Defs

📁 Source: Mathlib/Algebra/GroupWithZero/Action/Defs.lean

Statistics

Metric	Count
Definitions intSMulWithZero, natSMulWithZero, toAddMonoidEnd, toAddMonoidHom, toDistribSMul, toMulAction, DistribSMul, compFun, toAddMonoidHom, toSMulZeroClass, distribMulAction, distribSMul, mulActionWithZero, smulWithZero, smulZeroClass, distribMulAction, distribSMul, distribSMulLeft, mulActionWithZero, smulWithZero, smulZeroClassLeft, toMulActionWithZero, toOppositeMulActionWithZero, MulActionWithZero, compHom, toMulAction, toSMulWithZero, toOppositeSMulWithZero, toSMulWithZero, compHom, toSMulZeroClass, SMulZeroClass, compFun, toSMul, toZeroHom, smulZeroClass, instSMulZeroClass	37
Theorems int_smulCommClass, int_smulCommClass', nat_smulCommClass, nat_smulCommClass', ext, ext_iff, smul_add, smul_zero, toAddMonoidEnd_apply, toAddMonoidHom_apply, ext, ext_iff, smul_add, toAddMonoidHom_apply, nontrivial, smul_zero, subsingleton, zero_smul, single_apply_smul, zero_smul, smul_zero, toZeroHom_apply, boole_smul, ite_zero_smul, left_ne_zero_of_smul, right_ne_zero_of_smul, smul_add, smul_div₀', smul_eq_zero_iff_eq, smul_eq_zero_of_left, smul_eq_zero_of_right, smul_inv₀, smul_inv₀', smul_ite_zero, smul_ne_zero_iff_ne, smul_neg, smul_sub, smul_zero, zero_smul	39
Total	76

AddGroup

Definitions

Name	Category	Theorems
intSMulWithZero 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
int_smulCommClass 📖	mathematical	—	SMulCommClass SubNegMonoid.toZSMul toSubNegMonoid SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid DistribSMul.toSMulZeroClass	—	AddMonoidHom.map_zsmul
int_smulCommClass' 📖	mathematical	—	SMulCommClass SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid toSubNegMonoid DistribSMul.toSMulZeroClass SubNegMonoid.toZSMul	—	SMulCommClass.symm int_smulCommClass

AddMonoid

Definitions

Name	Category	Theorems
natSMulWithZero 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
nat_smulCommClass 📖	mathematical	—	SMulCommClass toNSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero toAddZeroClass DistribSMul.toSMulZeroClass	—	AddMonoidHom.map_nsmul
nat_smulCommClass' 📖	mathematical	—	SMulCommClass SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero toAddZeroClass DistribSMul.toSMulZeroClass toNSMul	—	SMulCommClass.symm nat_smulCommClass

DistribMulAction

Definitions

Name	Category	Theorems
toAddMonoidEnd 📖	CompOp	4 math math: toAddMonoidEnd_apply, AddMonoid.End.natCast_def, AddMonoid.End.intCast_def, AddSubgroup.pointwise_smul_def
toAddMonoidHom 📖	CompOp	1 math math: toAddMonoidHom_apply
toDistribSMul 📖	CompOp	6779 math, 1 bridge math: AnalyticWithinAt.const_smul, MultilinearMap.map_piecewise_smul, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, Matrix.l2_opNorm_toEuclideanCLM, AffineIndependent.smul, LinearMap.det_toContinuousLinearMap, HasDerivAt.fun_neg, LieSubmodule.coe_smul, SubMulAction.zero_mem, units_inv_smul, TestFunction.lineDerivCLM_apply_of_le, absorbent_iff_eventually_nhdsNE_zero, MeasureTheory.Measure.integral_comp_inv_smul, SkewMonoidAlgebra.mapDomain_smul, CategoryTheory.ShortComplex.opcyclesMap_smul, StarConvex.preimage_add_right, iteratedDeriv_scomp_two, HasDerivAt.isLittleO, LinearMap.IsSymmetric.clm_adjoint_eq, Finset.expect_ite_mem, ContinuousLinearMap.rayleigh_smul, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, ContinuousMap.toLp_inj, Real.hasDerivAt_fourier, InnerProductSpace.Core.inner_smul_right, AffineSpace.asymptoticNhds_smul, Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe, ContinuousMultilinearMap.map_piecewise_smul, LinearIsometryEquiv.strictConvex_preimage, TemperedDistribution.lineDerivOpCLM_eq, IsIntegralCurve.comp_mul, vsub_midpoint, LinearMap.restrictScalars_toMatrix, Orientation.oangle_sign_smul_add_right, DiffContOnCl.smul, MeasureTheory.Lp.toTemperedDistributionCLM_apply, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, HasStrictDerivAt.fun_pow', ConvexCone.convex, Convex.translate_preimage_right, MeasureTheory.setIntegral_tilted, RootPairing.rootForm_self_smul_coroot, CochainComplex.HomComplex.δ_units_smul, FormalMultilinearSeries.comp_rightInv_aux1, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, Seminorm.isBounded_const, PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective, LinearMap.mkContinuous₂_norm_le', AffineMap.lineMap_apply_module, LinearMap.SeparatingRight.toMatrix₂', HasDerivWithinAt.clog_real, ContinuousMultilinearMap.norm_mkPiRing, taylor_integral_remainder, CFC.posPart_smul_of_nonpos, Finsupp.linearCombination_apply_of_mem_supported, ContinuousLinearMap.derivWithin_of_bilinear, Submodule.mem_colon_span_singleton, ConvexOn.smul'', EuclideanGeometry.dist_smul_vadd_sq, StrictConcaveOn.sub, Bundle.ContMDiffRiemannianMetric.isVonNBounded, HasDerivWithinAt.clm_comp, SchwartzMap.lineDerivOpCLM_eq, PointedCone.toConvexCone_closure_pointed, NonUnitalAlgHom.map_smul, real_inner_div_norm_mul_norm_eq_neg_one_iff, HasDerivWithinAt.congr_of_mem, LinearEquiv.congrRight₂_refl, Convex.neg, iSupIndep.dfinsupp_lsum_injective, ConvexOn.mul_concaveOn', hasDerivWithinAt_Iio_iff_Iic, LinearMap.BilinForm.isOrtho_smul_right, HasStrictFDerivAt.fun_mul', Derivation.apply_eval_eq, LinearMap.mkContinuous₂_apply, LieDerivation.coe_smul, Module.End.exp_mul_of_derivation, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, Bundle.ContMDiffRiemannianMetric.contMDiff, InnerProductSpace.isPositive_rankOne_self, AffineMap.lineMap_vsub_left, DFinsupp.lsum_lsingle, MonoidAlgebra.liftMagma_apply_apply, MeasureTheory.condExpL1_smul, Seminorm.absorbent_closedBall_zero, LinearMap.ortho_smul_right, ModuleCat.FilteredColimits.colimit_smul_mk_eq, ordinaryHypergeometric_sum_eq, AlgEquiv.moduleEndSelfOp_apply_apply, Matrix.SeparatingLeft.toBilin', MeasureTheory.Lp.instIsScalarTower, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, QuadraticMap.smul_toBilin, CategoryTheory.ShortComplex.homologyMap_smul, Module.Basis.mem_submodule_iff, HasFDerivWithinAt.continuousMultilinearMap_apply, Polynomial.smeval_monomial_mul, RootPairing.pairing_smul_root_eq_of_not_linearIndependent, MDifferentiableOn.clm_postcomp, OrthonormalBasis.orthogonalProjection_eq_sum, hasDerivWithinAt_ofNat, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', Seminorm.bound_of_shell, Matrix.frobeniusIsBoundedSMul, HasCompactSupport.convolution_integrand_bound_left, LinearMap.BilinForm.toMatrix_toBilin, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, MeasureTheory.Martingale.smul, LinearMap.IsSymmetric.inner_map_polarization, HasDerivAt.const_sub, hasDerivWithinAt_add_const_iff, LinearOrder.strictConcaveOn_of_lt, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, SameRay.nonneg_smul_left, Convex.intrinsicClosure, MeasureTheory.integral_convexOn_of_integrand_ae, mellin_eq_fourier, Real.sSup_smul_of_nonpos, SchwartzMap.instLineDerivLeftSMulReal, NonUnitalStarSubalgebra.instSMulMemClass, Module.mem_annihilator, Matrix.SeparatingRight.toLinearMap₂, AnalyticOnNhd.smul, HasDerivAtFilter.sum, Ideal.Cotangent.lift_comp_toCotangent, PolyEquivTensor.toFunBilinear_apply_eq_sum, Rep.MonoidalClosed.linearHomEquiv_symm_hom, binomialSeries_eq_ordinaryHypergeometricSeries, Polynomial.lcoeff_comp_mapAlgHom_eq, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, StarAddMonoid.toStarModuleNNRat, StarAlgEquiv.ofLeftInverse'_apply, Ideal.tensorCotangentEquiv_tmul, SchwartzMap.integral_sesq_fourier_fourier, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, OreLocalization.oreDiv_add_char, Asymptotics.IsBigOTVS.congr', Submodule.isScalarTower, PowerSeries.IsRestricted.smul, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Filter.IsBoundedUnder.smul_tendsto_zero, MeasureTheory.charFun_eq_fourierIntegral', Submodule.smul_def, DiffContOnCl.circleAverage_poissonKernel_smul', Real.hasFDerivAt_fourierChar_neg_bilinear_left, HasDerivWithinAt.Iio_of_Iic, RootPairing.Polarization_apply, PolynomialModule.comp_single, hasStrictDerivAt_intCast, Balanced.smul_mem_iff, segment_subset_closedBall_right, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, NonUnitalAlgHom.mk_coe, isSMulRegular_iff_mem_nonZeroSMulDivisors, MeasureTheory.convolution_eq_right', TrivSqZeroExt.snd_pow, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, smul_eq_zero_iff_eq, MeasureTheory.eLpNormEssSup_const_smul, BilinForm.toMatrix_symm, gauge_def', Submodule.set_smul_le_iff, AffineMap.coe_smul, Asymptotics.isBigO_const_smul_right, MeasureTheory.hausdorffMeasure_segment, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, CategoryTheory.Linear.instMonoHSMulHomOfInvertible, IsSMulRegular.skewMonoidAlgebra, SimpleGraph.lapMatrix_toLinearMap₂', curveIntegral_smul, Quaternion.snd_imJ_dualNumberEquiv_symm, IntervalIntegrable.smul_continuousOn, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1, Orientation.inner_rotation_pi_div_two_right_smul, MultilinearMap.map_update_smul, Orientation.oangle_add_left_smul_rotation_pi_div_two, RootPairing.coroot_eq_polarizationEquiv_apply_root, derivWithin_smul, Real.fderiv_fourierIntegral, hasStrictFDerivAt_list_prod_finRange', MeasureTheory.integral_smul_nnreal_measure, ContinuousMultilinearMap.map_smul_univ, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, MvPolynomial.rTensor_apply_tmul_apply, InnerProductSpace.rankOne_one_left_eq_innerSL, LinearIndependent.pair_add_smul_right_iff, Seminorm.le_finset_sup_apply, Asymptotics.IsThetaTVS.trans_isBigOTVS, FormalMultilinearSeries.smul_apply, Complex.circleTransformDeriv_eq, LinearMap.IsSymmetric.restrictScalars, Seminorm.norm_sub_map_le_sub, bddBelow_smul_iff_of_neg, StrongDual.norm_extendRCLike, IsBaseChange.comp_iff, addMonoidHomLequivNat_symm_apply, HasFiniteFPowerSeriesAt.neg, Submodule.mem_ideal_smul_span_iff_exists_sum, Matrix.separatingRight_toLinearMap₂'_iff, LinearMap.baseChange_smul, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, Balanced.smul_congr, MvPolynomial.rTensorAlgEquiv_apply, Algebra.Generators.H1Cotangent.