gelfandStarTransform_naturality`, `ModularForm.prod_slash_sum_weights`, `gelfandStarTransform_apply_apply`, `HasFDerivWithinAt.const_mul`, `ContinuousMultilinearMap.norm_mkPiAlgebra_le`, `spectrum.isOpen_resolventSet`, `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`, `RCLike.toIsStrictOrderedModule`, `binomialSeries_radius_eq_one`, `intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip`, `HasDerivAt.comp_hasFDerivWithinAt`, `HasFDerivAt.restrictScalars`, `FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto`, `HasStrictFDerivAt.list_prod'`, `SchwartzMap.fourier_lineDerivOp_eq`, `Complex.starConvex_one_slitPlane`, `TemperedDistribution.instLineDerivLeftSMulReal`, `hasStrictDerivAt_exp_smul_const`, `SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv`, `norm_algebraMap_nnreal`, `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`, `fderivWithin_finset_prod`, `Matrix.PosSemidef.det_sqrt`, `convex_halfSpace_re_le`, `hasFDerivAt_ringInverse`, `MeasureTheory.convolution_precompR_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`, `Matrix.PosSemidef.posSemidef_sqrt`, `continuousOn_cfc_setProd`, `fderiv_mul_const'`, `spectrum.spectralRadius_lt_of_forall_lt`, `ContinuousAlternatingMap.norm_restrictScalars`, `ContinuousAlternatingMap.isUniformEmbedding_restrictScalars`, `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`, `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`, `Matrix.PosSemidef.sqrt_eq_one_iff`, `fderiv_pow`, `Matrix.PosSemidef.sqrt_sq`, `SchwartzMap.pairing_apply`, `HasFDerivAt.pow`, `spectrum.eventually_isUnit_resolvent`, `fderivWithin_inv'`, `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'`, `Matrix.PosSemidef.eq_sqrt_iff_sq_eq`, `fderiv_mul`, `HasCompactSupport.hasFDerivAt_convolution_right`, `StarAlgebra.elemental.bijective_characterSpaceToSpectrum`, `gelfandTransform_map_star`, `NumberField.mixedEmbedding.convexBodySumFun_smul`, `continuousOn_cfc_nnreal`, `NumberField.mixedEmbedding.logMap_real_smul`, `ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq`, `nnnorm_algebraMap`, `LinearMap.extendTo𝕜_apply`, `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`, `hasFDerivAt_list_prod'`, `hasFDerivAt_integral_of_dominated_loc_of_lip'`, `fderiv_mul'`, `HasFDerivWithinAt.cexp`, `IsSelfAdjoint.cfc_arg`, `spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius`, `SchwartzMap.smulRightCLM_apply_apply`, `NormedSpace.expSeries_summable'`, `MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp`, `ContinuousLinearMap.coe_restrict_scalarsL'`, `HasDerivAt.complexToReal_fderiv`, `inner_smul_real_right`, `hasFDerivAt_exp_smul_const'`, `FormalMultilinearSeries.ofScalars_norm_le`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos`, `SchwartzMap.smulLeftCLM_const`, `FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto`, `hasFDerivWithinAt_pow'`, `convex_halfSpace_im_lt`, `HasFDerivAt.cexp`, `StarSubalgebra.spectrum_eq`, `fderivWithin_mul_const'`, `fderivWithin_smul`, `cfcHom_real_eq_restrict`, `CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary`, `hasFDerivAt_list_prod_finRange'`, `IsSelfAdjoint.spectrumRestricts`, `ordinaryHypergeometric_radius_top_of_neg_nat₂`, `Complex.restrictScalars_one_smulRight`, `Matrix.IsHermitian.cfcAux_apply`, `SchwartzMap.fourierInv_lineDerivOp_eq`, `CFC.log_monotoneOn`, `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`, `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`, `ContinuousMultilinearMap.norm_mkPiAlgebra`, `fderiv_pow_ring'`, `QuasispectrumRestricts.real_iff`, `TemperedDistribution.instLineDerivSMulReal`, `spectrum.isBounded`, `IsSelfAdjoint.sq_spectrumRestricts`, `WeakDual.CharacterSpace.compContinuousMap_apply`, `Subalgebra.frontier_subset_frontier`, `ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq`, `HasFPowerSeriesAt.restrictScalars`, `ContDiffAt.restrictScalars_iteratedFDeriv`, `binomialSeries_radius_eq_top_of_nat`, `hasFDerivAt_pow`, `NumberField.mixedEmbedding.norm_smul`, `PositiveLinearMap.gnsStarAlgHom_apply`, `ConvexOn.convex_re_epigraph`, `SchwartzMap.integral_pow_mul_iteratedFDeriv_le`, `spectrum.nonempty`, `HasFDerivWithinAt.restrictScalars`, `CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le`, `nnnorm_cfc_nnreal_lt`, `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`, `Matrix.PosSemidef.isUnit_sqrt_iff`, `spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius`, `nnnorm_cfc_nnreal_le`, `RCLike.wInner_const_right`, `NormedSpace.exp_hasFPowerSeriesAt_zero`, `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`, `NormedSpace.norm_expSeries_summable'`, `formalMultilinearSeries_geometric_eq_ofScalars`, `fderivWithin_multiset_prod`, `HasFDerivAt.mul`, `selfAdjoint.star_coe_unitarySelfAddISMul`, `convex_halfSpace_im_ge`, `ContinuousLinearMap.extendTo𝕜_apply`, `CStarAlgebra.rpow_neg_one_le_rpow_neg_one`, `hasStrictFDerivAt_pow'`, `instRegularNormedAlgebra`, `convex_halfSpace_re_lt`, `CStarAlgebra.mul_star_le_algebraMap_norm_sq`, `ContinuousAlternatingMap.restrictScalarsLI_apply`, `Complex.restrictScalars_toSpanSingleton`, `fderiv_fun_mul'`, `IsSelfAdjoint.instIsometricContinuousFunctionalCalculus`, `RCLike.instStarModuleReal`, `upperHemicontinuous_spectrum_nnreal`, `Matrix.PosSemidef.sq_sqrt`, `norm_algebraMap`, `hasFDerivAt_exp_smul_const`, `fderiv_finset_prod`, `hasStrictFDerivAt_list_prod_attach'`, `HasFPowerSeriesWithinAt.restrictScalars`, `nnnorm_cfc_le`, `Unitization.nnreal_cfcₙ_eq_cfc_inr`, `hasStrictFDerivAt_ringInverse`, `CStarAlgebra.norm_le_iff_le_algebraMap`, `HasStrictDerivAt.comp_hasStrictFDerivAt`, `HasDerivWithinAt.comp_hasFDerivWithinAt`, `CFC.log_smul'`, `isConformalMap_complex_linear_conj`, `Matrix.PosSemidef.inv_sqrt`, `IsSelfAdjoint.spectralRadius_eq_nnnorm`, `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`, `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`, `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`, `StarSubalgebra.mem_spectrum_iff`, `ContinuousLinearMap.coe_restrictScalarsL`, `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`, `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`, `Matrix.IsHermitian.cfcAux_id`, `RCLike.real_smul_ofReal`, `SchwartzMap.fderivCLM_fourier_eq`, `SchwartzMap.derivCLM_apply`, `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`, `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`, `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`, `spectrum.instCompactSpaceNNReal`, `HasFDerivWithinAt.fun_pow'`, `IsSelfAdjoint.toReal_spectralRadius_eq_norm`, `differentiableAt_iff_restrictScalars`, `NormedSpace.expSeries_radius_pos`, `SchwartzMap.tsupport_derivCLM_subset`, `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`, `Real.hasFDerivAt_fourierChar_neg_bilinear_right`, `RCLike.ofReal_im_ax`, `unitary.norm_sub_one_lt_two_iff`, `hasStrictFDerivAt_inv'`, `SchwartzMap.smulLeftCLM_sub`, `SchwartzMap.smulLeftCLM_apply_apply`, `SchwartzMap.fourier_fderivCLM_eq`, `hasStrictFDerivAt_exp_smul_const`, `dist_algebraMap`, `Complex.hasStrictFDerivAt_log_real`, `HasStrictFDerivAt.mul`, `gelfandTransform_isometry`, `Quaternion.coe_ofComplex`, `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`, `Matrix.PosSemidef.sqrt_mul_self`, `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`, `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`, `CStarAlgebra.toStarModule`, `isConformalMap_complex_linear`, `SchwartzMap.smulLeftCLM_apply`, `ContinuousAlternatingMap.uniformContinuous_restrictScalars`, `HasStrictFDerivAt.fun_mul`, `hasFDerivWithinAt_pow`, `SchwartzMap.smulLeftCLM_compL_smulLeftCLM`, `coe_algEquiv_lpBCF_symm`, `HasFDerivWithinAt.mul'`, `TemperedDistribution.derivCLM_apply_apply`, `HasFDerivAtFilter.restrictScalars`, `IsStarNormal.instIsometricContinuousFunctionalCalculus`, `RCLike.ofRealCLM_coe`, `HasStrictDerivAt.complexToReal_fderiv`, `convex_halfSpace_re_gt`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp`, `fderivWithin_mul'`, `HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq`, `tendsto_algebraMap_cobounded`, `Unitary.argSelfAdjoint_coe`, `dist_algebraMap'`, `hasFDerivAt_inv'`, `RCLike.conj_smul`, `spectrum.resolvent_isBigO_inv`, `WeakDual.CharacterSpace.compContinuousMap_id`, `SchwartzMap.integral_clm_comp_laplacian_right_eq_left`, `Matrix.IsHermitian.mulVec_eigenvectorBasis`, `spectrum.map_polynomial_aeval`, `Subalgebra.SeparatesPoints.rclike_to_real`, `BoundedContinuousFunction.separatesPoints_charPoly`, `CStarAlgebra.exists_sum_four_unitary`, `RCLike.real_smul_eq_coe_mul`, `RCLike.ofRealAm_coe`, `IsSelfAdjoint.le_algebraMap_norm_self`, `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`, `isConformalMap_iff_is_complex_or_conj_linear`, `algebraMap_cobounded_le_cobounded`, `IsometricContinuousFunctionalCalculus.isGreatest_spectrum`, `fderivWithin_restrictScalars_comp`, `HasFDerivAt.mul'`, `Matrix.PosDef.posDef_sqrt`, `continuousFunctionalCalculus_map_id`, `coe_algEquiv_lpBCF`, `Complex.exists_norm_sub_smul_one_eq_zero`, `hasFDerivAt_list_prod_attach'`, `CFC.conjugate_rpow_neg_one_half`, `LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv`, `RCLike.re_extendTo𝕜'ₗ`, `FormalMultilinearSeries.ofScalars_norm_eq_mul`, `CFC.log_smul`, `HasDerivWithinAt.comp_hasFDerivAt_of_eq`, `binomialSeries_radius_ge_one`, `fderivWithin_fun_mul`, `CFC.complex_exp_eq_normedSpace_exp`, `le_iff_norm_sqrt_mul_rpow`, `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`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin`, `spectrum.mem_resolventSet_of_norm_lt_mul`, `norm_cfc_lt`, `HasCompactSupport.hasFDerivAt_convolution_left`, `NumberField.mixedEmbedding.convexBodyLT'_convex`, `selfAdjoint.expUnitary_coe`, `fderivWithin_mul`, `Matrix.PosSemidef.sqrt_eq_iff_eq_sq`, `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`, `le_iff_norm_sqrt_mul_sqrt_inv`, `HasFDerivWithinAt.list_prod'`, `fderiv_inv'`, `unitary.spectrum_subset_slitPlane_iff_norm_lt_two`, `fderivWithin_pow'`, `hasFDerivAt_finset_prod`
`toNormedSpace` 📖	CompOp	243 math math: `ContinuousLinearMap.mulLeftRight_isBoundedBilinear`, `RCLike.map_apply`, `RCLike.ofRealCLM_apply`, `Ideal.toCharacterSpace_apply_eq_zero_of_mem`, `RCLike.reCLM_apply`, `hasStrictFDerivAt_list_prod_finRange'`, `ContMDiffMap.coeFnAlgHom_apply`, `iteratedDerivWithin_const_mul_field`, `RCLike.ofRealLI_apply`, `hasFDerivAt_multiset_prod`, `SchwartzMap.pairing_apply_apply`, `RCLike.conjCLE_norm`, `ordinaryHypergeometric_radius_top_of_neg_nat₃`, `ContinuousLinearMap.integral_apply`, `analyticOnNhd_inverse`, `SchwartzMap.lineDerivOp_fourier_eq`, `RCLike.map_same_eq_id`, `deriv_mul_const_field`, `ContinuousLinearMap.opNorm_lsmul_apply_le`, `SchwartzMap.bilinLeftCLM_apply`, `MeasureTheory.integral_const_mul`, `iteratedDeriv_div_const`, `differentiableWithinAt_inv`, `FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal`, `AnalyticOnNhd.eval_linearMap'`, `MeasureTheory.integral_div`, `Manifold.IsImmersionAtOfComplement.ofOpen`, `gelfandStarTransform_naturality`, `cfcₙ_integral`, `ContinuousMultilinearMap.norm_mkPiAlgebra_le`, `RCLike.reCLM_norm`, `cfcₙ_setIntegral`, `formalMultilinearSeries_geometric_apply_norm_le`, `ordinaryHypergeometricSeries_radius_eq_one`, `MeromorphicAt.inv_iff`, `RCLike.conjCLE_apply`, `isScalarTower_closedBall_closedBall_closedBall`, `NormedSpace.exp_hasFPowerSeriesOnBall`, `isScalarTower_sphere_closedBall_closedBall`, `binomialSeries_radius_eq_one`, `FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto`, `SchwartzMap.fourier_lineDerivOp_eq`, `hasStrictDerivAt_exp_smul_const`, `hasStrictDerivAt_exp_smul_const'`, `SchwartzMap.smulLeftCLM_real_smul`, `spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul`, `hasStrictFDerivAt_multiset_prod`, `integral_smul_const`, `hasFDerivAt_ringInverse`, `differentiableWithinAt_pow`, `FiniteDimensional.rclike_to_real`, `hasStrictFDerivAt_exp`, `deriv_const_mul_field'`, `RCLike.conjLIE_apply`, `ContinuousMapZero.integral_apply`, `Complex.differentiable_exp`, `RCLike.imLm_coe`, `ContinuousLinearMap.lsmul_flip_inj`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero`, `WeakDual.CharacterSpace.homeoEval_naturality`, `RCLike.conjCLE_coe`, `Units.instIsManifoldModelWithCornersSelf`, `fderiv_inverse`, `hasStrictFDerivAt_exp_smul_const'`, `analyticAt_smul`, `SchwartzMap.pairing_apply`, `derivWithin_div_const`, `AnalyticOnNhd.eval_linearMap`, `RCLike.rank_le_two`, `FormalMultilinearSeries.ofScalars_radius_eq_of_tendsto`, `RCLike.reCLM_coe`, `isScalarTower_sphere_sphere_sphere`, `fderiv_pow_ring`, `ContinuousLinearMap.lsmul_apply`, `deriv_const_mul_field`, `integral_conj`, `IsometricContinuousFunctionalCalculus.toNonUnital`, `AlgHom.instContinuousLinearMapClassOfAlgHomClass`, `hasFDerivAt_list_prod'`, `Units.instLieGroupModelWithCornersSelf`, `SchwartzMap.smulRightCLM_apply_apply`, `hasFDerivAt_exp_smul_const'`, `FormalMultilinearSeries.ofScalars_norm_le`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos`, `SchwartzMap.smulLeftCLM_const`, `FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto`, `Complex.differentiableAt_exp`, `hasFDerivWithinAt_pow'`, `isScalarTower_closedBall_ball_ball`, `hasFDerivAt_list_prod_finRange'`, `MeromorphicOn.inv_iff`, `ordinaryHypergeometric_radius_top_of_neg_nat₂`, `SchwartzMap.fourierInv_lineDerivOp_eq`, `RCLike.finrank_le_two`, `differentiableOn_pow`, `hasDerivAt_exp_smul_const`, `derivWithin_mul_const_field`, `logDeriv_apply`, `RCLike.sqrt_map`, `NormedSpace.expSeries_radius_eq_top`, `Complex.contDiff_exp`, `contDiffAt_inv`, `ContinuousMultilinearMap.norm_mkPiAlgebra`, `fderiv_pow_ring'`, `WeakDual.CharacterSpace.compContinuousMap_apply`, `contDiff_smul_const`, `binomialSeries_radius_eq_top_of_nat`, `hasFDerivAt_pow`, `spectrum.hasDerivAt_resolvent`, `cfc_integral`, `RCLike.realLinearIsometryEquiv_symm_apply`, `instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial`, `isScalarTower_sphere_sphere_closedBall`, `ContinuousMultilinearMap.integral_apply`, `RCLike.complexLinearIsometryEquiv_symm_apply`, `MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto`, `NormedSpace.exp_hasFPowerSeriesAt_zero`, `isScalarTower_sphere_sphere_ball`, `formalMultilinearSeries_geometric_apply_norm`, `AnalyticOnNhd.eval_polynomial`, `hasFDerivAt_exp_zero`, `contDiffOn_inv`, `hasStrictFDerivAt_pow'`, `isScalarTower_sphere_closedBall_ball`, `instRegularNormedAlgebra`, `Manifold.IsImmersionOfComplement.ofOpen`, `hasFDerivAt_exp_smul_const`, `hasStrictFDerivAt_list_prod_attach'`, `hasFPowerSeriesOnBall_inv_one_sub`, `hasFPowerSeriesOnBall_inverse_one_sub`, `RCLike.ofRealCLM_norm`, `Complex.sqrt_map`, `hasStrictFDerivAt_ringInverse`, `hasStrictFDerivAt_finset_prod`, `SchwartzMap.tsupport_smulLeftCLM_subset`, `NumberField.canonicalEmbedding.mem_rat_span_latticeBasis`, `differentiable_pow`, `FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto`, `Manifold.IsImmersionAtOfComplement.of_opens`, `differentiableOn_inverse`, `spectrum.differentiableOn_inverse_one_sub_smul`, `RCLike.reLm_coe`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin_le`, `integral_coe_re_add_coe_im`, `AlgHom.coe_toContinuousLinearMap`, `hahnEmbedding_isOrderedModule_rat`, `SchwartzMap.pairing_continuous_left`, `hasFDerivAt_pow'`, `SchwartzMap.lineDerivOp_fourierInv_eq`, `ContinuousLinearMap.opNorm_lsmul_le`, `WeakDual.CharacterSpace.norm_le_norm_one`, `hasStrictFDerivAt_exp_zero`, `formalMultilinearSeries_geometric_radius`, `WeakDual.CharacterSpace.mem_spectrum_iff_exists`, `analyticOn_inv`, `instSMulCommClass_sphere_ball_ball`, `contDiff_mul`, `differentiableWithinAt_inverse`, `SchwartzMap.fderivCLM_fourier_eq`, `RCLike.map_nonneg_iff`, `contDiff_smul`, `iteratedDeriv_mul_const_field`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le`, `differentiableAt_pow`, `AlgHom.toContinuousLinearMap_norm`, `NormedSpace.continuousOn_exp`, `hasStrictFDerivAt_list_prod`, `ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty`, `RCLike.imCLM_coe`, `isScalarTower_sphere_ball_ball`, `NormedSpace.expSeries_radius_pos`, `analyticAt_mul`, `Manifold.IsImmersionOfComplement.id`, `RCLike.toContinuousLinearMap_complexLinearIsometryEquiv`, `integral_ofReal`, `analyticAt_inv`, `contDiffAt_ringInverse`, `Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv`, `WeakDual.CharacterSpace.equivAlgHom_coe`, `ordinaryHypergeometric_radius_top_of_neg_nat₁`, `Units.contMDiff_val`, `analyticAt_inverse_one_sub`, `hasStrictFDerivAt_inv'`, `analyticAt_inv_one_sub`, `iteratedDeriv_const_mul_field`, `SchwartzMap.fourier_fderivCLM_eq`, `hasStrictFDerivAt_exp_smul_const`, `hasDerivAt_exp_smul_const'`, `WeakDual.CharacterSpace.compContinuousMap_comp`, `WeakDual.CharacterSpace.equivAlgHom_symm_coe`, `hasStrictFDerivAt_list_prod'`, `setIntegral_re_add_im`, `SchwartzMap.smulLeftCLM_ofReal`, `Manifold.IsImmersionOfComplement.of_opens`, `hasStrictFDerivAt_pow`, `AnalyticOn.eval_polynomial`, `ContinuousLinearMap.opNorm_lsmul`, `FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto`, `isScalarTower_closedBall_closedBall_ball`, `analyticOnNhd_inv`, `hasFDerivWithinAt_pow`, `instNonemptySeedRatReal`, `integral_re`, `NormedSpace.exp_analytic`, `differentiableAt_inv`, `RCLike.ofRealCLM_coe`, `hasFDerivAt_inv'`, `WeakDual.CharacterSpace.exists_apply_eq_zero`, `WeakDual.CharacterSpace.compContinuousMap_id`, `differentiableAt_inverse`, `integral_re_add_im`, `SchwartzMap.fourier_convolution`, `AnalyticOnNhd.eval_continuousLinearMap'`, `hasFDerivAt_exp`, `deriv_mul_const_field'`, `WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace`, `FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto`, `derivWithin_const_mul_field`, `RCLike.span_one_I`, `analyticAt_inverse`, `hasFDerivAt_list_prod_attach'`, `iteratedDerivWithin_mul_const_field`, `RCLike.re_extendTo𝕜'ₗ`, `FormalMultilinearSeries.ofScalars_norm_eq_mul`, `AnalyticOnNhd.eval_continuousLinearMap`, `binomialSeries_radius_ge_one`, `deriv_div_const`, `RCLike.realLinearIsometryEquiv_apply`, `one_le_formalMultilinearSeries_geometric_radius`, `RCLike.imCLM_apply`, `cfc_setIntegral`, `differentiableOn_inv`, `ContinuousMultilinearMap.norm_mkPiAlgebraFin`, `MeasureTheory.integral_mul_const`, `MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto`, `integral_im`, `intervalIntegral.integral_const_mul`, `TemperedDistribution.smulLeftCLM_apply_apply`, `NumberField.mixedEmbedding.mem_rat_span_latticeBasis`, `FormalMultilinearSeries.ofScalars_norm`, `RCLike.complexLinearIsometryEquiv_apply`, `fderiv_inv'`, `hasFDerivAt_finset_prod`

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	1076 math math: `MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact`, `Polynomial.fderiv`, `IsLocalMaxOn.fderivWithin_nonpos`, `hasFDerivAt_iff_hasDerivAt`, `MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnreal`, `Real.differentiableOn_arcosh`, `Real.hasDerivAt_arccos`, `ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior`, `MeasureTheory.tendsto_integral_thickenedIndicator_of_isClosed`, `MeasureTheory.integral_eq_iff_of_ae_le`, `Polynomial.differentiableWithinAt`, `MeasureTheory.setIntegral_tilted`, `Seminorm.isBounded_const`, `isConformalMap_conj`, `ContinuousMultilinearMap.norm_mkPiRing`, `NormedSpace.isBounded_polar_of_mem_nhds_zero`, `differentiableAt_comp_neg`, `Real.iteratedDerivWithin_cos_Ioo`, `LeftInvariantDerivation.lift_zero`, `Real.differentiable_arctan`, `Real.differentiableAt_mulExpNegMulSq`, `Complex.restrictScalars_one_smulRight'`, `MeasureTheory.setIntegral_nonpos_ae`, `IsSelfAdjoint.quasispectrumRestricts`, `LinearMap.coe_toSeminorm`, `RCLike.ofRealCLM_apply`, `Real.iteratedDeriv_odd_cos`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `Real.differentiableAt_arcsin`, `Complex.linearEquiv_det_conjLIE`, `LeftInvariantDerivation.leibniz`, `smooth_barycentric_coord`, `Real.contDiffOn_log`, `Complex.iteratedDeriv_even_cosh`, `ConvexOn.rightDeriv_le_slope_of_mem_interior`, `Function.FactorizedRational.divisor`, `hasDerivAt_sqrt_mul_log`, `ConvexOn.differentiableWithinAt_Iio_of_mem_interior`, `ContinuousLinearMap.opNorm_bound_of_ball_bound`, `Complex.ofRealCLM_coe`, `MeromorphicAt.analyticAt`, `RightDerivMeasurableAux.D_subset_differentiable_set`, `Real.deriv_negMulLog`, `meromorphicOrderAt_const_ofNat`, `Real.analyticOn_cos`, `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`, `Real.deriv_binEntropy`, `smoothSheafCommRing.nonunits_stalk`, `MeasureTheory.convolution_mul`, `Complex.ofRealLI_apply`, `expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul`, `BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub`, `deriv_mem_iff`, `Real.analyticOnNhd_sin`, `Real.hasStrictDerivAt_rpow_const_of_ne`, `StrongDual.polarSubmodule_eq_setOf`, `ContinuousLinearMap.hasDerivAtFilter`, `HasDerivWithinAt.complexToReal_fderiv'`, `PMF.bernoulli_expectation`, `ContDiffBumpBase.smooth`, `Real.analyticOn_cosh`, `continuousOn_dslope`, `Complex.analyticOn_sin`, `isClosedEmbedding_cfcₙAux`, `LeftInvariantDerivation.coe_derivation`, `MeasureTheory.integral_mul_norm_le_Lp_mul_Lq`, `LinearMap.adjoint_innerₛₗ_apply`, `Real.differentiable_sinh`, `hasDerivAt_neg'`, `AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn`, `ContinuousLinearMap.toBilinForm_apply`, `ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm`, `expNegInvGlue.not_analyticAt_zero`, `NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm`, `AkraBazziRecurrence.differentiableAt_one_add_smoothingFn`, `LeftInvariantDerivation.left_invariant'`, `derivWithin_fderivWithin`, `Real.deriv_log`, `FormalMultilinearSeries.derivSeries_coeff_one`, `Complex.ofRealCLM_norm`, `HasDerivAt.comp_ofReal`, `rotation_injective`, `iteratedDeriv_pow`, `AffineMap.hasDerivWithinAt`, `LeftInvariantDerivation.left_invariant`, `Complex.iteratedDeriv_odd_sinh`, `MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt`, `MeasureTheory.toReal_rnDeriv_tilted_left`, `Complex.convexHull_reProdIm`, `Complex.conjLIE_apply`, `one_mem_posTangentConeAt_iff_frequently`, `Real.hasDerivAt_sin`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal`, `Real.differentiableOn_log`, `Real.iteratedDeriv_even_cosh`, `Real.differentiableOn_arcsin`, `Complex.hasStrictFDerivAt_exp_real`, `AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn`, `MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart`, `monomial_has_deriv_aux`, `Real.contDiffAt_tan`, `Real.hasDerivAt_mul_log`, `iter_deriv_zpow'`, `MeasureTheory.integral_tilted`, `Real.deriv_arccos`, `Real.hasStrictDerivAt_sinh`, `isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts`, `ConvexOn.univ_sSup_of_countable_affine_eq`, `Real.analyticWithinAt_sinh`, `cfcₙHom_nnreal_eq_restrict`, `IsLocalFrameOn.coeff_apply_of_mem`, `Real.contDiffAt_rpow_const_of_le`, `deriv_sqrt_mul_log`, `ContinuousLinearMap.norm_extendTo𝕜`, `IsLocalMax.fderiv_eq_zero`, `differentiable_descPochhammer_eval`, `innerₛₗ_apply_apply`, `Real.hasStrictFDerivAt_rpow_of_pos`, `hasFDerivWithinAt_inv`, `smoothSheafCommRing.instLocalRing_stalk`, `Real.analyticAt_cos`, `rotation_apply`, `toMatrix_rotation`, `Real.differentiableWithinAt_arccos_Ici`, `Real.sinc_eq_dslope`, `MeasureTheory.measure_integral_le_pos`, `exists_deriv_eq_zero`, `ContinuousMultilinearMap.norm_smulRightL_le`, `differentiableAt_comp_add_const`, `QuadraticForm.equivalent_signType_weighted_sum_squared`, `RCLike.reCLM_norm`, `Real.hasDerivAt_arcosh`, `Complex.analyticWithinAt_cosh`, `ConvexOn.monotoneOn_rightDeriv`, `Real.iteratedDerivWithin_cos_Icc`, `fderiv_eq_deriv_mul`, `MeasureTheory.exists_average_le`, `Polynomial.differentiableOn_aeval`, `IsLocalExtr.lineDeriv_eq_zero`, `MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_part`, `analyticAt_rexp`, `Complex.contDiff_cosh`, `IsExtrOn.lineDerivWithin_eq_zero`, `iteratedDerivWithin_eq_iteratedFDerivWithin`, `VectorFourier.fourierPowSMulRight_eq_comp`, `Complex.analyticOn_cosh`, `Real.analyticAt_sinh`, `Real.hasStrictDerivAt_arccos`, `MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le`, `Complex.reCLM_nnnorm`, `MeasureTheory.integral_norm_eq_lintegral_enorm`, `QuadraticForm.equivalent_one_neg_one_weighted_sum_squared`, `MeromorphicOn.divisor_natCast`, `Complex.deriv_ofReal_cpow_const`, `PiTensorProduct.mapL_smul`, `Real.norm_deriv_mulExpNegMulSq_le_one`, `LeftInvariantDerivation.lift_add`, `meromorphicOrderAt_ne_top_iff`, `VectorFourier.fourierIntegral_continuousLinearMap_apply`, `Real.not_continuousAt_deriv_mul_log_zero`, `Complex.analyticOn_sinh`, `ContinuousLinearMapWOT.inducingFn_apply`, `LeftInvariantDerivation.lift_smul`, `MeasureTheory.Measure.integral_toReal_rnDeriv'`, `analyticOnNhd_rexp`, `BoundedContinuousFunction.integral_const_sub`, `spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul`, `Real.differentiableAt_rpow_const_of_ne`, `WeakDual.toStrongDual_inj`, `AntitoneOn.derivWithin_nonpos`, `Real.hasDerivAt_arsinh`, `hasDerivAt_id'`, `CompactlySupportedContinuousMap.toRealLinearMap_apply_apply`, `ContinuousLinearMap.deriv`, `deriv_norm_ofReal_cpow`, `MeasureTheory.convolution_lsmul`, `Real.contDiffAt_sqrt`, `MeasureTheory.L1.dist_eq_integral_dist`, `Real.deriv_sqrt_aux`, `deriv_fderiv`, `MeasureTheory.integral_eq_zero_iff_of_nonneg`, `HasStrictDerivAt.real_of_complex`, `Real.deriv_rpow_const`, `FormalMultilinearSeries.norm_apply_eq_norm_coef`, `range_cfcₙHom`, `Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzero`, `HasDerivAt.differentiableAt`, `ContinuousLinearMap.hasDerivAt`, `AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn`, `Complex.reCLM_coe`, `MeasureTheory.ofReal_setAverage`, `Real.deriv_sinh`, `WeakDual.coe_toStrongDual`, `Matrix.linfty_opNNNorm_eq_opNNNorm`, `ModularGroup.lcRow0Extend_symm_apply`, `Complex.analyticAt_sin`, `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`, `MeasureTheory.llr_tilted_right`, `Polynomial.deriv_aeval`, `IsLocalFrameOn.coeff_congr`, `LinearMap.hasStrictDerivAt`, `Complex.equivRealProdCLM_symm_apply`, `CompactlySupportedContinuousMap.coe_toRealLinearMap`, `differentiableOn_dslope_of_notMem`, `IsLocalExtr.fderiv_eq_zero`, `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`, `MeasureTheory.lpNorm_one_eq_integral_norm`, `RCLike.imLm_coe`, `Real.differentiable_cos`, `Function.FactorizedRational.meromorphicOrderAt_eq`, `iteratedDeriv_fun_id_zero`, `ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior`, `MeromorphicOn.divisor_sub_const_self`, `Matrix.linfty_opNNNorm_toMatrix`, `analyticOrderAt_ne_zero`, `WeakDual.CharacterSpace.homeoEval_naturality`, `FormalMultilinearSeries.coeff_eq_zero`, `analyticOrderAt_centeredMonomial`, `Complex.contDiffAt_log`, `Real.analyticAt_sin`, `LeftInvariantDerivation.evalAt_coe`, `MeasureTheory.integral_tendsto_of_tendsto_of_antitone`, `MeasureTheory.integral_tendsto_of_tendsto_of_monotone`, `Polynomial.differentiable_aeval`, `hasDerivAt_deriv_iff`, `Complex.differentiable_iteratedDeriv_sin`, `hasDerivAtFilter_neg`, `Real.analyticOnNhd_cosh`, `Real.hasDerivAt_binEntropy`, `hasDerivAt_gronwallBound_shift`, `MeasureTheory.norm_integral_le_integral_norm`, `meromorphicOrderAt_const_natCast`, `Real.hasDerivAt_qaryEntropy`, `continuousAt_dslope_same`, `hasDerivWithinAt_pow`, `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`, `cfcₙAux_id`, `NormedSpace.inclusionInDoubleDual_norm_le`, `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`, `MeasureTheory.norm_integral_le_of_norm_le`, `MeasureTheory.Measure.integral_toReal_rnDeriv`, `Seminorm.comp_smul`, `MeromorphicOn.analyticAt_mem_codiscreteWithin`, `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`, `RealRMK.integral_rieszMeasure`, `LinearMap.deriv`, `contDiff_iff_iteratedDeriv`, `LeftInvariantDerivation.map_zero`, `NormedSpace.polar_ball_subset_closedBall_div`, `Real.differentiable_exp`, `fdifferential_apply`, `Real.hasStrictDerivAt_arcosh`, `LinearMap.extendTo𝕜_apply`, `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'`, `hasDerivAt_update`, `iteratedDeriv_fun_id`, `Seminorm.bound_of_continuous`, `HasDerivWithinAt.complexToReal_fderiv`, `Complex.ofRealCLM_nnnorm`, `Complex.imCLM_norm`, `Real.deriv2_binEntropy`, `LinearMap.toSeminorm_comp`, `IsExtrOn.lineDeriv_eq_zero`, `MeasureTheory.measure_le_setAverage_pos`, `meromorphicNFAt_inv`, `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`, `Polynomial.fderiv_aeval`, `orthogonalBilin_innerₗ`, `ContinuousLinearMap.norm_smulRight_apply`, `Real.hasStrictDerivAt_cosh`, `ConvexOn.real_univ_sSup_of_countable_affine_eq`, `Module.Basis.equivFunL_symm_apply_repr`, `MeasureTheory.integral_pos_iff_support_of_nonneg_ae`, `iter_deriv_zpow`, `Complex.analyticOnNhd_sin`, `MeasureTheory.integral_indicator_one`, `QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared`, `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`, `HasDerivAt.complexToReal_fderiv'`, `hasStrictFDerivAt_iff_hasStrictDerivAt`, `contDiff_nat_iff_iteratedDeriv`, `HasDerivAt.complexToReal_fderiv`, `ContinuousLinearMapWOT.isInducing_inducingFn`, `Real.deriv_mulExpNegMulSq`, `StrongDual.polarSubmodule_eq_polar`, `MeasureTheory.Integrable.exists_boundedContinuous_integral_sub_le`, `meromorphicOrderAt_inv`, `MeasureTheory.SignedMeasure.re_toComplexMeasure`, `AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn`, `Real.deriv_qaryEntropy`, `Real.deriv_arctan`, `monotoneOn_deriv_descPochhammer_eval`, `LinearMap.toMatrix_innerₛₗ_apply`, `MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le`, `MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt`, `PointwiseConvergenceCLM.equivWeakDual_symm_apply`, `AffineMap.hasDerivAt`, `Real.iteratedDerivWithin_sinh_Icc`, `iteratedDerivWithin_zpow`, `meromorphicOrderAt_eq_int_iff`, `AffineMap.differentiableAt`, `meromorphicNFAt_iff_analyticAt_or`, `WeakDual.isSeqCompact_closedBall`, `Real.differentiableAt_log_iff`, `hasStrictDerivAt_zpow`, `LinearIsometry.toSpanSingleton_apply`, `hasFDerivAtFilter_iff_hasDerivAtFilter`, `Polynomial.hasFDerivAt`, `Distribution.mapCLM_apply`, `Real.hasStrictDerivAt_const_rpow_of_neg`, `hasDerivAt_inv`, `AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn`, `ConvexOn.sSup_of_nat_affine_eq`, `Real.contDiff_arsinh`, `MeasureTheory.tilted_apply_eq_ofReal_integral`, `contMDiff_smul`, `MeromorphicOn.divisor_ofNat`, `Real.contDiffAt_arcsin_iff`, `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`, `MeasureTheory.Measure.setIntegral_toReal_rnDeriv'`, `Module.Basis.equivFunL_apply`, `ConvexOn.differentiableWithinAt_Ioi_of_mem_interior`, `LinearMap.hasDerivWithinAt`, `ContinuousMap.adjoin_id_eq_span_one_union`, `measurableSet_of_differentiableWithinAt_Ici_of_isComplete`, `IsSelfAdjoint.spectrumRestricts`, `Seminorm.const_isBounded`, `meromorphicTrailingCoeffAt_const`, `Complex.restrictScalars_one_smulRight`, `ContinuousLinearMapWOT.isEmbedding_inducingFn`, `HasDerivWithinAt.differentiableWithinAt`, `ZSpan.coe_floor_self`, `Real.iteratedDerivWithin_sin_Icc`, `Real.iteratedDeriv_odd_sinh`, `iteratedFDeriv_eq_equiv_comp`, `linear_isometry_complex`, `meromorphicTrailingCoeffAt_inv`, `MeromorphicAt.id`, `Real.hasDerivAt_cos`, `analyticOnNhd_cexp`, `exists_dual_vector`, `meromorphicNFOn_inv`, `Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range`, `Real.differentiableWithinAt_arcsin_Ici`, `iteratedDerivWithin_one_div`, `Real.hasDerivWithinAt_arcsin_Ici`, `rotationOf_rotation`, `IsMIntegralCurveAt.hasMFDerivAt`, `SpectrumRestricts.real_iff`, `IsLocalFrameOn.eventually_eq_sum_coeff_smul`, `MeasureTheory.tilted_apply`, `MeasureTheory.lpNorm_nnreal_eq_integral_norm_rpow`, `Function.FactorizedRational.analyticAt`, `Real.differentiableAt_cosh`, `MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm`, `Polynomial.hermite_eq_deriv_gaussian'`, `Real.analyticOnNhd_arsinh`, `MonotoneOn.derivWithin_nonneg`, `MeasureTheory.log_rnDeriv_tilted_left_self`, `CompactlySupportedContinuousMap.integralLinearMap_apply`, `Real.analyticAt_arcosh`, `MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le`, `LinearMap.adjoint_toSpanSingleton`, `Real.deriv_exp`, `ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply`, `Real.contDiff_sin`, `QuasispectrumRestricts.real_iff`, `Polynomial.differentiableAt_aeval`, `hasDerivAt_id`, `Real.hasDerivAt_rpow_const`, `IsMinOn.lineDeriv_eq_zero`, `deriv_update`, `Real.iter_deriv_exp`, `Real.differentiable_iteratedDeriv_cos`, `Polynomial.hasFDerivAt_aeval`, `exists_dual_vector''`, `deriv_zpow'`, `LeftInvariantDerivation.map_add`, `MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part`, `MeasureTheory.exists_integral_le`, `isTheta_deriv_rpow_const_atTop`, `Polynomial.deriv_gaussian_eq_hermite_mul_gaussian`, `hasDerivAt_exp`, `Complex.analyticOn_cos`, `contDiffOn_succ_iff_deriv_of_isOpen`, `LeftInvariantDerivation.coe_add`, `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`, `LinearIsometry.coe_toSpanSingleton`, `Real.contDiff_cos`, `deriv_neg''`, `IsLocalFrameOn.coeff_apply_of_notMem`, `Seminorm.closedBall_smul`, `isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts`, `fderiv_inv`, `MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction`, `MeasureTheory.L1.integral_eq_norm_posPart_sub`, `IsOpen.measure_eq_biSup_integral_continuous`, `iteratedDeriv_eq_equiv_comp`, `Real.iteratedDeriv_even_cos`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply`, `MeasureTheory.SimpleFunc.norm_integral_le_integral_norm`, `MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart`, `ContinuousLinearMap.norm_extendTo𝕜'_bound`, `Complex.iteratedDeriv_add_one_sinh`, `Real.differentiableAt_arctan`, `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`, `Complex.iteratedDeriv_add_one_sin`, `Real.rightDeriv_mul_log`, `ContinuousLinearEquiv.coord_toSpanNonzeroSingleton`, `fdifferential_comp`, `LeftInvariantDerivation.coe_injective`, `MeasureTheory.setIntegral_nonpos`, `fderiv_apply_one_eq_deriv`, `meromorphicTrailingCoeffAt_id_sub_const`, `Real.analyticWithinAt_cos`, `Complex.analyticAt_sinh`, `LeftInvariantDerivation.coe_neg`, `StrongDual.toLpₗ_apply`, `Real.differentiableWithinAt_arcsin_Iic`, `Polynomial.hermite_eq_deriv_gaussian`, `Complex.conjCLE_nnorm`, `Polynomial.differentiableOn`, `HasStrictDerivAt.complexToReal_fderiv'`, `IsLocalFrameOn.coeff_apply_zero_at`, `Orientation.inner_mul_areaForm_sub'`, `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`, `IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt`, `deriv_neg'`, `Real.differentiable_sin`, `AnalyticAt.of_meromorphicOrderAt_pos`, `ContinuousLinearEquiv.toSpanNonzeroSingleton_coord`, `Polynomial.hasDerivWithinAt_aeval`, `rotation_trans`, `Real.not_differentiableAt_inv_log_zero`, `Real.deriv_mul_log`, `Real.contDiffAt_rpow_const`, `Polynomial.hasStrictDerivAt_aeval`, `MeasureTheory.integral_rnDeriv_mul_log`, `ContinuousLinearMap.norm_extendTo𝕜'`, `differentiableAt_iff_comp_const_sub`, `Complex.restrictScalars_toSpanSingleton`, `MeasureTheory.SimpleFunc.integral_eq_lintegral`, `MeromorphicOn.countable_compl_analyticAt_inter`, `IsMaxOn.lineDerivWithin_eq_zero`, `MeasureTheory.setIntegral_nonneg_of_ae_restrict`, `MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd`, `Real.differentiableAt_tan`, `Real.differentiable_cosh`, `MeasureTheory.setLIntegral_tilted`, `NumberField.finite_of_discr_bdd`, `cfcHom_nnreal_eq_restrict`, `fderiv_deriv`, `MeasureTheory.integral_le_measure`, `MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt`, `Complex.contDiffAt_tan`, `Complex.analyticWithinAt_sinh`, `Complex.analyticOnNhd_cosh`, `coord_norm'`, `spec_cfcₙAux`, `ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior`, `MeasureTheory.ofReal_integral_norm_eq_lintegral_enorm`, `LeftInvariantDerivation.map_smul`, `Real.hasDerivAt_log`, `MeasureTheory.ofReal_setIntegral_one`, `rotationOf_coe`, `deriv_single`, `StrongDual.norm_toLpₗ_le`, `Module.Basis.parallelepiped_eq_map`, `MeasureTheory.toReal_laverage`, `Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational`, `MeromorphicOn.divisor_fun_inv`, `ProperCone.dual_flip_dual`, `RCLike.ofRealCLM_norm`, `ContDiffBump.contDiffAt`, `MeasureTheory.rnDeriv_tilted_left`, `MeasureTheory.convolution_lsmul_swap`, `Real.hasStrictDerivAt_arctan`, `Complex.contDiff_sinh`, `StrongDual.toLpₗ_of_not_memLp`, `isConformalMap_complex_linear_conj`, `analyticOrderAt_id`, `IsLocalMax.lineDeriv_eq_zero`, `instContMDiffInv₀ModelWithCornersSelf`, `MeasureTheory.setIntegral_nonpos_le`, `Real.iteratedDeriv_odd_cosh`, `deriv_zpow`, `StrongDual.mem_polarSubmodule`, `exists_dual_vector'`, `FormalMultilinearSeries.apply_eq_prod_smul_coeff`, `Real.analyticOn_sin`, `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`, `IsLocalMin.deriv_eq_zero`, `Real.hasDerivAt_cosh`, `Real.tendsto_deriv_mul_log_atTop`, `LeftInvariantDerivation.coe_smul`, `innerₗ_apply_apply`, `MeasureTheory.integral_eq_zero_iff_of_nonneg_ae`, `MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity'`, `hfdifferential_apply`, `analyticOn_cexp`, `CompactlySupportedContinuousMap.toNNRealLinear_apply`, `bilinFormOfRealInner_orthogonal`, `Complex.conjCLE_enorm`, `Real.differentiableWithinAt_arccos_Iic`, `spectrum.differentiableOn_inverse_one_sub_smul`, `Real.iteratedDerivWithin_sinh_Ioo`, `ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom`, `expNegInvGlue.contDiff`, `RCLike.reLm_coe`, `ContinuousLinearMap.toBilinForm_injective`, `Real.contDiffOn_arccos`, `toSpanSingleton_derivWithin`, `MeromorphicOn.eventually_analyticAt_or_mem_compl`, `MeasureTheory.setIntegral_gt_gt`, `MeasureTheory.setIntegral_nonneg_ae`, `MeasureTheory.setIntegral_nonpos_of_ae`, `NumberField.linearDisjoint_of_isGalois_isCoprime_discr`, `Real.iteratedDeriv_even_sinh`, `ConvexOn.univ_sSup_affine_eq`, `linearEquiv_det_rotation`, `Real.differentiable_mulExpNegMulSq`, `Real.differentiableAt_arccos`, `ConvexOn.real_univ_sSup_of_nat_affine_eq`, `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`, `MeasureTheory.Measure.exists_regular_eq_of_compactSpace`, `ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior`, `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`, `Real.hasStrictDerivAt_cos`, `iter_deriv_inv`, `exists_deriv_eq_zero'`, `AkraBazziRecurrence.deriv_smoothingFn`, `Real.not_differentiableAt_rpow_const_zero`, `MeasureTheory.setIntegral_nonneg`, `RightDerivMeasurableAux.differentiable_set_eq_D`, `MeasureTheory.mul_meas_ge_le_integral_of_nonneg`, `hasDerivWithinAt_zpow`, `Monotone.deriv_nonneg`, `Real.contDiff_arctan`, `MeasureTheory.setIntegral_tilted'`, `HasDerivAt.real_of_complex`, `measurableSet_of_differentiableWithinAt_Ioi`, `Real.iteratedDeriv_add_one_sin`, `Real.differentiable_iteratedDeriv_sin`, `AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn`, `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`, `Real.iteratedDeriv_even_sin`, `MeasureTheory.setIntegral_ge_of_const_le_real`, `Real.analyticOnNhd_cos`, `ModularGroup.tendsto_lcRow0`, `NormedSpace.sInter_polar_eq_closedBall`, `Complex.imCLM_coe`, `expNegInvGlue.contDiff_polynomial_eval_inv_mul`, `DoubleCentralizer.coe_eq_algebraMap`, `deriv_pow_field`, `Polynomial.hasDerivAt_aeval`, `hasDerivAt_gronwallBound`, `isBigO_deriv_ofReal_cpow_const_atTop`, `MeasureTheory.exists_le_setAverage`, `hasDerivAt_ofReal_cpow_const`, `Real.differentiableAt_tan_of_mem_Ioo`, `Real.not_continuousAt_deriv_qaryEntropy_zero`, `LeftInvariantDerivation.map_sub`, `MeasureTheory.L1.SimpleFunc.integral_eq_lintegral`, `Real.contDiff_cosh`, `MeromorphicOn.extract_zeros_poles`, `cfcₙAux_mem_range_inr`, `ContinuousMap.adjoin_id_eq_span_one_add`, `LeftInvariantDerivation.map_neg`, `BoundedContinuousFunction.integral_add_const`, `MeasureTheory.L1.norm_of_fun_eq_integral_norm`, `Real.analyticAt_arsinh`, `norm_deriv_eq_norm_fderiv`, `AkraBazziRecurrence.differentiableAt_smoothingFn`, `ContinuousLinearMap.nnnorm_smulRight_apply`, `MeasureTheory.setIntegral_one_eq_measureReal`, `deriv_id`, `Matrix.toLin_finTwoProd_toContinuousLinearMap`, `Real.deriv_cos`, `iteratedDeriv_exp_const_mul`, `Real.differentiableAt_binEntropy`, `QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared`, `Real.hasDerivAt_arctan'`, `differentiable_neg`, `hasDerivAt_neg`, `BoundedContinuousFunction.toReal_lintegral_coe_eq_integral`, `Polynomial.hasStrictDerivAt`, `Real.deriv2_qaryEntropy`, `Real.differentiableAt_exp`, `Real.hasStrictDerivAt_arcsin`, `AffineMap.hasStrictDerivAt`, `InnerProductSpace.toLinearMap_rankOne`, `Real.abs_iteratedDeriv_sin_le_one`, `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`, `iteratedDerivWithin_eq_equiv_comp`, `Polynomial.differentiableAt`, `MeasureTheory.exists_setAverage_le`, `CompactlySupportedContinuousMap.toReal_smul`, `MeasureTheory.lintegral_tilted`, `Real.analyticAt_cosh`, `Real.contDiffAt_rpow_const_of_ne`, `MeasureTheory.L1.SimpleFunc.norm_eq_integral`, `MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top`, `MeasureTheory.llr_tilted_left`, `Matrix.linfty_opNorm_eq_opNorm`, `MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction`, `Real.deriv_cos'`, `MeasureTheory.measure_le_integral_pos`, `isBigO_deriv_rpow_const_atTop`, `hasDerivAt_pow`, `contDiff_succ_iff_deriv`, `Real.deriv_rpow_const'`, `MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg`, `Real.differentiableAt_arcosh`, `IsLocalMaxOn.fderivWithin_eq_zero`, `LinearMap.isSymmetric_iff_sesqForm`, `hasDerivWithinAt_derivWithin_iff`, `hasStrictDerivAt_exp`, `MeasureTheory.lintegral_coe_le_coe_iff_integral_le`, `Real.hasStrictDerivAt_sqrt`, `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`, `MeasureTheory.exists_notMem_null_integral_le`, `Polynomial.hasFDerivWithinAt_aeval`, `Complex.iteratedDeriv_even_sin`, `Real.hasDerivAt_exp`, `hasStrictDerivAt_inv`, `MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae`, `Polynomial.contDiff_aeval`, `LinearMap.continuous_of_isClosed_ker`, `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`, `CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal`, `LinearMap.continuous_iff_isClosed_ker`, `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`, `VectorFourier.fourierIntegral_continuousMultilinearMap_apply`, `MeasureTheory.exists_le_integral`, `LinearMap.toSeminorm_apply`, `hasDerivAt_ofReal_cpow_const'`, `MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff`, `LeftInvariantDerivation.toDerivation_injective`, `Real.analyticOn_arsinh`, `Real.analyticWithinAt_sin`, `Complex.conjCLE_norm`, `LeftInvariantDerivation.evalAt_mul`, `iteratedDeriv_id`, `exists_extension_norm_eq`, `Complex.iteratedDeriv_add_one_cosh`, `NormedSpace.closedBall_inv_subset_polar_closedBall`, `MeasureTheory.convolution_mul_swap`, `ContinuousLinearMap.norm_smulRightL_le`, `AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn`, `Complex.imCLM_enorm`, `analyticOrderAt_eq_zero`, `hasDerivAt_single`, `det_rotation`, `IsMaxOn.lineDeriv_eq_zero`, `integral_complex_ofReal`, `Real.iteratedDeriv_odd_sin`, `RCLike.toContinuousLinearMap_complexLinearIsometryEquiv`, `integral_ofReal`, `Complex.ofRealCLM_enorm`, `CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun`, `MeasureTheory.ComplexMeasure.re_apply`, `Polynomial.differentiableWithinAt_aeval`, `MeasureTheory.measure_average_le_pos`, `Real.analyticOn_sinh`, `Real.differentiableAt_sinh`, `Real.differentiable_iteratedDeriv_sinh`, `FormalMultilinearSeries.coeff_iterate_fslope`, `Complex.analyticWithinAt_sin`, `MeasureTheory.measure_setAverage_le_pos`, `conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj`, `MeasureTheory.Integrable.measure_le_integral`, `rotation_symm`, `IsLocalFrameOn.coeff_eq_of_eq`, `ContinuousLinearMap.isAdjointPair_inner`, `Complex.equivRealProdCLM_symm_apply_im`, `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'`, `LinearMap.mem_span_iff_bound`, `MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap`, `hasDerivAt_mul_const`, `deriv_inv'`, `deriv_descPochhammer_eval_eq_sum_prod_range_erase`, `iteratedDeriv_cexp_const_mul`, `iteratedDeriv_fun_pow_zero`, `Complex.hasStrictFDerivAt_log_real`, `Real.analyticWithinAt_arcosh`, `Real.hasStrictDerivAt_tan`, `iter_deriv_inv_linear`, `MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_integral`, `AffineMap.differentiable`, `WeakDual.toStrongDual_apply`, `MeasureTheory.lpNorm_eq_integral_norm_rpow_toReal`, `Real.hasDerivAt_arctan`, `hasDerivWithinAt_id`, `ContinuousMultilinearMap.smulRightL_apply`, `innerₛₗ_apply_coe`, `IsLocalMinOn.fderivWithin_nonneg`, `AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn`, `Complex.reCLM_norm`, `Real.analyticWithinAt_arsinh`, `ContinuousMapZero.toNNReal_neg_smul`, `differentiableAt_of_deriv_ne_zero`, `MeasureTheory.exists_upperSemicontinuous_le_integral_le`, `Real.iteratedDerivWithin_cosh_Ioo`, `meromorphicOrderAt_const_intCast`, `LinearMap.toSeminormFamily_apply`, `MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure`, `exists_eq_const_mul_setIntegral_of_nonneg`, `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`, `Real.differentiableAt_qaryEntropy`, `ContinuousLinearMap.lsmul_flip_apply`, `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`, `LinearPMap.mem_adjoint_domain_iff`, `differentiableWithinAt_zpow`, `contDiffOn_infty_iff_deriv_of_isOpen`, `ContinuousMultilinearMap.norm_smulRight`, `DifferentiableAt.conformalAt`, `Real.analyticOnNhd_sinh`, `MeasureTheory.rnDeriv_tilted_right`, `LeftInvariantDerivation.commutator_apply`, `NNRealRMK.integral_rieszMeasure`, `ContinuousMapZero.elemental_eq_top`, `ContinuousMapZero.adjoin_id_dense`, `ContinuousLinearMap.hasDerivWithinAt`, `LeftInvariantDerivation.commutator_coe_derivation`, `NormedSpace.polar_closedBall`, `ContinuousMapZero.toNNReal_smul`, `MeasureTheory.setIntegral_nonneg_of_ae`, `coe_innerₛₗ_apply`, `Complex.analyticAt_cos`, `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`, `ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id`, `Module.Basis.opNorm_le`, `Real.differentiable_rpow_const`, `UniformCauchySeqOnFilter.one_smulRight`, `isConformalMap_complex_linear`, `MeasureTheory.ofReal_average`, `analyticWithinAt_cexp`, `Real.analyticWithinAt_cosh`, `hasDerivWithinAt_inv`, `hasStrictDerivAt_id`, `Complex.iteratedDeriv_odd_cosh`, `IsExtrFilter.lineDeriv_eq_zero`, `Complex.contDiff_sin`, `Complex.contDiff_cos`, `deriv_neg`, `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`, `LinearMap.hasDerivAtFilter`, `iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod`, `MeasureTheory.exists_le_average`, `MeasureTheory.setIntegral_le_nonneg`, `IsLocalFrameOn.coeff_sum_eq`, `RCLike.ofRealCLM_coe`, `HasStrictDerivAt.complexToReal_fderiv`, `ConvexOn.exists_affine_le_of_lt`, `RealRMK.le_rieszMeasure_tsupport_subset`, `ConvexOn.real_sSup_of_nat_affine_eq`, `MeasureTheory.integral_norm_eq_pos_sub_neg`, `norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin`, `Real.not_continuousAt_deriv_qaryEntropy_one`, `differentiableAt_dslope_of_ne`, `MeasureTheory.tilted_apply_eq_ofReal_integral'`, `hasDerivAt_zpow`, `MeasureTheory.exists_upperSemicontinuous_lt_integral_gt`, `MeasureTheory.integral_llr_tilted_right`, `Real.contDiffAt_arcsin`, `differentiableAt_iff_comp_const_add`, `signedDist_apply_linear`, `Real.differentiableAt_sin`, `integral_re_add_im`, `ZSpan.coe_fract_self`, `MeasureTheory.tendsto_integral_norm_approxOn_sub`, `LeftInvariantDerivation.toFun_eq_coe`, `Complex.reCLM_enorm`, `Real.hasDerivAt_sinh`, `MeasureTheory.rnDeriv_tilted_left_self`, `Real.deriv_cosh`, `Real.exists_extension_norm_eq`, `AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn`, `Real.deriv_sin`, `AffineMap.deriv`, `MeasureTheory.SimpleFunc.integral_eq_lintegral'`, `ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior`, `MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp`, `expNegInvGlue.differentiable_polynomial_eval_inv_mul`, `MeromorphicOn.eventually_analyticAt`, `Polynomial.hasDerivWithinAt`, `differentiableAt_iff_comp_sub_const`, `Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support`, `LinearMap.isAdjointPair_inner`, `Real.analyticOnNhd_arcosh`, `AnalyticOnNhd.eval_mvPolynomial`, `ContinuousLinearMap.hasStrictDerivAt`, `MeasureTheory.setIntegral_nonpos_of_ae_restrict`, `hasFDerivAt_inv`, `Real.deriv_mul_log_zero`, `MeasureTheory.Measure.setIntegral_toReal_rnDeriv`, `ContinuousLinearMap.smulRightL_apply_apply`, `Real.hasDerivAt_sqrt`, `analyticOn_rexp`, `ContinuousLinearMap.toSpanSingletonCLE_apply_apply`, `ValueDistribution.logCounting_inv`, `Real.hasDerivWithinAt_arccos_Iic`, `measurableSet_of_differentiableWithinAt_Ici`, `Real.contDiffOn_arcsin`, `ConvexOn.sSup_affine_eq`, `Real.contDiffAt_arccos_iff`, `deriv_sqrt_mul_log'`, `Real.differentiableAt_binEntropy_iff_ne_zero_one`, `ContinuousLinearMap.toSpanSingletonCLE_symm_apply`, `Real.deriv_tan`, `isConformalMap_iff_is_complex_or_conj_linear`, `hasFPowerSeriesAt_iff'`, `hasStrictDerivAt_exp_zero`, `differentiableAt_comp_sub_const`, `smooth_functions_tower`, `Real.contDiffAt_rpow_of_ne`, `Real.hasStrictDerivAt_exp`, `MeasureTheory.integral_exp_pos`, `LinearMap.mem_span_iff_continuous`, `Complex.analyticOnNhd_sinh`, `Complex.analyticWithinAt_cos`, `ConvexOn.real_sSup_affine_eq`, `RCLike.re_extendTo𝕜'ₗ`, `isBoundedBilinearMap_smulRight`, `MeasureTheory.lintegral_coe_eq_integral`, `MeasureTheory.integral_coe_le_of_lintegral_coe_le`, `MeasureTheory.toReal_rnDeriv_tilted_right`, `ContDiffBump.contDiffWithinAt`, `LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop`, `LeftInvariantDerivation.coeFnAddMonoidHom_apply`, `Complex.det_conjLIE`, `RCLike.realLinearIsometryEquiv_apply`, `ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior`, `ContinuousLinearMap.norm_smulRightL_apply`, `differentiableAt_iff_comp_neg`, `hasFPowerSeriesAt_iff`, `NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal`, `hasStrictDerivAt_pow`, `Derivation.evalAt_apply`, `derivWithin_mem_iff`, `ConvexOn.univ_sSup_of_nat_affine_eq`, `ConvexOn.slope_le_leftDeriv_of_mem_interior`, `MeasureTheory.integral_toReal`, `NormedSpace.dual_def`, `Seminorm.smul_le_smul`, `exists_eq_const_mul_setIntegral_of_ae_nonneg`, `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`, `MeasureTheory.tilted_apply'`, `Real.hasDerivWithinAt_arcsin_Iic`, `MeasureTheory.exists_notMem_null_average_le`, `differentiableWithinAt_Ioi_iff_Ici`, `integral_im`, `differentiableOn_zpow`, `Real.iteratedDerivWithin_sin_Ioo`, `Complex.conjCLE_coe`, `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`, `MeasureTheory.SignedMeasure.im_toComplexMeasure`, `RCLike.complexLinearIsometryEquiv_apply`, `iter_deriv_pow`, `Real.deriv2_negMulLog`, `Urysohns.CU.lim_eq_midpoint`, `fderiv_eq_smul_deriv`, `MeasureTheory.toReal_setLAverage`, `Real.smoothTransition.contDiff`, `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`, `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	5741 math, 1 bridge math: `Polynomial.fderiv`, `Matrix.l2_opNorm_toEuclideanCLM`, `OrthonormalBasis.singleton_repr`, `Pi.comul_eq_adjoint`, `Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁`, `instSeparatingDual`, `TangentBundle.continuousLinearMapAt_model_space`, `hasFDerivAt_iff_hasDerivAt`, `ContinuousLinearEquiv.antilipschitz`, `MeasureTheory.Measure.integral_comp_inv_smul`, `VectorBundleCore.toFiberBundleCore_coordChange`, `ContMDiffAt.coordChangeL`, `iteratedDeriv_scomp_two`, `MeromorphicOn.deriv`, `TensorProduct.mapInclIsometry_apply`, `ContinuousLinearMap.rayleigh_smul`, `Real.differentiableOn_arcosh`, `Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint`, `NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm`, `Real.hasDerivAt_arccos`, `WeakFEPair.differentiableAt_Λ`, `ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior`, `LinearIsometryEquiv.strictConvex_preimage`, `TemperedDistribution.lineDerivOpCLM_eq`, `PiTensorProduct.mapL_id`, `closure_diff_intrinsicFrontier`, `Submodule.starProjection_apply_eq_isComplProjection`, `Orientation.oangle_sign_smul_add_right`, `DiffContOnCl.smul`, `MeasureTheory.Lp.toTemperedDistributionCLM_apply`, `fderiv_iteratedFDeriv`, `Polynomial.differentiableWithinAt`, `Trivialization.pullback_linear`, `MeasureTheory.setIntegral_tilted`, `FormalMultilinearSeries.comp_rightInv_aux1`, `ContinuousLinearMap.hasFPowerSeriesOnBall`, `MDifferentiable.coordChangeL`, `Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul`, `TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq`, `hasStrictFDerivAt_const_add_iff`, `Seminorm.isBounded_const`, `MeasureTheory.L1.SimpleFunc.norm_Integral_le_one`, `isConformalMap_conj`, `hasStrictFDerivAt_apply`, `differentiableWithinAt_finCons'`, `Orthonormal.linearIndependent`, `ContinuousMultilinearMap.norm_mkPiRing`, `differentiableAt_comp_const_add`, `fderiv_snd`, `LinearIsometryEquiv.hasStrictFDerivAt`, `Bundle.Trivial.continuousLinearEquivAt_trivialization`, `EuclideanGeometry.dist_smul_vadd_sq`, `Bundle.ContMDiffRiemannianMetric.isVonNBounded`, `isBounded_polar_of_mem_nhds_zero`, `SchwartzMap.lineDerivOpCLM_eq`, `deriv_sub_const_fun`, `real_inner_div_norm_mul_norm_eq_neg_one_iff`, `TensorProduct.enorm_lid`, `ConformalAt.differentiableAt`, `Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent`, `differentiableAt_comp_neg`, `MeasureTheory.condExpInd_of_measurable`, `MeromorphicAt.fun_iterated_deriv`, `hasDerivWithinAt_Iio_iff_Iic`, `TensorProduct.inner_tmul`, `AffineMap.hasStrictDerivAt_lineMap`, `ContinuousLinearMap.isPositive_iff_eq_sum_rankOne`, `HasMFDerivAt.mul`, `Bundle.ContMDiffRiemannianMetric.contMDiff`, `continuousOn_stereoToFun`, `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`, `Orthonormal.inner_left_finsupp`, `ProbabilityTheory.isGaussian_iff_gaussian_charFun`, `ContinuousLinearMap.mulLeftRight_isBoundedBilinear`, `Real.differentiable_arctan`, `norm_cfcₙHom`, `ProperCone.innerDual_le_innerDual`, `Filter.EventuallyEq.derivWithin_eq_of_nhds`, `RCLike.map_apply`, `Real.differentiableAt_mulExpNegMulSq`, `NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace`, `OrthonormalBasis.orthogonalProjection_eq_sum`, `hasDerivWithinAt_ofNat`, `IsStarNormal.instNonUnitalContinuousFunctionalCalculus`, `ContinuousLinearMap.analyticWithinAt_bilinear`, `Complex.restrictScalars_one_smulRight'`, `MeasureTheory.aestronglyMeasurable_condExpInd`, `HasCompactSupport.convolution_integrand_bound_left`, `ContinuousLinearMap.compSL_apply`, `ContinuousLinearMap.continuous₂`, `MeasureTheory.Martingale.smul`, `LinearMap.IsSymmetric.inner_map_polarization`, `ContinuousLinearEquiv.differentiable`, `ContinuousLinearMap.opNorm_prod`, `hasDerivWithinAt_add_const_iff`, `IsSelfAdjoint.quasispectrumRestricts`, `LinearMap.coe_toSeminorm`, `ContinuousLinearMap.integral_compLp`, `FormalMultilinearSeries.comp_partialSum`, `mellin_eq_fourier`, `SchwartzMap.instLineDerivLeftSMulReal`, `tendsto_birkhoffAverage_apply_sub_birkhoffAverage'`, `LinearMap.adjoint_adjoint`, `HasFTaylorSeriesUpTo.differentiable`, `DoubleCentralizer.star_snd`, `ContinuousLinearMap.norm_inr_le_one`, `Affine.Simplex.orthogonalProjectionSpan_map`, `taylorWithin_succ`, `TensorProduct.ext_iff_inner_left`, `MeasureTheory.Measure.addHaar_image_continuousLinearMap`, `EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal`, `differentiableOn_star_iff`, `derivWithin_zero_of_frequently_mem`, `InnerProductSpace.toLinearIsometry_toDual`, `RCLike.ofRealCLM_apply`, `SchwartzMap.integral_sesq_fourier_fourier`, `HasMFDerivAt.add`, `Real.dimH_of_mem_nhds`, `Filter.IsBoundedUnder.smul_tendsto_zero`, `MeasureTheory.charFun_eq_fourierIntegral'`, `hasFDerivAt_comp_add_right`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `InnerProductSpace.span_gramSchmidtNormed`, `Real.differentiableAt_arcsin`, `LinearIsometryEquiv.analyticOnNhd`, `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`, `Ideal.toCharacterSpace_apply_eq_zero_of_mem`, `MeasureTheory.condExpInd_ae_eq_condExpIndSMul`, `MeasureTheory.convolution_eq_right'`, `hasStrictFDerivAt_exp_of_mem_ball`, `hasFDerivAt_iff_hasGradientAt`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn`, `Isometry.preimage_perpBisector`, `RCLike.reCLM_apply`, `smooth_barycentric_coord`, `NumberField.Units.finrank_eq_rank`, `ContinuousMultilinearMap.cpolynomialOn`, `LinearIsometry.norm_compContinuousAlternatingMap`, `MeasureTheory.hausdorffMeasure_segment`, `MeasureTheory.integrable_withDensity_iff_integrable_coe_smul`, `IsHilbertSum.surjective_isometry`, `curveIntegral_smul`, `Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face`, `Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub`, `ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric`, `Submodule.reflection_trans_reflection`, `dist_midpoint_right`, `Orientation.inner_rotation_pi_div_two_right_smul`, `extDeriv_constOfIsEmpty`, `Orientation.oangle_add_left_smul_rotation_pi_div_two`, `CFC.monotoneOn_one_sub_one_add_inv`, `Bundle.Trivial.symmL_trivialization`, `Real.fourierIntegral_comp_linearIsometry`, `Real.fderiv_fourierIntegral`, `Submodule.orthogonalDecomposition_symm_apply`, `hasStrictFDerivAt_list_prod_finRange'`, `Affine.Simplex.sSameSide_excenter_singleton_point`, `MeasureTheory.integral_smul_nnreal_measure`, `OrthogonalFamily.linearIsometry_apply_single`, `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`, `AffineIsometryEquiv.coe_symm_toAffineEquiv`, `Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot`, `NonUnitalCStarAlgebra.toStarModule`, `Complex.circleTransformDeriv_eq`, `hasDerivAt_sqrt_mul_log`, `LinearMap.IsSymmetric.restrictScalars`, `ContinuousAffineMap.fderiv`, `ConvexOn.differentiableWithinAt_Iio_of_mem_interior`, `ContinuousLinearMap.continuous_det`, `HasFiniteFPowerSeriesAt.neg`, `IsometryEquiv.toRealLinearIsometryEquiv_symm_apply`, `ZSpan.volume_real_fundamentalDomain`, `isSeparable_range_derivWithin`, `PiTensorProduct.mapLMonoidHom_apply`, `Complex.ofRealCLM_coe`, `Complex.kahler`, `MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left`, `ClosedSubmodule.toSubmodule_orthogonal_eq`, `ContinuousLinearMap.map_add_add`, `ContinuousAlternatingMap.norm_constOfIsEmpty`, `fderivWithin_comp_add_left`, `MeasureTheory.Measure.integral_comp_mul_right`, `RightDerivMeasurableAux.D_subset_differentiable_set`, `ContinuousLinearMap.sSup_unit_ball_eq_norm`, `Complex.areaForm`, `intervalIntegral.inv_smul_integral_comp_div_add`, `ContinuousAlternatingMap.norm_ofSubsingleton_id_le`, `WeakDual.isCompact_polar`, `MeromorphicOn.divisor_fun_smul`, `finrank_real_complex_fact'`, `Real.deriv_negMulLog`, `Real.hasDerivAt_sigmoid`, `Manifold.IsImmersionAtOfComplement.target_subset_preimage_target`, `EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center`, `ContinuousMultilinearMap.norm_iteratedFDerivComponent_le`, `Dual.isClosed_image_polar_of_mem_nhds`, `ContinuousLinearMap.analyticWithinAt`, `ContinuousAffineMap.differentiableWithinAt`, `ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap`, `ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff`, `Real.fourierIntegralInv_eq'`, `AffineMap.hasDerivAtFilter`, `PositiveLinearMap.apply_le_of_isSelfAdjoint`, `Matrix.IsHermitian.det_abs`, `RCLike.ofRealLI_apply`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm`, `LinearMap.IsPositive.ne_zero_iff`, `HasCompactSupport.integral_Ioi_deriv_eq`, `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`, `LinearMap.isPositive_adjoint_comp_self`, `ProbabilityTheory.covarianceBilinDual_apply'`, `Manifold.IsImmersionAt.map_target_subset_target`, `Real.nnnorm_deriv_mulExpNegMulSq_le_one`, `Submodule.toLinearEquiv_orthogonalDecomposition_symm`, `ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm`, `OrthonormalBasis.repr_injective`, `LinearMap.IsSymmetric.isFinitelySemisimple`, `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`, `hasFTaylorSeriesUpToOn_top_iff_right`, `MeasureTheory.charFunDual_apply`, `ContinuousLinearMap.IsPositive.inner_left_eq_inner_right`, `Complex.ofRealLI_apply`, `Affine.Simplex.circumcenter_map`, `expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul`, `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`, `FormalMultilinearSeries.radius_pi_eq_iInf`, `ContinuousLinearMap.norm_inl_le_one`, `MeasureTheory.norm_condExpL2_le`, `contDiffAt_norm_smul_iff`, `ProbabilityTheory.IsGaussian.integrable_dual`, `ContinuousLinearEquiv.contDiff_comp_iff`, `NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne`, `SchwartzMap.pairing_apply_apply`, `Submodule.instStrictConvexSpace`, `InnerProductSpace.isIdempotentElem_rankOne_self`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply`, `Matrix.cstar_nnnorm_def`, `MeasureTheory.weightedSMul_apply`, `ContinuousMultilinearMap.norm_map_snoc_le`, `AbsolutelyContinuousOnInterval.integral_deriv_eq_sub`, `ContinuousLinearMap.comp_condExp_comm`, `ImplicitFunctionData.isInvertible_fderiv_prodFun`, `Trivialization.continuousLinearMapAt_apply`, `intervalIntegral.integral_hasFDerivAt_of_tendsto_ae`, `iteratedFDerivWithin_eventually_congr_set`, `ApproximatesLinearOn.lipschitz`, `Real.hasStrictDerivAt_rpow_const_of_ne`, `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`, `ContDiff.hasStrictFDerivAt`, `Affine.Simplex.inv_height_eq_sum_mul_inv_dist`, `Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite`, `FormalMultilinearSeries.changeOriginSeriesTerm_apply`, `Matrix.l2_opNorm_mulVec`, `Meromorphic.deriv`, `HasFTaylorSeriesUpTo.cont`, `ImplicitFunctionData.isCompl_ker`, `EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne`, `ContinuousLinearMap.hasDerivAtFilter`, `DoubleCentralizer.intCast_snd`, `Real.fourierIntegral_eq`, `PeriodPair.basis_one`, `mdifferentiableWithinAt_iff_of_mem_maximalAtlas`, `MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one`, `DoubleCentralizer.range_toProdMulOpposite`, `ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall`, `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`, `Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude`, `Orientation.kahler_comp_rightAngleRotation'`, `dist_sq_lineMap_lineMap_of_inner_eq_zero`, `circleIntegral_def_Icc`, `MeasureTheory.inner_condExpL2_left_eq_right`, `MeasureTheory.integral_unique`, `Orientation.rotation_eq_self_iff`, `setIntegral_withDensity_eq_setIntegral_smul₀`, `Affine.Simplex.excenter_singleton_mem_affineSpan_range`, `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`, `Orientation.two_zsmul_oangle_smul_left_of_ne_zero`, `differentiableWithinAt_neg_iff`, `circleIntegrable_iff`, `ProbabilityTheory.covarianceBilinDual_apply`, `Submodule.reflection_orthogonal_apply`, `hasFDerivAt_stereoInvFunAux`, `SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left`, `ContinuousLinearMap.comp_memLp`, `IsOpen.exists_subset_affineIndependent_span_eq_top`, `Real.fderiv_fourierChar_neg_bilinear_right_apply`, `LinearMap.IsSymmetric.diagonalization_apply_self_apply`, `EuclideanGeometry.orthogonalProjection_congr`, `LinearMap.IsPositive.re_inner_nonneg_right`, `intervalIntegral.integral_deriv_of_contDiffOn_uIcc`, `Unitization.real_cfcₙ_eq_cfc_inr`, `real_inner_smul_self_left`, `norm_iteratedFDeriv_mul_le`, `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`, `DoubleCentralizer.natCast_fst`, `hasFPowerSeriesOnBall_pi_iff`, `SmoothPartitionOfUnity.contMDiffAt_finsum`, `LinearMap.IsSymmetric.im_inner_self_apply`, `ContinuousLinearMap.IsPositive.toLinearMap`, `AnalyticOnNhd.iteratedFDeriv_of_isOpen`, `ContinuousLinearMap.norm_compLp_le`, `Submodule.toLinearEquiv_orthogonalDecomposition`, `Continuous.convolution_integrand_fst`, `ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries`, `Affine.Simplex.dist_point_faceOppositeCentroid`, `differentiableWithinAt_abs_pos`, `continuousOn_dslope`, `ContinuousLinearEquiv.symm_toDiffeomorph`, `ContDiffMapSupportedIn.structureMapCLM_apply`, `OrthonormalBasis.toBasis_tensorProduct`, `TensorProduct.congrIsometry_refl_refl`, `ContinuousAlternatingMap.opNNNorm_pi`, `HasFPowerSeriesWithinAt.const_smul`, `norm_smul_inv_norm'`, `MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero`, `LipschitzWith.ae_lineDeriv_sum_eq`, `SchwartzMap.lineDerivOp_fourier_eq`, `Orientation.inner_mul_inner_add_areaForm_mul_areaForm`, `Orientation.areaForm_le`, `isClosedEmbedding_cfcₙAux`, `det_fderivPolarCoordSymm`, `setIntegral_withDensity_eq_setIntegral_toReal_smul`, `deriv_comp_const_sub`, `TensorProduct.enorm_comm`, `innerSL_apply_apply`, `Submodule.isOrtho_sup_right`, `HasFPowerSeriesWithinOnBall.restrictScalars`, `isVonNBounded_iff`, `ContinuousLinearEquiv.subsingleton_or_norm_symm_pos`, `aemeasurable_smul_const`, `LinearIsometry.rTensor_def`, `EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right`, `Affine.Simplex.incenter_map`, `SchwartzMap.integral_bilin_fourierInv_eq`, `LinearMap.adjoint_innerₛₗ_apply`, `TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars`, `Real.differentiable_sinh`, `HasFTaylorSeriesUpTo.hasFDerivAt`, `ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap`, `hasDerivAt_neg'`, `ContMDiffWithinAt.mfderivWithin_const`, `MeasureTheory.Measure.toSphere_apply_aux`, `Orientation.neg_rotation`, `Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv`, `AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn`, `Unitization.splitMul_apply`, `GaussianFourier.integral_cexp_neg_mul_sq_norm`, `tendsto_integral_peak_smul_of_integrable_of_tendsto`, `inner_eq_norm_mul_iff`, `ContinuousLinearMap.toBilinForm_apply`, `RCLike.map_same_eq_id`, `differentiable_fun_neg_iff`, `ProbabilityTheory.covarianceBilin_apply_eq_cov`, `ProbabilityTheory.covarianceBilin_self`, `DoubleCentralizer.nnnorm_def'`, `ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm`, `LinearMap.adjoint_eq_toCLM_adjoint`, `ClosedSubmodule.orthogonal_gc`, `LinearMap.isPositive_id`, `dist_left_midpoint`, `AffineSubspace.left_mem_perpBisector`, `bilinearIteratedFDerivTwo_eq_iteratedFDeriv`, `NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm`, `image_isVonNBounded_iff`, `EuclideanGeometry.preimage_inversion_perpBisector_inversion`, `eqOn_dslope_sub_smul`, `deriv_mul_const_field`, `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`, `DoubleCentralizer.zero_snd`, `LeftInvariantDerivation.left_invariant'`, `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`, `derivWithin_natCast`, `CFC.nnnorm_sqrt`, `IsometryEquiv.toRealLinearIsometryEquiv_apply`, `MeasureTheory.condExpIndL1Fin_smul`, `GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace`, `InnerProductSpace.span_gramSchmidtNormed_range`, `ContinuousLinearMap.opNorm_comp_linearIsometryEquiv`, `ProbabilityTheory.uncenteredCovarianceBilin_apply`, `Submodule.orthogonal_disjoint`, `InnerProductGeometry.angle_smul_right_of_pos`, `TemperedDistribution.lineDerivOp_fourier_eq`, `WeakFEPair.symm_Λ₀_eq`, `ContDiffPointwiseHolderAt.isBigO`, `Real.deriv_log`, `LinearMap.isSelfAdjoint_toContinuousLinearMap_iff`, `ContDiff.differentiable_deriv_two`, `SchwartzMap.decay'`, `Module.Basis.ofZLatticeBasis_apply`, `ContinuousAlternatingMap.map_insertNth`, `intervalIntegral.integral_comp_sub_div`, `FormalMultilinearSeries.derivSeries_coeff_one`, `VonNeumannAlgebra.ext_iff`, `Filter.EventuallyEq.lineDerivWithin_eq`, `Complex.ofRealCLM_norm`, `Submodule.starProjection_add_starProjection_orthogonal`, `Matrix.spectrum_toLpLin`, `HasDerivAt.comp_ofReal`, `OrderedFinpartition.norm_compAlongOrderedFinpartition_le`, `tangentConeAt_nonempty_of_properSpace`, `instIsZLatticeComap`, `not_differentiableAt_norm_zero`, `mdifferentiableOn_symm_coordChangeL`, `ContinuousLinearMap.opNorm_lsmul_apply_le`, `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`, `BoxIntegral.unitPartition.mem_smul_span_iff`, `intervalIntegral.integral_comp_mul_sub`, `SchwartzMap.bilinLeftCLM_apply`, `derivWithin_congr`, `InnerProductSpace.toDual_symm_apply`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_zero`, `IsConformalMap.is_complex_or_conj_linear`, `NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne`, `HasGradientAt.hasDerivAt'`, `derivWithin_comp_const_sub`, `IsHilbertSum.linearIsometryEquiv_symm_apply`, `Affine.Triangle.sbtw_touchpoint_singleton`, `Affine.Triangle.dist_point_faceOppositeCentroid`, `OrderedFinpartition.norm_applyOrderedFinpartition_le`, `ContinuousLinearMap.cpolynomialAt`, `HasMFDerivWithinAt.prodMk`, `differentiableOn_pi`, `AffineMap.hasDerivWithinAt`, `Submodule.starProjection_singleton`, `HasFPowerSeriesAt.eventually_hasSum`, `LeftInvariantDerivation.left_invariant`, `ContinuousLinearMap.comp_condExp_add_const_comm`, `Bundle.RiemannianMetric.isVonNBounded`, `ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le`, `Orientation.tan_oangle_add_right_smul_rotation_pi_div_two`, `Affine.Simplex.mem_circumsphere`, `hasStrictFDerivAt_snd`, `Complex.convexHull_reProdIm`, `toIsBoundedSMul`, `Complex.conjLIE_apply`, `one_mem_posTangentConeAt_iff_frequently`, `Real.hasDerivAt_sin`, `HasFPowerSeriesAt.neg`, `CPolynomialOn.iterated_deriv`, `ContDiff.continuous_deriv_one`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal`, `EuclideanGeometry.orthogonalProjection_contLinear`, `curveIntegralFun_smul`, `hasDerivAt_exp_zero_of_radius_pos`, `Module.Basis.exists_opNorm_le`, `ClosedSubmodule.mem_orthogonal'`, `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`, `EuclideanGeometry.Sphere.mem_commonExtTangents_iff`, `derivWithin_fun_const_smul_field`, `OrthogonalFamily.orthonormal_sigma_orthonormal`, `mdifferentiableWithinAt_iff_target_inter`, `differentiableWithinAt_fun_neg_iff`, `InnerProductSpace.canonicalCovariantTensor_eq_sum`, `MeasureTheory.charFun_eq_fourierIntegral`, `ContinuousAlternatingMap.piLIE_apply_apply`, `Matrix.PosSemidef.sqrt_eq_zero_iff`, `Real.differentiableOn_log`, `ProbabilityTheory.integral_continuousLinearMap_gaussianReal`, `combo_mem_ball_of_ne`, `UniqueMDiffOn.uniqueDiffOn`, `FDerivMeasurableAux.le_of_mem_A`, `lintegral_fderiv_lineMap_eq_edist`, `EuclideanGeometry.oangle_sign_eq_zero_iff_collinear`, `ContinuousLinearMap.isBigOWith_id`, `TemperedDistribution.smulLeftCLM_compL_smulLeftCLM`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_left`, `curveIntegrable_fun_neg_iff`, `hasDerivWithinAt_zero`, `ContDiffAt.hasStrictDerivAt`, `ContinuousLinearEquiv.coe_toDiffeomorph_symm`, `Submodule.reflection_symm`, `OrthonormalBasis.det_eq_neg_det_of_opposite_orientation`, `LinearMap.IsSymmetric.orthogonalFamily_eigenspaces`, `MeasureTheory.isAddHaarMeasure_hausdorffMeasure`, `TensorProduct.ext_iff_inner_right_threefold'`, `tangentCoordChange_def`, `signedDist_right_congr`, `Filter.EventuallyEq.lineDeriv_eq`, `differentiableWithinAt_inv`, `CurveIntegrable.zero`, `ContinuousMultilinearMap.contDiffAt`, `hasDerivAtFilter_ofNat`, `ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq`, `OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₃`, `curveIntegrable_smul_iff`, `TensorProduct.toLinearEquiv_lidIsometry`, `HasFPowerSeriesOnBall.restrictScalars`, `GaussianFourier.integral_cexp_neg_mul_sq_norm_add`, `Real.differentiableOn_arcsin`, `ContinuousLinearMap.opNNNorm_le_iff`, `derivWithin_zero_of_frequently_const`, `ContinuousLinearMap.isometry_mul_flip`, `DiffContOnCl.differentiableAt'`, `ZSpan.smul`, `AnalyticOnNhd.eval_linearMap'`, `EuclideanGeometry.reflection_map`, `HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt`, `Module.Basis.ofZLatticeComap_apply`, `AffineEquiv.continuous_of_finiteDimensional`, `conformal_const_smul`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective`, `ContinuousLinearMap.adjoint_id`, `Complex.hasStrictFDerivAt_exp_real`, `InnerProductSpace.smul_left`, `ClosedSubmodule.inf_orthogonal`, `balanced_ball_zero`, `iteratedFDerivWithin_succ_eq_comp_left`, `ContinuousLinearMap.isPositive_natCast`, `tendsto_birkhoffAverage_apply_sub_birkhoffAverage`, `ContinuousMultilinearMap.opNorm_zero_iff`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt`, `AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn`, `hasStrictFDerivAt_exp_smul_const_of_mem_ball'`, `MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart`, `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`, `CStarModule.innerSL_apply`, `MeromorphicOn.fun_smul`, `monomial_has_deriv_aux`, `LinearIsometryEquiv.conjStarAlgEquiv_apply`, `MeasureTheory.smul_convolution`, `Bundle.ContinuousLinearMap.vectorBundle`, `Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff`, `Real.vector_fourierIntegral_eq_integral_exp_smul`, `LinearMap.toMatrixOrthonormal_reindex`, `contDiff_one_iff_fderiv`, `MeasureTheory.ConvolutionExistsAt.integrable`, `nndist_midpoint_right`, `Real.hasDerivAt_mul_log`, `Real.fourier_real_eq_integral_exp_smul`, `EuclideanGeometry.Sphere.mem_tangentsFrom_iff`, `ProbabilityTheory.covarianceOperator_apply`, `InnerProductGeometry.angle_smul_left_of_neg`, `iter_deriv_zpow'`, `differentiableWithinAt_abs`, `MeasureTheory.integral_tilted`, `ContDiffAt.laplacian_CLM_comp_left`, `CStarAlgebra.span_nonneg_inter_unitBall`, `hasLineDerivAt_iff_isLittleO_nhds_zero`, `Real.deriv_arccos`, `Complex.differentiableOn_dslope`, `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`, `isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts`, `HasFiniteFPowerSeriesOnBall.sum`, `LocallyBoundedVariationOn.ae_differentiableWithinAt`, `MeasureTheory.Measure.toSphere_real_apply_univ`, `ContinuousLinearMap.opNorm_mul_flip_apply`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars`, `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`, `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`, `stronglyMeasurable_derivWithin_Ioi`, `SchwartzMap.fderivCLM_apply`, `hasStrictDerivAt_abs_pos`, `deriv_sqrt_mul_log`, `ContinuousLinearMap.smul_compLp`, `hasDerivWithinAt_abs_pos`, `Submodule.norm_starProjection_apply_le`, `ContinuousLinearMap.norm_extendTo𝕜`, `IsLocalMax.fderiv_eq_zero`, `ContinuousLinearMap.contMDiff`, `ContinuousLinearMap.mdifferentiable`, `HasSum.hasSum_at_zero`, `Pretrivialization.continuousLinearMap_symm_apply'`, `HasFPowerSeriesAt.add`, `differentiableWithinAt_sub_const_iff`, `differentiable_descPochhammer_eval`, `VectorBundleCore.coordChange_self`, `EuclideanGeometry.Sphere.mem_commonTangents_iff`, `differentiable_fst`, `ContinuousAlternatingMap.curryLeft_smul`, `fderiv_const_smul_field`, `HasFTaylorSeriesUpToOn.comp_continuousAffineMap`, `LinearIsometry.map_starProjection'`, `intervalIntegral.deriv_integral_right`, `tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support`, `antideriv_bernoulliFun`, `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`, `Affine.Simplex.excenterWeightsUnnorm_reindex`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn`, `OrthonormalBasis.repr_self`, `PointwiseConvergenceCLM.tendsto_nhds`, `Submodule.symmetric_isOrtho`, `iteratedDeriv_scomp_three`, `ContDiffAt.continuousAt_fderiv`, `hasDerivWithinAt_pi`, `IsometryEquiv.midpoint_fixed`, `lineDifferentiableWithinAt_congr_set`, `Real.integrable_prod_sub`, `Orientation.oangle_smul_left_of_neg`, `isVonNBounded_ball`, `OrthogonalFamily.norm_sq_diff_sum`, `MDifferentiable.smul`, `deriv_const'`, `norm_smul_inv_norm`, `ContinuousLinearEquiv.comp_hasFDerivAt_iff`, `ContinuousLinearMap.eq_adjoint_iff`, `deriv.star`, `ContDiffAt.fderiv_succ`, `Orientation.volumeForm_map`, `rotation_apply`, `toMatrix_rotation`, `PiTensorProduct.toDualContinuousMultilinearMap_apply_apply`, `MeasureTheory.Measure.addHaar_ball_of_pos`, `SchwartzMap.toLpCLM_apply`, `LinearMap.IsSymmetric.directSum_decompose_apply`, `deriv_abs_neg`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le`, `Real.differentiableWithinAt_arccos_Ici`, `HasFPowerSeriesAt.comp`, `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`, `Unitary.coe_linearIsometryEquiv_apply`, `OrthonormalBasis.toBasis_adjustToOrientation`, `MeasureTheory.convolution_tendsto_right`, `gelfandStarTransform_apply_apply`, `Submodule.reflection_singleton_apply`, `RCLike.nonUnitalContinuousFunctionalCalculus`, `smul_unitClosedBall_of_nonneg`, `HasFTaylorSeriesUpToOn.zero_eq'`, `SchwartzMap.compCLMOfContinuousLinearEquiv_apply`, `AffineIsometryEquiv.pointReflection_midpoint_left`, `HarmonicAt.analyticAt_complex_partial`, `HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal`, `interior_convexHull_nonempty_iff_affineSpan_eq_top`, `ContDiff.continuous_deriv`, `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`, `isClosed_setOf_tendsto_birkhoffAverage`, `MeasureTheory.weightedSMul_nonneg`, `signedDist_left_congr`, `MeasureTheory.convolution_integrand_bound_right_of_le_of_subset`, `ContinuousMap.toLp_norm_le`, `exists_deriv_eq_zero`, `FormalMultilinearSeries.id_apply_one'`, `ContinuousMultilinearMap.norm_smulRightL_le`, `tensorIteratedFDerivTwo_eq_iteratedFDeriv`, `AnalyticOnNhd.iteratedFDeriv`, `ContinuousLinearEquiv.contDiffAt_comp_iff`, `Affine.Simplex.ExcenterExists.touchpoint_map`, `WeakFEPair.h_feq`, `differentiableAt_smul_iff`, `ContinuousLinearMap.precompL_apply`, `DoubleCentralizer.nnnorm_snd`, `Orientation.inner_rightAngleRotation_swap'`, `differentiableAt_comp_add_const`, `EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw`, `ContinuousLinearEquiv.isBigO_comp`, `MeasureTheory.Measure.addHaar_preimage_smul`, `setIntegral_withDensity_eq_setIntegral_toReal_smul'`, `QuadraticForm.equivalent_signType_weighted_sum_squared`, `OrthonormalBasis.measurePreserving_repr`, `InformationTheory.leftDeriv_klFun_one`, `Module.Basis.parallelepiped_reindex`, `Submodule.reflection_apply`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars`, `curveIntegralFun_segment`, `SchwartzMap.integral_fourierInv_smul_eq`, `RCLike.reCLM_norm`, `Besicovitch.SatelliteConfig.exists_normalized_aux2`, `differentiable_finCons'`, `signedDist_triangle`, `Submodule.orthogonal_eq_bot_iff`, `TensorProduct.adjoint_map`, `Real.hasDerivAt_arcosh`, `curveIntegral_neg`, `tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn`, `VectorBundleCore.contMDiffOn_coordChange`, `FormalMultilinearSeries.radius_le_smul`, `LinearIsometryEquiv.lTensor_apply`, `EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint`, `InnerProductSpace.gramSchmidt_def`, `ConvexOn.monotoneOn_rightDeriv`, `intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right`, `CStarMatrix.toCLM_injective`, `iteratedFDerivWithin_succ_const`, `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`, `hasDerivAt_iff_isLittleO`, `Affine.Simplex.orthogonalProjectionSpan_eq_point`, `LocallyBoundedVariationOn.ae_differentiableAt`, `MonotoneOn.intervalIntegrable_deriv`, `Unitary.linearIsometryEquiv_coe_apply`, `isBounded_iff_subset_smul_closedBall`, `LDL.lowerInv_eq_gramSchmidtBasis`, `ContDiffAt.differentiableAt`, `Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux`, `hasFPowerSeriesAt_const`, `hasStrictFDerivAt_pi'`, `fderiv_eq_deriv_mul`, `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`, `FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius`, `ContinuousMultilinearMap.curry0_apply`, `hasFDerivAtFilter_sub_const_iff`, `Affine.Simplex.sSameSide_incenter_point`, `norm_iteratedFDerivWithin_zero`, `iteratedFDerivWithin_of_isOpen`, `ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear`, `FormalMultilinearSeries.radius_compNeg`, `EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq`, `setIntegral_withDensity_eq_setIntegral_toReal_smul₀`, `Polynomial.differentiableOn_aeval`, `SchwartzMap.integral_bilin_fourierIntegral_eq`, `fourier_gaussian_innerProductSpace`, `EuclideanGeometry.oangle_midpoint_right`, `Affine.Simplex.ExcenterExists.excenter_map`, `mdifferentiableAt_iff`, `LinearIsometryEquiv.adjoint_eq_symm`, `NumberField.mixedEmbedding.negAt_apply_snd`, `extDeriv_fun_smul`, `TensorProduct.mapIsometry_id_id`, `ContinuousAlternatingMap.toAlternatingMap_curryLeft`, `Orientation.neg_rotation_neg_pi_div_two`, `Matrix.toEuclideanLin_apply`, `IsContDiffImplicitAt.hasFDerivAt`, `iteratedDerivWithin_eq_iteratedFDerivWithin`, `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`, `hasFDerivWithinAt_pi'`, `IsHilbertSum.hasSum_linearIsometryEquiv_symm`, `ContinuousLinearMap.opNorm_mul`, `Submodule.IsOrtho.map_iff`, `DoubleCentralizer.smul_toProd`, `InnerProductSpace.harmonicOnNhd_comp_CLE_iff`, `sameRay_iff_inv_norm_smul_eq_of_ne`, `ContinuousAlternatingMap.constOfIsEmptyLIE_apply`, `norm_sum_lt_of_strictConvexSpace`, `iteratedDerivWithin_eq_iterate`, `UniformConvexOn.strictConvexOn`, `TemperedDistribution.smulLeftCLM_neg`, `Orientation.oangle_sign_sub_smul_left`, `intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge'`, `MeasureTheory.SimpleFunc.integral_eq_sum_filter`, `PiTensorProduct.mapL_one`, `Real.hasStrictDerivAt_arccos`, `DoubleCentralizer.toProdMulOpposite_injective`, `deriv_const_add'`, `RCLike.conjCLE_apply`, `ContinuousLinearMap.norm_fst_le`, `MeasureTheory.Measure.quasiMeasurePreserving_smul`, `ContMDiffAt.mfderiv_apply`, `hasFDerivAt_snd`, `Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne`, `MeasureTheory.dominatedFinMeasAdditive_condExpInd`, `Complex.reCLM_nnnorm`, `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`, `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`, `ImplicitFunctionData.range_leftDeriv`, `aemeasurable_lineDeriv_uncurry`, `Function.HasTemperateGrowth.toTemperedDistribution_apply`, `Euclidean.closedBall_eq_image`, `Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite`, `ContinuousLinearMap.flipMultilinear_apply_apply`, `ContinuousMultilinearMap.uncurrySum_apply`, `Orthonormal.inner_left_fintype`, `NumberField.mixedEmbedding.negAt_preimage`, `InformationTheory.not_differentiableWithinAt_klFun_Iio_zero`, `HasLineDerivAt.tendsto_slope_zero_right`, `ContDiffPointwiseHolderAt.differentiableAt`, `ZLattice.comap_toAddSubgroup`, `QuadraticForm.equivalent_one_neg_one_weighted_sum_squared`, `HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope`, `compactOperator_topologicalClosure`, `Complex.deriv_ofReal_cpow_const`, `Submodule.coe_orthogonalDecomposition_symm`, `Affine.Simplex.excenterExists_reindex`, `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'`, `MeasureTheory.charFunDual_pi'`, `ContinuousLinearMap.adjointAux_norm`, `differentiable_apply`, `CStarMatrix.norm_def'`, `derivWithin_univ`, `NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae`, `Submodule.range_starProjection`, `MeasureTheory.Measure.addHaar_ball_mul`, `fderiv_neg`, `Real.norm_deriv_mulExpNegMulSq_le_one`, `LinearIsometryEquiv.inner_map_eq_flip`, `MeasureTheory.convolution_smul`, `Quaternion.linearIsometryEquivTuple_symm_apply`, `hasDerivAtFilter_natCast`, `Affine.Simplex.ninePointCircle_eq_circumsphere_medial`, `meromorphicOrderAt_ne_top_iff`, `HasFPowerSeriesAt.differentiableAt`, `MeasureTheory.SignedMeasure.singularPart_smul`, `Pi.counit_eq_adjoint`, `WithLp.unitization_algebraMap`, `ProbabilityTheory.covarianceBilin_apply_basisFun_self`, `LinearMap.toMatrixOrthonormal_apply_apply`, `MeasureTheory.condExpInd_nonneg`, `ContinuousLinearMap.fpowerSeries_apply_zero`, `tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux`, `Orientation.areaForm_to_volumeForm`, `stereoInvFunAux_apply`, `StrongFEPair.functional_equation`, `VectorPrebundle.mk_contMDiffCoordChange`, `derivWithin.fun_neg`, `Submodule.exists_add_mem_mem_orthogonal`, `PiTensorProduct.projectiveSeminorm_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'`, `EuclideanGeometry.Sphere.IsTangentAt.mem_space`, `iteratedDerivWithin_one`, `Affine.Simplex.circumcenter_reindex`, `LinearMap.IsSymmetric.coe_re_inner_self_apply`, `circleIntegral.integral_sub_inv_smul_sub_smul`, `ContinuousLinearMap.comp_memLp'`, `SchwartzMap.fourier_lineDerivOp_eq`, `Manifold.IsImmersionAtOfComplement.map_target_subset_target`, `ContinuousLinearMapWOT.inducingFn_apply`, `EuclideanGeometry.affineSpan_of_orthocentricSystem`, `TemperedDistribution.instLineDerivLeftSMulReal`, `ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith`, `CStarMatrix.inner_toCLM_conjTranspose_left`, `AffineSubspace.mem_perpBisector_iff_inner_eq_zero`, `Orientation.areaForm_neg_orientation`, `hasStrictDerivAt_exp_smul_const`, `AffineBasis.interior_convexHull`, `EuclideanGeometry.inversion_vsub_center`, `isBoundedBilinearMap_comp`, `aestronglyMeasurable_lineDeriv`, `set_smul_sphere_zero`, `Orientation.rightAngleRotation_trans_rightAngleRotation`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx`, `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`, `Trivialization.continuousLinearEquivAt_apply`, `hasLineDerivWithinAt_smul_iff`, `Asymptotics.IsTheta.smul`, `TemperedDistribution.fourierInv_lineDerivOp_eq`, `MDifferentiable.const_smul`, `MeasureTheory.condExpL2_indicator_ae_eq_smul`, `Affine.Simplex.excenter_eq_affineCombination`, `conformalAt_const_smul`, `Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius`, `IsMIntegralCurveOn.hasDerivWithinAt`, `FormalMultilinearSeries.rightInv_removeZero`, `isCompactOperator_iff_isCompact_closure_image_ball`, `ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply`, `DoubleCentralizer.norm_def`, `ClosedSubmodule.orthogonal_closure''`, `hasStrictDerivAt_exp_smul_const'`, `SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable`, `NumberField.mixedEmbedding.negAt_signSet_apply_isComplex`, `LinearIsometry.toAffineIsometry_toAffineMap`, `MeromorphicAt.fun_smul`, `LinearIsometryEquiv.adjoint_toLinearMap_eq_symm`, `SchwartzMap.smulLeftCLM_real_smul`, `Real.dimH_univ_eq_finrank`, `InnerProductSpace.toDualMap_apply_apply`, `EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents`, `Submodule.le_orthogonal_orthogonal`, `MeasureTheory.Measure.integral_comp_inv_mul_left`, `ContDiffBump.measure_closedBall_div_le_integral`, `Orientation.kahler_eq_zero_iff`, `PositiveLinearMap.preGNS_norm_def`, `LinearMap.eq_adjoint_iff_basis_left`, `contDiff_succ_iff_fderiv`, `PositiveLinearMap.leftMulMapPreGNS_apply`, `ContinuousLinearMap.opNNNorm_prod`, `ContinuousLinearEquiv.comp_differentiableOn_iff`, `MeasureTheory.measure_smul_average`, `MeasureTheory.condExpL1CLM_of_aestronglyMeasurable'`, `MDifferentiableOn.smul`, `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`, `smul_closedBall'`, `signedDist_apply_apply`, `spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul`, `ZSpan.quotientEquiv_apply_mk`, `LinearMap.IsSymmetricProjection.isIdempotentElem`, `Real.differentiableAt_rpow_const_of_ne`, `deriv.fun_neg'`, `Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem`, `Orientation.oangle_smul_left_self_of_nonneg`, `Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl`, `ProbabilityTheory.gaussianReal_map_continuousLinearMap`, `WeakDual.toStrongDual_inj`, `EuclideanSpace.volume_closedBall_fin_three`, `AntitoneOn.derivWithin_nonpos`, `Real.hasDerivAt_arsinh`, `ContinuousLinearMap.mulLeftRight_apply`, `norm_lineDeriv_le_of_lipschitz`, `SchwartzMap.differentiable`, `LinearIsometryEquiv.fderiv`, `Orientation.areaForm_swap`, `curveIntegral_fun_smul`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum`, `ContinuousLinearMap.holderₗ_apply_apply`, `hasFDerivAt_add_const_iff`, `taylor_tendsto`, `NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq`, `dslope_sub_smul`, `hasDerivAt_id'`, `rescale_to_shell_semi_normed_zpow`, `ContinuousMultilinearMap.unit_le_opNorm`, `ext_inner_map`, `ProbabilityTheory.covarianceOperator_zero`, `Bundle.ContinuousRiemannianMetric.symm`, `ContinuousMultilinearMap.curryRight_norm`, `mellin_hasDerivAt_of_isBigO_rpow`, `ContinuousLinearMap.analyticOn_bilinear`, `LinearIsometryEquiv.measurePreserving`, `Submodule.instHasOrthogonalProjectionOfCompleteSpace`, `CompactlySupportedContinuousMap.toRealLinearMap_apply_apply`, `AffineIsometryEquiv.pointReflection_toAffineEquiv`, `FDerivMeasurableAux.norm_sub_le_of_mem_A`, `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`, `MeasureTheory.convolution_lsmul`, `TemperedDistribution.instFourierAdd`, `Complex.sameRay_of_arg_eq`, `hasFDerivAt_sub_const_iff`, `NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm`, `curveIntegral_fun_zero`, `meromorphicNFOn_smul_iff_right_of_analyticOnNhd`, `ModelWithCorners.uniqueDiffOn_preimage`, `LinearMap.nonneg_iff_isPositive`, `EuclideanGeometry.Sphere.IsDiameter.wbtw`, `hasDerivAt_abs_neg`, `Affine.Simplex.mongePoint_mem_mongePlane`, `Orientation.kahler_swap`, `coe_innerSL_apply`, `Orientation.det_rotation`, `strongConcaveOn_zero`, `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`, `Real.deriv_sqrt_aux`, `OrthonormalBasis.prod_apply`, `iteratedFDeriv_add_apply`, `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`, `ContDiffWithinAt.hasFDerivWithinAt_nhds`, `Affine.Simplex.excenterWeightsUnnorm_map`, `EuclideanGeometry.Sphere.IsExtTangentAt.wbtw`, `HasStrictDerivAt.real_of_complex`, `ContinuousLinearMap.isClosed_image_coe_closedBall`, `DoubleCentralizer.central`, `Matrix.PosSemidef.det_sqrt`, `MeasureTheory.integral_condExpL2_eq`, `HasFPowerSeriesOnBall.coeff_zero`, `ContinuousLinearMap.instStarOrderedRing`, `BoxIntegral.HasIntegral.smul`, `Real.deriv_rpow_const`, `CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM`, `TemperedDistribution.instFourierSMul`, `integral_smul_const`, `FormalMultilinearSeries.norm_apply_eq_norm_coef`, `VectorBundleCore.localTriv_symm_fst`, `range_cfcₙHom`, `HasFPowerSeriesWithinOnBall.differentiableOn`, `HasMFDerivWithinAt.prodMap`, `hasDerivWithinAt_abs`, `hasFPowerSeriesOnBall_const`, `hasFDerivAtFilter_iff_isLittleO`, `Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius`, `ContinuousLinearEquiv.one_le_norm_mul_norm_symm`, `TensorProduct.lidIsometry_apply`, `ContDiffMapSupportedIn.seminorm_le_iff`, `NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis`, `Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub`, `ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le`, `ContinuousLinearMap.hasDerivAt`, `hasDerivAt_of_tendstoUniformly`, `BoundedVariationOn.intervalIntegrable_deriv`, `Orientation.volumeForm_def`, `Trivialization.comp_continuousLinearEquivAt_eq_coord_change`, `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`, `CompletelyPositiveMap.instLinearMapClassComplex`, `Real.deriv_sinh`, `iteratedFDeriv_sum`, `hasFDerivAt_ringInverse`, `LinearMap.IsPositive.inner_nonneg_left`, `norm_cfcₙ_lt`, `ContinuousMultilinearMap.opNorm_smul_le`, `contDiffAt_one_iff`, `Function.HasTemperateGrowth.fun_smul`, `ContinuousLinearMap.instCStarRingId`, `WeakDual.coe_toStrongDual`, `eq_zero_iff_forall_dual_eq_zero`, `hasFDerivAt_finCons`, `HasMFDerivWithinAt.neg`, `ModularGroup.lcRow0Extend_symm_apply`, `AffineIsometryEquiv.map_vsub`, `hasFDerivWithinAt_finCons`, `dist_left_midpoint_eq_dist_right_midpoint`, `norm_injOn_ray_right`, `InformationTheory.hasDerivAt_klFun`, `MeasureTheory.setIntegral_condExpL2_indicator`, `InnerProductSpace.nnnorm_rankOne`, `stronglyMeasurable_lineDeriv`, `ContinuousMultilinearMap.norm_restr`, `ContinuousMultilinearMap.norm_image_sub_le`, `ProbabilityTheory.isPosSemidef_covarianceBilin`, `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`, `MeasureTheory.SimpleFunc.setToSimpleFunc_add_left`, `EuclideanGeometry.oangle_eq_pi_iff_sbtw`, `ae_differentiableAt_norm`, `hasDerivAt_of_tendstoLocallyUniformlyOn`, `hasDerivAtFilter_iff_tendsto_slope`, `ContinuousLinearMap.norm_toSpanSingleton`, `AffineMap.differentiableWithinAt`, `intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left`, `AffineIsometryEquiv.toContinuousAffineEquiv_symm`, `HasGradientWithinAt.differentiableWithinAt`, `ContinuousLinearMap.setIntegral_compLp`, `LinearMap.trace_eq_sum_inner`, `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`, `ContinuousLinearEquiv.isBigO_sub`, `Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter`, `MeasureTheory.integral_singleton'`, `HasCompactSupport.hasDerivAt_convolution_right`, `InnerProductSpace.isSymmetricProjection_rankOne_self`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe`, `hasDerivWithinAt_neg`, `HasFTaylorSeriesUpToOn.eventually_hasFDerivAt`, `Orientation.volumeForm_zero_pos`, `differentiableWithinAt_pow`, `ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp`, `Bundle.ContinuousRiemannianMetric.continuous`, `hasMFDerivAt_neg`, `Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere`, `AnalyticAt.deriv`, `ContinuousLinearEquiv.hasMFDerivAt`, `MeasureTheory.ConvolutionExistsAt.integrable_swap`, `SchwartzMap.laplacianCLM_eq'`, `Polynomial.deriv_aeval`, `VectorBundleCore.trivializationAt_coordChange_eq`, `hasGradientWithinAt_iff_hasFDerivWithinAt`, `DoubleCentralizer.nnnorm_def`, `norm_inner_eq_norm_iff`, `Real.circleAverage_eq_circleIntegral`, `HasFiniteFPowerSeriesOnBall.eq_partialSum`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left`, `MeasureTheory.charFunDual_prod`, `ContinuousLinearMap.measurable_apply₂`, `IsLocalFrameOn.coeff_congr`, `continuousOn_tangentCoordChange`, `EuclideanGeometry.Sphere.orthRadius_center`, `NumberField.Units.span_basisOfIsMaxRank`, `LinearIsometryEquiv.smul_apply`, `nnnorm_cfcₙ_nnreal_lt`, `inner_eq_norm_mul_iff_div`, `Submodule.topologicalClosure_eq_self`, `LinearMap.hasStrictDerivAt`, `LinearIsometryEquiv.contDiff`, `ContDiff.continuous_fderiv_apply`, `FiniteDimensional.RCLike.properSpace_submodule`, `AffineMap.hasDerivAt_lineMap`, `Function.hasTemperateGrowth_iff_isBigO`, `range_stereographic_symm`, `FiniteDimensional.rclike_to_real`, `Complex.equivRealProdCLM_symm_apply`, `TemperedDistribution.instContinuousFourier`, `mellinInv_eq_fourierIntegralInv`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_const`, `ProbabilityTheory.strong_law_ae`, `HasGradientAtFilter.hasDerivAtFilter'`, `Module.Basis.prod_addHaar`, `PiLp.volume_preserving_toLp`, `CompactlySupportedContinuousMap.coe_toRealLinearMap`, `differentiableOn_dslope_of_notMem`, `IsLocalExtr.fderiv_eq_zero`, `derivWithin_congr_set'`, `ZSpan.measureReal_fundamentalDomain`, `EuclideanGeometry.orthogonalProjection_apply'`, `SmoothPartitionOfUnity.contDiffAt_finsum`, `ContMDiffAt.smul`, `isOpenEmbedding_stereographic_symm`, `intervalIntegral.integral_hasDerivWithinAt_left`, `LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional`, `HasFPowerSeriesOnBall.fderiv_eq`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le`, `strictConvex_closedBall`, `NumberField.Units.basisOfIsMaxRank_apply`, `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`, `differentiableAt_star_iff`, `VectorBundle.trivialization_linear'`, `SchwartzMap.smulLeftCLM_sum`, `PiTensorProduct.projectiveSeminorm_tprod_le`, `LinearIsometryEquiv.comp_hasFDerivWithinAt_iff'`, `AffineMap.hasDerivWithinAt_lineMap`, `PeriodPair.basis_zero`, `mfderiv_prod_eq_add_comp`, `has_fderiv_at_filter_real_equiv`, `NumberField.mixedEmbedding.negAt_signSet_apply_isReal`, `Matrix.PosSemidef.posSemidef_sqrt`, `aestronglyMeasurable_deriv`, `Real.hasDerivWithinAt_arccos_Ici`, `RightDerivMeasurableAux.differentiable_set_subset_D`, `unitary.linearIsometryEquiv_coe_symm_apply`, `PiTensorProduct.tprodL_toFun`, `MeasureTheory.setIntegral_condExpInd`, `ContinuousLinearMap.isPositive_def`, `LipschitzWith.ae_lineDifferentiableAt`, `ContinuousLinearMap.nnnorm_toSpanSingleton`, `EuclideanGeometry.oangle_midpoint_rev_left`, `ContinuousLinearEquiv.hasMFDerivWithinAt`, `ContinuousAlternatingMap.alternatizeUncurryFin_smul`, `InformationTheory.leftDeriv_klFun`, `contDiffAt_map_inverse`, `tendsto_integral_exp_smul_cocompact`, `MeasureTheory.integral_comp_rpow_Ioi_of_pos`, `Affine.Triangle.touchpoint_singleton_sbtw`, `SchwartzMap.toBoundedContinuousFunctionCLM_apply`, `curveIntegral_segment`, `TestFunction.postcompCLM_apply`, `hasDerivAt_iff_tendsto_slope_left_right`, `BoundedContinuousFunction.instStarModule`, `deriv_id''`, `HasFTaylorSeriesUpToOn.hasFDerivWithinAt`, `ContinuousAlternatingMap.norm_restrictScalars`, `OrthonormalBasis.coe_ofRepr`, `Submodule.starProjection_top'`, `ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range`, `aemeasurable_deriv_with_param`, `Orientation.rotation_symm`, `EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection`, `OrthonormalBasis.toBasis_mulOpposite`, `Submodule.adjoint_subtypeL`, `hasStrictFDerivAt_exp`, `Affine.Simplex.exradius_map`, `IsCoercive.range_eq_top`, `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'`, `Orientation.oangle_eq_zero_iff_sameRay`, `RCLike.conjLIE_apply`, `Submodule.reflection_orthogonalComplement_singleton_eq_neg`, `ContinuousLinearEquiv.comp_fderiv`, `convexOn_univ_norm`, `derivWithin.neg`, `Complex.orthonormalBasisOneI_repr_apply`, `ContinuousLinearMap.isBigO_id`, `NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq`, `ContDiffAt.fderiv_right`, `Complex.differentiable_exp`, `AnalyticOn.compContinuousLinearMap`, `hasStrictFDerivAt_iff_isLittleO`, `MeasureTheory.convolution_def`, `Affine.Triangle.dist_circumcenter_reflection_orthocenter`, `MeasureTheory.norm_condExpL2_coe_le`, `Pretrivialization.continuousLinearMapCoordChange_apply`, `ContinuousMultilinearMap.curryLeft_norm`, `MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le`, `MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable`, `InnerProductSpace.trace_rankOne`, `HasFPowerSeriesOnBall.differentiableOn`, `ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp`, `MeasureTheory.Submartingale.smul_nonneg`, `RCLike.imLm_coe`, `deriv.neg`, `ContinuousMultilinearMap.uncurry0_norm`, `openSegment_subset_ball_of_ne`, `HasFPowerSeriesWithinOnBall.prod`, `normalize_smul`, `MeasureTheory.integrable_withDensity_iff_integrable_smul'`, `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`, `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`, `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'`, `Orientation.rotation_map`, `Orientation.oangle_rotation_left`, `hasFDerivAt_norm_rpow`, `derivWithin_ofNat`, `dist_birkhoffAverage_apply_birkhoffAverage`, `ContinuousLinearMap.compL_apply`, `ContinuousLinearMap.lsmul_flip_inj`, `mellinInv_eq_fourierInv`, `ZSpan.repr_ceil_apply`, `MeasureTheory.Measure.addHaar_preimage_continuousLinearMap`, `HasFPowerSeriesOnBall.uniform_geometric_approx`, `ProperCone.innerDual_zero`, `LinearIsometry.inner_map_map`, `DoubleCentralizer.neg_snd`, `Affine.Simplex.excenterWeights_reindex`, `ContDiffMapSupportedIn.structureMapLM_eq_of_scalars`, `ZLattice.comap_equiv_apply`, `EuclideanGeometry.collinear_of_angle_eq_zero`, `ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior`, `sameRay_iff_of_norm_eq`, `ContinuousLinearMap.analyticAt`, `iteratedFDeriv_succ_const`, `EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center`, `fourier_gaussian_innerProductSpace'`, `norm_smul_of_nonneg`, `ContDiffAt.iteratedFDeriv_right`, `dist_affineCombination_lt_of_strictConvexSpace`, `VectorFourier.fourierIntegral_const_smul`, `ContDiffBump.convolution_tendsto_right`, `Matrix.linfty_opNNNorm_toMatrix`, `HasFTaylorSeriesUpToOn.cont`, `dist_lineMap_left`, `inCoordinates_apply_eq₂`, `measurable_deriv`, `Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm`, `ContDiffAt.contDiffAt_norm_smul`, `Real.fourier_real_eq`, `AnalyticOnNhd.fderiv_of_isOpen`, `ContinuousAlternatingMap.le_opNorm`, `Affine.Simplex.ExcenterExists.isTangentAt_touchpoint`, `Asymptotics.IsEquivalent.smul`, `differentiableAt_apply`, `MeasureTheory.L1.integral_def`, `Affine.Simplex.inradius_reindex`, `FormalMultilinearSeries.hasSum`, `hasDerivAt_abs_rpow`, `ContinuousLinearMap.IsPositive.conj_adjoint`, `ContinuousLinearMap.flip_apply`, `MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg`, `Matrix.toEuclideanCLM_toLp`, `WeakDual.CharacterSpace.homeoEval_naturality`, `signedDist_eq_zero_of_orthogonal`, `EuclideanGeometry.preimage_inversion_perpBisector`, `CPolynomialOn.iteratedFDeriv`, `NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis`, `realPart.norm_le`, `ContinuousLinearMap.isPositive_id`, `ZSpan.volume_fundamentalDomain`, `FormalMultilinearSeries.coeff_eq_zero`, `ProbabilityTheory.covarianceBilin_zero`, `RCLike.conjCLE_coe`, `Ioo_smul_sphere_zero`, `HasFPowerSeriesOnBall.sum`, `Real.tendsto_integral_gaussian_smul'`, `contDiffOn_stereoToFun`, `Real.hasFDerivAt_fourier`, `VectorFourier.differentiable_fourierIntegral`, `Affine.Simplex.incenter_mem_interior`, `Real.finrank_eq_int_finrank_of_discrete`, `Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter`, `LeftInvariantDerivation.evalAt_coe`, `derivWithin_const_add`, `Unitary.coe_symm_linearIsometryEquiv_apply`, `fderiv_inverse`, `Affine.Simplex.altitudeFoot_map`, `smul_sphere'`, `hasStrictFDerivAt_exp_smul_const'`, `SchwartzMap.smulLeftCLM_fun_neg`, `HasFPowerSeriesOnBall.fderiv`, `LinearMap.adjoint_rTensor`, `ZSpan.measure_fundamentalDomain`, `lineDerivWithin_of_isOpen`, `dist_midpoint_midpoint_le`, `Matrix.PosSemidef.sqrt_eq_one_iff`, `LinearMap.IsPositive.add`, `ImplicitFunctionData.leftDeriv_fderiv_implicitFunction`, `Real.deriv_Gamma_nat`, `HilbertBasis.hasSum_orthogonalProjection`, `ContinuousLinearMap.bilinearRestrictScalars_apply_apply`, `LinearMap.adjoint_inner_right`, `MeasureTheory.mem_lpMeas_indicatorConstLp`, `iteratedFDeriv_const_smul_apply'`, `InnerProductSpace.adjoint_rankOne`, `FormalMultilinearSeries.compAlongComposition_nnnorm`, `PiLp.hasFDerivAt_toLp`, `stereoInvFun_apply`, `PiTensorProduct.mapL_coe`, `Isometry.mapsTo_perpBisector`, `EuclideanGeometry.Cospherical.affineIndependent_of_ne`, `Filter.EventuallyEq.hasDerivAt_iff`, `Manifold.IsImmersionAt.writtenInCharts`, `InnerProductSpace.rankOne_eq_zero`, `ContinuousLinearMap.lipschitz`, `Polynomial.differentiable_aeval`, `ProbabilityTheory.isGaussian_map_equiv_iff`, `DoubleCentralizer.range_toProd`, `Affine.Simplex.circumcenter_eq_point`, `Real.fourierIntegral_convergent_iff'`, `Matrix.PosSemidef.sqrt_sq`, `hasDerivAt_deriv_iff`, `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`, `MeasureTheory.integral_indicatorConstLp`, `MeasureTheory.Measure.toSphere_apply_univ`, `Real.hasDerivAt_binEntropy`, `Submodule.norm_sq_eq_add_norm_sq_starProjection`, `hasDerivAt_gronwallBound_shift`, `AffineIsometry.linear_eq_linearIsometry`, `inner_map_polarization'`, `Bundle.ContMDiffRiemannianMetric.symm`, `ContMDiffOn.coordChangeL`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `MeasureTheory.charFunDual_eq_prod_iff`, `InnerProductSpace.inner_right_rankOne_apply`, `HilbertBasis.hasSum_repr`, `ContDiff.differentiable_iteratedFDeriv`, `SchwartzMap.pairing_apply`, `Real.fourier_comp_linearIsometry`, `MeasureTheory.Measure.integral_comp_smul`, `MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt`, `Asymptotics.isBigOTVS_iff_isBigO`, `ContinuousMultilinearMap.isLeast_opNorm`, `ContDiff.continuous_fderiv`, `mdifferentiableAt_hom_bundle`, `setIntegral_withDensity_eq_setIntegral_smul₀'`, `Real.hasDerivAt_qaryEntropy`, `innerSL_inj`, `AffineIsometryEquiv.coe_ofEq_apply`, `continuousAt_dslope_same`, `PositiveLinearMap.preGNS_inner_def`, `MeasureTheory.condExpIndSMul_smul`, `AffineIsometryEquiv.vaddConst_toAffineEquiv`, `hasDerivAt_add_const_iff`, `hasDerivWithinAt_pow`, `CStarAlgebra.instNonnegSpectrumClassComplexNonUnital`, `MeasureTheory.ae_ae_add_linearMap_mem_iff`, `real_inner_div_norm_mul_norm_eq_one_iff`, `TensorProduct.ext_iff_inner_left_threefold`, `MDifferentiableAt.differentiableWithinAt_writtenInExtChartAt`, `MeasureTheory.lintegral_nnnorm_condExpL2_le`, `EuclideanGeometry.oangle_eq_zero_iff_wbtw`, `Monotone.ae_hasDerivAt`, `StrongDual.toLp_of_not_memLp`, `AffineSubspace.isometryEquivMap.toAffineMap_eq`, `DoubleCentralizer.add_fst`, `MeasureTheory.integrable_withDensity_iff_integrable_smul₀'`, `differentiableWithinAt_of_derivWithin_ne_zero`, `LinearMap.IsSymmetric.coe_toSelfAdjoint`, `one_mem_posTangentConeAt_iff_mem_closure`, `quasispectrum.isCompact`, `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`, `ContDiffMapSupportedIn.uniformSpace_eq_iInf`, `hasFDerivAt_apply`, `derivWithin_div_const`, `Matrix.piLp_ofLp_toEuclideanLin`, `cfcₙAux_id`, `LinearMap.IsSymmetric.diagonalization_symm_apply`, `PiTensorProduct.liftIsometry_tprodL`, `maximal_orthonormal_iff_basis_of_finiteDimensional`, `TensorProduct.norm_comm`, `contDiffWithinAt_iff_of_ne_infty`, `inclusionInDoubleDual_norm_le`, `AnalyticOnNhd.eval_linearMap`, `LinearIsometryEquiv.coe_toMeasurableEquiv`, `hasFTaylorSeriesUpToOn_pi'`, `RCLike.rank_le_two`, `curveIntegral_segment_const`, `hasDerivWithinAt_one`, `mfderiv_sub`, `deriv_comp_add_const`, `VectorBundleCore.localTriv_symm_apply`, `WeakDual.isCompact_closedBall`, `MeasureTheory.L1.integral_eq_setToL1`, `ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv`, `ContinuousLinearMap.isPositive_toLinearMap_iff`, `Affine.Simplex.signedInfDist_apply_self`, `BoxIntegral.BoxAdditiveMap.volume_apply`, `TangentBundle.trivializationAt_apply`, `PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm`, `ConvexOn.sSup_of_countable_affine_eq`, `VectorFourier.iteratedFDeriv_fourierIntegral`, `TestFunction.coe_ofSupportedInCLM`, `Real.differentiableAt_rpow_of_ne`, `RCLike.reCLM_coe`, `ContDiffBump.normed_convolution_eq_right`, `ProbabilityTheory.gaussianReal_map_linearMap`, `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'`, `ContDiffMapSupportedIn.continuous_iff_comp_withOrder`, `HasLineDerivAt.tendsto_slope_zero`, `AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub`, `ContinuousLinearMap.holder_smul_left`, `exists_mem_interior_convexHull_affineBasis`, `ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear`, `ContinuousLinearMap.precompR_apply`, `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`, `Seminorm.comp_smul`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd'`, `hasDerivAtFilter_one`, `Real.fourierIntegral_iteratedDeriv`, `intervalIntegral.smul_integral_comp_mul_sub`, `Real.fourierInv_comp_linearIsometry`, `MeasureTheory.hasFDerivAt_convolution_right_with_param`, `ContinuousLinearEquiv.differentiableAt`, `CStarAlgebra.span_nonneg_inter_unitClosedBall`, `ProbabilityTheory.IsGaussian.charFun_eq'`, `Real.deriv_inv_log`, `ProbabilityTheory.covarianceBilinDual_eq_covariance`, `ContMDiffAt.mfderiv_const`, `AnalyticOn.domDomCongr_iteratedFDeriv`, `Matrix.PosSemidef.eq_sqrt_iff_sq_eq`, `signedDist_zero`, `MeasureTheory.condExpL1CLM_indicatorConstLp`, `Asymptotics.IsLittleO.isLittleOTVS`, `hasDerivAt_ofNat`, `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`, `IsLocalExtr.deriv_eq_zero`, `IsLocalMax.deriv_eq_zero`, `Matrix.l2_opNNNorm_mulVec`, `aestronglyMeasurable_derivWithin_Ioi`, `MeasureTheory.integrable_comp`, `NumberField.mixedEmbedding.span_idealLatticeBasis`, `NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis`, `hasFDerivAt_prodMk_left`, `AffineIsometryEquiv.toContinuousAffineEquiv_refl`, `AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn`, `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`, `ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap`, `SchwartzMap.norm_iteratedFDeriv_le_seminorm`, `ProbabilityTheory.covarianceBilinDual_zero`, `Submodule.norm_orthogonalProjection_apply_le`, `Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff`, `StarAlgebra.elemental.bijective_characterSpaceToSpectrum`, `Affine.Simplex.incenter_notMem_affineSpan_face`, `RealRMK.integral_rieszMeasure`, `LinearMap.deriv`, `VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas`, `Continuous.fderiv`, `CFC.continuous_abs`, `contDiff_iff_iteratedDeriv`, `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`, `norm_fderiv_le_of_lipschitz`, `InnerProductSpace.toDualMap_apply`, `hasFDerivWithinAt_finCons'`, `Real.differentiable_exp`, `TangentBundle.coordChange_model_space`, `normalize_smul_of_pos`, `ContinuousLinearMap.adjoint_inner_left`, `MeasureTheory.condExpInd_disjoint_union`, `PointwiseConvergenceCLM.isInducing_inducingFn`, `ImplicitFunctionData.hasStrictFDerivAt_implicitFunction_fderiv`, `FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le`, `TensorProduct.inner_mapIncl_mapIncl`, `Orientation.oangle_rotation_oangle_right`, `ProbabilityTheory.differentiableOn_mgf`, `ContinuousLinearMap.isBoundedBilinearMap`, `WeakFEPair.Λ₀_eq`, `fdifferential_apply`, `ContinuousMultilinearMap.opNorm_nonneg`, `ball_normSeminorm`, `HasFPowerSeriesWithinOnBall.sum`, `InnerProductSpace.AlgebraOfCoalgebra.mul_def`, `fderivWithin_const_add`, `Real.hasStrictDerivAt_arcosh`, `LinearMap.extendTo𝕜_apply`, `Filter.EventuallyEq.iteratedFDerivWithin`, `Filter.EventuallyEq.lineDerivWithin_eq_nhds`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right`, `compContinuousLinearMap_zero`, `HasLineDerivWithinAt.smul`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply`, `Real.differentiableAt_cos`, `FormalMultilinearSeries.apply_eq_pow_smul_coeff`, `EuclideanGeometry.image_inversion_perpBisector`, `hasDerivAtFilter_id`, `innerₗ_apply`, `FormalMultilinearSeries.le_radius_compContinuousLinearMap`, `Differentiable.fderiv_two`, `continuousMultilinearCurryFin0_symm_apply`, `MeasureTheory.setIntegral_condExpIndSMul`, `ContinuousLinearEquiv.integrable_comp_iff`, `Orientation.rightAngleRotation_symm`, `MeasureTheory.weightedSMul_empty`, `MeasureTheory.integrable_withDensity_iff_integrable_smul₀`, `inv_norm_smul_mem_unitClosedBall`, `Affine.Simplex.mongePlane_def`, `Affine.Triangle.acuteAngled_iff_angle_lt`, `ModularGroup.lcRow0Extend_apply`, `MDifferentiableOn.coordChangeL`, `Real.deriv_log'`, `hasDerivAt_update`, `ContinuousLinearMap.IsPositive.isSymmetric`, `ContinuousAlternatingMap.ofSubsingletonLIE_apply`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply`, `FormalMultilinearSeries.compAlongComposition_bound`, `continuousMultilinearCurryRightEquiv_symm_apply`, `OrthonormalBasis.equiv_apply`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le`, `Seminorm.bound_of_continuous`, `ContinuousLinearMap.lipschitz_apply`, `ContDiff.euclidean_dist`, `Trivialization.prod.isLinear`, `inner_eq_sum_norm_sq_div_four`, `MeasureTheory.lpMeasToLpTrimLie_symm_indicator`, `AnalyticWithinAt.differentiableWithinAt`, `intervalIntegral.integral_comp_add_mul`, `fderiv_pow_ring`, `constFormalMultilinearSeries_apply_zero`, `hasFTaylorSeriesUpToOn_top_iff'`, `ContinuousLinearMap.lsmul_apply`, `MeasureTheory.setIntegral_rnDeriv_smul`, `inTangentCoordinates_eq`, `LinearIsometryEquiv.conjStarAlgEquiv_trans`, `FormalMultilinearSeries.radius_smul_eq`, `selfAdjoint.unitarySelfAddISMul_coe`, `Bundle.ContMDiffRiemannianMetric.pos`, `AffineIsometryEquiv.ofEq_symm`, `Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded`, `HasDerivWithinAt.complexToReal_fderiv`, `signedDist_triangle_left`, `ContinuousLinearMap.bilinearComp_zero_right`, `Complex.IsExactOn.differentiableOn`, `TemperedDistribution.fourier_toTemperedDistributionCLM_eq`, `LinearMap.IsSymmetric.continuous`, `IsContMDiffRiemannianBundle.exists_contMDiff`, `Affine.Simplex.excenterExists_map`, `DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul`, `deriv_const_mul_field`, `hasDerivAtFilter_add_const_iff`, `isBounded_iff_asymptoticCone_subset_singleton`, `LinearIsometry.extend_apply`, `ProbabilityTheory.instIsGaussianMapHSub`, `Complex.ofRealCLM_nnnorm`, `Complex.imCLM_norm`, `Real.deriv2_binEntropy`, `InnerProductSpace.rank_rankOne`, `LinearMap.isSymmetric_sum`, `MDifferentiableAt.const_smul`, `LinearMap.toSeminorm_comp`, `ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply`, `Submodule.isOrtho_top_left`, `gauge_closure_zero`, `IsometricContinuousFunctionalCalculus.toNonUnital`, `contMDiffAt_coordChangeL`, `VectorFourier.fourierIntegral_convergent_iff`, `InnerProductSpace.toDual_apply_apply`, `Affine.Simplex.vectorSpan_isOrtho_altitude_direction`, `AlgHom.instContinuousLinearMapClassOfAlgHomClass`, `ContinuousLinearMap.adjointAux_apply`, `ContinuousLinearMap.nonneg_iff_isPositive`, `Real.hasDerivAt_arcsin`, `Orientation.inner_rotation_pi_div_two_right`, `integral_comp_polarCoord_symm`, `Affine.Simplex.exsphere_reindex`, `coe_lpBCFₗᵢ`, `ContinuousAffineMap.norm_contLinear_le`, `ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self`, `gauge_ball`, `CompactlySupportedContinuousMap.toRealPositiveLinear_apply`, `Submodule.linearEquiv_det_reflection`, `LinearMap.isSymmetric_linearIsometryEquiv_conj_iff`, `Trivialization.symmL_continuousLinearMapAt`, `FiniteDimensional.of_isCompact_closedBall₀`, `ProperCone.innerDual_singleton`, `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`, `HasLineDerivAt.tendsto_slope_zero_left`, `ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear`, `ContDiffWithinAt.continuousLinearMap_comp`, `ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall`, `derivWithin_const_smul_field`, `OrthonormalBasis.volume_parallelepiped`, `ContinuousAlternatingMap.norm_ofSubsingleton`, `Real.hasDerivAt_tan`, `OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply`, `hasFDerivAt_list_prod'`, `Submodule.toLinearMap_starProjection_eq_isComplProjection`, `hasStrictFDerivAt_finCons`, `Affine.Simplex.altitudeFoot_mem_affineSpan`, `InnerProductSpace.rankOne_def`, `MDifferentiableWithinAt.coordChangeL`, `TensorProduct.nnnorm_map`, `Module.Basis.ofZLatticeBasis_span`, `Orientation.oangle_rotation`, `Real.deriv_tan_sub_id`, `ContinuousLinearMap.coe_flipₗᵢ'`, `HasMFDerivAt.prodMap`, `mul_gauge_le_norm`, `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`, `Polynomial.fderiv_aeval`, `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`, `norm_deriv_le_of_lipschitzOn`, `dist_birkhoffAverage_birkhoffAverage`, `NumberField.mixedEmbedding.mem_span_latticeBasis`, `hasDerivAt_const`, `dslope_sub_smul_of_ne`, `deriv_add_const'`, `TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx'`, `Module.Basis.equivFunL_symm_apply_repr`, `AffineIsometry.coe_toAffineMap`, `fderiv_const_add`, `IsometryEquiv.map_midpoint`, `LinearIsometryEquiv.conjStarAlgEquiv_ext_iff`, `OrthonormalBasis.repr_apply_apply`, `hasFDerivWithinAt_const_add_iff`, `iteratedDerivWithin_of_isOpen_eq_iterate`, `UniformSpace.Completion.norm_toComplL`, `ContDiffOn.differentiableOn`, `ProbabilityTheory.covarianceBilin_comm`, `iter_deriv_zpow`, `ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply`, `Orientation.inner_rotation_pi_div_two_left`, `ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker`, `natCast_le_analyticOrderAt`, `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`, `MDifferentiable.differentiable`, `ClosedSubmodule.orthogonal_eq_inter`, `PositiveLinearMap.toPreGNS_ofPreGNS`, `ContinuousMultilinearMap.prodL_apply`, `Orientation.kahler_neg_orientation`, `FormalMultilinearSeries.radius_inv_eq_limsup`, `Real.hasStrictDerivAt_log`, `hasFDerivWithinAt_iff_hasDerivWithinAt`, `mdifferentiableWithinAt_iff_image`, `affinity_unitBall`, `MonotoneOn.intervalIntegrable_slope`, `convex_eball`, `nndist_left_midpoint`, `hasFTaylorSeriesUpToOn_succ_iff_right`, `ContinuousLinearMap.coe_flipMultilinearEquiv`, `Affine.Triangle.circumsphere_eq_of_dist_of_oangle`, `NonUnitalAlgHom.coe_Lmul`, `NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex`, `ContinuousMultilinearMap.norm_map_init_le`, `NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed`, `LeftInvariantDerivation.left_invariant''`, `ContinuousAlternatingMap.hasStrictFDerivAt`, `ContinuousAffineMap.hasStrictFDerivAt`, `SchwartzMap.fourierInv_apply_eq`, `SchwartzMap.smulRightCLM_apply_apply`, `Real.differentiableOn_Gamma_Ioi`, `Real.differentiableOn_mul_log`, `LinearIsometryEquiv.conjStarAlgEquiv_refl`, `CurveIntegrable.fun_zero`, `InnerProductSpace.laplacian_smul`, `hasStrictFDerivAt_iff_hasStrictDerivAt`, `MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin`, `ProbabilityTheory.setIntegral_tilted_mul_eq_mgf'`, `contDiff_nat_iff_iteratedDeriv`, `eventually_singleton_add_smul_subset`, `LinearMap.IsSymmetric.toSelfAdjoint_apply`, `EuclideanGeometry.image_inversion_sphere_dist_center`, `InnerProductSpace.volume_ball`, `EuclideanGeometry.orthogonalProjection_subtype`, `NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem`, `iteratedFDeriv_neg_apply`, `circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const`, `Submodule.coe_orthogonalDecomposition`, `VectorField.lieBracket_eq`, `fderiv_norm_smul_neg`, `SchwartzMap.toTemperedDistributionCLM_apply_apply`, `HasDerivAt.complexToReal_fderiv`, `differentiableAt_fst`, `ContinuousLinearMapWOT.isInducing_inducingFn`, `fderivWithin_fderivWithin_eq_of_eventuallyEq`, `integrableOn_Ioi_deriv_ofReal_cpow`, `EuclideanGeometry.Sphere.sbtw_secondInter`, `PositiveLinearMap.exists_norm_apply_le`, `DoubleCentralizer.star_fst`, `Real.fourierIntegral_real_eq_integral_exp_smul`, `Real.deriv_mulExpNegMulSq`, `StrongDual.polarSubmodule_eq_polar`, `Submodule.finrank_orthogonal_span_singleton`, `PiTensorProduct.liftEquiv_symm_apply`, `ContinuousLinearMap.fpowerSeries_apply_add_two`, `TestFunction.coe_ofSupportedInLM`, `Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero`, `NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top`, `LinearMap.isPositive_natCast`, `inner_smul_real_right`, `Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum`, `TensorProduct.toLinearEquiv_congrIsometry`, `AnalyticAt.analyticOrderAt_deriv_add_one`, `ContinuousMultilinearMap.opNorm_zero`, `hasFDerivAt_exp_smul_const'`, `dense_differentiableAt_norm`, `MeromorphicAt.iterated_deriv`, `MeasureTheory.SignedMeasure.re_toComplexMeasure`, `TemperedDistribution.smulLeftCLM_sub`, `CStarAlgebra.instNonnegSpectrumClass`, `Submodule.isOrtho_iSup_left`, `ContinuousLinearMap.hasFiniteFPowerSeriesOnBall`, `IsCoercive.bounded_below`, `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'`, `hasFDerivAt_finCons'`, `Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint`, `LinearMap.toMatrixOrthonormal_symm_apply`, `Real.deriv_qaryEntropy`, `ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear`, `contDiffPointwiseHolderAt_iff`, `ContinuousLinearMap.IsStarNormal.orthogonal_range`, `Real.deriv_arctan`, `hasSum_cauchyPowerSeries_integral`, `AffineSubspace.isPreconnected_setOf_wOppSide`, `ContinuousLinearMap.aestronglyMeasurable_comp₂`, `differentiableWithinAt_comp_sub`, `Matrix.posDef_gram_iff_linearIndependent`, `monotoneOn_deriv_descPochhammer_eval`, `MeasureTheory.Lp.instFourierSMul`, `SchwartzMap.smulLeftCLM_const`, `hasStrictFDerivAt_piLp`, `MeasureTheory.integral_fintype`, `LinearMap.toMatrix_innerₛₗ_apply`, `strictConvexSpace_iff`, `intervalIntegral.smul_integral_comp_sub_mul`, `AffineSubspace.toContinuousAffineMap_subtypeₐᵢ`, `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`, `Orientation.rightAngleRotation_map'`, `TensorProduct.toLinearEquiv_commIsometry`, `EuclideanGeometry.oangle_midpoint_left`, `NumberField.mixedEmbedding.negAt_apply_isComplex`, `AffineMap.hasDerivAt`, `hasDerivWithinAt_congr_set`, `ProbabilityTheory.isGaussian_iff_charFun_eq`, `Orientation.inner_rotation_pi_div_two_left_smul`, `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`, `LinearIsometry.norm_iteratedFDeriv_comp_left`, `fourierIntegral_eq_half_sub_half_period_translate`, `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`, `ContinuousLinearEquiv.dimH_image`, `meromorphicOrderAt_eq_int_iff`, `ContinuousLinearMap.norm_precompR_le`, `dist_lineMap_right`, `hasFDerivWithinAt_pow'`, `ContDiffMapSupportedIn.structureMapLM_apply_withOrder`, `HasFTaylorSeriesUpToOn.continuousLinearMap_comp`, `AffineMap.differentiableAt`, `hasStrictDerivAt_finCons'`, `ProbabilityTheory.instIsGaussianDirac`, `dist_iteratedFDerivWithin_zero`, `curveIntegral_restrictScalars`, `HasFPowerSeriesOnBall.hasSum`, `ContinuousLinearMap.isBoundedLinearMap_comp_right`, `Matrix.PosSemidef.toLinearMap₂'_zero_iff`, `Submodule.starProjection_isSymmetric`, `Submodule.starProjection_apply`, `ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear`, `HasFPowerSeriesWithinAt.pi`, `MeasureTheory.Measure.addHaar_parallelepiped`, `isVonNBounded_iff'`, `Polynomial.rootSet_derivative_subset_convexHull_rootSet`, `Submodule.HasOrthogonalProjection.map_linearIsometryEquiv'`, `VonNeumannAlgebra.mem_carrier`, `WeakDual.isSeqCompact_closedBall`, `differentiableOn_fun_neg_iff`, `hasStrictDerivAt_finCons`, `enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc`, `PiTensorProduct.liftEquiv_apply`, `DoubleCentralizer.add_snd`, `EuclideanGeometry.preimage_inversion_sphere_dist_center`, `MeasureTheory.norm_condExpInd_apply_le`, `has_antideriv_at_fourier_neg`, `Real.differentiableAt_log_iff`, `hasFTaylorSeriesUpTo_top_iff'`, `hasStrictDerivAt_zpow`, `fderivWithin_iteratedFDerivWithin`, `CStarModule.norm_inner_le`, `Orientation.rotation_neg_orientation_eq_neg`, `rescale_to_shell`, `ContinuousLinearMap.rayleighQuotient_add`, `ContinuousMultilinearMap.contDiff`, `Matrix.instNonnegSpectrumClass`, `LinearIsometry.toSpanSingleton_apply`, `hasFDerivAt_iff_tendsto`, `Orientation.eq_rotation_self_iff`, `VonNeumannAlgebra.centralizer_centralizer`, `WeakDual.exists_countable_separating`, `NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces`, `mdifferentiable_iff`, `LinearMap.isSelfAdjoint_iff'`, `FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm`, `MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm`, `Orientation.areaForm'_apply`, `VectorBundleCore.coe_coordChange`, `hasFDerivAtFilter_iff_hasDerivAtFilter`, `MeasureTheory.hausdorffMeasure_lineMap_image`, `innerSLFlip_apply_apply`, `ContinuousLinearEquiv.mdifferentiableOn`, `ContinuousLinearMap.nnnorm_holder_apply_apply_le`, `AffineMap.lipschitzWith_of_finiteDimensional`, `mdifferentiableWithinAt_iff_differentiableWithinAt`, `Affine.Triangle.dist_orthocenter_reflection_circumcenter`, `OrthogonalFamily.hasSum_linearIsometry`, `Polynomial.hasFDerivAt`, `Asymptotics.isTheta_const_smul_left`, `intervalIntegral.integral_smul_measure`, `isOpen_setOf_affineIndependent`, `signedDist_smul_of_pos`, `Distribution.mapCLM_apply`, `finrank_euclideanSpace`, `FormalMultilinearSeries.norm_compContinuousLinearMap_le`, `Real.hasStrictDerivAt_const_rpow_of_neg`, `hasDerivAt_inv`, `LinearMap.IsPositive.isSelfAdjoint`, `ContinuousLinearMap.bilinear_hasTemperateGrowth`, `IsContinuousRiemannianBundle.exists_continuous`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin`, `Filter.EventuallyEq.hasLineDerivWithinAt_iff_of_mem`, `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`, `Submodule.fst_orthogonalDecomposition_apply`, `ContinuousLinearMap.prodMapL_apply`, `ContinuousLinearMap.uncurryLeft_apply`, `HilbertBasis.dense_span`, `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`, `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`, `ContinuousAlternatingMap.curryLeft_compContinuousLinearMap`, `NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply`, `signedDist_lineMap_lineMap`, `Complex.ofRealCLM_apply`, `contMDiffOn_continuousLinearMapCoordChange`, `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`, `InnerProductSpace.continuousLinearMapOfBilin_zero`, `differentiableAt_complex_iff_differentiableAt_real`, `ContinuousMultilinearMap.compContinuousLinearMapLRight_apply`, `PiTensorProduct.mapL_mul`, `cfcHom_real_eq_restrict`, `intervalIntegral.inv_smul_integral_comp_sub_div`, `ContinuousLinearMap.toLinearMap_innerSL_apply`, `UniformConvexOn.convexOn`, `differentiableAt_comp_const_sub`, `Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius`, `HasFPowerSeriesAt.hasStrictDerivAt`, `Submodule.orthogonalFamily_self`, `NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem`, `ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self`, `NumberField.Units.regOfFamily_of_isMaxRank`, `Module.Basis.equivFunL_apply`, `CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary`, `inner_map_complex`, `hasFDerivAt_list_prod_finRange'`, `ContDiffOn.differentiableOn_one`, `ConvexOn.differentiableWithinAt_Ioi_of_mem_interior`, `NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum`, `LinearMap.IsSymmetric.adjoint_eq`, `Trivialization.continuousLinearEquivAt_apply'`, `BoundedContinuousFunction.probCharDual_zero`, `LinearMap.isPositive_sum`, `ContinuousMultilinearMap.flipLinear_apply_apply`, `Submodule.starProjection_norm_le`, `mfderiv_add`, `ContinuousAlternatingMap.norm_toContinuousMultilinearMap`, `HasGradientAt.hasFDerivAt`, `ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall`, `LinearMap.hasDerivWithinAt`, `CStarMatrix.toCLM_apply_single`, `PiLp.volume_preserving_ofLp`, `hasSum_two_pi_I_cauchyPowerSeries_integral`, `rescale_to_shell_semi_normed`, `FormalMultilinearSeries.comp_id`, `differentiableWithinAt_star_iff`, `ContinuousMultilinearMap.hasStrictFDerivAt`, `Submodule.inner_orthogonalProjection_eq_of_mem_right`, `Submodule.reflection_reflection`, `fderivWithin_comp_smul_eq_fderivWithin_smul`, `ContinuousLinearMap.isLeast_opNNNorm`, `sameRay_iff_norm_add`, `ContinuousMap.adjoin_id_eq_span_one_union`, `measurableSet_of_differentiableWithinAt_Ici_of_isComplete`, `signedDist_vadd_left_swap`, `IsSelfAdjoint.spectrumRestricts`, `Submodule.isOrtho_iff_le`, `MeasureTheory.condExp_smul`, `imaginaryPart.norm_le`, `Seminorm.const_isBounded`, `hasFTaylorSeriesUpTo_succ_nat_iff_right`, `Polynomial.eq_centerMass_of_eval_derivative_eq_zero`, `iteratedFDeriv_add`, `VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip`, `hasFDerivWithinAt_piLp`, `MeasureTheory.norm_weightedSMul_le`, `Complex.restrictScalars_one_smulRight`, `ContinuousLinearMapWOT.isEmbedding_inducingFn`, `differentiableOn_piLp`, `differentiableAt_abs_neg`, `ClosedSubmodule.iInf_orthogonal`, `Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero`, `hasDerivAt_fourier_neg`, `Orientation.rotation_zero`, `ProbabilityTheory.isGaussian_gaussianReal`, `HasFiniteFPowerSeriesOnBall.differentiableOn`, `HasFPowerSeriesOnBall.neg`, `deriv_abs_zero`, `VectorFourier.fderiv_fourierIntegral`, `ContinuousLinearMap.uncurryBilinear_apply`, `LinearMap.IsSymmetric.isSymmetric_smul_iff`, `VectorBundle.continuousOn_coordChange'`, `LinearMap.isPositive_linearIsometryEquiv_conj_iff`, `ZSpan.coe_floor_self`, `HasCompactSupport.enorm_le_lintegral_Ici_deriv`, `ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm`, `ContinuousLinearMap.mfderiv_eq`, `MeasureTheory.integral_posConvolution`, `hasStrictDerivAt_abs`, `nndist_midpoint_midpoint_le'`, `hasFDerivAt_const_add_iff`, `OrthonormalBasis.equiv_self_rfl`, `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`, `InnerProductSpace.harmonicAt_comp_CLE_iff`, `InnerProductSpace.coe_gramSchmidtBasis`, `Bundle.RiemannianMetric.symm`, `dist_homothety_self`, `ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear`, `isVonNBounded_of_isBounded`, `strongConcaveOn_iff_convex`, `iteratedFDeriv_eq_equiv_comp`, `Affine.Simplex.height_map`, `Submodule.reflection_inv`, `linear_isometry_complex`, `MeasureTheory.condExpIndL1_smul`, `Unitization.norm_eq_sup`, `ProbabilityTheory.isGaussian_map`, `instIsZLatticeRealSpan`, `Affine.Simplex.orthogonalProjection_circumcenter`, `Real.hasDerivAt_cos`, `ContinuousMap.toLp_norm_eq_toLp_norm_coe`, `Matrix.ofLp_toEuclideanCLM`, `hasFTaylorSeriesUpToOn_succ_nat_iff_right`, `Fourier.fourierIntegral_const_smul`, `hasDerivAtFilter_iff_isLittleO`, `CStarMatrix.toCLM_apply_eq_sum`, `AffineIsometry.map_vsub`, `PiTensorProduct.mapL_comp`, `Submodule.norm_starProjection`, `differentiableOn_pow`, `isCompactOperator_iff_image_closedBall_subset_compact`, `HasFPowerSeriesWithinAt.sub`, `ClosedSubmodule.sup_orthogonal`, `FormalMultilinearSeries.isLittleO_one_of_lt_radius`, `LinearMap.IsSymmetric.orthogonalFamily_eigenspaces'`, `hasDerivAt_exp_smul_const`, `Meromorphic.fun_smul`, `MeasureTheory.weightedSMul_add_measure`, `Unitary.linearIsometryEquiv_coe_symm_apply`, `MeasureTheory.Measure.NullMeasurableSet.const_smul`, `mdifferentiableOn_iff_of_subset_source`, `WithCStarModule.pi_norm`, `Filter.EventuallyEq.derivWithin_eq`, `ContDiff.comp_continuousLinearMap`, `exists_dual_vector`, `nndist_center_homothety`, `NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm`, `ContDiffMapSupportedIn.locallyConvexSpace`, `hasFDerivWithinAt_comp_smul_smul_iff`, `NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff`, `Orientation.oangle_rotation_oangle_left`, `ContinuousLinearMap.rayleighQuotient_le_norm`, `OrthonormalBasis.det_to_matrix_orthonormalBasis`, `smul_unitBall_of_pos`, `differentiableAt_const_add_iff`, `ContinuousLinearEquiv.comp_right_hasFDerivAt_iff`, `AffineIsometryEquiv.symm_constVSub`, `stronglyMeasurable_lineDeriv_uncurry`, `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`, `norm_inner_eq_norm_tfae`, `Real.circleAverage_def`, `derivWithin_zero_of_notMem_closure`, `ContinuousMultilinearMap.opNorm_pi`, `curveIntegral_fun_add`, `ContinuousLinearEquiv.lipschitz`, `iteratedDeriv_vcomp_three`, `Submodule.isCompl_orthogonal_of_hasOrthogonalProjection`, `RCLike.sqrt_map`, `Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff`, `Submodule.reflection_mul_reflection`, `Real.hasDerivWithinAt_arcsin_Ici`, `signedDist_vadd_right`, `UniqueDiffWithinAt.smul_iff`, `curveIntegral_fun_neg`, `InnerProductSpace.instIsContPerfPairRealInnerₗOfCompleteSpace`, `RCLike.inner_tmul_eq`, `AnalyticAt.analyticOrderAt_eq_natCast`, `inr_comp_cfcₙHom_eq_cfcₙAux`, `rotationOf_rotation`, `not_sameRay_iff_of_norm_eq`, `differentiableAt_finCons`, `InnerProductSpace.gramSchmidt_triangular`, `equicontinuous_TFAE`, `hasDerivAt_taylorWithinEval_succ`, `Submodule.starProjection_map_apply`, `CFC.monotoneOn_one_sub_one_add_inv_real`, `IsMIntegralCurveAt.hasMFDerivAt`, `Bornology.IsBounded.smul₀`, `LinearMap.star_eq_adjoint`, `PMF.integral_eq_tsum`, `SpectrumRestricts.real_iff`, `dist_self_homothety`, `contDiffWithinAt_succ_iff_hasFDerivWithinAt'`, `DiffContOnCl.circleAverage_smul_div`, `IsLocalFrameOn.eventually_eq_sum_coeff_smul`, `FiniteDimensional.of_isCompact_closedBall`, `Filter.EventuallyEq.iteratedFDerivWithin'`, `contDiffOn_succ_iff_hasFDerivWithinAt`, `fderivWithin_add_const`, `intervalIntegral.deriv_integral_left`, `differentiableWithinAt_euclidean`, `ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear`, `LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot'`, `intervalIntegral.integral_comp_div`, `ContinuousLinearMap.opNorm_add_le`, `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`, `Matrix.isPositive_toEuclideanLin_iff`, `ContDiffPointwiseHolderAt.continuousLinearMap_comp`, `ContinuousLinearMap.coe_restrictScalarsIsometry`, `TensorProduct.enorm_tmul`, `ContinuousLinearMap.memLp_of_bilin`, `HasFPowerSeriesOnBall.tendstoUniformlyOn`, `ContinuousLinearMap.norm_inr`, `MeasureTheory.setAverage_eq`, `SchwartzMap.smulLeftCLM_smulLeftCLM_apply`, `Submodule.starProjection_bot`, `ConvexBody.isBounded`, `NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap`, `ZSpan.isAddFundamentalDomain'`, `continuousMultilinearCurryFin0_apply`, `CStarMatrix.ofMatrix_eq_ofMatrixL`, `Affine.Simplex.touchpoint_mem_affineSpan`, `EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center`, `HasGradientAt.differentiableAt`, `ContDiffAt.hasStrictFDerivAt`, `PiTensorProduct.dualSeminorms_bounded`, `Conformal.differentiable`, `FormalMultilinearSeries.radius_neg`, `VectorPrebundle.pretrivialization_linear'`, `Real.differentiableAt_cosh`, `extDeriv_smul`, `EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear`, `homeomorphUnitSphereProd_symm_apply_coe`, `ProbabilityTheory.covarianceBilin_self_nonneg`, `Orientation.rightAngleRotation_rightAngleRotation`, `taylorWithinEval_succ`, `Submodule.orthogonal_closure`, `ProbabilityTheory.integral_linearMap_gaussianReal`, `LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace`, `TensorProduct.inner_assoc_assoc`, `ContinuousMultilinearMap.curryMidEquiv_apply`, `conformalAt_iff_isConformalMap_fderiv`, `StrictConvexSpace.strictConvex_closedBall`, `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`, `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`, `ContinuousLinearMap.reApplyInnerSelf_apply`, `ZSpan.fundamentalDomain_reindex`, `ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff'`, `Orientation.oangle_sign_smul_add_smul_smul_add_smul`, `ProbabilityTheory.indepFun_iff_charFunDual_prod'`, `Affine.Simplex.direction_mongePlane`, `DoubleCentralizer.algebraMap_snd`, `MeasureTheory.Measure.integral_comp_mul_left`, `AnalyticAt.analyticOrderNatAt_eq_iff`, `ProbabilityTheory.covarianceBilinDual_self_eq_variance`, `MonotoneOn.derivWithin_nonneg`, `ProperCone.innerDual_union`, `MeasureTheory.integrable_smul_const`, `hasFiniteFPowerSeriesOnBall_const`, `LinearMap.le_def`, `Affine.Simplex.dist_point_centroid`, `MeasureTheory.integral_condExpL2_eq_of_fin_meas_real`, `iteratedFDerivWithin_succ_apply_left`, `hasStrictFDerivAt_norm_sq`, `Submodule.starProjection_unit_singleton`, `Affine.Simplex.altitudeFoot_reindex`, `SchwartzMap.fourier_evalCLM_eq`, `HasCompactMulSupport.eq_one_or_finiteDimensional`, `LinearIsometryEquiv.comp_differentiableWithinAt_iff`, `support_deriv_subset`, `LinearMap.adjoint_toSpanSingleton`, `DoubleCentralizer.one_snd`, `ContinuousWithinAt.integral_sub_linear_isLittleO_ae`, `OrthonormalBasis.coe_toBasis`, `ContDiff.differentiable_iteratedDeriv`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear`, `Affine.Simplex.affineCombination_eq_touchpoint_iff`, `contDiffOn_infty_iff_fderiv_of_isOpen`, `hasDerivWithinAt_natCast`, `Real.deriv_exp`, `hasFDerivWithinAt_tangentCoordChange`, `ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply`, `Orientation.oangle_sign_smul_sub_left`, `ContinuousLinearEquiv.analyticOn`, `SchwartzMap.hasFDerivAt`, `ContinuousMultilinearMap.opNorm_add_le`, `fderiv_pow_ring'`, `QuasispectrumRestricts.real_iff`, `MeasureTheory.memL1_smul_of_L1_withDensity`, `ContinuousLinearMap.bilinearComp_apply`, `ContinuousMultilinearMap.instContinuousEval`, `differentiableAt_piLp`, `Submodule.reflection_sub`, `differentiableWithinAtProp_self_source`, `MeasureTheory.Measure.toSphere_apply'`, `TemperedDistribution.instLineDerivSMulReal`, `iteratedDeriv_comp_neg`, `ProbabilityTheory.differentiableAt_iteratedDeriv_mgf`, `SchwartzMap.evalCLM_apply_apply`, `Affine.Simplex.altitudeFoot_mem_altitude`, `MDifferentiableWithinAt.mfderivWithin`, `LinearMap.IsSymmetric.natCast`, `Orientation.rotation_eq_self_iff_angle_eq_zero`, `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`, `DiffContOnCl.smul_const`, `MeasureTheory.condExpIndL1_smul'`, `Polynomial.differentiableAt_aeval`, `isBounded_convexHull`, `MeasureTheory.Measure.toTemperedDistribution_apply`, `Filter.EventuallyEq.lineDifferentiableWithinAt_iff_of_mem`, `Complex.analyticOn_iff_differentiableOn`, `WeakDual.CharacterSpace.compContinuousMap_apply`, `tendsto_integral_exp_smul_cocompact_of_inner_product`, `LinearMap.re_inner_adjoint_mul_self_nonneg`, `hasDerivAt_id`, `differentiable_pi`, `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`, `InnerProductSpace.nullSubmodule_le_ker_toDualMap_left`, `DoubleCentralizer.algebraMap_toProd`, `Affine.Triangle.affineSpan_orthocenter_point_le_altitude`, `ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff`, `LinearMap.isPositive_self_comp_adjoint`, `Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded`, `differentiableAt_norm_smul`, `FiniteDimensional.of_locallyCompactSpace`, `FormalMultilinearSeries.id_comp`, `circleIntegral.integral_smul`, `Trivialization.baseSet_continuousLinearMap`, `ContinuousLinearMap.norm_map_tail_le`, `aestronglyMeasurable_lineDeriv_uncurry`, `deriv_update`, `Real.circleAverage_eq_integral_add`, `HasFPowerSeriesAt.restrictScalars`, `Real.iter_deriv_exp`, `contMDiffOn_symm_coordChangeL`, `hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `tangentBundleCore_coordChange_model_space`, `intervalIntegral.inv_smul_integral_comp_div_sub`, `Module.Basis.prod_parallelepiped`, `ContinuousLinearMap.instStarModuleId`, `Real.differentiable_iteratedDeriv_cos`, `nndist_lineMap_right`, `EuclideanGeometry.Cospherical.affineIndependent`, `Polynomial.hasFDerivAt_aeval`, `contMDiffAt_hom_bundle`, `EuclideanGeometry.orthogonalProjection_affineSpan_singleton`, `LinearIsometryEquiv.toLinearEquiv_lTensor`, `DoubleCentralizer.instIsCentralScalar`, `polar_closure`, `Matrix.linearIndependent_of_posDef_gram`, `ContDiffAt.restrictScalars_iteratedFDeriv`, `exists_dual_vector''`, `deriv_zpow'`, `PiTensorProduct.injectiveSeminorm_apply`, `ContinuousLinearMap.isBoundedLinearMap_comp_left`, `LinearIsometryEquiv.toLinearEquiv_smul`, `MeasureTheory.MemLp.continuousLinearMap_comp`, `ProbabilityTheory.IsGaussian.memLp_dual`, `norm_fderiv_iteratedFDeriv`, `MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real`, `isConnected_setOf_sameRay_and_ne_zero`, `curveIntegralFun_neg`, `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`, `ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply`, `hasFDerivAt_pow`, `LinearIsometryEquiv.analyticOn`, `TemperedDistribution.fourier_lineDerivOp_eq`, `LinearIsometryEquiv.analyticAt`, `convexHull_sphere_eq_closedBall`, `ProbabilityTheory.setIntegral_tilted_mul_eq_cgf'`, `Matrix.l2_opNNNorm_def`, `ContinuousMultilinearMap.instIsBoundedSMul`, `MeasureTheory.charFunDual_map_const_add`, `ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal`, `hasDerivAtFilter_sub_const_iff`, `EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two`, `MeasureTheory.charFunDual_map_add_const`, `spectrum.hasDerivAt_resolvent`, `ContinuousLinearMap.integrable_comp`, `ContinuousLinearMap.adjointAux_adjointAux`, `ImplicitFunctionData.differentiableAt_implicitFunction`, `Submodule.coe_inner`, `ContDiffMapSupportedIn.seminorm_le_iff_withOrder`, `Polynomial.deriv_gaussian_eq_hermite_mul_gaussian`, `Orientation.rotation_trans`, `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`, `hasFDerivAt_single`, `signedDist_lineMap_left`, `selfAdjoint.realPart_unitarySelfAddISMul`, `MeasureTheory.condExpL2_indicator_of_measurable`, `LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot`, `ProbabilityTheory.covarianceBilin_real_self`, `iteratedDeriv_vcomp_eq_sum_orderedFinpartition`, `LinearMap.eq_adjoint_iff`, `MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top`, `Real.tendsto_rightDeriv_mul_log_atTop`, `Real.hasStrictDerivAt_arsinh`, `PositiveLinearMap.gnsStarAlgHom_apply`, `Real.fourier_iteratedDeriv`, `iter_deriv_pow'`, `MeasureTheory.integral_comp_rpow_Ioi`, `ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin`, `convex_closedEBall`, `hasDerivAt_iff_tendsto_slope_zero`, `MeasureTheory.condExp_ae_eq_condExpL1CLM`, `Orthonormal.inner_right_finsupp`, `AffineIsometry.norm_map`, `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`, `HasFTaylorSeriesUpToOn.hasFDerivAt`, `WeakFEPair.hf_zero`, `RCLike.realLinearIsometryEquiv_symm_apply`, `LinearIsometry.norm_toContinuousLinearMap_comp`, `convex_ball`, `hasStrictFDerivAt_inv`, `real_inner_smul_right`, `ContinuousLinearMap.isBigOWith_comp`, `ContinuousLinearMap.flip_add`, `hasFiniteFPowerSeriesAt_const`, `continuous_clm_apply`, `ContinuousLinearMap.hasTemperateGrowth`, `Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay`, `AffineSubspace.isometryEquivMap.coe_apply`, `Orientation.oangle_sub_right_smul_rotation_pi_div_two`, `LinearIsometry.coe_toSpanSingleton`, `LinearMap.isPositive_iff_complex`, `VectorFourier.fourierSMulRight_apply`, `ContinuousLinearEquiv.isBigO_sub_rev`, `deriv_neg''`, `ContinuousLinearMap.isSelfAdjoint_iff'`, `Submodule.sndL_comp_coe_orthogonalDecomposition`, `DoubleCentralizer.pow_toProd`, `OrthonormalBasis.equiv_apply_euclideanSpace`, `measurable_fderiv_apply_const`, `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`, `eventually_norm_symmL_trivializationAt_self_comp_lt`, `OrthonormalBasis.det_adjustToOrientation`, `MeasureTheory.condExpL1CLM_indicatorConst`, `isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts`, `fderiv_inv`, `MeromorphicAt.fun_deriv`, `normalize_smul_of_neg`, `Complex.orthonormalBasisOneI_repr_symm_apply`, `tangentBundleCore_coordChange`, `derivWithin_comp_mul_left`, `MeasureTheory.L1.nnnorm_Integral_le_one`, `hasDerivAt_circleMap`, `instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial`, `curveIntegralFun_fun_zero`, `EuclideanGeometry.oangle_homothety`, `ContinuousLinearMap.bilinearComp_zero`, `MeasureTheory.integral_fun_norm_addHaar`, `Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff`, `MeasureTheory.setIntegral_ge_of_const_le`, `signedDist_anticomm`, `dslope_of_ne`, `ZSpan.map`, `HasCompactSupport.eq_zero_or_finiteDimensional`, `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`, `segment_subset_closedBall_left`, `ContinuousMultilinearMap.cpolynomialAt`, `Trivialization.continuousLinearMap_apply`, `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`, `ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm`, `HasFPowerSeriesWithinAt.differentiableWithinAt`, `ZSpan.exist_unique_vadd_mem_fundamentalDomain`, `ContinuousMultilinearMap.ratio_le_opNorm`, `ContDiff.iterate_deriv`, `ZSpan.fundamentalDomain_subset_parallelepiped`, `ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos`, `ContinuousLinearMap.norm_extendTo𝕜'_bound`, `sum_mem_ball_of_strictConvexSpace`, `ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff`, `MeasureTheory.hausdorffMeasure_homothety_image`, `ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap`, `Real.differentiableAt_arctan`, `Matrix.PosSemidef.isUnit_sqrt_iff`, `HasFTaylorSeriesUpToOn.differentiableAt`, `eq_lineMap_of_dist_eq_mul_of_dist_eq_mul`, `ContDiff.deriv'`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real`, `LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp`, `HasFiniteFPowerSeriesOnBall.neg`, `derivWithin_intCast`, `differentiableWithinAt_abs_neg`, `MeasureTheory.integral_comp`, `TemperedDistribution.instContinuousLineDeriv`, `RCLike.complexLinearIsometryEquiv_symm_apply`, `Real.differentiableOn_negMulLog`, `MeasureTheory.average_union_mem_segment`, `WithCStarModule.prod_norm`, `norm_derivWithin_eq_norm_fderivWithin`, `differentiableWithinAt_dslope_of_ne`, `iteratedFDeriv_zero_apply`, `ContinuousLinearMap.le_def`, `WeakDual.isClosed_closedBall`, `contDiff_succ_iff_fderiv_apply`, `hasDerivAt_fourier`, `coe_lpPiLpₗᵢ`, `VectorBundleCore.localTriv_apply`, `LinearIsometry.inr_apply`, `LinearMap.isPositive_zero`, `DoubleCentralizer.zero_fst`, `EuclideanGeometry.Sphere.direction_orthRadius_le_iff`, `NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces`, `fderiv_update`, `ContinuousLinearMap.IsPositive.re_inner_nonneg_left`, `Real.rightDeriv_mul_log`, `dist_add_dist_eq_iff`, `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`, `CStarMatrix.mul_entry_mul_eq_inner_toCLM`, `LinearIsometry.orthonormal_comp_iff`, `EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq`, `LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv`, `homeomorphSphereProd_symm_apply_coe`, `hom_trivializationAt`, `Diffeomorph.uniqueDiffOn_image`, `ContinuousLinearMap.le_opNorm₂`, `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`, `MeasureTheory.integrable_tilted_iff`, `ContinuousLinearMap.norm_iteratedFDeriv_comp_left`, `ContinuousLinearMap.norm_uncurryMid`, `ProbabilityTheory.covarianceOperator_inner`, `InnerProductSpace.rankOne_def'`, `ContDiff.fderiv_apply`, `ContinuousLinearMap.opNorm_mul_le`, `MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one`, `ContinuousLinearMap.uncurryLeft_norm`, `hasFDerivAtFilter_fst`, `Submodule.isClosed_orthogonal`, `differentiableWithinAt_comp_add_right`, `EuclideanGeometry.Sphere.IsDiameter.sbtw`, `ContinuousLinearMap.opNorm_subsingleton`, `mellin_eq_fourierIntegral`, `hasStrictDerivAt_abs_neg`, `Orientation.inner_rightAngleRotation_left`, `MeasureTheory.AEStronglyMeasurable.fourierPowSMulRight`, `ContinuousLinearMap.holder_smul_right`, `HasFPowerSeriesOnBall.tendstoUniformlyOn'`, `AffineSubspace.mem_perpBisector_iff_inner_eq_inner`, `Pretrivialization.continuousLinearMap.isLinear`, `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`, `HasFTaylorSeriesUpToOn.compContinuousLinearMap`, `HasFPowerSeriesOnBall.sub`, `EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius`, `SchwartzMap.integral_sesq_fourierIntegral_eq`, `contDiffAt_succ_iff_hasFDerivAt`, `ContinuousLinearMap.IsPositive.inner_nonneg_left`, `Real.fourierIntegral_eq'`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left`, `LinearMap.adjoint_lTensor`, `MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd`, `MeasureTheory.integrable_withDensity_iff_integrable_smul`, `CStarModule.norm_sq_eq`, `MeasureTheory.Integrable.convolution_integrand`, `norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul`, `OrthonormalBasis.map_apply`, `LinearMap.toMatrixOrthonormal_apply`, `hasFPowerSeriesOn_cauchy_integral`, `MeasureTheory.condExpL1CLM_lpMeas`, `measurableSet_of_differentiableAt`, `HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod`, `Module.Basis.coe_parallelepiped`, `Submodule.isSymmetricProjection_starProjection`, `ContinuousLinearMap.mdifferentiableWithinAt`, `SeparatingDual.completeSpace_continuousLinearMap_iff`, `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`, `ProbabilityTheory.deriv_mgf`, `SchwartzMap.integral_bilinear_laplacian_right_eq_left`, `ClosedSubmodule.mem_orthogonal_toSubmodule_iff`, `ZLattice.covolume_eq_det_mul_measureReal`, `hasDerivWithinAt_const`, `FormalMultilinearSeries.compAlongComposition_norm`, `ContinuousLinearMap.isometry_mul`, `VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral'`, `intervalIntegral.integral_comp_sub_mul`, `ContinuousLinearMap.isOpen_injective`, `mdifferentiableWithinAt_iff'`, `NonUnitalCommCStarAlgebra.toStarModule`, `ContDiff.continuous_iteratedFDeriv'`, `OrthonormalBasis.sum_repr_symm`, `homeomorphUnitSphereProd_apply_fst_coe`, `LipschitzWith.ae_differentiableAt`, `StrongDual.toLpₗ_apply`, `Orientation.kahler_apply_self`, `Affine.Simplex.dist_circumcenter_eq_circumradius'`, `Real.differentiableWithinAt_arcsin_Iic`, `EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt`, `signedDist_triangle_right`, `Polynomial.hermite_eq_deriv_gaussian`, `Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev`, `Orthonormal.inner_left_sum`, `Orientation.inner_smul_rotation_pi_div_two_right`, `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`, `Pi.orthonormalBasis.toBasis`, `LinearIsometry.map_starProjection`, `IsLocalFrameOn.coeff_apply_zero_at`, `Orientation.inner_mul_areaForm_sub'`, `constFormalMultilinearSeries_apply_of_nonzero`, `hasFDerivAt_polarCoord_symm`, `fourierIntegral_gaussian_innerProductSpace`, `egauge_ball_one_le_of_one_lt_norm`, `HasFTaylorSeriesUpToOn.add`, `MeasureTheory.dist_convolution_le'`, `EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius`, `IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero`, `differentiableOn_neg`, `ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM`, `ZSpan.isAddFundamentalDomain`, `ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff`, `EuclideanGeometry.dist_orthogonalProjection_eq_infNndist`, `Asymptotics.IsBigO.hasFDerivWithinAt`, `dist_homothety_center`, `LinearMap.continuous_of_nonzero_on_open`, `Submodule.inf_orthogonal`, `ConvexOn.real_univ_sSup_affine_eq`, `MeasureTheory.weightedSMul_union`, `ProbabilityTheory.hasDerivAt_neg_exp_mul_exp`, `Real.deriv_arcsin`, `abs_signedDist_eq_dist_iff_vsub_mem_span`, `InnerProductSpace.innerSL_norm`, `MeasureTheory.uniformIntegrable_average`, `hasFDerivAt_exp_zero`, `differentiableAt_fun_neg_iff`, `LinearIsometryEquiv.strictConvex_image`, `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`, `EuclideanGeometry.Concyclic.Coplanar`, `Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint`, `InnerProductSpace.span_gramSchmidt_Iic`, `MDifferentiableAt.smul`, `LinearMap.IsSymmetric.direct_sum_isInternal`, `Submodule.det_reflection`, `ContinuousLinearMap.measurable_apply`, `selfAdjoint.star_coe_unitarySelfAddISMul`, `deriv_neg'`, `deriv_zero_of_frequently_const`, `Orientation.kahler_rotation_left'`, `MeasureTheory.Measure.addHaar_affineSubspace`, `Real.differentiable_sin`, `MeasureTheory.setIntegral_rnDeriv_smul'`, `FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp`, `ContinuousMultilinearMap.norm_ofSubsingleton_id_le`, `derivWithin_zero_of_not_accPt`, `ContinuousAlternatingMap.curryLeft_same`, `ContinuousMultilinearMap.curryRight_apply`, `TensorProduct.inner_comm_comm`, `ContDiff.fourierPowSMulRight`, `ContinuousLinearEquiv.toSpanNonzeroSingleton_coord`, `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`, `intervalIntegral.smul_integral_comp_mul_left`, `Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent`, `ContinuousLinearMap.extendTo𝕜_apply`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars`, `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`, `not_sameRay_iff_abs_lt_norm_sub`, `CPolynomialOn.deriv`, `EuclideanSpace.volume_ball_fin_three`, `Real.not_differentiableAt_inv_log_zero`, `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`, `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`, `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`, `DoubleCentralizer.one_fst`, `ContinuousLinearMap.norm_extendTo𝕜'`, `InnerProductGeometry.angle_smul_smul`, `HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope`, `AnalyticOnNhd.deriv_of_isOpen`, `NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis`, `LinearIsometry.coe_toAffineIsometry`, `differentiableAt_iff_comp_const_sub`, `Affine.Simplex.altitude_reindex`, `linearIndependent_of_ne_zero_of_inner_eq_zero`, `ModelWithCorners.convex_range`, `ContDiffMapSupportedIn.postcompCLM_apply`, `LinearPMap.isSelfAdjoint_def`, `TemperedDistribution.smulLeftCLM_add`, `DoubleCentralizer.coeHom_apply`, `ContinuousAlternatingMap.curryLeft_zero`, `signedDist_neg`, `IsContDiffImplicitAt.bijective`, `norm_lineDeriv_le_of_lipschitzOn`, `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`, `Orientation.normSq_kahler`, `ContinuousMultilinearMap.opNNNorm_prod`, `MDifferentiableWithinAt.differentiableWithinAt`, `ContinuousLinearEquiv.comp_right_differentiableOn_iff`, `ContinuousLinearMap.opENorm_comp_le`, `hasGradientAt_iff_hasFDerivAt`, `Asymptotics.IsTheta.isThetaTVS`, `Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl`, `curveIntegrable_neg_iff`, `ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul`, `NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single`, `HasFPowerSeriesOnBall.tendsto_partialSum`, `maximal_orthonormal_iff_orthogonalComplement_eq_bot`, `SmoothBumpFunction.contMDiff_smul`, `iteratedFDeriv_one_apply`, `ContinuousLinearEquiv.iteratedFDeriv_comp_left`, `gauge_unit_ball`, `Filter.Tendsto.zero_smul_isBoundedUnder_le`, `Submodule.reflection_orthogonal`, `hasFDerivAt_exp_smul_const_of_mem_ball`, `ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft`, `HasFPowerSeriesOnBall.factorial_smul`, `Real.differentiableAt_tan`, `ContinuousAlternatingMap.norm_image_sub_le'`, `Real.differentiable_cosh`, `NumberField.mixedEmbedding.negAt_symm`, `HasFPowerSeriesWithinAt.prod`, `VectorFourier.contDiff_fourierIntegral`, `ContMDiffMap.coe_smul`, `iteratedFDeriv_succ_apply_right`, `Submodule.isOrtho_top_right`, `FormalMultilinearSeries.leftInv_coeff_one`, `LinearMap.IsSymmetric.