δAux_mul, Pi.image_update_openSegment, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, ContinuousLinearMap.map_add_add, Set.smul_set_neg, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, SeminormFamily.basisSets_smul_right, MeasureTheory.Measure.integral_comp_mul_right, Convex.convex_isRCLikeNormedField, intervalIntegral.inv_smul_integral_comp_div_add, Antivary.smul_add_smul_le_smul_add_smul, MeromorphicOn.divisor_fun_smul, TrivSqZeroExt.lift_inlAlgHom_inrHom, Bornology.IsVonNBounded.of_sub_left, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, HasDerivWithinAt.div_const, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, StarAlgEquiv.ofStarAlgHom_symm_apply, Real.hasDerivAt_sigmoid, MeasureTheory.IntegrableOn.continuousOn_smul, taylorWithinEval_hasDerivAt_Ioo, AlternatingMap.map_vecCons_smul, ContDiffMapSupportedIn.seminorm_monoLM_eq, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, fderivWithin_fun_smul, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Module.End.smul_def, Finset.weightedVSubOfPoint_apply, HasDerivWithinAt.congr_mono, complexOfReal_hasDerivWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, MvPolynomial.scalarRTensor_apply_monomial_tmul, Real.fourierIntegralInv_eq', AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, LinearIndependent.pair_add_smul_left_iff, QuadraticMap.canLift, StrictConvex.is_linear_image, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, RingTheory.Sequence.isWeaklyRegular_cons_iff', SkewMonoidAlgebra.coeff_single_one_mul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, MeasureTheory.VectorMeasure.coe_smul, Finset.sum_smul, Quaternion.star_smul, hasDerivAt_integral_of_dominated_loc_of_lip, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, finsuppTensorFinsupp_apply, Convex.smul_preimage, AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff, curveIntegrable_segment, Submodule.toConvexCone_inf, ContDiffOn.smul_const, MvPolynomial.universalFactorizationMap_comp_map, Module.Basis.equivFun_symm_apply, MDifferentiableAt.cle_arrowCongr, Absorbs.eventually_nhds_zero, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul', PolynomialModule.smul_def, Seminorm.bot_eq_zero, Submodule.set_smul_span, Complex.integral_boundary_rect_eq_zero_of_differentiableOn, ContinuousLinearMap.continuousSMul, Ideal.relNorm_smul, hasFTaylorSeriesUpToOn_top_iff_right, Module.End.isNilpotent_restrict_genEigenspace_nat, Seminorm.smul_comp, CochainComplex.HomComplex.Cocycle.coe_smul, ConvexCone.mem_positive, LinearIsometry.map_smul, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, MeasureTheory.Lp.const_smul_mem_Lp, RootPairing.reflectionPerm_eq_iff_smul_root, IsBaseChange.finsuppPow, strictConvex_Iic, Matrix.separatingRight_toLinearMap₂_iff, AddSubgroupClass.coe_zmod_smul, absorbs_zero_iff, ConvexOn.smul, Module.End.HasUnifEigenvector.pow_apply, AffineSubspace.setOf_sSameSide_eq_image2, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, intervalIntegral.integral_hasDerivWithinAt_right, TrivSqZeroExt.snd_pow_eq_sum, Bornology.isVonNBounded_add_of_nonempty, norm_add_eq_iff_real, Monotone.quasiconcaveOn, Complex.integral_comp_pi_polarCoord_symm, FormalMultilinearSeries.radius_pi_eq_iInf, ProperCone.convex, contDiffAt_norm_smul_iff, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, addMonoidHomLequivInt_apply, SchwartzMap.pairing_apply_apply, MeasureTheory.integral_domSMul, InnerProductSpace.isIdempotentElem_rankOne_self, norm_iteratedFDerivWithin_smul_le, Submodule.tensorEquivSpan_apply_tmul, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, IsLprojection.Lnorm, AddCommGroup.intIsScalarTower, Polynomial.smul_mem_rootSet, MeasureTheory.weightedSMul_apply, NonUnitalSubalgebra.instIsScalarTower', LineDifferentiableWithinAt.smul, egauge_prod_mk, Differentiable.clm_comp, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport, LinearEquiv.congrRight_symm, LinearMap.BilinForm.toMatrixAux_eq, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, IsScalarTower.to_smulCommClass', ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, HasStrictDerivAt.pow, IsExposed.isExtreme, ContinuousLinearMap.isUniformEmbedding_restrictScalars, RingTheory.Sequence.isWeaklyRegular_cons_iff, ConvexCone.canLift, hasDerivWithinAt_taylorWithinEval, Matrix.toLinearMap₂'_comp, map_ratCast_smul, FormalMultilinearSeries.changeOriginSeriesTerm_apply, AffineSubspace.smul_mem_smul_iff₀, Asymptotics.isLittleOTVS_one, SkewMonoidAlgebra.support_single_mul, Seminorm.finset_sup_apply, HasDerivAt.hasDerivWithinAt, ContinuousLinearMap.hasDerivAtFilter, span_fourier_closure_eq_top, Real.fourierIntegral_eq, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, HasDerivWithinAt.fun_div, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, LinearMap.llcomp_apply, CategoryTheory.ShortComplex.Homotopy.smul_h₁, LinearMap.toMatrix₂_mul, StarConvex.affine_preimage, HasFPowerSeriesOnBall.add, LinearMap.BilinForm.smul_left_of_tower, HasDerivWithinAt.complexToReal_fderiv', circleIntegral_def_Icc, NumberField.RingOfIntegers.instSMulDistribClass, convexJoin_singletons, MeasureTheory.integral_unique, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, setIntegral_withDensity_eq_setIntegral_smul₀, Complex.hasSum_taylorSeries_of_entire, ContinuousMap.toLp_denseRange, IsCovariantDerivativeOn.difference_apply, ProbabilityTheory.hasSum_integral_poissonMeasure, Submodule.pow_pOrder_smul, Bornology.isVonNBounded_add_self, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, intervalIntegral.intervalIntegral_eq_integral_uIoc, Seminorm.ball_smul_closedBall, ContinuousLinearMap.integral_apply, CochainComplex.HomComplex.Cochain.leftShift_smul, FixedPoints.mem_addSubgroup, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, segment_inter_subset_endpoint_of_linearIndependent_sub, HasDerivAt.fun_finset_prod, LocalizedModule.restrictScalars_map_eq, circleIntegrable_iff, PolynomialModule.map_smul, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, convex_iff_sum_mem, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, ConcaveOn.mul_convexOn', NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded, ContMDiffCovariantDerivativeOn.affine_combination, WithSeminorms.mem_nhds_iff, Convex.vadd, LinearMap.IsSymmetric.diagonalization_apply_self_apply, TensorProduct.sum_tmul_basis_right_injective, LinearMap.extendScalarsOfIsLocalization_apply, Submodule.mem_colon', Memℓp.const_smul, StrictConvex.diff_interior_subset_extremePoints, Real.fourier_continuousLinearMap_apply, DirectSum.of_smul, Unitization.real_cfcₙ_eq_cfc_inr, real_inner_smul_self_left, neg_smul, fderivWithin_fun_pow', intervalIntegral.fderiv_integral_of_tendsto_ae, ZMod.invDFT_apply, SMulPosReflectLE_iff_smulPosReflectLT, Convex.combo_interior_closure_mem_interior, Representation.asAlgebraHom_single, NormedSpace.isBounded_iff_subset_smul_ball, HasFDerivWithinAt.clm_apply, Balanced.sub, hasFPowerSeriesOnBall_pi_iff, SmoothPartitionOfUnity.contMDiffAt_finsum, imaginaryPart_I_smul, Continuous.convolution_integrand_fst, ContinuousAlternatingMap.vecCons_smul, MDifferentiableOn.smul_const_section, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, Module.Ray.neg_units_smul, MvPolynomial.leibniz_iff_X, DilationEquiv.smulTorsor_symm_apply, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, Convex.convex_remove_iff_notMem_convexHull_remove, Representation.freeLift_single_single, ConvexOn.lt_left_of_right_lt', HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, LinearMap.BilinForm.congr_apply, diam_smul₀, Seminorm.uniformContinuous_of_forall, TensorAlgebra.toTrivSqZeroExt_ι, abs_smul, Polynomial.homogenize_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul, LieModule.traceForm_eq_sum_finrank_nsmul', DomMulAct.smul_linearMap_apply, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, AddSubgroup.smul_mem_pointwise_smul_iff, LinearMap.BilinForm.toMatrix_compRight, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, segment_translate_preimage, convexHull_eq_iInter, SeminormFamily.filter_eq_iInf, LinearMap.rTensor_smul_action, toMul_uzpow, aemeasurable_smul_const, DifferentiableWithinAt.fun_const_smul, SchwartzMap.integral_bilin_fourierInv_eq, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, HasFTaylorSeriesUpTo.hasFDerivAt, TensorProduct.AlgebraTensorModule.rid_tmul, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Ideal.smul_closure, MeasureTheory.Measure.toSphere_apply_aux, Bornology.IsVonNBounded.of_neg, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, PolynomialModule.comp_smul, Unitization.splitMul_apply, tendsto_integral_peak_smul_of_integrable_of_tendsto, ContMDiffOn.clm_postcomp, inner_eq_norm_mul_iff, Seminorm.restrictScalars_closedBall, smulPosMono_iff_smulPosStrictMono, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, Matrix.Semiring.smulCommClass, tendsto_smul_comp_nat_floor_of_tendsto_mul, LinearMap.adjoint_eq_toCLM_adjoint, Asymptotics.IsLittleOTVS.tendsto_div, DirectSum.instIsCentralScalar, Seminorm.bddAbove_range_iff, AntivaryOn.sub_smul_sub_nonpos, Module.Basis.basis_singleton_iff, convex_iff_pairwise_pos, NormedSpace.image_isVonNBounded_iff, VectorField.mpullbackWithin_smul, ContinuousMap.range_toLp, eqOn_dslope_sub_smul, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div, convex_Iic, Seminorm.closedBall_iSup, Differentiable.fun_smul, Subbimodule.smul_mem', TemperedDistribution.fourierMultiplierCLM_smul, hasDerivAt_bernoulliFun, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, derivWithin_fderivWithin, Matrix.toLinearMap₂_toMatrix₂, WithLp.isBoundedSMulSeminormedAddCommGroupToProd, Submodule.smul_mem_span_smul, intervalIntegral.integral_deriv_smul_comp', IsSelfAdjoint.smul_mem_skewAdjoint, DualNumber.range_lift, StarConvex.add_smul_mem, QuotSMulTop.equivTensorQuot_naturality, MeasureTheory.condExpIndL1Fin_smul, StrictConvexOn.neg, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, MultilinearMap.mkContinuousMultilinear_apply, AddSubgroup.mem_inv_pointwise_smul_iff, PosSMulReflectLE_iff_posSMulReflectLT, CliffordAlgebraDualNumber.equiv_symm_eps, Monovary.sum_smul_comp_perm_le_sum_smul, InnerProductGeometry.angle_smul_right_of_pos, tsum