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`, `mdifferentiableOn_continuousLinearMapCoordChange`, `derivWithin_one`, `hasDerivAtFilter_intCast`, `Orthonormal.inner_finsupp_eq_sum_left`, `cfcHom_nnreal_eq_restrict`, `fderiv_deriv`, `BoxIntegral.integral_smul`, `WithLp.unitizationAlgEquiv_symm_apply_ofLp`, `hasFPowerSeriesAt_pi_iff`, `mfderivWithin_eq_fderivWithin`, `norm_cfcₙ_le`, `ProbabilityTheory.integral_tilted_mul_eq_mgf`, `MeasureTheory.integral_simpleFunc_larger_space`, `hasDerivWithinAt_univ`, `LinearIsometryEquiv.hasFDerivAt`, `ContDiffBump.apply`, `ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm`, `Orientation.oangle_sign_add_smul_left`, `differentiableAt_add_const_iff`, `ContinuousLinearEquiv.contDiffWithinAt_comp_iff`, `Matrix.PosSemidef.sq_sqrt`, `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`, `InnerProductSpace.isStarProjection_rankOne_self`, `deriv_sub_const`, `coord_norm'`, `Trivialization.apply_eq_prod_continuousLinearEquivAt`, `ProperCone.relative_hyperplane_separation`, `OrderedFinpartition.compAlongOrderedFinpartitionL_apply`, `ContinuousAlternatingMap.piLIE_symm_apply_apply`, `ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le`, `LinearIsometry.integral_comp_comm`, `contDiff_clm_apply_iff`, `HasFPowerSeriesAt.hasFDerivAt`, `OrthonormalBasis.measurePreserving_repr_symm`, `hasStrictFDerivAt_finCons'`, `spec_cfcₙAux`, `ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior`, `ClosedSubmodule.orthogonal_eq_top_iff`, `UniformConcaveOn.strictConcaveOn`, `QuadraticMap.lineDifferentiableAt`, `EuclideanSpace.piLpCongrLeft_single`, `FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius`, `hasFDerivAt_exp_smul_const`, `LinearIsometryEquiv.norm_iteratedFDeriv_comp_right`, `HasFPowerSeriesOnBall.eventually_hasSum`, `DifferentiableWithinAtProp_self`, `signedDist_linear_apply`, `NumberField.mixedEmbedding.negAt_apply_isReal_and_mem`, `Orientation.rotation_eq_matrix_toLin`, `MeasureTheory.AEStronglyMeasurable.fourierSMulRight`, `FormalMultilinearSeries.zero_radius`, `Real.hasDerivAt_log`, `smul_unitBall`, `intervalIntegral.integral_const_of_cdf`, `IsSymmSndFDerivAt.iteratedFDeriv_cons`, `Orientation.inner_rightAngleRotation_swap`, `ContinuousLinearMap.hasFPowerSeriesAt_bilinear`, `intervalIntegral.integral_const'`, `ContinuousLinearMap.comp_analyticOn`, `hasStrictDerivAt_const`, `Bundle.Trivial.trivialization.isLinear`, `ContinuousLinearMap.coeFn_compLpL`, `hasStrictFDerivAt_list_prod_attach'`, `rotationOf_coe`, `MDifferentiableOn.differentiableOn`, `NumberField.mixedEmbedding.volume_negAt_plusPart`, `deriv_single`, `stronglyMeasurable_deriv`, `StrongDual.norm_toLpₗ_le`, `ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl`, `hasFDerivWithinAt_euclidean`, `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`, `ProperCone.innerDual_insert`, `range_deriv_subset_closure_span_image`, `Module.Basis.parallelepiped_eq_map`, `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`, `LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range`, `FormalMultilinearSeries.id_apply_zero`, `SchwartzMap.hasDerivAt`, `Submodule.starProjection_orthogonal`, `PiTensorProduct.mapLMultilinear_apply_apply`, `Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero`, `ContinuousLinearMap.instNonnegSpectrumClassRealId`, `iteratedDeriv_comp_two`, `Affine.Simplex.incenter_eq_affineCombination`, `ContinuousLinearMap.uncurryMid_apply`, `hasFDerivAt_update`, `signedDist_self`, `iteratedDeriv_eq_iterate`, `isBoundedBilinearMap_apply`, `HasFPowerSeriesWithinOnBall.coeff_zero`, `FormalMultilinearSeries.analyticOnNhd`, `fderiv_comp_add_right`, `Unitization.nnreal_cfcₙ_eq_cfc_inr`, `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`, `Matrix.IsHermitian.eigenvectorUnitary_coe`, `Submodule.ClosedComplemented.of_finiteDimensional`, `Complex.sqrt_map`, `InnerProductSpace.HarmonicOnNhd.const_smul`, `ContinuousAffineMap.hasFDerivAtFilter`, `hasStrictFDerivAt_ringInverse`, `MeasureTheory.setIntegral_indicatorConstLp`, `ContDiffOn.continuousOn_fderiv_of_isOpen`, `signedDist_vsub_self`, `ContinuousLinearMap.mul_apply'`, `EuclideanGeometry.inversion_mul`, `ContDiffOn.continuousLinearMap_comp`, `stereographic_target`, `MeasureTheory.SignedMeasure.rnDeriv_smul`, `Unitary.norm_map`, `ProbabilityTheory.isGaussian_conv`, `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`, `MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub`, `LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply`, `InnerProductSpace.rankOne_comp_rankOne`, `TemperedDistribution.fourierTransform_apply`, `ContinuousLinearMap.opNorm_zero`, `MeasureTheory.convolution_lsmul_swap`, `Orientation.oangle_add_right_smul_rotation_pi_div_two`, `not_sameRay_iff_norm_add_lt`, `Real.hasStrictDerivAt_arctan`, `HasFTaylorSeriesUpToOn.prodMk`, `ContinuousMultilinearMap.norm_iteratedFDeriv_le`, `ContDiffAt.domDomCongr_iteratedFDeriv`, `isSeparable_range_deriv`, `Orientation.inner_smul_rotation_pi_div_two_left`, `BoxIntegral.hasIntegral_const`, `ZLattice.volume_image_eq_volume_div_covolume`, `hasDerivAtFilter_finCons'`, `MeasureTheory.Supermartingale.smul_nonpos`, `MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul`, `LinearIsometry.toLinearMap_rTensor`, `Real.map_linearMap_volume_pi_eq_smul_volume_pi`, `PiLp.hasStrictFDerivAt_apply`, `CStarModule.norm_eq_csSup`, `hasStrictFDerivAt_fst`, `Matrix.toEuclideanLin_eq_toLin`, `setIntegral_withDensity_eq_setIntegral_smul`, `UniqueMDiffOn.uniqueDiffOn_inter_preimage`, `Affine.Simplex.sOppSide_point_excenter_singleton`, `DoubleCentralizer.pow_fst`, `mdifferentiableWithinAt_iff_target_inter'`, `StrongDual.toLpₗ_of_not_memLp`, `isConformalMap_complex_linear_conj`, `MeromorphicAt.meromorphicTrailingCoeffAt_smul`, `PiTensorProduct.mapL_apply`, `hasDerivWithinAt_finCons'`, `Euclidean.closedBall_eq_preimage`, `mellin_comp_rpow`, `Matrix.isHermitian_iff_isSymmetric`, `ContinuousAffineMap.hasFDerivAt`, `MeasureTheory.Submartingale.sum_smul_sub'`, `NumberField.mixedEmbedding.iUnion_negAt_plusPart_union`, `deriv.fun_neg`, `AffineSubspace.mem_perpBisector_iff_dist_eq'`, `Matrix.PosSemidef.inv_sqrt`, `ContinuousMultilinearMap.norm_iteratedFDeriv_le'`, `support_iteratedFDeriv_subset`, `MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball`, `hasStrictFDerivAt_finset_prod`, `AffineSubspace.isPreconnected_setOf_wSameSide`, `AnalyticOnNhd.deriv`, `Submodule.le_orthogonal_iff_le_orthogonal`, `fderiv_fun_neg`, `intervalIntegral.differentiable_integral_of_continuous`, `intervalIntegral.smul_integral_comp_mul_add`, `curveIntegral_zero`, `deriv_zpow`, `hasFDerivAt_comp_sub`, `LipschitzWith.locallyIntegrable_lineDeriv`, `InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis`, `Affine.Simplex.ninePointCircle_center_mem_affineSpan`, `Submodule.IsOrtho.comap_iff`, `InnerProductSpace.rankOne_comp`, `Submodule.mem_orthogonal`, `ContinuousAffineMap.norm_image_zero_le`, `StrongDual.mem_polarSubmodule`, `exists_dual_vector'`, `MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual`, `FormalMultilinearSeries.apply_eq_prod_smul_coeff`, `Asymptotics.IsTheta.const_smul_left`, `Orientation.kahler_rightAngleRotation_left`, `hasFPowerSeriesWithinAt_pi_iff`, `isCompactOperator_iff_isCompact_closure_image_closedBall`, `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`, `inner_smul_right`, `SchwartzMap.tsupport_smulLeftCLM_subset`, `HasMFDerivAt.sub`, `InnerProductSpace.toMatrix_rankOne`, `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`, `ContDiffMapSupportedIn.structureMapCLM_apply_withOrder`, `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`, `MeasureTheory.Measure.addHaar_smul_of_nonneg`, `OrthonormalBasis.reindex_toBasis`, `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`, `Real.fourierIntegral_convergent_iff`, `NumberField.canonicalEmbedding.mem_rat_span_latticeBasis`, `IsLocalMin.deriv_eq_zero`, `Real.hasDerivAt_cosh`, `Real.tendsto_deriv_mul_log_atTop`, `fderiv_const_sub`, `continuousMultilinearCurryLeftEquiv_apply`, `Orientation.abs_areaForm_of_orthogonal`, `LipschitzOnWith.ae_differentiableWithinAt_real`, `HasFPowerSeriesAt.deriv`, `upperHemicontinuous_quasispectrum_nnreal`, `LinearIsometryEquiv.symm_rTensor`, `LinearMap.isSymmetricProjection_iff`, `innerₗ_apply_apply`, `differentiable_pow`, `uniqueMDiffWithinAt_iff_inter_range`, `HasMFDerivWithinAt.add`, `Matrix.toEuclideanLin_conjTranspose_eq_adjoint`, `LinearMap.eq_adjoint_iff_basis`, `HasCompactSupport.iteratedFDeriv`, `TensorProduct.commIsometry_symm`, `isStarProjection_starProjection`, `MeasureTheory.integral_rnDeriv_smul`, `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`, `ContinuousLinearMap.integral_comp_L1_comm`, `curveIntegralFun_add`, `ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf`, `CompactlySupportedContinuousMap.toNNRealLinear_apply`, `ContinuousLinearMap.opNorm_zero_iff`, `Affine.Simplex.touchpoint_reindex`, `LinearEquiv.isSymmetric_symm_iff`, `MeasureTheory.Measure.map_addHaar_smul`, `aemeasurable_lineDeriv`, `InnerProductSpace.gramSchmidt_def''`, `Real.hasDerivAt_fourierChar`, `bilinFormOfRealInner_orthogonal`, `OrthonormalBasis.equiv_symm`, `AnalyticOnNhd.fderiv`, `WStarAlgebra.exists_predual`, `PMF.integral_eq_sum`, `MeasureTheory.average_add_measure`, `hasDerivAt_intCast`, `EuclideanGeometry.inner_weightedVSub`, `nndist_midpoint_midpoint_le`, `Orientation.kahler_rotation_left`, `PiTensorProduct.liftIsometry_symm_apply`, `nnnorm_cfcₙHom`, `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`, `EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp`, `Real.differentiableWithinAt_arccos_Iic`, `MeasureTheory.charFunDual_eq_pi_iff`, `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`, `Trivialization.continuousLinearEquivAt_prod`, `HasFPowerSeriesAt.const_smul`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder`, `intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Icc`, `Filter.EventuallyEq.lineDifferentiableWithinAt_iff`, `iteratedFDeriv_succ_eq_comp_right`, `SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv`, `ContinuousMultilinearMap.changeOriginSeries_support`, `ContinuousLinearEquiv.comp_hasFDerivAt_iff'`, `WeakFEPair.functional_equation₀`, `CFC.nnrpow_le_nnrpow`, `MeasureTheory.SimpleFunc.setToSimpleFunc_zero`, `Real.tendsto_integral_cexp_sq_smul`, `curveIntegralFun_sub`, `ContDiffMapSupportedIn.seminorm_apply`, `inner_map_self_eq_zero`, `FormalMultilinearSeries.isLittleO_of_lt_radius`, `tsupport_iteratedFDeriv_subset`, `OrthogonalFamily.eq_ite`, `convexHull_ediam`, `aemeasurable_withDensity_iff`, `ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom`, `Orientation.inner_sq_add_areaForm_sq`, `ContinuousMultilinearMap.hasFDerivAt`, `ODE.hasDerivWithinAt_picard_Icc`, `signedDist_smul_of_neg`, `ContinuousLinearMap.rotation_apply`, `Real.iteratedFDeriv_fourier`, `circleAverage_sub_sub_inv_smul_of_differentiable_on`, `DoubleCentralizer.algebraMap_fst`, `differentiableOn_euclidean`, `RCLike.reLm_coe`, `mdifferentiableWithinAt_iff_of_mem_source'`, `hasDerivWithinAt_diff_singleton`, `fderiv_continuousLinearEquiv_comp`, `differentiableAt_abs_pos`, `SchwartzMap.convolution_continuous_left`, `ContinuousLinearMap.adjoint_toSpanSingleton`, `hasStrictFDerivAt_exp_zero_of_radius_pos`, `ContinuousLinearMap.toBilinForm_injective`, `circleIntegral.integral_smul_const`, `InnerProductSpace.mem_span_gramSchmidt`, `ContinuousLinearMap.mfderivWithin_eq`, `ContinuousMultilinearMap.nnnorm_ofSubsingleton`, `inner_smul_real_left`, `aemeasurable_deriv`, `Complex.isConservativeOn_and_continuousOn_iff_isDifferentiableOn`, `ContinuousLinearMap.continuousOn_uncurry_of_multilinear`, `ContinuousLinearMap.norm_compContinuousAlternatingMap_le`, `ContDiff.continuous_iteratedFDeriv`, `mdifferentiableOn_iff_differentiableOn`, `TangentBundle.symmL_model_space`, `HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow`, `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`, `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`, `ContinuousAlternatingMap.isLeast_opNNNorm`, `NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace`, `MeasureTheory.SimpleFunc.integral_eq_sum_of_subset`, `EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff`, `HasFiniteFPowerSeriesOnBall.eq_partialSum'`, `mdifferentiableWithinAt_iff`, `LinearIsometry.enorm_toContinuousLinearMap`, `Unitization.instCStarRing`, `coe_lpBCFₗᵢ_symm`, `range_mfderiv_coe_sphere`, `Complex.wedgeIntegral_add_wedgeIntegral_eq`, `uniqueMDiffOn_iff_uniqueDiffOn`, `coe_lpPiLpₗᵢ_symm`, `differentiable_piLp`, `ClosedSubmodule.inf_orthogonal_eq_bot`, `HasFPowerSeriesOnBall.pi`, `Affine.Triangle.eulerPoint_eq_midpoint`, `ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply`, `Submodule.reflection_eq_self_iff`, `MeasureTheory.weightedSMul_union'`, `MeasureTheory.Measure.addHaar_closedBall_mul_of_pos`, `stereographic_source`, `ContinuousMultilinearMap.piₗᵢ_symm_apply`, `hom_trivializationAt_source`, `AlgHom.coe_toContinuousLinearMap`, `hahnEmbedding_isOrderedModule_rat`, `ContDiff.iteratedFDeriv_right'`, `NumberField.linearDisjoint_of_isGalois_isCoprime_discr`, `Affine.Simplex.sign_signedInfDist_touchpoint_empty`, `ContinuousLinearMap.norm_id_le`, `deriv.neg'`, `AnalyticAt.analyticOrderAt_ne_top`, `SchwartzMap.pairing_continuous_left`, `ConvexOn.univ_sSup_affine_eq`, `Matrix.ofLp_toEuclideanLin_apply`, `signedDist_vadd_right_swap`, `Real.hasFDerivAt_fourierIntegral`, `intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left`, `SchwartzMap.integralCLM_apply`, `linearEquiv_det_rotation`, `InnerProductSpace.rankOne_one_right_eq_toSpanSingleton`, `Real.differentiable_mulExpNegMulSq`, `Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint`, `hasDerivAt_one`, `FormalMultilinearSeries.radius_shift`, `EuclideanSpace.volume_ball_fin_two`, `ContinuousLinearEquiv.comp_right_differentiableAt_iff`, `Real.differentiableAt_arccos`, `ConvexOn.real_univ_sSup_of_nat_affine_eq`, `Complex.conjCLE_apply`, `polar_ball`, `HasFTaylorSeriesUpToOn.hasStrictFDerivAt`, `IsZLattice.span_top`, `Real.not_DifferentiableAt_log_mul_zero`, `innerSLFlip_apply`, `ContinuousLinearEquiv.differentiableOn`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective`, `FormalMultilinearSeries.div_le_radius_compContinuousLinearMap`, `ContinuousLinearEquiv.hasStrictFDerivAt`, `SmoothBumpCovering.comp_embeddingPiTangent_mfderiv`, `EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection`, `fderivWithin_derivWithin`, `Submodule.ker_starProjection`, `ContinuousLinearEquiv.mfderiv_eq`, `hasDerivAt_const_mul`, `Trivialization.coe_continuousLinearEquivAt_eq`, `hasLineDerivAt_iff_tendsto_slope_zero`, `differentiableAt_comp_add_right`, `InnerProductSpace.toContinuousLinearMap_toDualMap`, `MeasureTheory.SignedMeasure.singularPart_smul_nnreal`, `ProbabilityTheory.covarianceBilin_real`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp'`, `ProbabilityTheory.strong_law_Lp`, `EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center`, `ContinuousLinearEquiv.comp_contDiffWithinAt_iff`, `MeasureTheory.integral_const`, `Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset`, `ContinuousLinearMap.measurable_coe`, `Euclidean.ball_eq_preimage`, `ContinuousLinearMap.analyticOn`, `ContinuousLinearMap.nndist_le_opNNNorm`, `CStarAlgebra.star_left_conjugate_le_norm_smul`, `ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior`, `norm_iteratedFDeriv_prod_le`, `contDiff_nat_iff_continuous_differentiable`, `MeasureTheory.L1.SimpleFunc.setToL1S_zero_left`, `hasFDerivAt_pow'`, `absorbent_ball`, `SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv`, `SchwartzMap.lineDerivOp_fourierInv_eq`, `LinearIsometryEquiv.symm_conjStarAlgEquiv`, `OrderedFinpartition.compAlongOrderFinpartition_apply`, `Trivialization.continuousLinearEquivAt_symm_apply`, `Submodule.topologicalClosure_eq_top_iff`, `InformationTheory.rightDeriv_klFun_one`, `hasDerivAt_abs`, `NumberField.mixedEmbedding.stdBasis_apply_isReal`, `mdifferentiableOn_coordChangeL`, `HasFiniteFPowerSeriesOnBall.add`, `ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le`, `IsLocalFrameOn.eq_iff_coeff`, `iteratedDeriv_comp_const_sub`, `ContDiffAt.iteratedFDeriv_comp_perm`, `Polynomial.hasDerivAt`, `ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply`, `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`, `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`, `WeakDual.CharacterSpace.norm_le_norm_one`, `AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn`, `Matrix.linfty_opNorm_toMatrix`, `ConvexOn.real_sSup_of_countable_affine_eq`, `hasDerivAt_natCast`, `Submodule.reflection_bot`, `Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter`, `ContinuousMultilinearMap.opNNNorm_pi`, `innerSL_apply_norm`, `Real.hasDerivAt_Gamma_one`, `InnerProductSpace.toDual_apply_eq_toDualMap_apply`, `AffineSubspace.perpBisector_self`, `Real.fourier_bilin_convolution_eq_integral`, `AffineIsometryEquiv.toAffineEquiv_injective`, `closedBall_normSeminorm`, `Real.hasStrictDerivAt_cos`, `IntervalIntegrable.intervalIntegrable_slope`, `ContinuousLinearMap.isPositive_def'`, `LinearMap.adjoint_inner_left`, `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`, `ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap`, `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`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars`, `ContinuousLinearMap.inCoordinates_eq`, `meromorphicOrderAt_smul_of_ne_zero`, `lineDerivWithin_congr_set`, `HasFPowerSeriesAt.sub`, `RightDerivMeasurableAux.differentiable_set_eq_D`, `ContDiffAt.continuousLinearMap_comp`, `BoxIntegral.integralSum_smul`, `ContinuousMultilinearMap.norm_domDomCongr`, `hasDerivWithinAt_zpow`, `ZSpan.quotientEquiv.symm_apply`, `OrthogonalFamily.range_linearIsometry`, `EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq`, `Real.tendsto_integral_exp_smul_cocompact`, `mellin_convergent_iff_norm`, `Monotone.deriv_nonneg`, `MeasureTheory.setIntegral_tilted'`, `EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw`, `VectorBundleCore.IsContMDiff.contMDiffOn_coordChange`, `Submodule.ker_orthogonalProjection`, `EuclideanGeometry.oangle_midpoint_rev_right`, `Orientation.kahler_mul`, `LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional`, `ProbabilityTheory.iIndepFun_iff_charFunDual_pi'`, `lineDerivWithin_of_mem_nhds`, `Submodule.reflection_map_apply`, `sameRay_iff_norm_sub`, `HasDerivAt.real_of_complex`, `ProbabilityTheory.covarianceBilinDual_comm`, `TensorProduct.dist_tmul_le`, `ProbabilityTheory.isGaussian_iff_charFunDual_eq`, `ProbabilityTheory.iteratedDeriv_two_cgf`, `ContinuousOn.integral_sub_linear_isLittleO_ae`, `SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left`, `AffineIsometry.map_vadd`, `ContinuousMultilinearMap.curry0_norm`, `ContinuousLinearMap.opNNNorm_mul_flip_apply`, `ContinuousLinearMap.compLeftContinuousBounded_apply`, `Submodule.sup_orthogonal_of_hasOrthogonalProjection`, `measurableSet_of_differentiableWithinAt_Ioi`, `TensorProduct.norm_lid`, `MeasureTheory.lpTrimToLpMeas_ae_eq`, `ContinuousLinearMap.norm_fst`, `ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap`, `Real.differentiable_iteratedDeriv_sin`, `OrderedFinpartition.applyOrderedFinpartition_apply`, `ProbabilityTheory.deriv_mgf_zero`, `HasFPowerSeriesOnBall.hasFDerivAt`, `MeasureTheory.charFun_eq_charFunDual_toDualMap`, `AffineIsometry.toContinuousAffineMap_injective`, `SchwartzMap.instLocallyConvexSpace`, `differentiableAt_neg_iff`, `ContinuousLinearMap.opNNNorm_comp_le`, `Affine.Simplex.incenter_mem_affineSpan_range`, `Submodule.starProjection_orthogonalComplement_singleton_eq_zero`, `Submodule.isOrtho_iSup_right`, `TensorProduct.toLinearEquiv_assocIsometry`, `ContinuousMultilinearMap.analyticOn`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₂`, `Orientation.oangle_smul_smul_self_of_nonneg`, `HasMFDerivAt.prod`, `MeromorphicNFAt.smul_analytic`, `AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn`, `Real.deriv_sigmoid`, `Submodule.IsOrtho.disjoint`, `ContinuousMultilinearMap.curryMid_apply`, `iteratedDeriv_eq_iteratedFDeriv`, `ZLattice.volume_image_eq_volume_div_covolume'`, `ProperCone.dual_dual_flip`, `MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv`, `PiTensorProduct.mapL_opNorm`, `flip_innerₗ`, `ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior`, `EuclideanGeometry.orthogonalProjection_orthogonalProjection`, `iter_deriv_inv'`, `toMatrix_innerSL_apply`, `OrthonormalBasis.equiv_apply_basis`, `WeakDual.CharacterSpace.mem_spectrum_iff_exists`, `ClosedSubmodule.sInf_orthogonal`, `Affine.Simplex.eulerPoint_reindex`, `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`, `Orientation.volumeForm_robust'`, `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`, `ContinuousLinearEquiv.comp_contDiffOn_iff`, `ModelWithCorners.convex_range'`, `Dual.dual_norm_topology_le_weak_dual_topology`, `MDifferentiableAt.coordChangeL`, `dist_left_lineMap`, `Manifold.IsImmersionAt.target_subset_preimage_target`, `Submodule.starProjection_top`, `toLocallyConvexSpace`, `Affine.Simplex.excenterWeights_map`, `EulerSine.antideriv_sin_comp_const_mul`, `hasFDerivAt_sub_const`, `Submodule.iInf_orthogonal`, `ContinuousLinearMap.norm_restrictScalars`, `Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero`, `coe_normSeminorm`, `signedDist_vadd_left`, `ModularGroup.tendsto_lcRow0`, `AffineSpace.asymptoticNhds_le_cobounded`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn`, `Pretrivialization.continuousLinearMap_apply`, `derivWithin_sub_const_fun`, `ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear`, `sInter_polar_eq_closedBall`, `ContDiffBump.convolution_eq_right`, `TemperedDistribution.instFourierInvSMul`, `hasFDerivWithinAt_fst`, `ExistsContDiffBumpBase.w_def`, `measurable_derivWithin_Ioi`, `ProbabilityTheory.deriv_cgf`, `MeasureTheory.Measure.setIntegral_comp_smul`, `PositiveLinearMap.ofPreGNS_toPreGNS`, `Complex.imCLM_coe`, `ModelWithCorners.transContinuousLinearEquiv_range`, `isBoundedBilinearMap_inner`, `TensorProduct.nnnorm_assoc`, `WeakFEPair.hf_modif_FE`, `FormalMultilinearSeries.analyticAt_changeOrigin`, `ContinuousLinearMap.opNorm_mul_apply_le`, `Affine.Simplex.incenter_notMem_affineSpan_pair`, `PiTensorProduct.tprodL_apply`, `CStarMatrix.normedSpaceCore`, `intervalIntegral.integral_hasFDerivWithinAt`, `HasFPowerSeriesAt.tendsto_partialSum`, `Diffeomorph.uniqueDiffOn_preimage`, `deriv_pow_field`, `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'`, `norm_smul_le`, `HasFPowerSeriesAt.eventually_hasSum_sub`, `deriv_comp_neg`, `ProbabilityTheory.covarianceBilin_apply`, `DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul`, `fourierIntegral_half_period_translate`, `BoxIntegral.integralSum_sub_partitions`, `Polynomial.hasDerivAt_aeval`, `ContinuousLinearMap.comp_cpolynomialOn`, `AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero`, `ContinuousLinearMap.opNorm_smul_le`, `InnerProductSpace.span_gramSchmidt`, `MeasureTheory.withDensitySMulLI_apply`, `hasDerivAt_gronwallBound`, `hasDerivWithinAt_const_add_iff`, `MeasureTheory.Measure.addHaar_nnreal_smul`, `Affine.Simplex.touchpoint_eq_point_rev`, `EuclideanGeometry.hasFDerivAt_inversion`, `Orientation.kahler_map`, `isBigO_deriv_ofReal_cpow_const_atTop`, `MeasureTheory.convolutionExistsAt_iff_integrable_swap`, `ContinuousMultilinearMap.le_opNorm_mul_prod_of_le`, `PiLp.hasFDerivAt_ofLp`, `TemperedDistribution.instFourierInvAdd`, `dist_div_norm_sq_smul`, `torusIntegral_smul`, `ZLattice.comap_comp`, `stronglyMeasurable_derivWithin_Ici`, `norm_iteratedFDeriv_one`, `posTangentConeAt_mono`, `hasDerivAt_ofReal_cpow_const`, `LinearIsometryEquiv.comp_differentiable_iff`, `CFC.norm_abs`, `hasDerivAt_norm_rpow`, `Affine.Simplex.signedInfDist_reindex`, `ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite`, `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`, `ClosedSubmodule.orthogonal_toSubmodule_eq`, `ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply`, `ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal`, `differentiableAt_finCons'`, `ContinuousLinearMap.isPositive_iff`, `MeasureTheory.Measure.addHaar_submodule`, `TensorProduct.mapIsometry_apply`, `differentiableWithinAt_inverse`, `ContinuousMultilinearMap.compContinuousLinearMapL_apply`, `AnalyticAt.analyticAt_localInverse`, `ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp`, `signedDist_apply_linear_apply`, `VectorBundleCore.inCoordinates_eq`, `SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul`, `TemperedDistribution.fourierInv_apply`, `MeromorphicOn.extract_zeros_poles`, `VectorField.pullbackWithin_eq`, `cfcₙAux_mem_range_inr`, `ContinuousLinearMap.norm_bilinearRestrictScalars`, `PiTensorProduct.liftIsometry_apply_apply`, `ContinuousMultilinearMap.prodL_symm_apply`, `ContinuousMap.adjoin_id_eq_span_one_add`, `EuclideanGeometry.inversion_mem_perpBisector_inversion_iff`, `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`, `MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le`, `LinearMap.IsSymmetric.sub`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear`, `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`, `Unitization.nnnorm_eq_sup`, `Orientation.two_zsmul_oangle_smul_right_self`, `Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton`, `SchwartzMap.fourierTransformCLM_apply`, `AffineSubspace.signedInfDist_singleton`, `HasFPowerSeriesWithinOnBall.neg`, `norm_deriv_eq_norm_fderiv`, `Trivialization.symm_continuousLinearEquivAt_eq`, `EuclideanGeometry.angle_midpoint_eq_pi`, `DoubleCentralizer.zero_toProd`, `Orientation.coe_basisRightAngleRotation`, `MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux`, `PointwiseConvergenceCLM.tendsto_nhds_atTop`, `AkraBazziRecurrence.differentiableAt_smoothingFn`, `TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq`, `ContinuousLinearMap.bilinearComp_zero_left`, `ContinuousLinearMap.nnnorm_smulRight_apply`, `deriv_id`, `hasFPowerSeriesWithinOnBall_pi_iff`, `hasDerivAt_zero`, `LinearIsometryEquiv.smul_trans`, `SchwartzMap.fderivCLM_fourier_eq`, `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`, `Real.deriv_cos`, `IsCoercive.continuousLinearEquivOfBilin_apply`, `VectorBundleCore.continuousOn_coordChange`, `Affine.Simplex.affineCombination_touchpointWeights`, `MeasureTheory.integral_fun_fst`, `Orientation.volumeForm_zero_neg`, `SmoothPartitionOfUnity.contMDiff_finsum_smul`, `hasDerivWithinAt_inter'`, `MeasureTheory.pdf.integrable_pdf_smul_iff`, `Real.differentiableAt_binEntropy`, `AffineSubspace.subtypeₐᵢ_linearIsometry`, `Unitary.inner_map_map`, `ContDiffBump.dist_normed_convolution_le`, `Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero`, `QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared`, `mellin_differentiableAt_of_isBigO_rpow_exp`, `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`, `EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear`, `differentiable_neg`, `deriv_comp_mul_left`, `hasDerivAt_neg`, `LinearMap.IsSymmetric.id`, `OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary`, `hasDerivAtFilter_finCons`, `ContinuousLinearMap.adjoint_comp`, `deriv_bernoulliFun`, `PiTensorProduct.norm_eval_le_projectiveSeminorm`, `iteratedFDeriv_zero_eq_comp`, `isCompactOperator_iff_image_ball_subset_compact`, `intervalIntegral.integral_hasDerivAt_right`, `det_fderivPiPolarCoordSymm`, `isConformalMap_iff`, `hasFTaylorSeriesUpToOn_succ_iff_left`, `HasCompactSupport.hasDerivAt_convolution_left`, `measurableSet_lineDifferentiableAt`, `Polynomial.hasStrictDerivAt`, `IsConformalMap.comp`, `Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle`, `Real.deriv2_qaryEntropy`, `ContinuousLinearEquiv.isBigO_comp_rev`, `VectorFourier.integral_bilin_fourierIntegral_eq_flip`, `Real.differentiableAt_exp`, `Affine.Simplex.mongePoint_mem_affineSpan`, `Real.hasStrictDerivAt_arcsin`, `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`, `NumberField.mixedEmbedding.commMap_apply_of_isReal`, `EuclideanGeometry.Sphere.IsTangent.isTangentAt`, `AffineMap.hasStrictDerivAt`, `LipschitzWith.ae_differentiableAt_of_real`, `ProperCone.mem_innerDual`, `InnerProductSpace.toLinearMap_rankOne`, `instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional`, `ContinuousLinearMap.comp_hasFPowerSeriesOnBall`, `meromorphicNFAt_smul_iff_right_of_analyticAt`, `EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff`, `ContinuousLinearMap.adjointAux_inner_right`, `IsClosed.diffContOnCl_iff`, `HasDerivWithinAt.Ioi_iff_Ioo`, `MeromorphicOn.smul`, `Seminorm.finset_sup_smul`, `quasispectrum.isCompact_nnreal`, `HasMFDerivWithinAt.mul`, `Bundle.RiemannianMetric.pos`, `TemperedDistribution.instLineDerivSMulComplex`, `ContinuousLinearEquiv.isOpen`, `HilbertBasis.repr_self`, `CStarAlgebra.instNonnegSpectrumClass'`, `CStarAlgebra.conjugate_le_norm_smul`, `AnalyticAt.differentiableWithinAt`, `TensorProduct.commIsometry_apply`, `ContinuousLinearEquiv.coe_toDiffeomorph`, `deriv_intCast`, `Seminorm.isBounded_sup`, `NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm`, `norm_midpoint_lt_iff`, `continuousMultilinearCurryRightEquiv_symm_apply'`, `MeasureTheory.integral_comp_mul_right_Ioi`, `MeasureTheory.condExpInd_smul'`, `ContinuousLinearMap.isBigO_sub`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply`, `DoubleCentralizer.norm_fst`, `measurable_smul_const`, `WeakFEPair.functional_equation`, `MeasureTheory.Submartingale.sum_smul_sub`, `SchwartzMap.smul_apply`, `ContDiffMapSupportedIn.continuousSMul`, `Real.differentiable_iteratedDeriv_cosh`, `Real.hasStrictDerivAt_sin`, `TensorProduct.congrIsometry_symm`, `ContDiffMapSupportedIn.structureMapLM_zero_injective`, `toSpanSingleton_deriv`, `ContinuousLinearMapWOT.continuous_inducingFn`, `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`, `Affine.Simplex.incenter_reindex`, `Trivialization.continuousLinearMapAt_symmL`, `LinearMap.isStarProjection_toContinuousLinearMap_iff`, `ContinuousLinearMap.IsPositive.orthogonalProjection_comp`, `MeromorphicOn.divisor_smul`, `AffineSubspace.mem_perpBisector_iff_dist_eq`, `LinearMap.IsSymmetric.orthogonal_range`, `MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀`, `iteratedDerivWithin_eq_equiv_comp`, `ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le`, `Polynomial.differentiableAt`, `MeasureTheory.charFunDual_eq_pi_iff'`, `Besicovitch.card_le_of_separated`, `dimH_orthogonalProjection_le`, `BoundedContinuousFunction.toLp_norm_le`, `instDiscreteTopologySubtypeMemSubmoduleIntComap`, `Pretrivialization.continuousOn_continuousLinearMapCoordChange`, `ContDiffMapSupportedIn.seminorm_postcompLM_le`, `ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap`, `ContinuousMultilinearMap.bound`, `MeasureTheory.integral_countable`, `DoubleCentralizer.coe_fst`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap`, `ContDiffPointwiseHolderAt.fderiv`, `CompactlySupportedContinuousMap.toReal_smul`, `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`, `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`, `InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero`, `continuousOn_cfcₙ_nnreal`, `EuclideanGeometry.reflection_apply'`, `Complex.IsConservativeOn.hasDerivAt_wedgeIntegral`, `hasFDerivWithinAt_iff_hasGradientWithinAt`, `iteratedDerivWithin_succ`, `CurveIntegrable.smul`, `AffineIsometryEquiv.ofEq_rfl`, `BoxIntegral.Integrable.smul`, `TemperedDistribution.laplacian_toTemperedDistributionCLM_eq`, `ContinuousAffineMap.differentiableOn`, `Submodule.id_eq_sum_starProjection_self_orthogonalComplement`, `Submodule.isOrtho_bot_right`, `LinearMap.adjoint_comp`, `FormalMultilinearSeries.min_radius_le_radius_add`, `ContinuousAlternatingMap.opNorm_le_iff`, `hasStrictDerivAt_one`, `ContinuousAffineMap.norm_comp_le`, `IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus`, `signedDist_right_lineMap`, `ProbabilityTheory.uncenteredCovarianceBilin_zero`, `LinearMap.IsPositive.inner_nonneg_right`, `VonNeumannAlgebra.coe_toStarSubalgebra`, `Matrix.toEuclideanLin_apply_piLp_toLp`, `MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter`, `Real.differentiable_fourierChar`, `InnerProductSpace.span_gramSchmidt_Iio`, `mdifferentiableAt_iff_of_mem_source`, `ContinuousAlternatingMap.curryLeft_add`, `HasFPowerSeriesAt.pi`, `ProbabilityTheory.setIntegral_tilted_mul_eq_mgf`, `hasFDerivAt_comp_add_left`, `iteratedDerivWithin_succ'`, `smul_ball`, `LinearIsometryEquiv.lTensor_def`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn'`, `EuclideanGeometry.Sphere.mem_tangentSet_iff`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply`, `hasStrictDerivAt_pi`, `ContDiff.hasStrictDerivAt`, `LinearIsometry.strictConvexSpace_range_iff`, `VectorFourier.fourierPowSMulRight_apply`, `inner_eq_norm_mul_iff_real`, `Affine.Simplex.altitude_map`, `ContinuousAlternatingMap.prodLIE_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`, `LinearMap.isSymmetric_iff_isSelfAdjoint`, `Real.deriv_rpow_const'`, `ContinuousLinearMap.opNorm_le_iff_lipschitz`, `CPolynomialOn.fderiv`, `NumberField.mixedEmbedding.normAtPlace_negAt`, `Submodule.reflection_involutive`, `SchwartzMap.convolution_flip`, `Real.differentiableAt_arcosh`, `AffineIsometry.toAffineMap_injective`, `ContinuousLinearMap.opNorm_flip`, `Module.Basis.parallelepiped_map`, `AffineIsometryEquiv.toAffineEquiv_refl`, `AlternatingMap.measure_def`, `ContDiffAt.differentiableAt_one`, `MeasureTheory.charFunDual_dirac`, `continuousOn_integral_bilinear_of_locally_integrable_of_compact_support`, `VectorPrebundle.continuousOn_coordChange`, `Filter.Tendsto.integral_sub_linear_isLittleO_ae`, `LinearMap.isSymmetric_iff_sesqForm`, `FormalMultilinearSeries.radius_compContinuousLinearMap_le`, `hasDerivWithinAt_derivWithin_iff`, `hasDerivAt_sub_const_iff`, `hasStrictDerivAt_exp`, `ContinuousLinearMap.IsPositive.adjoint_conj`, `measurable_fderiv_with_param`, `LinearIsometryEquiv.reflections_generate_dim`, `Complex.isometryOfOrthonormal_apply`, `IsConformalMap.smul`, `iteratedFDeriv_prodMk`, `nndist_lineMap_lineMap`, `intervalIntegral.smul_integral_comp_mul_right`, `LinearMap.isSymmetricProjection_iff_eq_coe_starProjection`, `Complex.sameRay_iff`, `SchwartzMap.lineDerivOp_apply_eq_fderiv`, `deriv_add_const`, `intervalIntegral.integral_comp_div_add`, `Real.hasStrictDerivAt_sqrt`, `mdifferentiableAt_iff_differentiableAt`, `EuclideanGeometry.Sphere.isTangentAt_center_iff`, `ContinuousLinearMap.exist_extension_of_finiteDimensional_range`, `LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range`, `hasFDerivWithinAt_pi`, `BoxIntegral.integral_const`, `intervalIntegral.integral_smul_const`, `MeasureTheory.hausdorffMeasure_orthogonalProjection_le`, `Polynomial.deriv`, `ContinuousMultilinearMap.uncurry0_apply`, `differentiableWithinAt_apply`, `ContinuousLinearMap.isPositive_iff'`, `LinearIsometryEquiv.comp_hasFDerivAt_iff`, `derivWithin_const_add_fun`, `Real.hasDerivAt_tan_of_mem_Ioo`, `OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le`, `Submodule.finrank_add_finrank_orthogonal`, `NumberField.mixedEmbedding.finrank`, `Orientation.two_zsmul_oangle_smul_right_of_ne_zero`, `ContinuousLinearMap.star_eq_adjoint`, `SchwartzMap.integral_fourier_smul_eq`, `Real.dimH_segment`, `Real.iter_deriv_rpow_const`, `AffineMap.differentiableOn`, `Complex.imCLM_nnnorm`, `Submodule.orthogonal_eq_top_iff`, `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`, `ContMDiffWithinAt.coordChangeL`, `Polynomial.hasFDerivWithinAt_aeval`, `HasFPowerSeriesWithinAt.neg`, `Orientation.inner_rightAngleRotation_right`, `continuousOn_cfcₙ_setProd`, `Real.hasDerivAt_exp`, `volume_euclideanSpace_eq_dirac`, `derivWithin_comp_add_const`, `LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces`, `NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply`, `derivWithin.star`, `hasStrictDerivAt_inv`, `asymptoticCone_subset_singleton_of_bounded`, `OrderedFinpartition.applyOrderedFinpartition_update_left`, `LinearMap.continuous_of_isClosed_ker`, `Unitization.complex_cfcₙ_eq_cfc_inr`, `orthogonalFamily_iff_pairwise`, `ZSpan.map_fundamentalDomain`, `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`, `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`, `ContinuousLinearMap.norm_compSL_le`, `MeasureTheory.norm_condExpInd_le`, `ContinuousLinearEquiv.uniqueDiffOn_preimage_iff`, `VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral`, `ContDiffMapSupportedIn.withSeminorms`, `differentiableWithinAt_snd`, `Submodule.isOrtho_sSup_left`, `Bundle.Trivial.trivialization.coordChangeL`, `MeasureTheory.withDensityᵥ_smul`, `ContDiffAt.exists_eventually_eq_hasDerivAt`, `CStarAlgebra.norm_negPart_le`, `ContinuousMultilinearMap.analyticWithinAt`, `NumberField.mixedEmbedding.negAt_apply_norm_isReal`, `fderiv_star`, `MeasureTheory.integrable_comp_smul_iff`, `derivWithin_fun_const_smul'`, `MeasureTheory.Measure.addHaar_preimage_linearEquiv`, `innerₛₗ_apply`, `hasFDerivAtFilter_iff_tendsto`, `InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis`, `ProbabilityTheory.setIntegral_tilted_mul_eq_cgf`, `Affine.Simplex.orthogonalProjectionSpan_reindex`, `innerSL_apply`, `OrthonormalBasis.coe_toBasis_repr`, `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`, `InnerProductSpace.isIdempotentElem_rankOne_self_iff`, `Filter.EventuallyEq.iteratedFDeriv`, `ContinuousLinearMap.opNorm_nonneg`, `MeasureTheory.hausdorffMeasure_affineSegment`, `Pretrivialization.continuousLinearMap_symm_apply`, `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`, `ContinuousLinearMap.coe_flipₗᵢ`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty`, `inner_map_polarization`, `HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace`, `Submodule.inner_starProjection_left_eq_right`, `ContinuousLinearMap.normOneClass`, `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`, `Real.iteratedFDeriv_fourierIntegral`, `MeasureTheory.integrableOn_condExpL2_of_measure_ne_top`, `differentiableAt_snd`, `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`, `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`, `IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero_symm`, `differentiableWithinAt_smul_iff`, `LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry`, `Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne`, `MeasureTheory.condExpInd_disjoint_union_apply`, `ContinuousLinearMap.analyticOn_uncurry_of_multilinear`, `iteratedDeriv_one`, `EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two`, `FormalMultilinearSeries.changeOrigin_eval`, `LinearMap.toSeminorm_ball_zero`, `differentiableWithinAt_add_const_iff`, `Real.differentiableAt_negMulLog`, `continuousAt_hom_bundle`, `LinearIsometryEquiv.hasFDerivWithinAt`, `ContinuousAlternatingMap.norm_alternatizeUncurryFin_le`, `Submodule.fstL_comp_coe_orthogonalDecomposition`, `StrongConvexOn.strictConvexOn`, `iter_deriv_inv_linear_sub`, `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`, `LinearIsometryEquiv.symm_units_smul`, `IsHilbertSum.linearIsometryEquiv_symm_apply_single`, `AffineIsometryEquiv.map_vadd`, `VonNeumannAlgebra.mem_commutant_iff`, `UnitAddTorus.mFourierBasis_repr`, `HasFPowerSeriesAt.prod`, `LinearMap.toSeminorm_apply`, `hasDerivAt_ofReal_cpow_const'`, `hasStrictDerivAt_natCast`, `LinearIsometryEquiv.toLinearIsometry_rTensor`, `VectorPrebundle.contMDiffOn_contMDiffCoordChange`, `LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum`, `Orientation.areaForm_apply_self`, `CFC.sqrt_le_sqrt`, `MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff`, `Submodule.starProjection_minimal`, `DiffContOnCl.differentiableAt`, `EuclideanGeometry.orthogonalProjection_linear`, `HasFPowerSeriesAt.isBigO_sub_partialSum_pow`, `ContinuousLinearMap.contMDiffWithinAt`, `Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff`, `lineDeriv_smul`, `MeasureTheory.integrable_rnDeriv_smul_iff`, `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`, `MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot`, `Affine.Simplex.sSameSide_point_excenter_singleton`, `mdifferentiableAt_coordChangeL`, `hasDerivAt_finCons'`, `ProbabilityTheory.variance_linearMap_gaussianReal`, `MeasureTheory.Lp.toTemperedDistribution_toLp_eq`, `fourierBasis_repr`, `LeftInvariantDerivation.evalAt_mul`, `AffineSubspace.signedInfDist_def`, `MeasureTheory.Measure.addHaar_closedBall`, `ContinuousLinearMap.unit_le_opNorm`, `NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply`, `HasFPowerSeriesWithinAt.add`, `Submodule.starProjection_mem_subspace_eq_self`, `Affine.Simplex.acuteAngled_reindex_iff`, `Complex.norm_deriv_le_of_forall_mem_sphere_norm_le`, `MeasureTheory.BoundedContinuousFunction.inner_toLp`, `ContinuousLinearMap.adjoint_inner_right`, `Submodule.angle_coe`, `exists_extension_norm_eq`, `Real.tendsto_integral_gaussian_smul`, `HasMFDerivAt.prodMk`, `CStarModule.continuous_inner`, `ContinuousLinearMap.norm_id`, `FormalMultilinearSeries.id_apply_of_one_lt`, `ContinuousMultilinearMap.nnnorm_ofSubsingleton_id`, `HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt`, `TensorProduct.norm_tmul`, `ContDiff.contDiff_fderiv_apply`, `hasStrictDerivAt_exp_zero_of_radius_pos`, `LinearMap.isPositive_iff`, `MeasureTheory.L1.norm_Integral_le_one`, `ContinuousLinearMap.measurable_apply'`, `VectorFourier.fourierIntegral_comp_add_right`, `closedBall_inv_subset_polar_closedBall`, `ContDiffMapSupportedIn.postcompLM_apply`, `Affine.Simplex.mem_altitude`, `Affine.Simplex.isDiameter_ninePointCircle`, `ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero`, `ContDiff.dimH_range_le`, `signedDist_lineMap_right`, `analyticOrderAt_smul`, `ContinuousLinearMap.norm_smulRightL_le`, `TemperedDistribution.laplacian_apply_apply`, `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`, `HasFPowerSeriesOnBall.image_sub_sub_deriv_le`, `Complex.imCLM_enorm`, `TemperedDistribution.smulLeftCLM_smulLeftCLM_apply`, `hasDerivAtFilter_const`, `LinearIsometryEquiv.symm_smul_apply`, `SchwartzMap.tsupport_derivCLM_subset`, `Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle`, `Filter.Tendsto.cesaro_smul`, `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`, `ContinuousLinearMap.coe_symm_flipMultilinearEquiv`, `Continuous.fourierPowSMulRight`, `differentiableOn_apply`, `LinearIsometryEquiv.star_eq_symm`, `ContinuousLinearEquiv.dimH_preimage`, `hasStrictFDerivAt_add_const_iff`, `SchwartzMap.integral_smul_laplacian_right_eq_left`, `differentiableAt_pi`, `hasStrictDerivAt_exp_of_mem_ball`, `FormalMultilinearSeries.radius_prod_eq_min`, `OrthonormalBasis.coe_equiv_euclideanSpace`, `differentiable_norm_rpow`, `VectorFourier.fourierIntegral_probChar`, `AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv`, `ContinuousLinearEquiv.continuousAlternatingMapCongr_apply`, `Affine.Simplex.sign_signedInfDist_incenter`, `Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter`, `Orientation.rightAngleRotation_map`, `VectorFourier.norm_fourierSMulRight_le`, `continuousWithinAt_hom_bundle`, `AlternatingMap.measure_parallelepiped`, `EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power`, `IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary`, `ContinuousAffineMap.hasFDerivWithinAt`, `NonUnitalCommCStarAlgebra.toSMulCommClass`, `ContinuousAlternatingMap.nnnorm_ofSubsingleton`, `RCLike.toContinuousLinearMap_complexLinearIsometryEquiv`, `MeasureTheory.charFunDual_map`, `hasFDerivWithinAt_add_const_iff`, `HasFiniteFPowerSeriesOnBall.fderiv'`, `Orientation.two_zsmul_oangle_smul_left_self`, `Orientation.kahler_rotation_right`, `Complex.ofRealCLM_enorm`, `Submodule.orthogonalProjectionFn_eq`, `Fourier.fourierIntegral_def`, `intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le`, `ContinuousMultilinearMap.currySum_apply`, `isOpenMap_barycentric_coord`, `TensorProduct.nnnorm_comm`, `Submodule.IsOrtho.ge`, `Affine.Simplex.signedInfDist_affineCombination`, `TemperedDistribution.lineDerivOp_apply_apply`, `CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun`, `MeasureTheory.ComplexMeasure.re_apply`, `Polynomial.differentiableWithinAt_aeval`, `Submodule.bot_orthogonal_eq_top`, `signedDist_apply`, `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`, `measurable_fderiv`, `continuousMultilinearCurryRightEquiv_apply'`, `ContinuousLinearMap.flipₗᵢ'_symm`, `le_egauge_ball_one`, `Orthonormal.comp_linearIsometryEquiv`, `TemperedDistribution.lineDerivOp_fourierInv_eq`, `Submodule.map_orthogonal`, `fourierCoeffOn_eq_integral`, `ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero`, `DoubleCentralizer.natCast_snd`, `VonNeumannAlgebra.coe_commutant`, `ContDiffMapSupportedIn.bounded_iteratedFDeriv`, `AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm`, `HasFTaylorSeriesUpToOn.differentiableOn`, `MeasureTheory.SimpleFunc.integral_const`, `MeromorphicAt.deriv`, `HasFiniteFPowerSeriesOnBall.hasFDerivAt`, `ProbabilityTheory.variance_dual_prod`, `ProbabilityTheory.isGaussian_map_equiv`, `differentiableWithinAt_const_sub_iff`, `EuclideanGeometry.dist_affineCombination`, `hasStrictDerivAt_zero`, `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`, `AffineSubspace.direction_perpBisector`, `Besicovitch.multiplicity_le`, `FormalMultilinearSeries.coeff_iterate_fslope`, `AffineSubspace.angle_coe`, `LinearMap.IsSymmetric.conj_inner_sym`, `HasFPowerSeriesAt.eq_zero`, `ContinuousLinearMap.coeFn_compLp`, `ContinuousLinearMap.flip_zero`, `FormalMultilinearSeries.leftInv_removeZero`, `deriv_const_smul'`, `intervalIntegral.integral_comp_mul_right`, `hasStrictDerivAt_exp_smul_const_of_mem_ball'`, `rotation_symm`, `OrthonormalBasis.same_orientation_iff_det_eq_det`, `ContinuousLinearMap.extendTo𝕜'_apply`, `hasFDerivWithinAt_comp_sub`, `derivWithin_comp_sub_const`, `ClosedSubmodule.orthogonal_disjoint`, `CompletelyPositiveMap.map_cstarMatrix_nonneg'`, `IsLocalFrameOn.coeff_eq_of_eq`, `ContDiff.differentiable_iteratedDeriv'`, `Affine.Simplex.ninePointCircle_map`, `iteratedFDerivWithin_const_of_ne`, `ContinuousMultilinearMap.norm_ofSubsingleton`, `ContinuousLinearMap.isAdjointPair_inner`, `VectorFourier.norm_fourierPowSMulRight_le`, `TensorProduct.norm_map`, `EuclideanGeometry.dist_smul_vadd_eq_dist`, `derivWithin_Ioi_eq_Ici`, `dist_birkhoffAverage_birkhoffAverage_le`, `Complex.equivRealProdCLM_symm_apply_im`, `ContinuousLinearMap.coe_le_coe_iff`, `AddChar.linearIndependent`, `MeasureTheory.integral_singleton`, `ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply`, `intervalIntegral.integral_comp_div_sub`, `hasFDerivAtFilter_finCons'`, `ContinuousLinearEquiv.analyticWithinAt`, `nndist_homothety_center`, `ProbabilityTheory.norm_uncenteredCovarianceBilin_le`, `ConvexBody.hausdorffDist_coe`, `Real.hasFDerivAt_fourierChar_neg_bilinear_right`, `EuclideanGeometry.orthogonalProjection_eq_self_iff`, `LinearIsometryEquiv.differentiableAt`, `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`, `HasFPowerSeriesAt.coeff_zero`, `Submodule.orthogonal_le_orthogonal_iff`, `DoubleCentralizer.sub_snd`, `ModelWithCorners.coe_transContinuousLinearEquiv`, `Submodule.orthogonal_le_iff_orthogonal_le`, `ContDiffOn.comp_continuousLinearMap`, `VectorFourier.norm_fourierSMulRight`, `Polynomial.differentiable`, `InnerProductSpace.volume_closedBall`, `ContinuousLinearEquiv.coord_norm'`, `HasFPowerSeriesOnBall.hasSum_sub`, `ContinuousLinearMap.nnnorm_id`, `differentiableOn_abs`, `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`, `div_le_egauge_closedBall`, `intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left`, `hasStrictFDerivAt_inv'`, `AffineIsometryEquiv.coe_vaddConst'`, `LinearMap.mem_span_iff_bound`, `homeomorphSphereProd_apply_fst_coe`, `uniqueMDiffWithinAt_iff_uniqueDiffWithinAt`, `hasFDerivAt_exp_smul_const_of_mem_ball'`, `hasDerivAt_mul_const`, `MeasureTheory.Lp.toTemperedDistribution_apply`, `SchwartzMap.smulLeftCLM_sub`, `Submodule.snd_orthogonalDecomposition_apply`, `TemperedDistribution.smulLeftCLM_const`, `SchwartzMap.smulLeftCLM_apply_apply`, `deriv_inv'`, `deriv_descPochhammer_eval_eq_sum_prod_range_erase`, `strongConvexOn_iff_convex`, `Module.Basis.ofZLatticeBasis_repr_apply`, `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'`, `SchwartzMap.fourier_fderivCLM_eq`, `Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv`, `ConvexBody.hausdorffEDist_coe`, `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`, `SchwartzMap.fourier_convolution_apply`, `Complex.hasStrictFDerivAt_log_real`, `MeasureTheory.SimpleFunc.setToSimpleFunc_const'`, `iteratedFDeriv_two_apply`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap`, `LinearIsometry.norm_toContinuousLinearMap_le`, `Real.hasStrictDerivAt_tan`, `AffineSubspace.isometryEquivMap.apply_symm_apply`, `Submodule.starProjection_le_starProjection_iff`, `iteratedFDerivWithin_zero_fun`, `real_inner_smul_left`, `CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one`, `TemperedDistribution.smulLeftCLM_sum`, `intervalIntegral.integral_hasStrictDerivAt_left`, `NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis`, `ContinuousLinearMap.analyticOnNhd`, `fderiv_fst`, `iter_deriv_inv_linear`, `ProbabilityTheory.deriv_cgf_zero`, `AffineMap.differentiable`, `ContDiffOn.continuousOn_deriv_of_isOpen`, `Orientation.oangle_rotation_self_right`, `ContinuousAlternatingMap.differentiable`, `WeakDual.toStrongDual_apply`, `LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul`, `hom_trivializationAt_apply`, `AffineEquiv.coe_toHomeomorphOfFiniteDimensional`, `ContinuousLinearEquiv.uniqueDiffOn_image_iff`, `NumberField.mixedEmbedding.euclidean.finrank`, `LinearMap.eq_adjoint_iff_basis_right`, `ContinuousLinearMap.hasMFDerivWithinAt`, `ContinuousLinearEquiv.nnnorm_symm_pos`, `InnerProductSpace.laplacian_smul_nhds`, `MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball`, `Real.differentiable_fourierChar_neg_bilinear_left`, `Submodule.instOrthogonalCompleteSpace`, `FormalMultilinearSeries.enorm_compContinuousLinearMap_le`, `ConvexBody.hausdorffEdist_coe`, `AffineBasis.centroid_mem_interior_convexHull`, `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`, `MeasureTheory.Measure.addHaar_closedBall_mul`, `hasDerivAt_exp_smul_const'`, `dist_right_lineMap`, `hasFDerivAtFilter_const_add_iff`, `DoubleCentralizer.instStarModule`, `WeakDual.CharacterSpace.compContinuousMap_comp`, `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`, `innerₛₗ_apply_coe`, `AnalyticOn.differentiableOn`, `mellin_differentiableAt_of_isBigO_rpow`, `TestFunction.instContinuousSMulReal`, `MeasureTheory.integral_comp_mul_left_Ioi`, `AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn`, `Complex.reCLM_norm`, `ContinuousLinearMap.norm_snd_le`, `Submodule.orthogonalDecomposition_apply`, `iteratedFDeriv_succ_eq_comp_left`, `LinearIsometryEquiv.comp_hasFDerivWithinAt_iff`, `Submodule.isOrtho_self`, `LinearIsometryEquiv.toLinearIsometry_lTensor`, `ContinuousMapZero.toNNReal_neg_smul`, `ContinuousLinearMap.smul_compLpL`, `MeasureTheory.SimpleFunc.map_integral`, `differentiableAt_of_deriv_ne_zero`, `FormalMultilinearSeries.summable_norm_mul_pow`, `ContinuousLinearMap.contMDiffOn`, `ProbabilityTheory.instIsGaussianMapHAdd`, `VonNeumannAlgebra.instStarMemClass`, `ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv`, `contMDiffOn_coordChangeL`, `NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm`, `ext_iff`, `OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self`, `ContinuousLinearMap.nnbound`, `stronglyMeasurable_deriv_with_param`, `ContinuousLinearMap.opNorm_mulLeftRight_le`, `DoubleCentralizer.intCast_fst`, `MeasureTheory.measure_smul_setAverage`, `ClosedSubmodule.orthogonal_closure`, `ContDiffPointwiseHolderAt.iteratedFDeriv`, `ContinuousLinearMap.norm_compLpL_le`, `MeasureTheory.Integrable.comp_smul`, `ZSpan.vadd_mem_fundamentalDomain`, `LinearMap.toSeminormFamily_apply`, `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`, `derivWithin_add_const`, `TemperedDistribution.fourier_apply`, `fderiv_comp_add_left`, `ContinuousMultilinearMap.piₗᵢ_apply`, `meromorphicAt_smul_iff_of_ne_zero`, `Matrix.PosSemidef.sqrt_mul_self`, `Orientation.areaForm_rightAngleRotation_right`, `MeasureTheory.setIntegral_condExpL1CLM`, `SchwartzMap.lineDerivOp_apply`, `OrthonormalBasis.orientation_adjustToOrientation`, `ContDiffAt.continuousAt_iteratedFDeriv`, `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`, `Module.Basis.map_addHaar`, `AffineIsometryEquiv.norm_map`, `ContinuousLinearMap.cpolynomialOn`, `ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le`, `MeasureTheory.Integrable.fourier_smul`, `fderiv_comp_sub`, `ContinuousAlternatingMap.nnnorm_constOfIsEmpty`, `hasStrictFDerivAt_list_prod'`, `Real.differentiableAt_qaryEntropy`, `ContinuousLinearMap.le_opENorm`, `continuousMultilinearCurryFin1_symm_apply`, `MeasureTheory.Measure.setIntegral_comp_smul_of_pos`, `EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal`, `differentiableWithinAt_comp_add_left`, `Trivialization.symmL_apply`, `ContinuousMultilinearMap.opNorm_le_iff`, `AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff`, `MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound`, `intervalIntegral.integral_comp_mul_add`, `FormalMultilinearSeries.radius_pi_le`, `hom_trivializationAt_baseSet`, `MeasureTheory.lpMeasToLpTrim_ae_eq`, `Submodule.orthogonal_eq_inter`, `VectorFourier.integral_fourierIntegral_smul_eq_flip`, `ContinuousLinearMap.mdifferentiableOn`, `MeasureTheory.eLpNorm_condExpL2_le`, `Affine.Simplex.touchpoint_mem_affineSpan_simplex`, `ContinuousLinearMap.lsmul_flip_apply`, `aemeasurable_derivWithin_Ici`, `Orientation.inner_smul_rotation_pi_div_two_smul_left`, `closure_diff_intrinsicInterior`, `ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft`, `hasDerivAt_iff_tendsto`, `ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe`, `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`, `ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply`, `MeasureTheory.condExp_bot'`, `ContinuousAlternatingMap.unit_le_opNorm`, `SchwartzMap.smulLeftCLM_ofReal`, `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`, `Trivialization.prod_apply'`, `ContinuousLinearMap.sSup_unitClosedBall_eq_norm`, `mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop`, `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`, `intervalIntegral.integral_hasDerivAt_left`, `ContinuousLinearMap.norm_map_iff_adjoint_comp_self`, `Matrix.toEuclideanLin_eq_toLin_orthonormal`, `isTheta_deriv_ofReal_cpow_const_atTop`, `MeasureTheory.lpMeasToLpTrim_smul`, `Real.hasStrictDerivAt_const_rpow`, `Submodule.starProjection_orthogonal_val`, `VectorField.lieBracketWithin_eq`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap`, `MeasureTheory.integral_finset`, `Affine.Simplex.circumsphere_reindex`, `isStarProjection_iff_eq_starProjection`, `ContinuousLinearMap.norm_adjoint_comp_self`, `LinearPMap.mem_adjoint_domain_iff`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith`, `Orientation.inner_smul_rotation_pi_div_two_smul_right`, `LinearMap.IsSymmetricProjection.le_iff_range_le_range`, `derivWithin_congr_set`, `hasDerivWithinAt_intCast`, `differentiableWithinAt_zpow`, `ContinuousAt.integral_sub_linear_isLittleO_ae`, `CircleIntegrable.out`, `VonNeumannAlgebra.instSubringClass`, `contDiffOn_infty_iff_deriv_of_isOpen`, `EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace`, `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`, `ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm`, `mdifferentiableWithinAt_iff_of_mem_source`, `Bundle.ContinuousLinearMap.memTrivializationAtlas`, `MeasureTheory.Measure.toSphere_eq_zero_iff_finrank`, `ContinuousMapZero.elemental_eq_top`, `ContinuousMapZero.adjoin_id_dense`, `Complex.rightAngleRotation`, `EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq`, `ContinuousAlternatingMap.bound`, `Affine.Simplex.circumradius_reindex`, `ContinuousLinearMap.hasDerivWithinAt`, `differentiableWithinAt_piLp`, `LinearIsometry.rTensor_apply`, `hasStrictFDerivAt_pow`, `FormalMultilinearSeries.derivSeries_apply_diag`, `polar_closedBall`, `derivWithin_comp_const_add`, `Submodule.norm_orthogonalProjection`, `AnalyticAt.fderiv`, `ContinuousLinearEquiv.differentiableWithinAt`, `ContinuousMapZero.toNNReal_smul`, `fderiv_comp_smul`, `Submodule.instHasOrthogonalProjectionTop`, `AffineSubspace.signedInfDist_apply_self`, `EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection`, `ContinuousLinearMap.opNorm_lsmul`, `LinearIsometry.toLinearMap_lTensor`, `EuclideanGeometry.orthogonalProjection_mem_orthogonal`, `HasFPowerSeriesWithinOnBall.hasSum`, `coe_innerₛₗ_apply`, `ProbabilityTheory.covarianceBilinDual_of_not_memLp`, `FormalMultilinearSeries.norm_changeOriginSeriesTerm`, `PiLp.hasStrictFDerivAt_ofLp`, `TemperedDistribution.smulLeftCLM_smul`, `ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply`, `ContinuousLinearMap.norm_id_of_nontrivial_seminorm`, `curveIntegral_add`, `HasGradientAt.hasDerivAt`, `TensorProduct.nndist_tmul_le`, `ProbabilityTheory.strong_law_ae_of_measurable`, `InnerProductGeometry.angle_eq_pi_iff`, `ModularGroup.lcRow0_apply`, `hasDerivAt_exp_zero`, `HasFTaylorSeriesUpTo.zero_eq'`, `deriv_circleMap_eq_zero_iff`, `Complex.imCLM_apply`, `MeasureTheory.charFun_map_eq_charFunDual_smul`, `ContinuousLinearEquiv.analyticAt`, `InnerProductSpace.continuousLinearMapOfBilin_apply`, `NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace`, `HasCompactSupport.deriv`, `ContinuousMultilinearMap.norm_def`, `double_dual_bound`, `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`, `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`, `ProperCone.innerDual_iUnion`, `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`, `ContinuousLinearMap.norm_snd`, `ZSpan.repr_floor_apply`, `Submodule.HasOrthogonalProjection.map_linearIsometryEquiv`, `WeakDual.isSeqCompact_polar`, `MeasureTheory.condExpIndSMul_ae_eq_smul`, `HasFTaylorSeriesUpTo.fderiv`, `ContinuousLinearMap.iteratedFDeriv_comp_right`, `CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁`, `Quaternion.linearIsometryEquivTuple_apply`, `norm_fderiv_le_of_lip'`, `EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff`, `DiffContOnCl.differentiableOn`, `ContinuousMultilinearMap.apply_zero_uncurry0`, `PiTensorProduct.injectiveSeminorm_tprod_le`, `IsOpen.affineSpan_eq_top`, `lipschitzWith_lineMap`, `Filter.EventuallyEq.hasLineDerivAt_iff`, `ContDiff.continuousLinearMap_comp`, `ContinuousLinearMap.norm_holderL_le`, `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`, `instNonemptySeedRatReal`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip`, `HasGradientAt.fderiv_apply`, `SchwartzMap.instFourierInvSMul`, `ContinuousAlternatingMap.instContinuousEval`, `ContinuousLinearMap.comp_analyticOnNhd`, `TemperedDistribution.derivCLM_apply_apply`, `OrthonormalBasis.tensorProduct_apply`, `TorusIntegrable.function_integrable`, `LinearIsometryEquiv.integrable_comp_iff`, `deriv_neg`, `range_derivWithin_subset_closure_span_image`, `AffineIsometryEquiv.toContinuousAffineEquiv_injective`, `ContinuousAlternatingMap.norm_compContinuousLinearMap_le`, `ContDiffWithinAt.differentiableWithinAt'`, `MeasureTheory.Supermartingale.smul_nonneg`, `abs_signedDist_le_dist`, `norm_iteratedFDeriv_zero`, `Orientation.norm_kahler`, `dist_midpoint_left`, `NumberField.mixedEmbedding.disjoint_span_commMap_ker`, `Polynomial.hasFDerivWithinAt`, `MeasureTheory.condExpIndSMul_smul'`, `Real.hasStrictFDerivAt_rpow_of_neg`, `LinearMap.hasDerivAt`, `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`, `MeasureTheory.weightedSMul_smul_measure`, `LinearMap.hasDerivAtFilter`, `iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod`, `intervalIntegral.integral_hasFDerivAt`, `ProperCone.innerDual_toSubmodule`, `CurveIntegrable.sub`, `InnerProductSpace.HarmonicAt.comp_CLM`, `differentiableAt_inv`, `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`, `MeasureTheory.hausdorffMeasure_homothety_preimage`, `ContinuousLinearEquiv.comp_contDiffAt_iff`, `ContinuousAlternatingMap.hasFDerivAt`, `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`, `ContinuousLinearMap.analyticAt_bilinear`, `EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq`, `eventually_norm_trivializationAt_lt`, `TensorProduct.congrIsometry_apply`, `integral_withDensity_eq_integral_smul₀`, `ZMod.dft_eq_fourier`, `ContinuousLinearEquiv.comp_right_hasFDerivAt_iff'`, `ConvexOn.exists_affine_le_of_lt`, `ProbabilityTheory.IsGaussian.charFunDual_eq'`, `HasFPowerSeriesAt.hasStrictFDerivAt`, `OrthonormalBasis.det_to_matrix_orthonormalBasis_real`, `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`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp`, `hasDerivAt_exp_of_mem_ball`, `ContinuousLinearMap.bound`, `hasStrictDerivAt_exp_smul_const_of_mem_ball`, `ContinuousLinearMap.isPositive_one`, `ContinuousLinearMap.isPositive_sum`, `DoubleCentralizer.isUniformEmbedding_toProdMulOpposite`, `Real.hasDerivAt_Gamma_nat`, `Orientation.oangle_smul_right_self_of_nonneg`, `CStarAlgebra.instNonnegSpectrumClassComplexUnital`, `ZSpan.fract_eq_fract`, `hasDerivAt_pi`, `nndist_right_midpoint`, `MeasureTheory.ContinuousMap.inner_toLp`, `gradient_eq_deriv`, `differentiableAt_abs`, `Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff`, `LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'`, `ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars`, `ConvexOn.real_sSup_of_nat_affine_eq`, `MeasureTheory.integrable_fun_norm_addHaar`, `hasFDerivAt_inv'`, `LinearMap.toMatrix_adjoint`, `ProbabilityTheory.isPositive_covarianceOperator`, `MeasureTheory.dominatedFinMeasAdditive_weightedSMul`, `Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter`, `hasDerivWithinAt_finCons`, `Affine.Simplex.height_reindex`, `WeakDual.CharacterSpace.exists_apply_eq_zero`, `norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin`, `FormalMultilinearSeries.rightInv_coeff`, `Real.not_continuousAt_deriv_qaryEntropy_one`, `differentiableAt_dslope_of_ne`, `Affine.Simplex.inradius_map`, `Complex.map_isometryOfOrthonormal`, `Meromorphic.smul`, `OpenPartialHomeomorph.unitBallBall_symm_apply`, `quasispectrum.instCompactSpaceNNReal`, `hasDerivAt_zpow`, `TemperedDistribution.fourierTransformInv_apply`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand'`, `Orientation.oangle_neg_orientation_eq_neg`, `FormalMultilinearSeries.summable_norm_apply`, `Orientation.oangle_sign_smul_add_smul_left`, `ContinuousMultilinearMap.norm_constOfIsEmpty`, `uniqueDiffOn_extChartAt_target`, `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`, `measurable_derivWithin_Ici`, `ContinuousLinearMap.isPositive_adjoint_comp_self`, `SchwartzMap.integral_clm_comp_laplacian_right_eq_left`, `ContinuousLinearMap.integral_comp_comm`, `hasFDerivWithinAt_iff_tendsto`, `FormalMultilinearSeries.compAlongOrderedFinpartition_apply`, `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`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn'`, `ClosedSubmodule.orthogonal_closure'`, `differentiableAt_inverse`, `Matrix.l2_opNorm_def`, `fderivWithin_comp_add_right`, `Real.fourierInv_eq'`, `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`, `nnnorm_cfcₙ_le`, `continuous_stereoInvFun`, `MellinConvergent.cpow_smul`, `parallelepiped_orthonormalBasis_one_dim`, `ContinuousLinearMap.iteratedFDeriv_comp_left`, `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`, `Complex.reCLM_enorm`, `MeasureTheory.integral_fun_snd`, `ContinuousMultilinearMap.opNorm_prod`, `MeasureTheory.condExpInd_empty`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt`, `Real.hasDerivAt_sinh`, `MeasureTheory.condExpL1CLM_smul`, `isConformalMap_const_smul`, `real_inner_smul_self_right`, `hasDerivWithinAt_iff_tendsto_slope'`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand`, `dist_smul_add_one_sub_smul_le`, `norm_innerSL_le`, `MeromorphicAt.smul`, `AffineSubspace.subtypeₐᵢ_toAffineMap`, `VectorFourier.hasFDerivAt_fourierChar_smul`, `OrthonormalBasis.measurePreserving_measurableEquiv`, `Orientation.rotation_pi`, `Real.fourierIntegral_real_eq`, `ContinuousLinearMap.isLeast_opNorm`, `InformationTheory.not_differentiableAt_klFun_zero`, `fderiv_const_smul_of_field`, `Real.deriv_cosh`, `PeriodPair.lattice_eq_span_range_basis`, `FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm`, `IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus`, `ContinuousLinearMap.IsPositive.isSelfAdjoint`, `MeasureTheory.measure_unitBall_eq_integral_div_gamma`, `HasLineDerivAt.smul`, `Real.exists_extension_norm_eq`, `OrthonormalBasis.sum_repr'`, `continuousMultilinearCurryRightEquiv_apply`, `antilipschitzWith_lineMap`, `Submodule.coe_orthogonalProjection_apply`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_right`, `Submodule.starProjection_coe_eq_isCompl_projection`, `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`, `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`, `Submodule.ClosedComplemented.of_quotient_finiteDimensional`, `SchwartzMap.integral_smul_deriv_right_eq_neg_left`, `ContinuousLinearMap.apply_apply'`, `HasFPowerSeriesWithinAt.hasFDerivWithinAt`, `LinearIsometryEquiv.norm_iteratedFDeriv_comp_left`, `ProbabilityTheory.covarianceBilinDual_of_not_memLp'`, `LinearMap.posSemidef_toMatrix_iff`, `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`, `SchwartzMap.fourier_convolution`, `tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn`, `ContDiff.differentiable_one`, `HasMFDerivWithinAt.prod`, `AnalyticOnNhd.eval_continuousLinearMap'`, `SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul`, `norm_lineDeriv_le_of_lip'`, `Orientation.rotation_symm_apply`, `AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul`, `AnalyticOnNhd.iterated_deriv`, `ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior`, `MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp`, `VectorFourier.integrable_fourierPowSMulRight`, `Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear`, `Orthonormal.inner_right_fintype`, `HasMFDerivAt.mul'`, `ContinuousLinearMap.flipₗᵢ_symm`, `ImplicitFunctionData.rightDeriv_fderiv_implicitFunction`, `expNegInvGlue.differentiable_polynomial_eval_inv_mul`, `WeakFEPair.f_modif_aux2`, `Asymptotics.isTheta_const_smul_right`, `continuousOn_cfcₙ_nnreal_setProd`, `ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz`, `posTangentConeAt_univ`, `OrthonormalBasis.abs_det_adjustToOrientation`, `mellin_cpow_smul`, `HasGradientWithinAt.hasFDerivWithinAt`, `ContinuousLinearMap.dist_le_opNorm`, `FormalMultilinearSeries.rightInv_coeff_one`, `hasFDerivAt_exp`, `ContinuousAlternatingMap.opNNNorm_prod`, `ContDiffWithinAt.differentiableWithinAt`, `Pi.orthonormalBasis_repr`, `deriv_mul_const_field'`, `EuclideanGeometry.inversion_eq_lineMap`, `Polynomial.hasDerivWithinAt`, `ZSpan.mem_fundamentalDomain`, `IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single`, `differentiableAt_iff_comp_sub_const`, `InnerProductGeometry.IsConformalMap.preserves_angle`, `uniqueDiffWithinAt_extChartAt_target`, `ApproximatesLinearOn.lipschitzOnWith`, `CFC.norm_sqrt`, `LipschitzOnWith.ae_differentiableWithinAt`, `Orthonormal.tmul`, `norm_fderiv_norm_id_rpow`, `NumberField.Units.basisOfIsMaxRank_fundSystem`, `LinearMap.isAdjointPair_inner`, `MeasureTheory.condExpIndL1Fin_smul'`, `LinearMap.IsPositive.adjoint_conj`, `ContinuousLinearMap.norm_holder_apply_apply_le`, `LinearMap.isPositive_one`, `NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily`, `Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset`, `Affine.Simplex.affineSpan_pair_eq_altitude_iff`, `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`, `ContinuousLinearMap.analyticAt_uncurry_of_multilinear`, `AffineIsometry.coe_toContinuousAffineMap`, `WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace`, `dist_sq_lineMap_of_inner_eq_zero`, `hasDerivWithinAt_iff_tendsto_slope`, `hasFDerivAtFilter_pi'`, `measurable_fderiv_apply_const_with_param`, `constFormalMultilinearSeries_apply_succ`, `ImplicitFunctionData.hasStrictFDerivAt_rightFun`, `aestronglyMeasurable_deriv_with_param`, `signedDist_left_lineMap`, `FormalMultilinearSeries.continuousOn`, `hasFDerivAt_inv`, `Affine.Simplex.direction_altitude`, `LinearIsometryEquiv.symm_lTensor`, `Real.deriv_mul_log_zero`, `ContinuousLinearMap.coe_ofIsClosedGraph`, `ProbabilityTheory.Kernel.integral_withDensity`, `ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap`, `NumberField.mixedEmbedding.norm_negAt`, `Orientation.oangle_sign_smul_sub_right`, `DoubleCentralizer.toProdHom_apply`, `ContinuousAlternatingMap.enorm_toContinuousMultilinearMap`, `Submodule.isOrtho_bot_left`, `DoubleCentralizer.mul_snd`, `ContinuousLinearMap.fpowerSeries_apply_one`, `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`, `ContinuousLinearMap.toSpanSingletonCLE_apply_apply`, `derivWithin_inter`, `constFormalMultilinearSeries_zero`, `intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right`, `OpenPartialHomeomorph.unitBallBall_apply`, `Affine.Simplex.circumcenter_eq_centroid`, `Real.fourierIntegralInv_eq`, `MeasureTheory.weightedSMul_zero_measure`, `Asymptotics.IsBigO.isBigOTVS`, `taylor_within_apply`, `Real.hasDerivWithinAt_arccos_Iic`, `ContDiffBump.convolution_tendsto_right_of_continuous`, `Affine.Simplex.excenter_reindex`, `WithCStarModule.prod_inner`, `measurableSet_of_differentiableWithinAt_Ici`, `LinearIsometryEquiv.toContinuousLinearEquiv_smul`, `ContinuousAlternatingMap.compContinuousLinearMapCLM_apply`, `ContinuousMultilinearMap.norm_compContinuousLinearMap_le`, `ContinuousLinearMap.opNNNorm_mul_apply`, `fderivInnerCLM_apply`, `AffineIsometry.image_intrinsicFrontier`, `ContinuousMultilinearMap.curryFinFinset_apply`, `deriv_zero_of_frequently_mem`, `EuclideanGeometry.orthogonalProjection_eq_iff_mem`, `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`, `eq_midpoint_of_dist_eq_half`, `MeasureTheory.integral_smul_measure`, `deriv_sqrt_mul_log'`, `Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl`, `VectorBundleCore.coordChange_comp`, `derivWithin_const_sub`, `SchwartzMap.denseRange_toLpCLM`, `ConformalAt.const_smul`, `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`, `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`, `isConformalMap_iff_is_complex_or_conj_linear`, `AnalyticAt.hasStrictFDerivAt`, `ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp`, `ContinuousLinearMap.apply_apply`, `ContinuousLinearEquiv.comp_differentiableWithinAt_iff`, `intrinsicClosure_eq_closure`, `RCLike.span_one_I`, `Asymptotics.isThetaTVS_iff_isTheta`, `hasFDerivAt_pi'`, `OrthogonalFamily.summable_iff_norm_sq_summable`, `ContinuousLinearMap.norm_map_removeNth_le`, `ContinuousMultilinearMap.hasStrictFDerivAt_uncurry`, `iteratedFDeriv_neg`, `ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply`, `HasGradientAtFilter.hasDerivAtFilter`, `IsSymmSndFDerivWithinAt.eq`, `CurveIntegrable.add`, `PiTensorProduct.mapLMultilinear_opNorm`, `hasDerivWithinAt_inter`, `ContinuousMultilinearMap.norm_image_sub_le'`, `Affine.Triangle.sSameSide_affineSpan_pair_incenter_point`, `hasFPowerSeriesAt_iff'`, `LinearIsometryEquiv.differentiableOn`, `Real.fourier_eq'`, `Real.differentiable_fourier`, `IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀`, `MeasureTheory.charFunDual_eq_prod_iff'`, `hasDerivAt_exp_smul_const_of_mem_ball`, `MeasureTheory.lpMeasToLpTrimLie_symm_toLp`, `LinearIsometryEquiv.conjStarAlgEquiv_apply_apply`, `hasStrictDerivAt_exp_zero`, `deriv_const_smul_field`, `NonUnitalCStarAlgebra.toSMulCommClass`, `Submodule.orthogonalProjection_norm_le`, `DoubleCentralizer.intCast_toProd`, `ContinuousAffineMap.differentiableAt`, `Matrix.PosDef.posDef_sqrt`, `WeakFEPair.Λ_residue_k`, `MeasureTheory.StronglyMeasurable.norm_approxBounded_le`, `Function.HasTemperateGrowth.isBigO_uniform`, `differentiableOn_snd`, `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`, `FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius`, `fderiv_single`, `hom_trivializationAt_target`, `finrank_euclideanSpace_fin`, `mdifferentiable_iff_differentiable`, `Submodule.orthogonalProjection_orthogonal`, `Real.hasStrictDerivAt_exp`, `CFC.norm_nnrpow`, `differentiableWithinAt_const_add_iff`, `Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter`, `le_egauge_closedBall_one`, `hasFDerivAt_list_prod_attach'`, `InformationTheory.deriv_klFun`, `mdifferentiableOn_iff_of_mem_maximalAtlas`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd`, `LinearIsometryEquiv.rTensor_def`, `MeasureTheory.norm_condExpL2_le_one`, `ContinuousLinearEquiv.mdifferentiableAt`, `HasCompactSupport.convolution_integrand_bound_right`, `differentiable_sigmoid`, `LinearMap.mem_span_iff_continuous`, `HasFPowerSeriesWithinOnBall.hasFDerivWithinAt`, `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`, `OrthonormalBasis.repr_reindex`, `MeasureTheory.condExpL2_comp_continuousLinearMap`, `hasLineDerivWithinAt_congr_set`, `LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv`, `ConvexOn.real_sSup_affine_eq`, `RCLike.re_extendTo𝕜'ₗ`, `InnerProductSpace.symm_toEuclideanLin_rankOne`, `isBoundedBilinearMap_smulRight`, `MeasureTheory.charFun_map_smul`, `isOpen_setOf_linearIndependent`, `ZSpan.setFinite_inter`, `LinearIsometryEquiv.differentiableWithinAt`, `convex_closedBall`, `AffineIsometry.id_toAffineMap`, `differentiableOn_const_add_iff`, `AnalyticOnNhd.eval_continuousLinearMap`, `hasStrictFDerivAt_pi`, `Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero`, `Submodule.isOrtho_sup_left`, `ProbabilityTheory.uncenteredCovarianceBilinDual_zero`, `ContinuousLinearMap.adjoint_innerSL_apply`, `ZLattice.coe_comap`, `sameRay_iff_norm_smul_eq`, `Submodule.IsOrtho.comap`, `hasFDerivAt_iff_isLittleO_nhds_zero`, `fderivWithin_comp_sub`, `OrthogonalFamily.inner_right_fintype`, `ProbabilityTheory.integral_tilted_mul_self`, `integrableOn_Ioi_deriv_norm_ofReal_cpow`, `ContDiffMapSupportedIn.structureMapLM_apply`, `CStarAlgebra.span_unitary`, `AffineSubspace.right_mem_perpBisector`, `ContinuousLinearMap.circleAverage_comp_comm`, `EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt`, `derivWithin_const_smul'`, `VectorPrebundle.contMDiffCoordChange_apply`, `isBoundedLinearMap_prod_multilinear`, `nndist_homothety_self`, `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'`, `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`, `MonotoneOn.ae_differentiableWithinAt`, `hasDerivWithinAt_iff_tendsto`, `MeasureTheory.condExpL2_const_inner`, `curveIntegrable_restrictScalars_iff`, `LinearMap.IsSymmetric.intCast`, `WeakFEPair.differentiable_Λ₀`, `MeasureTheory.integral_countable'`, `IsCoercive.isClosed_range`, `RCLike.realLinearIsometryEquiv_apply`, `TemperedDistribution.laplacianCLM_apply`, `isBigO_rpow_zero_log_smul`, `contMDiffWithinAt_hom_bundle`, `mdifferentiableOn_iff_of_subset_source'`, `ProperCone.innerDual_innerDual`, `TensorProduct.ext_iff_inner_right_threefold`, `mem_contMDiffFiberwiseLinear_iff`, `intervalIntegral.integral_deriv_of_contDiffOn_Icc`, `NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne`, `curveIntegralFun_def`, `ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior`, `ContinuousLinearMap.norm_smulRightL_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_apply`, `ContinuousLinearMap.intervalIntegral_comp_comm`, `hasDerivAt_finCons`, `Orientation.areaForm_rightAngleRotation_left`, `ContinuousLinearMap.contMDiffAt`, `CStarAlgebra.exists_sum_four_nonneg`, `isOpen_setOf_nat_le_rank`, `FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin`, `SchwartzMap.smulLeftCLM_smul`, `CurveIntegrable.neg`, `differentiableAt_iff_comp_neg`, `isClosed_setOf_isCompactOperator`, `DoubleCentralizer.coe_snd`, `ContinuousMultilinearMap.fin0_apply_norm`, `LinearIsometry.angle_map`, `hasFPowerSeriesAt_iff`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_one`, `NumberField.mixedEmbedding.disjoint_negAt_plusPart`, `NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal`, `MeasureTheory.integral_convolution`, `ContinuousLinearMap.le_opNorm_enorm`, `HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum`, `Filter.EventuallyEq.nhdsNE_deriv`, `MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le`, `fderiv_norm_sq_apply`, `Submodule.starProjection_eq_self_iff`, `LipschitzWith.ae_differentiableAt_real`, `RCLike.imCLM_apply`, `hasStrictDerivAt_pow`, `RightDerivMeasurableAux.le_of_mem_A`, `OrthonormalBasis.tensorProduct_repr_tmul_apply`, `Derivation.evalAt_apply`, `derivWithin_mem_iff`, `EuclideanGeometry.Sphere.finrank_orthRadius`, `PositiveLinearMap.preGNS_norm_sq`, `ContinuousMultilinearMap.norm_curryMid`, `ConvexOn.univ_sSup_of_nat_affine_eq`, `differentiableOn_inv`, `ContinuousLinearEquiv.comp_right_differentiable_iff`, `aestronglyMeasurable_withDensity_iff`, `ConvexOn.slope_le_leftDeriv_of_mem_interior`, `ContinuousAlternatingMap.ratio_le_opNorm`, `diffContOnCl_univ`, `Affine.Simplex.points_vsub_eulerPoint`, `TensorProduct.assocIsometry_symm_apply`, `hasFDerivAt_exp_of_mem_ball`, `InnerProductGeometry.angle_smul_left_of_pos`, `InnerProductSpace.gramSchmidt_mem_span`, `ModelWithCorners.uniqueDiffOn`, `norm_iteratedFDeriv_fderiv`, `MeasureTheory.Lp.toTemperedDistribution_smul_eq`, `dual_def`, `LinearMap.IsSymmetric.add`, `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`, `fderiv_norm_sq`, `Filter.EventuallyEq.hasDerivAtFilter_iff`, `Seminorm.smul_le_smul`, `instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace`, `LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces`, `differentiableWithinAtProp_self_target`, `MeasureTheory.Measure.toSphere_apply_univ'`, `HasMFDerivAt.const_smul`, `WeakDual.CharacterSpace.instStarHomClass`, `TensorProduct.toLinearMap_mapInclIsometry`, `NonUnitalCommCStarAlgebra.toIsScalarTower`, `AnalyticOnNhd.differentiableOn`, `MeasureTheory.condExp_bot_ae_eq`, `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`, `Orientation.inner_mul_inner_add_areaForm_mul_areaForm'`, `EuclideanGeometry.angle_eq_pi_iff_sbtw`, `MeasureTheory.condExpL1_eq`, `norm_deriv_le_of_lip'`, `orthonormal_span`, `ModularGroup.smul_eq_lcRow0_add`, `ContinuousLinearMap.innerSL_apply_comp`, `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`, `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`, `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`, `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`, `hasFDerivWithinAt_comp_add_left`, `MeasureTheory.condExpL2_indicator_nonneg`, `ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply`, `ContinuousLinearMap.adjoint_adjoint`, `Affine.Triangle.orthocenter_reindex`, `HasCompactSupport.hasFDerivAt_convolution_left`, `differentiableOn_zpow`, `Affine.Simplex.circumradius_map`, `DoubleCentralizer.add_toProd`, `CFC.abs_eq_zero_iff`, `Bundle.ContinuousRiemannianMetric.isVonNBounded`, `Matrix.PosSemidef.sqrt_eq_iff_eq_sq`, `TemperedDistribution.smulLeftCLM_apply_apply`, `Complex.conjCLE_coe`, `NumberField.mixedEmbedding.mem_rat_span_latticeBasis`, `nndist_lineMap_left`, `hasFDerivAt_pi`, `Orientation.inner_mul_areaForm_sub`, `differentiableOn_fst`, `contDiff_one_iff_deriv`, `Circle.norm_smul`, `ProbabilityTheory.covarianceOperator_of_not_memLp`, `AffineIsometryEquiv.pointReflection_midpoint_right`, `hasFDerivWithinAt_snd`, `MeasureTheory.Measure.addHaar_closedBall'`, `uniformConvexOn_zero`, `IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap`, `ContMDiff.coordChangeL`, `deriv2_sqrt_mul_log`, `mellin_comp_mul_left`, `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`, `hasFTaylorSeriesUpToOn_pi`, `ZSpan.fundamentalDomain_ae_parallelepiped`, `MeasureTheory.SignedMeasure.im_toComplexMeasure`, `NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces`, `ContinuousLinearMap.orthogonal_ker`, `NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne`, `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`, `contDiffWithinAt_succ_iff_hasFDerivWithinAt`, `Filter.EventuallyEq.hasDerivWithinAt_iff`, `Filter.EventuallyEq.hasLineDerivWithinAt_iff`, `Asymptotics.IsBigO.hasFDerivAt`, `BoundedContinuousFunction.probCharDual_apply`, `hasFDerivWithinAt_apply`, `Real.deriv2_negMulLog`, `intervalIntegral.inv_smul_integral_comp_add_div`, `InnerProductSpace.norm_rankOne`, `NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces`, `Urysohns.CU.lim_eq_midpoint`, `measurableSet_of_differentiableAt_with_param`, `ContMDiffMap.coeFnLinearMap_apply`, `Submodule.isHilbertSumOrthogonal`, `DoubleCentralizer.neg_fst`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le`, `EuclideanGeometry.Sphere.self_mem_orthRadius`, `PiTensorProduct.mapLMultilinear_toFun_apply`, `CStarMatrix.inner_toCLM_conjTranspose_right`, `Affine.Simplex.insphere_reindex`, `HasFiniteFPowerSeriesOnBall.fderiv`, `ContinuousLinearEquiv.norm_pos`, `real_inner_I_smul_self`, `LinearIsometry.lTensor_def`, `ContinuousAffineMap.toConstProdContinuousLinearMap_snd`, `Orthonormal.inner_right_sum`, `mellin_comp_mul_right`, `NonUnitalStarAlgHom.instContinuousLinearMapClassComplex`, `GaussianFourier.integral_rexp_neg_mul_sq_norm`, `ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff`, `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`, `ContinuousMultilinearMap.uncurryRight_norm`, `ContinuousLinearMap.flipAlternating_apply_apply`, `MeasureTheory.Measure.addHaar_real_closedBall`, `tangentBundleCore_coordChange_achart`, `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`, `ContinuousLinearMap.coeFn_compLp'`, `Unitization.cfcₙ_eq_cfc_inr`, `MeasureTheory.average_eq`, `ContinuousLinearEquiv.mfderivWithin_eq`, `EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self`, `curveIntegralFun_zero`, `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`, `IsSymmSndFDerivAt.eq`, `le_iff_norm_sqrt_mul_sqrt_inv`, `Submodule.orthogonalProjectionFn_mem`, `LinearMap.IsPositive.re_inner_nonneg_left`, `iteratedFDeriv_const_of_ne`, `hasDerivWithinAt_sub_const_iff`, `intervalIntegral.smul_integral_comp_add_mul`, `Complex.restrictScalars_toSpanSingleton'`, `Real.differentiableAt_negMulLog_iff`, `NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal`, `QuadraticMap.hasLineDerivAt`, `fderiv_inv'`, `MeasureTheory.Measure.integral_comp_inv_mul_right`, `ContinuousLinearEquiv.contDiff`, `ContinuousLinearMapWOT.ext_inner_iff`, `Besicovitch.SatelliteConfig.exists_normalized_aux3`, `ContinuousLinearMap.coeFn_ofIsClosedGraph`, `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`, `ProbabilityTheory.integral_tilted_mul_eq_cgf`, `Real.deriv2_mul_log`, `LinearIsometryEquiv.coe_symm_toMeasurableEquiv`, `AffineIsometryEquiv.coe_toAffineEquiv`, `FormalMultilinearSeries.comp_assoc`, `PiTensorProduct.tprodL_coe`, `ModelWithCorners.extChartAt_transContinuousLinearEquiv_target`, `MeasureTheory.Measure.addHaar_smul`, `HasFPowerSeriesWithinAt.comp`, `Submodule.mem_iff_norm_starProjection`, `differentiable_neg_iff`, `Complex.reCLM_apply`, `Real.hasDerivAt_negMulLog`, `AffineIsometryEquiv.coe_toContinuousAffineEquiv`, `Orientation.abs_volumeForm_apply_le`, `Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff`, `continuousMultilinearCurryFin1_apply`, `IsCoercive.antilipschitz`, `PiLp.hasStrictFDerivAt_toLp`, `Complex.conjLIE_symm`, `LeftInvariantDerivation.evalAt_apply`, `hasStrictDerivAt_neg`, `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`, `Trivialization.coordChangeL_prod`, `aemeasurable_derivWithin_Ioi`, `MeasureTheory.Measure.addHaar_image_homothety`, `MeasureTheory.setIntegral_const`, `norm_combo_lt_of_ne`, `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` `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`, `ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear`, `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`, `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	386 math math: `contDiffAt_snd`, `TangentBundle.tangentMap_tangentBundle_pure`, `contMDiff_prod_assoc`, `NumberField.mixedEmbedding.fundamentalDomain_integerLattice`, `instLieGroup`, `Bundle.ContMDiffRiemannianMetric.contMDiff`, `Bundle.mdifferentiableAt_proj`, `contDiff_fst`, `ContinuousAlternatingMap.opNorm_prod`, `Trivialization.mdifferentiableAt_section_iff`, `ContinuousLinearMap.analyticWithinAt_bilinear`, `ContMDiffMul.prod`, `ContinuousLinearMap.opNorm_prod`, `ContinuousLinearMap.norm_inr_le_one`, `ModelWithCorners.range_prod`, `Bundle.contMDiffOn_zeroSection`, `ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap`, `MDifferentiableAt.mfderiv_prod`, `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`, `ContDiffBumpBase.smooth`, `MDifferentiableOn.prodMk_space`, `Manifold.IsImmersionOfComplement.prodMap`, `contMDiff_addInvariantVectorField`, `Trivialization.mdifferentiableOn_section_baseSet_iff`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_zero`, `HasMFDerivWithinAt.prodMk`, `contDiffWithinAt_fst`, `ContMDiffAdd.prod`, `ContMDiffMul.contMDiff_mul`, `Bundle.contMDiffWithinAt_zeroSection`, `mdifferentiableOn_snd`, `contMDiff_mul`, `contMDiff_mulInvariantVectorField`, `contMDiffWithinAt_snd`, `contMDiffWithinAt_prod_iff`, `UniqueMDiffOn.prod`, `IsLocalFrameOn.contMDiffAt_of_coeff`, `contMDiff_equivTangentBundleProd_symm`, `contDiff_prodAssoc`, `mdifferentiableWithinAt_section`, `Trivialization.contMDiffAt_iff`, `MDifferentiableWithinAt.prodMk_space`, `Trivialization.contMDiffOn_symm_trans`, `ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear`, `ContDiffAt.prodMap`, `ContinuousLinearMap.norm_fst_le`, `ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear`, `Trivialization.contMDiff_iff`, `ContMDiffAdd.contMDiff_add`, `Manifold.IsSmoothEmbedding.prodMap`, `ContDiffAt.fst''`, `Trivialization.contMDiffOn_section_iff`, `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`, `HasMFDerivWithinAt.prodMap`, `mdifferentiableAt_addInvariantVectorField`, `ContDiff.prodMk`, `ContMDiff.contMDiff_tangentMap`, `MeasureTheory.charFunDual_prod`, `Module.Basis.prod_addHaar`, `mdifferentiableAt_fst`, `analyticOnNhd_snd`, `MDifferentiableOn.prodMk`, `MDifferentiableAt.prodMap'`, `NumberField.mixedEmbedding.fundamentalDomain_idealLattice`, `AnalyticWithinAt.prod`, `ContMDiffAt.prodMap`, `HasFPowerSeriesWithinOnBall.prod`, `mdifferentiableAt_totalSpace`, `mdifferentiableOn_fst`, `mdifferentiable_mulInvariantVectorField`, `contDiff_prodMk_right`, `contDiffOn_fst`, `mdifferentiableOn_prod_module_iff`, `ContDiff.prodMap`, `ContDiffWithinAt.prodMap`, `MDifferentiableAt.prodMk`, `analyticAt_smul`, `Diffeomorph.prodCongr_symm`, `Trivialization.mdifferentiableAt_totalSpace_iff`, `MeasureTheory.charFunDual_eq_prod_iff`, `ContDiff.fst'`, `mdifferentiableAt_hom_bundle`, `IsLocalFrameOn.mdifferentiableAt_of_coeff_aux`, `mdifferentiable_fst`, `ContDiffPointwiseHolderAt.snd`, `modelWithCorners_prod_coe`, `ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear`, `Bundle.TotalSpace.isManifold`, `IsBoundedBilinearMap.contDiff`, `contMDiff_vectorSpace_iff_contDiff`, `mdifferentiableAt_snd`, `mfderiv_prodMap`, `ContMDiffWithinAt.prodMk_space`, `UniqueMDiffWithinAt.bundle_preimage'`, `AnalyticAt.prod`, `IsContMDiffRiemannianBundle.exists_contMDiff`, `ModelWithCorners.prod_symm_apply`, `contMDiff_snd`, `contMDiffAt_prod_iff`, `MDifferentiableOn.clm_prodMap`, `tangentMap_prodSnd`, `ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear`, `ContMDiffAt.prodMk_space`, `HasMFDerivAt.prodMap`, `IsLocalFrameOn.mdifferentiableOn_of_coeff`, `ModelWithCorners.prod_source`, `ContinuousMultilinearMap.prodL_apply`, `hasMFDerivWithinAt_fst`, `WithLp.contDiff_toLp`, `snd_integral`, `MDifferentiableOn.prodMap`, `ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear`, `IsContDiffImplicitAt.implicitFunction_apply`, `mdifferentiableAt_prod_module_iff`, `swap_integral`, `Trivialization.contMDiffOn_localFrame_baseSet`, `ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear`, `ContDiffPointwiseHolderAt.prodMk`, `ContDiffWithinAt.prodMap'`, `IsBoundedBilinearMap.isBoundedLinearMap_deriv`, `modelWithCorners_prod_coe_symm`, `IsContDiffImplicitAt.implicitFunctionData_pt`, `MDifferentiable.prodMk_space`, `contMDiff_smul`, `Bundle.mdifferentiableWithinAt_proj`, `IsLocalFrameOn.contMDiffOn`, `ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear`, `MDifferentiableWithinAt.prodMk`, `Bundle.contMDiffWithinAt_totalSpace`, `Diffeomorph.coe_prodComm`, `Bundle.mdifferentiableOn_proj`, `ContMDiffOn.prodMk_space`, `SmoothBumpCovering.embeddingPiTangent_injective_mfderiv`, `ContinuousLinearMap.norm_inr`, `ContinuousLinearMap.analyticOnNhd_bilinear`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear`, `equivTangentBundleProd_symm_apply_snd`, `WithLp.contDiff_ofLp`, `iteratedFDerivWithin_prodMk`, `Module.Basis.prod_parallelepiped`, `IsLocalFrameOn.contMDiffAt`, `contMDiffAt_hom_bundle`, `ContMDiffOn.prodMap`, `ContMDiffRing.contMDiff_mul`, `contMDiff_prod_iff`, `FiberBundle.extChartAt`, `NumberField.mixedEmbedding.fundamentalDomain_stdBasis`, `mfderiv_prod_right`, `MDifferentiable.clm_prodMap`, `SmoothBumpCovering.embeddingPiTangent_ker_mfderiv`, `IsContDiffImplicitAt.implicitFunctionData_rightFun_apply`, `analyticAt_fst`, `Bundle.contMDiffWithinAt_proj`, `ModelWithCorners.boundary_of_boundaryless_left`, `modelWithCornersSelf_prod`, `Bundle.contMDiffAt_totalSpace`, `analyticWithinAt_fst`, `MDifferentiableAt.prodMk_space`, `WithLp.analyticOn_toLp`, `ContDiffAt.snd'`, `contDiff_add`, `Trivialization.contMDiffOn_section_baseSet_iff`, `UniqueMDiffOn.tangentBundle_proj_preimage`, `MeasureTheory.average_pair`, `mdifferentiable_snd`, `mdifferentiableAt_prod_iff`, `MDifferentiable.prodMk`, `OpenPartialHomeomorph.extend_prod`, `contMDiffWithinAt_fst`, `ContinuousMultilinearMap.analyticOn_uncurry_of_linear`, `Bundle.contMDiffOn_proj`, `ContinuousMultilinearMap.opNNNorm_prod`, `ContMDiffWithinAt.prodMk`, `Bundle.contMDiff_proj`, `HasFPowerSeriesWithinAt.prod`, `contMDiffOn_fst`, `ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear`, `contDiffAt_inner`, `NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis`, `NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice`, `contMDiffOn_prod_iff`, `ContinuousLinearMap.hasFPowerSeriesAt_bilinear`, `contMDiffAt_section_of_mem_baseSet`, `Manifold.IsImmersionAt.prodMap`, `IsManifold.prod`, `HasFTaylorSeriesUpToOn.prodMk`, `mfderivWithin_prodMap`, `integral_pair`, `SmoothBumpCovering.embeddingPiTangent_injOn`, `UniqueMDiffWithinAt.bundle_preimage`, `contMDiffAt_vectorSpace_iff_contDiffAt`, `Manifold.IsImmersion.prodMap`, `Bundle.mdifferentiableWithinAt_zeroSection`, `mfderiv_snd`, `ContMDiffAt.clm_prodMap`, `mdifferentiable_addInvariantVectorField`, `Trivialization.continuousLinearEquivAt_prod`, `ContDiffAt.prodMap'`, `modelWithCorners_prod_toPartialEquiv`, `fst_integral`, `SmoothBumpCovering.comp_embeddingPiTangent_mfderiv`, `Trivialization.mdifferentiableWithinAt_section_iff`, `ExistsContDiffBumpBase.y_smooth`, `Bundle.contMDiff_zeroSection`, `contDiff_inner`, `FiberBundle.extChartAt_target`, `IsContDiffImplicitAt.contDiffAt`, `contMDiffAt_localFrame_of_mem`, `mdifferentiableWithinAt_snd`, `mfderiv_prodMk`, `hasMFDerivWithinAt_snd`, `contMDiff_prod_module_iff`, `mdifferentiableAt_section`, `ContinuousLinearMap.norm_fst`, `Bundle.mdifferentiable_proj`, `ModelWithCorners.boundary_of_boundaryless_right`, `NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice`, `ModelWithCorners.range_eq_univ_prod`, `ModelWithCorners.prod_apply`, `ContMDiff.clm_prodMap`, `SmoothBumpCovering.embeddingPiTangent_injective`, `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`, `Trivialization.contMDiffWithinAt_iff`, `UniqueMDiffOn.bundle_preimage`, `Bundle.contMDiffAt_section`, `ModelWithCorners.boundary_prod`, `ContinuousLinearMap.fpowerSeriesBilinear_radius`, `contDiff_smul`, `equivTangentBundleProd_eq_tangentMap_prod_tangentMap`, `contDiffOn_snd`, `ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap`, `mdifferentiable_prod_iff`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap`, `mdifferentiableOn_prod_iff`, `mdifferentiableAt_mulInvariantVectorField`, `mfderivWithin_prodMk`, `ImplicitFunctionData.contDiff_implicitFunction`, `contMDiffAt_prod_module_iff`, `Trivialization.mdifferentiableOn_section_iff`, `IsContDiffImplicitAt.implicitFunctionData_rightFun_pt`, `ContinuousAlternatingMap.prodLIE_apply`, `ContMDiffAt.prodMap'`, `iteratedFDeriv_prodMk`, `IsContDiffImplicitAt.implicitFunctionData_leftFun_apply`, `tangentMap_prodFst`, `ContMDiffOn.contMDiffOn_tangentMapWithin`, `ContMDiffWithinAt.prodMap'`, `mdifferentiableWithinAt_fst`, `Trivialization.contMDiffAt_section_iff`, `IsLocalFrameOn.contMDiffOn_of_coeff`, `ModelWithCorners.BoundarylessManifold.prod`, `ContinuousLinearMap.analyticOn_uncurry_of_multilinear`, `contMDiff_add`, `HasFPowerSeriesAt.prod`, `Diffeomorph.prodComm_symm`, `instLieAddGroup`, `HasMFDerivAt.prodMk`, `ContDiff.contDiff_fderiv_apply`, `Trivialization.contMDiffOn_symm`, `FormalMultilinearSeries.radius_prod_eq_min`, `analyticAt_mul`, `NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis`, `ContMDiffAt.prodMk`, `Bundle.contMDiffAt_proj`, `Trivialization.contMDiffOn_iff`, `contMDiffAt_addInvariantVectorField`, `contMDiff_tangentBundleModelSpaceHomeomorph`, `ContMDiffWithinAt.clm_prodMap`, `mdifferentiableWithinAt_prod_module_iff`, `hasMFDerivAt_snd`, `ContDiff.snd'`, `MDifferentiableWithinAt.prodMap`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap`, `Bundle.contMDiffWithinAt_section`, `Bundle.mdifferentiableOn_zeroSection`, `Trivialization.mdifferentiableWithinAt_totalSpace_iff`, `ContMDiffSection.mdifferentiable'`, `ContinuousLinearMap.norm_snd_le`, `contMDiff_tangentBundleModelSpaceHomeomorph_symm`, `IsContDiffImplicitAt.implicitFunction_def`, `mfderiv_fst`, `ContDiffOn.prodMk`, `ContMDiffSection.mdifferentiableAt`, `contDiffWithinAt_snd`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap`, `ContMDiffOn.clm_prodMap`, `Bundle.Prod.contMDiffVectorBundle`, `AnalyticOn.prod`, `UniqueMDiffWithinAt.prod`, `mdifferentiable_prod_module_iff`, `equivTangentBundleProd_symm_apply_proj`, `ContMDiffSection.mdifferentiable`, `ContinuousLinearMap.norm_snd`, `contDiff_snd`, `ContMDiff.prodMk_space`, `ContMDiffWithinAt.prodMap`, `ContDiffWithinAt.prodMk`, `Bundle.mdifferentiable_zeroSection`, `contMDiffAt_fst`, `mdifferentiableWithinAt_prod_iff`, `IsLocalFrameOn.mdifferentiableAt_of_coeff`, `ContinuousLinearMap.analyticAt_bilinear`, `contDiffOn_fderivWithin_apply`, `ContDiffAt.prodMk`, `tangentMap_prod_right`, `contMDiffOn_vectorSpace_iff_contDiffOn`, `ContDiffOn.prodMap`, `contDiffAt_fst`, `ContinuousMultilinearMap.opNorm_prod`, `tangentMap_prod_left`, `SmoothBumpCovering.embeddingPiTangent_coe`, `ContinuousAlternatingMap.prodLIE_symm_apply`, `ContMDiffSection.contMDiff_toFun`, `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`, `MDifferentiableWithinAt.clm_prodMap`, `contMDiffOn_prod_module_iff`, `ContDiffPointwiseHolderAt.fst`, `MDifferentiableWithinAt.prodMap'`, `mdifferentiableWithinAt_hom_bundle`, `IsLocalFrameOn.contMDiffAt_of_coeff_aux`, `Trivialization.contMDiffOn`, `ContDiffAt.snd''`, `contMDiffOn_section_of_mem_baseSet₀`, `Real.contDiffAt_rpow_of_ne`, `contMDiff_fst`, `Bundle.mdifferentiableAt_zeroSection`, `boundary_product`, `contDiff_prodMk_left`, `MDifferentiableAt.prodMap`, `Trivialization.mdifferentiable`, `VectorBundle.prod`, `isBoundedLinearMap_prod_multilinear`, `ContMDiff.prodMap`, `contMDiff_snd_tangentBundle_modelSpace`, `contMDiffWithinAt_hom_bundle`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_one`, `NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis`, `analyticOn_snd`, `contMDiffAt_snd`, `Trivialization.contMDiffWithinAt_section`, `extChartAt_prod`, `IsContDiffImplicitAt.implicitFunctionData_leftFun_pt`, `analyticOn_fst`, `WithLp.analyticOn_ofLp`, `norm_jacobiTheta₂_term_fderiv_le`, `analyticAt_snd`, `Manifold.LiftSourceTargetPropertyAt.prodMap`, `ProbabilityTheory.indepFun_iff_charFunDual_prod`, `contMDiffOn_section_of_mem_baseSet`, `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	1 math math: `ContinuousLinearMap.norm_extendTo𝕜`

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	2 math math: `ContinuousLinearMap.norm_extendTo𝕜`, `ContinuousLinearMap.extendTo𝕜_apply`
`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` `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` `instSemiringNNReal` `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` `instCommSemiringNNReal` `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` `instCommSemiringNNReal` `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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