_const_smul', StrongDual.norm_extendRCLike_bound, TemperedDistribution.lineDerivOp_fourier_eq, Units.smul_coe, Matrix.mul_smul, WeakFEPair.symm_Λ₀_eq, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, SpecialLinearGroup.mem_center_iff_spec, Seminorm.smul_inf, Matrix.separatingRight_toBilin_iff, Ideal.mem_pointwise_smul_iff_inv_smul_mem, Submodule.Quotient.instIsBoundedSMul, intervalIntegral.integral_comp_sub_div, Subsemiring.mem_smul_pointwise_iff_exists, HasDerivAt.comp_ofReal, tangentConeAt_nonempty_of_properSpace, AdicCompletion.instIsScalarTower_1, convexJoin_singleton_left, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, intervalIntegral.integral_comp_mul_left, AnalyticAt.fun_const_smul, Submodule.ideal_span_singleton_smul, Continuous.integral_hasStrictDerivAt, LinearMap.ofIsCompl_smul, AffineBasis.coe_smul, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, deriv_const_smul, fderiv_clm_comp, StrictConcaveOn.sub_convexOn, Submodule.top_eq_ofList_cons_smul_iff, BoxIntegral.unitPartition.mem_smul_span_iff, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, TensorProduct.smul_tmul, intervalIntegral.integral_comp_mul_sub, mdifferentiableWithinAt_smul_const_section, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, RingAut.smul_def, AlternatingMap.smulRight_apply, Ideal.exists_smul_eq_of_isGaloisGroup, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, IsConformalMap.is_complex_or_conj_linear, Bornology.isVonNBounded_pi_iff, fderiv_continuousAlternatingMap_apply_const, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', Fintype.expect_dite_eq, Module.Basis.isScalarTower_of_nonempty, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, LinearMap.BilinForm.toMatrix'_symm, Prod.image_mk_openSegment_left, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, TrivSqZeroExt.inv_inl, HasDerivAt.clm_apply, SemilinearMapClass.toMulActionSemiHomClass, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_symm_apply_mk_tmul, ContDiffMapSupportedIn.seminorm_fderivLM_le, toMatrix_distrib_mul_action_toLinearMap, LinearMap.IsRefl.ker_flip_eq_bot, RKHS.coe_smul, Bundle.RiemannianMetric.isVonNBounded, vadd_right_mem_affineSpan_pair, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContDiffMapSupportedIn.seminorm_fderivLM_top, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Convex.affine_image, NormedSpace.toIsBoundedSMul, UniformConvergenceCLM.smul_apply, LinearMap.smul_comp, Fintype.mem_span_image_iff_exists_fun, HasFPowerSeriesAt.neg, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux, Seminorm.continuous_of_forall', AlgEquiv.apply_smulCommClass', curveIntegralFun_smul, addInvariantVectorField_smul, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt, RootPairing.span_orbit_eq_top, VertexOperator.of_coeff_apply_coeff, neg_strictConvexOn_iff, Module.Basis.smul_eq_zero, smul_lt_smul_of_neg_left, MeasureTheory.Measure.domSMul_apply, groupHomology.single_isCycle₂_iff_inv, egauge_ball_le_of_one_lt_norm, Ideal.subset_pointwise_smul_iff, CategoryTheory.Quotient.Linear.smul_eq, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, ContinuousAffineMap.smul_apply, MvPolynomial.algHom_ext'_iff, Polynomial.natDegree_smul, MonovaryOn.sum_smul_comp_perm_le_sum_smul, hasDerivWithinAt_iff_isLittleO, TensorPower.gMul_eq_coe_linearMap, GeneralSchauderBasis.proj_apply, hasStrictFDerivAt_iff_isLittleOTVS, CStarMatrix.mapₗ_reindexₐ, ContinuousAlternatingMap.smul_apply, derivWithin_fun_const_smul_field, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, LinearMap.BilinForm.IsRefl.groupSMul, StarAlgEquiv.ofStarAlgHom_apply, LinearMap.BilinForm.toMatrix'_apply, Submodule.mem_smul_span_singleton, Finsupp.sum_smul_index_linearMap', MeasureTheory.IntegrableOn.smul_continuousOn, ContinuousAlternatingMap.piLIE_apply_apply, AffineSubspace.wOppSide_smul_vsub_vadd_left, ContinuousLinearMap.applySMulCommClass', PreInnerProductSpace.Core.smul_left, inv_intCast_smul_eq, extremePoints_prod, Subsemiring.smul_mem_pointwise_smul_iff, combo_mem_ball_of_ne, lintegral_fderiv_lineMap_eq_edist, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, LinearMap.BilinForm.SeparatingRight.toMatrix, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, balancedCoreAux_maximal, hasDerivWithinAt_zero, HasStrictDerivAt.pow', TestFunction.monoCLM_eq_zero, CategoryTheory.Abelian.Ext.smul_hom, coe_convexAddSubmonoid, TopologicalGroup.IsSES.integral_inducedMeasure, LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero', hasDerivAt_star_conj_iff, AbsolutelyContinuousOnInterval.const_smul, ContDiffAt.hasStrictDerivAt, Seminorm.neg_ball, TrivSqZeroExt.inv_one, RatFunc.mk_smul, LinearEquiv.congrRight₂_apply, FormalMultilinearSeries.hasSum_of_finite, CStarMatrix.mul_smul, LieAlgebra.of_smul, SpecialLinearGroup.mem_center_iff, StrictConcaveOn.translate_right, hasDerivAtFilter_ofNat, SkewMonoidAlgebra.support_mul_single, Asymptotics.IsBigO.smul, AdicCompletion.val_smul_eq_evalₐ_smul, instStarModuleNNRealOfReal, VectorField.mlieBracket_smul_left, Matrix.Nondegenerate.toLinearMap₂, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, Seminorm.continuous', FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, Complex.hasSum_taylorSeries_on_ball, Submodule.mem_span_image_iff_exists_fun, QuadraticMap.map_smul_of_tower, Asymptotics.IsBigOTVS.add, MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff, HasFPowerSeriesOnBall.restrictScalars, smul_nonneg_iff_neg_imp_nonpos, StrictConcaveOn.inf, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, ContinuousLinearMap.isometry_mul_flip, Quaternion.snd_re_dualNumberEquiv_symm, ZSpan.smul, HasStrictFDerivAt.mul', Module.AEval.of_symm_smul, Mathlib.Tactic.Module.NF.eval_neg, Module.Ray.units_smul_of_neg, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, AlgebraicGeometry.StructureSheaf.const_add, LocalizedModule.mk_add_mk, conformal_const_smul, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, HasStrictFDerivAt.comp_hasStrictDerivAt, ContinuousLinearMap.adjoint_id, ClosedSubmodule.inf_orthogonal, LinearMap.coe_toContinuousLinearMap', ContDiffWithinAt.fun_smul, balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, ConvexCone.coe_zero, CharacterModule.smul_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Module.Free.instFaithfulSMulOfNontrivial, contDiffOn_iff_continuousOn_differentiableOn, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, convexJoin_segments, ClosedSubmodule.instSMulMemClass, Submodule.comap_le_comap_smul, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, CStarModule.innerSL_apply, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt, QuadraticMap.toBilinHom_apply, MeromorphicOn.fun_smul, monomial_has_deriv_aux, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, LieRinehartAlgebra.LieRinehartRing.leibniz_smul_right, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.smul_convolution, Bundle.ContinuousLinearMap.vectorBundle, Real.vector_fourierIntegral_eq_integral_exp_smul, VectorField.mlieBracketWithin_const_smul_right, HasDerivWithinAt.sub, PadicInt.mahlerTerm_apply, LinearMap.toMatrixOrthonormal_reindex, AlternatingMap.map_update_smul, WithLp.smul_snd, MeasureTheory.ConvolutionExistsAt.integrable, Fintype.linearIndependent_iff', Complex.taylorSeries_eq_of_entire, egauge_add_add_le, HVertexOperator.coeff_isPWOsupport, exists_pos_right_iff_sameRay, QuadraticMap.associated_eq_self_apply, Real.fourier_real_eq_integral_exp_smul, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, Monotone.quasilinearOn, Asymptotics.IsBigOWith.const_smul_self, Asymptotics.isLittleOTVS_prodMk_left, ExteriorAlgebra.toTrivSqZeroExt_comp_map, AntivaryOn.sum_comp_perm_smul_eq_sum_smul_iff, inner_smul_left_eq_star_smul, ProbabilityTheory.covarianceOperator_apply, BoundedContinuousFunction.toContinuousMapLinearMap_apply, nndist_smul₀, InnerProductGeometry.angle_smul_left_of_neg, Module.exists_smul_eq_zero_and_mk_eq, Asymptotics.IsBigOTVS.comp_tendsto, MeasureTheory.integral_tilted, Submodule.span_smul_eq_of_isUnit, WithSeminorms.continuousSMul, IsSl2Triple.lie_lie_smul_f, LinearMap.ortho_smul_left, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, ContinuousMultilinearMap.mkPiRing_apply, Ideal.LiesOver.smul, hasDerivAt_of_hasDerivAt_of_ne, LinearMap.lTensor_smul, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, AddMonoidHom.coe_smul', MeasureTheory.average_mem_openSegment_compl_self, TestFunction.continuous_iff_continuous_comp, HasFiniteFPowerSeriesOnBall.sum, MeasureTheory.L1.integral_smul, Distribution.IsVanishingOn.smulLeftCLM, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, inv_natCast_smul_eq, DifferentiableOn.smul_const, Quaternion.imJ_fst_dualNumberEquiv, InnerProductSpace.inner_left_rankOne_apply, cfcₙHom_nnreal_eq_restrict, star_dotProduct_toMatrix₂_mulVec, TestFunction.toBoundedContinuousFunctionCLM_apply, Conformal.const_smul, MeasureTheory.Lp.instFourierInvSMul, CochainComplex.HomComplex.Cocycle.coe_units_smul, Bornology.isVonNBounded_neg, AlternatingMap.smul_apply, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, ContinuousLinearMap.smul_compLp, difference_quotients_converge_uniformly, TrivSqZeroExt.snd_list_prod, hasDerivWithinAt_abs_pos, HasDerivWithinAt.sub_const, ContinuousLinearMap.norm_extendTo𝕜, LocalizedModule.lift'_smul, HasSum.hasSum_at_zero, Seminorm.continuousAt_zero_of_forall', HasFPowerSeriesAt.add, lineDifferentiableAt_smul_iff, TrivSqZeroExt.fstHom_comp_map, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, Matrix.conjTranspose_natCast_smul, LinearMap.sum_repr_mul_repr_mulₛₗ, ContinuousLinearMap.hasBasis_nhds_zero, Bornology.IsVonNBounded.of_add_right, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, Module.End.apply_smulCommClass', HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, CochainComplex.HomComplex.Cochain.units_smul_comp, AddCircle.integral_haarAddCircle, InnerProductSpace.HarmonicAt.const_smul, Matrix.Represents.smul, Seminorm.ball_mem_nhds, eventually_nhds_norm_smul_sub_lt, CentroidHom.smul_def, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, Module.IsTorsionFree.isSMulRegular, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, ContMDiffAt.clm_postcomp, QuadraticMap.associated_rightInverse, scalarSMulCLE_symm_apply, Real.fourier_deriv, ContMDiffWithinAt.clm_postcomp, iteratedDeriv_scomp_three, fderiv_fun_pow', hasDerivWithinAt_pi, Matrix.toBilin_symm, StarAddMonoid.toStarModuleRat, Real.integrable_prod_sub, Orientation.oangle_smul_left_of_neg, NormedSpace.isVonNBounded_ball, locallyConvexSpace_iff, MDifferentiable.smul, strictConvex_Icc, antivary_iff_smul_rearrangement, norm_smul_inv_norm, Submodule.pointwise_smul_def, ContinuousLinearMap.eq_adjoint_iff, ConcaveOn.smul_convexOn', IsLocalizedModule.mk'_eq_zero', tangentConeAt_univ, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, convexHull_union_neg_eq_absConvexHull, SubMulAction.neg_mem, ContinuousLinearMap.toSpanSingleton_apply, ConcaveOn.add_const, smul_vsub_rev_vadd_mem_affineSpan_pair, KaehlerDifferential.isScalarTower', Submodule.mem_torsion_iff, derivWithin.scomp, DifferentiableOn.circleIntegral_sub_inv_smul, Derivation.linearEquiv_coe_to_linearMap_comp, Submodule.isTorsion'_powers_iff, Submodule.sum_smul_mem, Prod.segment_subset, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, smul_nonpos_iff, HasFPowerSeriesAt.comp, HasFDerivAt.continuousMultilinear_apply_const, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousLinearMap.IsPositive.smul_of_nonneg, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, InnerProductSpace.rankOne_apply, Convex.combo_eq_smul_sub_add, ConcaveOn.smul_convexOn, LieModule.shiftedGenWeightSpace.toEnd_eq, FormalMultilinearSeries.sum_of_finite, RingTheory.Sequence.isRegular_cons_iff, Ideal.finsuppTotal_apply_eq_of_fintype, ConcaveOn.comp_linearMap, HahnSeries.instSMulCommClass, ContinuousLinearEquiv.map_smul, extremePoints_pi, Submodule.reflection_singleton_apply, SkewMonoidAlgebra.mapDomain_mul, IntermediateField.isScalarTower, smul_unitClosedBall_of_nonneg, HasFTaylorSeriesUpToOn.zero_eq', KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, Asymptotics.IsLittleOTVS.trans_isThetaTVS, Fintype.expect_ite_eq, MulSemiringActionHom.map_smulₛₗ, MultilinearMap.map_insertNth_smul, QuotSMulTop.equivTensorQuot_naturality_mk, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, Subring.mem_pointwise_smul_iff_inv_smul_mem, isIntegralCurveAt_comp_mul_ne_zero, smulMemClass, HasStrictDerivAt.clm_comp, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, LieModule.Cohomology.twoCochain_alt, PiLp.isBoundedSMulSeminormedAddCommGroupToPi, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, Module.endTensorEndAlgHom_apply, inv_intCast_smul_comm, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, ContDiffMapSupportedIn.monoLM_apply, HasDerivWithinAt.Iic_of_Iio, ContinuousMultilinearMap.norm_smulRightL_le, Multiset.sum_smul_sum, balancedCore_nonempty_iff, StrictConvex.affine_image, WeakFEPair.h_feq, derivWithin_clm_comp, LinearMap.ker_restrictScalars, differentiableAt_smul_iff, Antitone.convex_le, ContinuousLinearMap.precompL_apply, Seminorm.closedBall_smul_ball, egauge_univ, Algebra.normalizedTrace_algebraMap, Subalgebra.coe_pointwise_smul, IsSelfAdjoint.adjoint_eq, Antitone.quasiconvexOn, Submodule.smul_mem', Submodule.mem_ideal_smul_span_iff_exists_sum', MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', mem_tangentConeAt_of_segment_subset, Asymptotics.IsLittleOTVS.prodMk, TrivSqZeroExt.fst_exp, DirectSum.mk_smul, curveIntegralFun_segment, HasDerivWithinAt.clm_apply, SchwartzMap.integral_fourierInv_smul_eq, Submodule.smul_iSup', DifferentiableAt.hasDerivAt, MonovaryOn.sum_comp_perm_smul_le_sum_smul, OrderDual.instIsStrictOrderedModule, RootPairing.coroot_eq_smul_coroot_iff, RKHS.kernel_apply, HasDerivAt.finCons, Seminorm.bound_of_continuous_normedSpace, Besicovitch.SatelliteConfig.exists_normalized_aux2, AlternatingMap.coe_smul, HasDerivAtFilter.add, groupHomology.isBoundary₁_of_mem_boundaries₁, exists_nonneg_left_iff_sameRay, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, LinearMap.BilinForm.isOrtho_smul_left, FormalMultilinearSeries.radius_le_smul, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, toAddMonoidHom_apply, Absorbs.of_neg_neg, MDifferentiable.clm_postcomp, IsArtinian.exists_pow_succ_smul_dvd, TrivSqZeroExt.map_inr, AntivaryOn.smul_add_smul_le_smul_add_smul, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, MeasureTheory.VectorMeasure.smul_apply, CStarMatrix.toCLM_injective, biUnion_associatedPrimes_eq_compl_regular, Asymptotics.IsLittleOTVS.insert, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, Complex.integral_circleTransform, ContinuousLinearMap.isPositive_self_comp_adjoint, iteratedDeriv_scomp_eq_sum_orderedFinpartition, convexOn_univ_dist, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, Matrix.SeparatingLeft.toLinearMap₂', MeasureTheory.Measure.IsAddHaarMeasure.domSMul, hasDerivAt_iff_isLittleO, LinearMap.rTensor_comp_flip_mk, Absorbs.eventually_nhdsNE_zero, Unitization.sqrt_inr, UniqueDiffWithinAt.smul, TopModuleCat.continuousSMul, LocallyConvexSpace.convex_basis_zero, NormedSpace.isBounded_iff_subset_smul_closedBall, KaehlerDifferential.isLocalizedModule_of_isLocalizedModule, hasFPowerSeriesAt_const, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, UniformOnFun.continuousSMul_induced_of_image_bounded, Subalgebra.inclusion.isScalarTower_left, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, Finsupp.linearCombination_smul, ConcaveOn.smul'', HasFDerivWithinAt.fun_const_smul, neg_one_smul, HasStrictFDerivAt.const_smul, Fintype.bilinearCombination_apply_single, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, LinearMap.BilinForm.nondegenerate_toMatrix_iff, Subring.mem_pointwise_smul_iff_inv_smul_mem₀, FormalMultilinearSeries.radius_compNeg, Fintype.expect_ite_zero, LinearMap.toMatrixₛₗ₂'_symm, NormedAddGroupHom.smul_apply, IsBoundedBilinearMap.smul_left, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, quasispectrum.mem_iff_of_isUnit, SchwartzMap.integral_bilin_fourierIntegral_eq, TopologicalGroup.IsSES.pushforward_def, SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM, Real.fourierIntegral_continuousMultilinearMap_apply, ProbabilityTheory.HasGaussianLaw.smul, StrictConcaveOn.lt_map_sum, MonotoneOn.convex_ge, QuotSMulTop.map_comp_mkQ, HasStrictDerivAt.fun_sum, LinearIsometryEquiv.adjoint_eq_symm, smul_mem_closure_star_mul, extDeriv_fun_smul, VectorField.mpullback_const_smul_apply, Ideal.finsuppTotal_apply, IsLocalizedModule.exist_integer_multiples, ContinuousAlternatingMap.toAlternatingMap_curryLeft, TensorProduct.flip_mk_surjective, LinearMap.separatingRight_toMatrix₂'_iff, StrictConvex.neg, Bornology.IsVonNBounded.image_multilinear', Finset.expect_ite_zero, Submodule.biSup_eq_range_dfinsupp_lsum, Quaternion.imI_fst_dualNumberEquiv, HasDerivAt.congr_of_eventuallyEq, mem_tangentConeAt_of_pow_smul, LinearMap.IsPositive.isPositive_smul_iff, analyticOrderAt_smul_eq_top_of_left, mem_openSegment_sub_add, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, WithSeminorms.tendsto_nhds', isAdjointPair_toLinearMap₂, ContinuousLinearMap.opNorm_mul, MvPowerSeries.smul_eq_C_mul, skewAdjoint.val_smul, LieModule.Cohomology.d₂₃_apply, Seminorm.pullback_apply, DoubleCentralizer.smul_toProd, collinear_iff_of_mem, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, sameRay_iff_inv_norm_smul_eq_of_ne, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, norm_sum_lt_of_strictConvexSpace, Seminorm.bddAbove_of_absorbent, smul_rayOfNeZero, UniformConvexOn.strictConvexOn, TemperedDistribution.smulLeftCLM_neg, Module.Dual.im_extendRCLike_apply, InnerProductSpace.Core.inner_smul_ofReal_right, Orientation.oangle_sign_sub_smul_left, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', MeasureTheory.SimpleFunc.integral_eq_sum_filter, egauge_zero_zero, Differentiable.fun_const_smul, Matrix.conjTranspose_inv_intCast_smul, TestFunction.lineDerivOpCLM_eq_lineDerivCLM, MDifferentiable.cle_arrowCongr, Asymptotics.IsLittleOTVS.neg_right, gauge_le_eq, segment_subset_convexHull, MeasureTheory.Measure.quasiMeasurePreserving_smul, HasSum.smul_eq, HasFTaylorSeriesUpTo.fderiv_eq, HasDerivAt.fun_pow', Unitization.nnnorm_def, LieModule.mem_weightSpace, instSMulCommClassMatrixFinOfNatNatProd, PowerSeries.le_order_smul, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, LieModule.Cohomology.d₁₂_apply_apply, Algebra.Extension.Cotangent.smul_eq_zero_of_mem, TestFunction.fderivCLM_ofSupportedIn, convexHull_toCone_eq_sInf, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson, ConcaveOn.inf, Finset.zero_mem_smul_finset_iff, LinearMap.smulRight_apply, HasFDerivAt.fun_smul, Module.AEval'.X_smul_of, Function.HasTemperateGrowth.toTemperedDistribution_apply, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, IsIntegralCurveOn.comp_mul, Orthonormal.inner_left_fintype, lie_smul, HasLineDerivAt.tendsto_slope_zero_right, TensorProduct.AlgebraTensorModule.map_smul_left, Balanced.convexHull, Complex.hasDerivAt_GammaIntegral, AntitoneOn.convex_le, fderiv_continuousAlternatingMapCompContinuousLinearMap, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, IncidenceAlgebra.instIsScalarTower, Absorbent.gauge_set_nonempty, Matrix.toBilin_apply, Submodule.pointwise_smul_toAddSubgroup, RatFunc.Luroth.algEquiv_apply, LinearMap.toMatrix₂'_compl₁₂, Convex.cthickening, PiTensorProduct.mapL_smul, Module.End.maxGenEigenspace_eq_maxGenEigenspace_zero, SchwartzMap.integral_sesq_fourier_eq, DFinsupp.instSMulPosMono, DualNumber.lift_apply_eps, Real.fderiv_fourier, CategoryTheory.ShortComplex.Homotopy.smul_h₂, ContinuousLinearMap.adjointAux_norm, MeasureTheory.L1.setToL1_smul_left, Representation.smul_ofModule_asModule, CStarMatrix.norm_def', KaehlerDifferential.instIsScalarTowerTensorProduct, algebra_compatible_smul, AntitoneOn.convex_gt, MeasureTheory.Integrable.smul_bdd, MDifferentiable.clm_bundle_apply₂, Fintype.expect_dite_eq', ContinuousLinearMap.smul_comp, MeasureTheory.convolution_smul, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, neg_smul_neg, hasDerivAtFilter_natCast, LinearMap.flip_injective_iff₁, Finsupp.linearCombination_one_tmul, CategoryTheory.Linear.units_smul_comp, meromorphicOrderAt_ne_top_iff, ContinuousAffineMap.smul_contLinear, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, ConvexCone.coe_map, HahnSeries.SummableFamily.hsum_smul_module, ContinuousAlternatingMap.instContinuousSMul, LinearMap.ker_smul', DualNumber.inv_eps, LinearMap.toMatrixOrthonormal_apply_apply, IsLocalizedModule.map_linearMap_of_isLocalization, HasFDerivAt.restrictScalars, balancedHull_subset_convexHull_union_neg, StrictConvex.extremePoints_eq_diff_interior, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, SameRay.exists_eq_smul_add, CategoryTheory.Functor.Linear.map_smul, stereoInvFunAux_apply, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, StrongFEPair.functional_equation, MulSemiringAction.toRingEquiv_apply, MonotoneOn.convex_le, norm_curveIntegral_segment_le, Ideal.smul_sup, Matrix.toLinearMapₛₗ₂'_single, LieAlgebra.bracket_ofTwoCocycle, Representation.ofDistribMulAction_apply_apply, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, Submodule.coe_torsion', LocalizedModule.mk_eq, IsLinearMap.isLinearMap_smul', MonoidAlgebra.instIsPushout, Matrix.nondegenerate_toBilin'_iff, TensorProduct.AlgebraTensorModule.restrictScalars_curry, HasFDerivAtFilter.isThetaTVS_sub, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH, MonotoneOn.quasiconvexOn, LinearMap.BilinForm.congr_comp, Finset.mem_convexHull', StarConvex.affine_image, iteratedDeriv_smul_const, circleIntegral.integral_sub_inv_smul_sub_smul, Action.smul_hom, HasStrictFDerivAt.list_prod', CliffordAlgebra.foldr'Aux_foldr'Aux, SchwartzMap.fourier_lineDerivOp_eq, DifferentiableAt.smul, HasFDerivWithinAt.isThetaTVS_sub, LinearMap.isBigOTVS_rev_comp, LinearMap.toContinuousBilinearMap_apply, Algebra.Extension.instIsScalarTowerH1CotangentOfCotangent, TemperedDistribution.instLineDerivLeftSMulReal, Submodule.span_singleton_eq_top_iff, CStarMatrix.inner_toCLM_conjTranspose_left, RootPairing.reflection_apply_root', hasStrictDerivAt_exp_smul_const, Submodule.FG.restrictScalars, PolynomialModule.monomial_smul_single, Subsemiring.smul_mem_pointwise_smul, Derivation.leibniz_div, EuclideanGeometry.inversion_vsub_center, Filter.EventuallyEq.ftaylorSeries, isBoundedBilinearMap_comp, StarConvex.smul_mem, lp.instIsCentralScalarPreLp, set_smul_sphere_zero, MeasureTheory.Integrable.essSup_smul, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, ContMDiff.smul, hasStrictDerivAt_add_const_iff, hasLineDerivWithinAt_smul_iff, Matrix.toLinearMap₂'_apply', Asymptotics.IsBigO.const_smul_left, Asymptotics.IsTheta.smul, TemperedDistribution.fourierInv_lineDerivOp_eq, MDifferentiable.const_smul, TrivSqZeroExt.lift_comp_inrHom, MeasureTheory.condExpL2_indicator_ae_eq_smul, Convex.openSegment_self_interior_subset_interior, SkewPolynomial.φ_iterate_apply, Asymptotics.IsBigOTVS.neg_right, ModuleCat.smulShortComplex_X₃_isAddCommGroup, conformalAt_const_smul, Submodule.span_smul_le, Ideal.pointwise_smul_subset_iff, IsMIntegralCurveOn.hasDerivWithinAt, IsLocalizedModule.mk'_add_mk', Polynomial.X_pow_smul_rTensor_monomial, FormalMultilinearSeries.rightInv_removeZero, IsUnit.smul_sub_iff_sub_inv_smul, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ClosedSubmodule.orthogonal_closure'', Submodule.smul_bot', instIsPushoutFractionRingPolynomial_1, HasDerivWithinAt.comp, hasStrictDerivAt_exp_smul_const', KaehlerDifferential.mapBaseChange_tmul, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, Module.DirectLimit.quotMk_of, openSegment_translate_image, egauge_univ_pi, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq, AffineSubspace.smul_vsub_vadd_mem, MeromorphicAt.fun_smul, Real.fourier_iteratedFDeriv, CFC.negPart_smul_of_nonpos, HasDerivAt.add, SchwartzMap.smulLeftCLM_real_smul, strictConvex_uIcc, MeasureTheory.Measure.integral_comp_inv_mul_left, HasMFDerivAt.smul, LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec, TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm, HasStrictDerivAt.div, NormMulClass.toNormSMulClass_op, RootPairing.pairing_one_four_iff', ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, MeasureTheory.measure_smul_average, MDifferentiableOn.smul, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, TrivSqZeroExt.fst_invOf, Ideal.instCovariantClassHSMulLe, Orientation.oangle_sign_sub_smul_right, hasDerivAtFilter_zero, Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone, segment_subset_convexJoin, StrictConvex.is_linear_preimage, Algebra.Generators.H1Cotangent.δAux_C, Complex.integral_comp_polarCoord_symm, NormedAddGroupHom.isCentralScalar, Seminorm.map_eq_zero_of_norm_zero, smul_closedBall', spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, QuadraticMap.associated_prod, HasFDerivAt.fun_const_smul, ConvexCone.coe_comap, LinearOrder.strictConvexOn_of_lt, Convex.combo_interior_closure_subset_interior, LocalizedModule.mk_cancel, PresheafOfModules.Sheafify.map_smul_eq, convex_iff_openSegment_subset, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Orientation.oangle_smul_left_self_of_nonneg, Monotone.convex_ge, UnitAddTorus.mFourierCoeff_toLp, NonUnitalSubalgebra.unitization_injective, Submodule.coe_toConvexCone, LinearMap.toMatrix_transpose, LinearMap.toMatrix₂_toLinearMapₛₗ₂, Submodule.smul_mem_pointwise_smul, ContinuousLinearMap.uniformContinuous_restrictScalars, Submodule.instSMulCommClass, TensorProduct.finsuppLeft_smul', MvPolynomial.sumAlgEquiv_comp_rename_inr, LieSubmodule.instSMulMemClass, SubmodulesBasis.smul, ContinuousLinearMap.mulLeftRight_apply, mem_openSegment_translate, PowerSeries.coe_smul, isModuleTopologyOfFiniteDimensional, MvPolynomial.aevalTower_toAlgHom, LinearMap.extendTo𝕜'_apply, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, MonotoneOn.convex_gt, fromTangentSpace_mfderiv_smul_apply, Differentiable.const_smul, Seminorm.ball_eq_emptyset, ArchimedeanClass.mk_le_mk_smul, taylor_tendsto, dslope_sub_smul, LinearMap.smul_compMultilinearMap, rescale_to_shell_semi_normed_zpow, HasFDerivAt.curveIntegral_segment_source, balancedCore_mem_nhds_zero, convexJoin_segment_singleton, SameRay.exists_eq_smul, DirectSum.instSMulCommClass, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, CentroidHom.instSMulCommClass_2, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, deriv_fun_smul, ConvexCone.salient_strictlyPositive, iteratedFDeriv_comp_const_smul, LocalizedModule.mem_ker_mkLinearMap_iff, Algebra.IsInvariant.exists_smul_of_under_eq, HasStrictDerivAt.mul, PresheafOfModules.Derivation.d_mul, Bundle.Trivialization.eq_sum_localFrame_coeff_smul, LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, MeasureTheory.convolution_lsmul, QuadraticMap.map_smul, MDifferentiableAt.clm_postcomp, fderiv_continuousAlternatingMap_apply, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, abs_nnqsmul, SeminormFamily.finset_sup_comp, Module.Dual.norm_extendRCLike_apply_sq, Submodule.mem_span_finset, Bornology.isVonNBounded_iff_absorbing_le, Module.AEval.instIsScalarTowerOrigPolynomial, CategoryTheory.Pretriangulated.Triangle.smul_hom₂, ContDiffMapSupportedIn.monoLM_eq_of_scalars, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, LieDerivation.coe_smul_linearMap, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim, Module.AEval.C_smul, Algebra.Extension.CotangentSpace.map_tmul, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, element_smul_restrictScalars, strongConcaveOn_zero, integral_withDensity_eq_integral_smul, Representation.ofMulAction_self_smul_eq_mul, intervalIntegral.integral_comp_add_div, Matrix.instSMulCommClassForall_1, convex_singleton, HasDerivAt.pow, deriv_fderiv, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, RegularNormedAlgebra.isometry_mul', fwdDiff_const_smul, convexJoin_singleton_segment, cauchyPowerSeries_apply, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, toAddMonoidEnd_apply, mem_smul_of_egauge_lt, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, DifferentiableAt.const_smul, RootPairing.mem_range_root_of_mem_range_reflection_of_mem_range_root, Rep.ihom_ev_app_hom, BoxIntegral.HasIntegral.smul, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, Ideal.range_mul, integral_smul_const, CStarModule.inner_smul_right_real, Module.exists_nontrivial_relation_of_finrank_lt_card, MDifferentiableWithinAt.clm_bundle_apply₂, TrivSqZeroExt.algHom_ext'_iff, fun_meromorphicOrderAt_smul, SameRay.inv_norm_smul_eq, ModuleCat.hom_smul, TestFunction.limitCLM_apply, Module.IsTorsionBySet.mk_smul, hasDerivWithinAt_abs, Algebra.TensorProduct.linearMap_comp_rid, hasFPowerSeriesOnBall_const, CentroidHom.toEnd_smul, QuadraticForm.polarBilin_tmul, HasFDerivAt.clm_apply, openSegment_eq_image', HasStrictDerivAt.const_mul, ContDiffMapSupportedIn.seminorm_le_iff, ConcaveOn.convex_strict_hypograph, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, NonUnitalStarSubalgebra.unitization_range, smul_nonpos_iff_pos_imp_nonpos, LinearMap.BilinForm.Nondegenerate.congr, MeasureTheory.Measure.integral_comp_smul_of_nonneg, VectorFourier.hasFDerivAt_fourierIntegral, DiffContOnCl.circleIntegral_sub_inv_smul, Submodule.smul_sup', HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, Submodule.comap_smul, TensorProduct.Algebra.smul_def, LinearMap.flip_surjective_iff₁, LaurentPolynomial.smeval_C_mul, Seminorm.ball_norm_mul_subset, IsLocalizedModule.exist_integer_multiples_of_finset, WeakDual.instContinuousConstSMul, List.sum_smul, ClosedSubmodule.inner_real_eq_re_inner, hasFDerivAt_ringInverse, ContinuousMultilinearMap.opNorm_smul_le, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, Matrix.toLinearMap₂'_apply, HasFDerivAt.continuousAlternatingMap_apply, MeasureTheory.convolution_precompR_apply, PolynomialModule.single_smul, SchwartzMap.compSubConstCLM_apply, LinearMap.BilinForm.separatingLeft_toMatrix'_iff, IsNilpotent.exp_smul_eq_sum, MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc, VectorFourier.fourierIntegral_iteratedFDeriv, TopologicalAddGroup.IsSES.pushforward_apply_apply, rank_lt_rank_dual', QuotSMulTop.map_surjective, InformationTheory.hasDerivAt_klFun, IsLocalizedModule.mk'_eq_mk'_iff, InnerProductSpace.nnnorm_rankOne, FreeLieAlgebra.liftAux_map_smul, Seminorm.closedBall_zero_eq_preimage_closedBall, MonotoneOn.quasilinearOn, fderiv_smul, ArithmeticFunction.one_smul', OrthonormalBasis.orthogonalProjection_apply_eq_sum, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, Filter.BoundedAtFilter.smul, NonUnitalSubalgebra.unitization_range, LieModule.LinearWeights.map_smul, SemimoduleCat.Algebra.instIsScalarTowerCarrier, instIsOrderedModule, ModuleCat.CoextendScalars.smul_apply, HasDerivAt.fun_pow, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, starConvex_compl_Ici, LocalizedModule.equivTensorProduct_symm_apply_tmul, ContinuousLinearMap.norm_toSpanSingleton, FormalMultilinearSeries.continuousOn_of_finite, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, TensorProduct.finsuppScalarRight_apply_tmul, Submodule.topologicalClosure_map, Submodule.toConvexCone_top, Representation.single_smul, OrderDual.instSMulPosStrictMono, FormalMultilinearSeries.ofScalars_series_of_subsingleton, Ideal.under_smul, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, affinity_unitClosedBall, ContinuousLinearMap.flip_smul, Module.FinitePresentation.linearEquivMap_symm_apply, ContDiffMapSupportedIn.coe_smul, HasDerivAtFilter.mono, PadicInt.mahlerSeries_apply, HasFDerivAt.isBigOTVS_sub, HasDerivWithinAt.fun_pow', LieModuleHom.coe_smul, Module.Dual.extendRCLike_apply, MeasureTheory.integral_singleton', HasCompactSupport.hasDerivAt_convolution_right, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, OreLocalization.oreDiv_add_char', HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, Finset.affineCombination_eq_linear_combination, HasDerivWithinAt.const_add, SameRay.pos_smul_left, Coalgebra.TensorProduct.lid_tmul, Module.Basis.constrL_apply, Module.AEval'.of_symm_X_smul, QuadraticMap.associated_apply, HasFDerivWithinAt.const_smul, LieModule.mem_genWeightSpace, ModuleFilterBasis.smul_right, MeasureTheory.ConvolutionExistsAt.integrable_swap, NormedSpace.expSeries_sum_eq, norm_inner_eq_norm_iff, IsLocalizedModule.finsetIntegerMultiple_image, RootPairing.weylGroup_apply_root, Real.circleAverage_eq_circleIntegral, HasFiniteFPowerSeriesOnBall.eq_partialSum, image_openSegment, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, hasDerivAt_tsum_of_isPreconnected, subset_balancedCore, Submodule.mul_mem_smul_iff, FormalMultilinearSeries.ofScalars_add, ContinuousAlternatingMap.coe_smul, ContMDiffCovariantDerivativeOn.finite_affine_combination, convexOn_dist, LinearIsometryEquiv.smul_apply, convexOn_iff_forall_pos, inner_eq_norm_mul_iff_div, convex_Ico, Submodule.topologicalClosure_eq_self, Submodule.smul_subset_smul, SameRay.nonneg_smul_right, LinearMap.hasStrictDerivAt, real_linearMap_map_smul_complex, LinearMap.BilinForm.mul_toMatrix'_mul, AffineMap.hasDerivAt_lineMap, fderivWithin_continuousAlternatingMap_apply_const_apply, MeasureTheory.setToFun_smul_left', ratCast_smul_eq, MeasureTheory.integral_smul, Seminorm.convexOn, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left', Subring.coe_pointwise_smul, mellinInv_eq_fourierIntegralInv, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, ProbabilityTheory.strong_law_ae, HasDerivWithinAt.fun_finset_prod, Convex.semilinear_image, Derivation.comp_aeval_eq, Algebra.Extension.Cotangent.val_smul''', HasDerivWithinAt.norm_sq, CStarModule.inner_smul_right_complex, HasGradientAtFilter.hasDerivAtFilter', instIsPushoutPolynomial_1, Seminorm.balanced_closedBall_zero, zmod_smul_mem, dualTensorHom_apply, BilinForm.mul_toMatrix_mul, LinearEquiv.mem_fixedSubmodule_transvection_iff, SmoothPartitionOfUnity.contDiffAt_finsum, IsInvariantSubring.smul_mem, ContMDiffAt.smul, Mathlib.Tactic.Module.NF.add_eq_eval₃, TrivSqZeroExt.map_comp_inlAlgHom, intervalIntegral.integral_hasDerivWithinAt_left, GeneralSchauderBasis.expansion, ofNat_smul_eq_nsmul, HasFPowerSeriesOnBall.fderiv_eq, Finsupp.weight_single, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, Seminorm.coe_restrictScalars, strictConvex_closedBall, NormedSpace.toNormSMulClass, Finset.sum_smul_const_vsub_eq_vsub_affineCombination, Quaternion.fst_imK_dualNumberEquiv_symm, midpoint_eq_smul_add, IsCovariantDerivativeOn.smul_const, Submodule.smul_le_self_of_tower, RootPairing.Equiv.root_indexEquiv_eq_smul, Asymptotics.IsLittleOTVS.zero, isBigO_rpow_top_log_smul, Module.FinitePresentation.exists_lift_of_isLocalizedModule, HasDerivAtFilter.fun_add, AffineMap.left_vsub_lineMap, SchwartzMap.smulLeftCLM_sum, Matrix.toLinearMap₂_compl₁₂, midpoint_sub_right, Submodule.smul_mem_span_smul_of_mem, AffineMap.hasDerivWithinAt_lineMap, AffineMap.smul_linear, Asymptotics.IsLittleOTVS.congr_left, ContinuousLinearMap.fderiv_of_bilinear, TestFunction.coe_smul, has_fderiv_at_filter_real_equiv, SkewMonoidAlgebra.nonUnitalAlgHom_ext'_iff, MeasureTheory.setIntegral_condExpInd, Seminorm.gaugeSeminorm_ball, MeasureTheory.Measure.addHaarScalarFactor_smul_congr, ContinuousLinearMap.nnnorm_toSpanSingleton, FixedPoints.mem_addSubmonoid, ContinuousAlternatingMap.alternatizeUncurryFin_smul, PresheafOfModules.map_smul, fderiv_mul_const', tendsto_integral_exp_smul_cocompact, Matrix.linftyOpIsBoundedSMul, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Complex.hasDerivAt_Gammaℝ_one, Matrix.toLinearMapₛₗ₂'_symm, ContDiffMapSupportedIn.monoCLM_eq_of_scalars, curveIntegral_segment, Module.Ray.linearEquiv_smul_eq_map, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, Submodule.mem_annihilator', hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, DualNumber.fst_eq_zero_iff_eps_dvd, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Asymptotics.isBigOTVS_iff_smallSets, Derivation.leibniz_inv, Real.fourierIntegral_continuousLinearMap_apply, smul_left_inj, LinearMap.isAlt_iff_eq_neg_flip, Submodule.adjoint_subtypeL, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, Mathlib.Tactic.LinearCombination.smul_lt_const, ConvexOn.sub, Polynomial.aevalTower_toAlgHom, HasDerivAtFilter.sub, midpoint_mem_openSegment, gauge_norm_smul, InnerProductSpace.Core.cauchy_schwarz_aux, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, ContinuousLinearMap.opNorm_mul_apply, ContinuousLinearMap.norm_smulRightL, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, TrivSqZeroExt.inl_mul_inr, DFinsupp.toFinsupp_smul, Asymptotics.IsBigOWith.const_smul_left, LinearMap.toBilin'Aux_toMatrixAux, TrivSqZeroExt.fst_list_prod, convexOn_univ_norm, HasFDerivWithinAt.fun_smul, AffineMap.lineMap_vsub_right, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, Module.End.intCast_def, Submodule.exists_isTorsionBy, intervalIntegral.integral_deriv_comp_smul_deriv', strictAnti_smul_left, MeasureTheory.convolution_def, LinearMap.toMatrix₂_compl₂, QuaternionAlgebra.star_smul', ContinuousMultilinearMap.curryLeft_norm, Seminorm.ball_zero_eq_preimage_ball, lp.norm_const_smul, finsuppTensorFinsuppLid_symm_single_smul, ContinuousLinearMap.compContinuousMultilinearMapL_apply, Module.reflection_mul_reflection_pow_apply, DFinsupp.sum_mapRange_index.linearMap, CategoryTheory.Abelian.Ext.mk₀_smul, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MeasureTheory.Submartingale.smul_nonneg, MDifferentiableWithinAt.cle_arrowCongr, Balanced.add, ConvexOn.openSegment_subset_strict_epigraph, TensorProduct.tmul_smul, CStarModule.inner_smul_left_complex, openSegment_subset_ball_of_ne, HasFPowerSeriesWithinOnBall.prod, units_smul_eq_self_iff, NormedSpace.normalize_smul, MDifferentiableWithinAt.clm_precomp, smul_add_smul_lt_smul_add_smul, HasDerivAt.fun_add, SchwartzMap.fourierMultiplierCLM_sum, MeasureTheory.integrable_withDensity_iff_integrable_smul', HasDerivAt.neg, ContMDiffVectorBundle.continuousLinearMap, DFinsupp.mapRange_smul, IsMIntegralCurveOn.comp_mul, DenseRange.topologicalClosure_map_submodule, Prod.image_mk_segment_left, Matrix.isBoundedSMul, HasDerivAt.star, MvPolynomial.scalarRTensor_apply_tmul, Matrix.conjTranspose_inv_natCast_smul, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, RootPairing.mem_range_coroot_of_mem_range_coreflection_of_mem_range_coroot, ConvexBody.coe_smul, Polynomial.smeval_smul, Convex.combo_self_interior_subset_interior, infEDist_smul₀, Bornology.IsVonNBounded.neg, ContinuousLinearMap.continuous_restrictScalars, UniqueDiffWithinAt.dense_tangentConeAt, hasStrictDerivAt_const_add_iff, InnerProductGeometry.angle_eq_zero_iff, RootPairing.EmbeddedG2.twoShortAddLongRoot_eq, smul_add_smul_le_smul_add_smul, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, Asymptotics.IsBigOTVS.fun_add, AnalyticAt.smul, hasLineDerivAt_smul_iff, VectorField.lieBracket_const_smul_left, SameRay.sameRay_nonneg_smul_left, LinearIndependent.pair_smul_iff, neg_convexOn_iff, ENNReal.smul_top, Submodule.mem_smul_iff_inv_mul_mem, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, Matrix.toLinearMapₛₗ₂'_aux_eq, ContinuousAlternatingMap.map_piecewise_smul, mellinInv_eq_fourierInv, units_smul_eq_neg_iff, HasFPowerSeriesOnBall.uniform_geometric_approx, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_monotoneOn, Module.End.algebraMap_isUnit_inv_apply_eq_iff', ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, IsNilpotent.exp_smul, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, CommRingCat.coproductCocone_inl, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, Convex.strictConvex, IsSl2Triple.mem_toLieSubalgebra_iff, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, HasDerivAtFilter.const_smul, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, NonUnitalAlgHom.coe_distribMulActionHom_mk, Submodule.mem_torsionBySet_iff, Asymptotics.isBigOTVS_fun_neg_left, Ideal.stabilizerEquiv_symm_apply_smul, norm_smul_of_nonneg, sub_smul, VectorFourier.fourierIntegral_const_smul, HasFPowerSeriesWithinAt.fderivWithin_eq, Convex.span_tangentConeAt, inCoordinates_apply_eq₂, Asymptotics.isBigOTVS_fun_neg_right, CompactlySupportedContinuousMap.instSMulCommClass, KaehlerDifferential.tensorKaehlerEquivBase_tmul, ContDiffAt.contDiffAt_norm_smul, Real.fourier_real_eq, CentroidHom.smul_apply, MeasureTheory.setToFun_smul, SkewMonoidAlgebra.coeff_mul_right, FormalMultilinearSeries.id_comp', Seminorm.rescale_to_shell_zpow, FormalMultilinearSeries.ofScalars_sub, Asymptotics.IsEquivalent.smul, MeasureTheory.distribHaarChar_apply, MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_poles, prodXSubSMul.smul, ContinuousMultilinearMap.range_toUniformOnFun, QuadraticMap.toQuadraticMap_associated, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, Convex.openSegment_interior_self_subset_interior, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, Matrix.toEuclideanCLM_toLp, PiTensorProduct.liftAux.smul, Algebra.traceForm_toMatrix, Seminorm.smul_closedBall_zero, HasDerivAt.comp, AddMonoid.End.smul_apply, Seminorm.balanced_ball_zero, hasSum_fourier_series_L2, DualNumber.lift_inlAlgHom_eps, DifferentiableWithinAt.hasDerivWithinAt, isSMulRegular_submodule_iff_right_eq_zero_of_smul, Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNil, mem_openSegment_of_ne_left_right, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, Ioo_smul_sphere_zero, HasFPowerSeriesOnBall.sum, Real.tendsto_integral_gaussian_smul', HasFDerivAt.comp_hasDerivAt, Mathlib.Tactic.Module.NF.eq_cons_const, Real.hasFDerivAt_fourier, LinearOrder.convexOn_of_lt, HasDerivWithinAt.mul, absorbs_iff_eventually_nhdsNE_zero, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, Matrix.toLin_scalar, Antitone.convex_lt, CategoryTheory.ShortComplex.Homotopy.smul_h₀, QuadraticMap.polar_smul, fderiv_inverse, smul_sphere', SchwartzMap.smulLeftCLM_fun_neg, ClosedSubmodule.mulI_sup, two_smul, Ideal.IsPrime.smul_iff, toBilin'Aux_toMatrixAux, PiLp.instNormSMulClass, MeasureTheory.setIntegral_countable, ContMDiffOn.clm_precomp, CategoryTheory.ShortComplex.Homotopy.smul_h₃, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, contDiffOn_nat_iff_continuousOn_differentiableOn, Module.Basis.isScalarTower_finsupp, CategoryTheory.ShortComplex.cyclesMap_smul, TensorProduct.finsuppLeft_symm_apply_single, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Submodule.smul_coe_torsionBy, Fintype.not_linearIndependent_iffₛ, BilinForm.dotProduct_toMatrix_mulVec, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, LinearMap.BilinForm.tensorDistrib_tmul, map_nnrat_smul, stereoInvFun_apply, monovaryOn_iff_forall_smul_nonneg, TrivSqZeroExt.mul_left_eq_one, StrictConvexOn.translate_left, analyticAt_smul, Seminorm.restrictScalars_ball, Filter.EventuallyEq.hasDerivAt_iff, LinearMap.trace_transpose', ConvexBody.coe_mk, LieAlgebra.Basis.baseSupp_apply_smul_f, InnerProductSpace.rankOne_eq_zero, egauge_le_one, Real.fourierIntegral_convergent_iff', fderivWithin_continuousMultilinear_apply_const_apply, LieModuleHom.smul_apply, Submodule.mem_annihilator, hasDerivAt_deriv_iff, Unitization.splitMul_injective_of_clm_mul_injective, RCLike.mul_wInner_left, Seminorm.continuous, Function.Antiperiodic.const_inv_smul₀, StrictConvexOn.translate_right, CliffordAlgebra.ι_mul_ι_mul_ι, ContinuousAlternatingMap.norm_curryLeft, Module.End.HasEigenvector.apply_eq_smul, MeasureTheory.integral_indicatorConstLp, inner_map_polarization', HasStrictDerivAt.clog_real, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal, hasDerivAt_of_hasDerivAt_of_ne', intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, LieDerivation.ofGradingSum_of, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, Module.Dual.transpose_apply, QuadraticMap.polar_smul_left_of_tower, ContinuousLinearMapWOT.smul_apply, MeasureTheory.Measure.integral_comp_smul, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, Asymptotics.isBigOTVS_iff_isBigO, LinearMap.isPosSemidef_iff_posSemidef_toMatrix, Asymptotics.IsLittleO.smul, setIntegral_withDensity_eq_setIntegral_smul₀', LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, Bornology.isVonNBounded_sub_of_nonempty, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, subset_tangentConeAt_prod_right, TrivSqZeroExt.snd_exp, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, MeasureTheory.condExpIndSMul_smul, fderivWithin_inv', KaehlerDifferential.isScalarTower_of_tower, TannakaDuality.FiniteGroup.sumSMulInv_apply, Submodule.isTorsion'_iff_torsion'_eq_top, hasDerivAt_add_const_iff, not_disjoint_segment_convexHull_triple, AlgEquiv.smul_def, MeasureTheory.Measure.hausdorffMeasure_smul₀, real_inner_div_norm_mul_norm_eq_one_iff, Monotone.ae_hasDerivAt, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, star_natCast_smul, ContinuousLinearMap.fderivWithin_of_bilinear, Module.Basis.smul_det, HasFPowerSeriesOnBall.compContinuousLinearMap, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonpos, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', lineMap_mem_openSegment, Fintype.sum_single_smul, QuadraticMap.associated_left_inverse, gaugeSeminorm_ball_one, LinearMap.BilinForm.smul_right_of_tower, ContinuousMultilinearMap.cons_smul, DiffContOnCl.deriv_eq_smul_circleIntegral, LinearMap.BilinForm.tensorDistribEquiv_apply, ContinuousLinearMap.applyFaithfulSMul, DifferentiableOn.deriv_eq_smul_circleIntegral, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Submodule.mem_span_singleton, iteratedFDerivWithin_smul_const_apply, Algebra.Generators.H1Cotangent.δAux_monomial, LinearMap.BilinForm.toMatrix_apply, PiTensorProduct.liftIsometry_tprodL, VectorField.mpullback_smul_apply, DualNumber.isNilpotent_iff_eps_dvd, TrivSqZeroExt.map_comp_inrHom, RootPairing.reflectionPerm_coroot, Disjoint.exists_open_convexes, UniformConvergenceCLM.continuousSMul, curveIntegral_segment_const, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, hasDerivWithinAt_one, BilinForm.toMatrix_toBilin, ConvexOn.smul_concaveOn', le_egauge_smul_left, sub_smul_slope_vadd, LieRinehartAlgebra.toIsScalarTower, Algebra.Extension.instIsScalarTowerCotangent, Bundle.Trivialization.eventually_eq_localFrame_sum_coeff_smul, DualNumber.isMaximal_span_singleton_eps, HahnSeries.SummableFamily.smul_hsum, Seminorm.finset_sup_apply_lt, Convex.second_derivative_within_at_symmetric, AffineSubspace.setOf_wOppSide_eq_image2, BoxIntegral.BoxAdditiveMap.volume_apply, spinGroup.conjAct_smul_range_ι, ConvexCone.isGenerating_bot, ProbabilityTheory.HasGaussianLaw.fun_smul, ModuleCat.Derivation.d_mul, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, MeasureTheory.Integrable.toL1_smul, LinearMap.BilinForm.IsRefl.smul, InnerProductSpace.rankOne_eq_rankOne_iff_comm, realPart_add_I_smul_imaginaryPart, ContinuousLinearMap.uniformContinuousConstSMul, Ideal.Quotient.smul_top, HasLineDerivAt.tendsto_slope_zero, Asymptotics.IsLittleOTVS.fst, SemilinearMapClass.map_smul_inv, HasDerivWithinAt.inner, LieDerivation.exp_map_apply, subset_tangentConeAt_prod_left, LocalizedModule.mk_cancel_common_left, strictConvex_Ioo, ConvexBody.convex, ContinuousLinearMap.holder_smul_left, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, sameRay_smul_left_iff, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable, LinearMap.BilinForm.IsPosSemidef.smul, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, Submodule.FG.restrictScalars_iff, Seminorm.comp_smul, LieRinehartRing.lie_smul_eq_mul', absorbent_nhds_zero, ContMDiffAt.const_smul_section, Submodule.pointwise_smul_toAddSubmonoid, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Real.fourierIntegral_iteratedDeriv, MultilinearMap.dfinsuppFamily_smul, intervalIntegral.smul_integral_comp_mul_sub, Derivation.leibniz', Derivation.leibniz_zpow, iteratedDerivWithin_smul_const, Mathlib.Tactic.Module.NF.sub_eq_eval₃, MeasureTheory.hasFDerivAt_convolution_right_with_param, InnerProductSpace.exists_of_rankOne_eq_rankOne, fderiv_pow', MeasureTheory.Lp.coeFn_smul, ContMDiffSection.coe_smul, Asymptotics.IsLittleO.isLittleOTVS, hasDerivAt_ofNat, SchwartzMap.postcompCLM_apply, Asymptotics.IsLittleOTVS.neg_left, Ideal.tensorCotangentHom_tmul, iteratedFDerivWithin_eq_equiv_comp, Matrix.smul_kroneckerTMul, LinearMap.toMatrix₂_comp, DifferentiableAt.isBigOTVS_sub, nhds_basis_balanced, LinearMap.restrictScalars_smul, Module.Quotient.mk_smul_mk, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, differentialIdeal_le_iff, IsLocalizedModule.exist_integer_multiples_of_finite, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, LinearMap.lsmul_flip_apply, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, IsModuleTopology.instProd, LinearIndependent.smul_left_injective, isLocalizedModule_iff, HahnEmbedding.Partial.exists_sub_mem_ball, Matrix.SeparatingRight.toLinearMap₂', Representation.asModuleEquiv_symm_map_smul, Asymptotics.IsLittleOTVS.pi, Submodule.mem_span_iff_exists_finset_subset, LinearEquiv.transvection.apply, DualNumber.lift_smul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, SameRay.exists_pos_right, MeasureTheory.SimpleFunc.integral_eq_sum, DoubleCentralizer.smul_fst, Coalgebra.sum_counit_smul, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, iteratedDerivWithin_const_smul_field, Submodule.mem_iSup_iff_exists_dfinsupp, Quaternion.imK_fst_dualNumberEquiv, LinearMap.exists_eq_smul_id_of_forall_notLinearIndependent, MvPolynomial.rTensor_apply_X_tmul, Bundle.Pretrivialization.continuousLinearMap.isLinear, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonneg, CFC.posPart_smul, TotallyBounded.isVonNBounded, UpperHalfPlane.hasStrictDerivAt_smul, smul_min_of_nonpos, NormedSpace.normalize_smul_of_pos, Seminorm.comp_zero, LinearMap.tensorProductEnd_apply, ContinuousLinearMap.adjoint_inner_left, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, lift_rank_lt_rank_dual', Subring.mem_inv_pointwise_smul_iff, PointwiseConvergenceCLM.isInducing_inducingFn, KaehlerDifferential.tensorKaehlerEquiv_tmul, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, DomMulAct.coe_smul_linearMap, Module.AEval'.X_pow_smul_of, Bornology.IsVonNBounded.image_multilinear, StarConvex.sub, groupHomology.isCycle₂_of_mem_cycles₂, LieRinehartAlgebra.Hom.map_smul_apply', Algebra.Generators.H1Cotangent.δAux_toAlgHom, ContDiffMapSupportedIn.seminorm_monoLM_le, Finsupp.linearCombination_single_index, intervalIntegral.integral_comp_smul_deriv'', Monovary.smul_add_smul_le_smul_add_smul, CochainComplex.HomComplex.Cochain.shift_smul, ContinuousLinearMap.isBoundedBilinearMap, WeakFEPair.Λ₀_eq, LinearMap.restrictScalars_self, ContinuousMultilinearMap.hasBasis_nhds_zero, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, LinearMap.BilinForm.separatingRight_toMatrix'_iff, LinearMap.extendTo𝕜_apply, RingTheory.Sequence.isWeaklyRegular_singleton_iff, HasDerivAt.sub, intervalIntegral.integral_comp_smul_deriv, SkewMonoidAlgebra.support_mul_single_eq_image, Module.piEquiv_apply_apply, LinearMap.BilinForm.smul_left, egauge_pi, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, Finsupp.lift_apply, ConvexOn.convex_epigraph, HasLineDerivWithinAt.smul, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, RatFunc.Luroth.algEquiv_algebraMap, Submodule.dualCoannihilator_map_linearEquiv_flip, mdifferentiable_smul_const_section, HasStrictDerivAt.sum, Polynomial.adjSylvester_comp_sylveserMap, Finset.expect_eq_single_of_mem, FormalMultilinearSeries.apply_eq_pow_smul_coeff, fderivWithin_continuousMultilinear_apply_const, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, MeasureTheory.setIntegral_condExpIndSMul, Finset.weightedVSub_smul, totallyBounded_absConvexHull, Prod.smul_mk_zero, Asymptotics.isBigOTVS_congr, ContinuousLinearMap.toSpanSingleton_smul, MulSemiringAction.charpoly_eq_prod_smul, MeasureTheory.integrable_withDensity_iff_integrable_smul₀, AdicCompletion.AdicCauchySequence.smul_apply, inv_norm_smul_mem_unitClosedBall, Seminorm.neg_mem_ball_zero, star_ratCast_smul, Submodule.mapsTo_smul_closure, IsArtinian.range_smul_pow_stabilizes, MulSemiringAction.smul_coeff_charpoly, Submodule.iSup_eq_range_dfinsupp_lsum, LinearMap.isScalarTower_of_injective, Ideal.torsionOf_eq_span_pow_pOrder, LinearMap.BilinForm.lieInvariant_iff, ContinuousLinearEquiv.symm_smul_apply, Asymptotics.isBigOTVS_neg_right, LieModule.Cohomology.twoCochain_skew, TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply, VectorField.lieBracketWithin_smul_left, LinearMap.BilinForm.dotProduct_toMatrix_mulVec, VectorField.mlieBracketWithin_const_smul_left, convex_halfSpace_ge, AffineMap.right_vsub_lineMap, Quaternion.re_fst_dualNumberEquiv, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ConvexOn.translate_left, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, MulSemiringActionHom.map_smul, TemperedDistribution.fourierMultiplierCLM_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, convex_list_sum, Seminorm.bound_of_continuous, ContDiff.euclidean_dist, HasStrictDerivAt.smul, inner_eq_sum_norm_sq_div_four, AntivaryOn.sum_smul_le_sum_comp_perm_smul, intervalIntegral.integral_comp_add_mul, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, constFormalMultilinearSeries_apply_zero, ConvexBody.ext_iff, hasDerivAt_tsum, DifferentiableAt.fderiv_restrictScalars, starConvex_iff_forall_ne_pos, AnalyticAt.fun_smul, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, Matrix.Module.smul_def, Representation.IntertwiningMap.smul_apply, MeasureTheory.setIntegral_rnDeriv_smul, LinearIsometryEquiv.conjStarAlgEquiv_trans, FormalMultilinearSeries.radius_smul_eq, RootPairing.smul_coroot_eq_of_root_add_root_eq, traceForm_dualSubmodule_adjoin, Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, ContinuousLinearMap.bilinearComp_zero_right, SkewMonoidAlgebra.single_mul_single, DivisibleHull.instIsStrictOrderedModuleNNRat, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, IsContMDiffRiemannianBundle.exists_contMDiff, ConcaveOn.comp_affineMap, Matrix.toBilin'_symm, Unitization.isStarProjection_inr_iff, ModuleCat.smulShortComplex_g, StarConvex.zero_smul, Function.support_smul, DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul, BaireSpace.instBarrelledSpace, hasDerivAtFilter_add_const_iff, TrivSqZeroExt.inl_smul, MultilinearMap.map_update_smul_left, hasDerivAt_jacobiTheta₂_fst, HomologicalComplex.units_smul_f_apply, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, HasDerivWithinAt.scomp_of_eq, LinearMap.toMatrix_smulBasis_left, MDifferentiableAt.const_smul, SkewMonoidAlgebra.support_single_mul_eq_image, MvPowerSeries.constantCoeff_smul, VertexOperator.ncoeff_apply, Module.Dual.transpose_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, IsSl2Triple.lie_h_e_smul, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, TrivSqZeroExt.inr_mul_inr, LinearMap.BilinForm.isSymm_iff_flip, convex_openSegment, Convex.taylor_approx_two_segment, DiffContOnCl.const_smul, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, LinearMap.flip_bijective_iff₁, subset_balancedHull, ConvexCone.pointed_positive, VectorFourier.fourierIntegral_convergent_iff, LinearMap.flip_bijective_iff₂, WithConv.matrixToLin'StarAlgEquiv_apply, IsLocalizedModule.subsingleton_iff, ContinuousLinearMap.adjointAux_apply, RCLike.real_smul_eq_coe_smul, integral_comp_polarCoord_symm, Set.zero_mem_smul_set_iff, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, IsCompactOperator.hasEigenvalue_or_mem_resolventSet, fderivWithin_fun_mul', CategoryTheory.Functor.map_smul, sup_eq_half_smul_add_add_abs_sub', Module.Basis.coe_smul, ProperCone.innerDual_singleton, VonNeumannAlgebra.coe_mk, Asymptotics.IsLittleO.smul_isBigO, MonotoneOn.convex_lt, HasFPowerSeriesWithinOnBall.sub, TemperedDistribution.fourierMultiplierCLM_const, MvPolynomial.tensorEquivSum_one_tmul_C, HasLineDerivAt.tendsto_slope_zero_left, StrictConvexOn.add, Submodule.coe_pointwise_smul, Balanced.subset_smul, ConcaveOn.mul', ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, derivWithin_const_smul_field, StrictConvexOn.map_sum_eq_iff, MvPolynomial.rTensor_apply_tmul, Antitone.convex_ge, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, hasFDerivAt_integral_of_dominated_loc_of_lip', CliffordAlgebra.invOf_ι_mul_ι_mul_ι, ConvexCone.coe_strictlyPositive, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, Asymptotics.isLittleO_const_smul_left, DifferentiableOn.fun_const_smul, RKHS.kerFun_dense, VectorField.mpullback_const_smul, InnerProductSpace.rankOne_def, HasDerivAt.smul_const, ConvexOn.add_strictConvexOn, BilinForm.toMatrix_comp, smul_vsub_vadd_mem_affineSpan_pair, HasDerivAtFilter.sub_const, smul_nonneg_of_nonpos_of_nonpos, ContinuousLinearMap.coe_flipₗᵢ', MDifferentiableAt.clm_bundle_apply₂, WeakFEPair.h_feq', star_nnrat_smul, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, uniqueDiffWithinAt_iff, SchwartzMap.convolution_apply, Polynomial.smul_mem_rootSet_iff, Submodule.IsPrincipal.mem_iff_eq_smul_generator, PointedCone.pointed_toConvexCone, fderivWithin_fderivWithin_eq_of_mem_nhds, LinearMap.lTensor_smul_action, transpose_dualTensorHom, Submodule.IsLattice.smul, ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, Set.zero_mem_smul_iff, contDiff_iff_continuous_differentiable, Asymptotics.IsLittleOTVS.exists_eventuallyLE_mul_ennreal, Finsupp.instFaithfulSMulOfNonempty, hasDerivAt_const, dslope_sub_smul_of_ne, Finset.centerMass_smul_left, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Submodule.coe_tensorSpanEquivSpan_apply_tmul, Module.End.aeval_apply_of_hasEigenvector, CategoryTheory.Abelian.Ext.smul_comp, QuadraticMap.associated_tmul, fderiv_mul', Filter.EventuallyEq.ftaylorSeriesWithin, UniformSpace.Completion.norm_toComplL, Seminorm.uniformContinuous_of_continuousAt_zero, IsRegular.smul_right_injective, fderivWithin_const_smul_of_field, Bornology.IsVonNBounded.tendsto_smallSets_nhds, Matrix.toLin_self, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, ContinuousMap.toLp_def, OrderDual.instSMulPosReflectLE, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, instSMulDistribClassAlgEquiv, Complex.hasDerivAt_Gammaℂ_one, MulSemiringAction.smul_charpoly, VectorField.lieBracket_fmul_left, Module.Basis.SmithNormalForm.snf, Asymptotics.IsBigOTVS.snd, iteratedDerivWithin_fun_const_smul_field, LieDerivation.exp_apply, sup_eq_half_smul_add_add_abs_sub, RootPairing.pairing_neg_one_neg_four_iff, SchwartzMap.integral_bilin_fourier_eq, HasFDerivWithinAt.lim, KaehlerDifferential.ker_map, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, ConcaveOn.quasiconcaveOn, DifferentiableOn.clm_comp, ContDiffMapSupportedIn.monoCLM_apply, ftaylorSeriesWithin_zero, ContinuousMultilinearMap.prodL_apply, Seminorm.add_comp, Finset.smul_neg, segment_eq_image, HasStrictDerivAt.mul_const, Matrix.conjTranspose_inv_ofNat_smul, InnerProductSpace.HarmonicContOnCl.const_smul, set_smul_mem_nhds_zero_iff, affinity_unitBall, convex_eball, instPosSMulStrictMono, LinearMap.separatingLeft_toMatrix₂'_iff, hasFTaylorSeriesUpToOn_succ_iff_right, StrictConcaveOn.convex_gt, ContinuousOn.clm_bundle_apply₂, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, StrictConvex.add_left, Seminorm.bddAbove_iff, Convex.is_linear_preimage, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, LinearEquiv.map_smulₛₗ, IsGaloisGroup.faithful, ModuleFilterBasis.smul_left', SchwartzMap.compCLMOfAntilipschitz_apply, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, HasDerivWithinAt.fun_neg, LinearIsometryEquiv.conjStarAlgEquiv_refl, HasDerivAt.tendsto_slope_zero_left, InnerProductSpace.laplacian_smul, MeasureTheory.setToFun_smul_left, HasDerivAt.complexToReal_fderiv', IsBaseChange.lift_comp, LinearMap.separatingRight_iff_flip_ker_eq_bot, AddMonoid.End.smul_def, MvPolynomial.mkDerivationₗ_monomial, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, starConvex_iff_openSegment_subset, mem_segment_iff_sameRay, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, derivWithin_fun_const_smul, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', ContinuousAlternatingMap.map_update_smul, eventually_singleton_add_smul_subset, MeasureTheory.L1.setToL1_smul_left', Matrix.fin_two_smul_prod, TensorProduct.finsuppScalarRight_smul, Module.Ray.units_smul_of_pos, Antivary.sum_smul_lt_sum_comp_perm_smul_iff, mem_extremePoints_iff_forall_segment, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, Asymptotics.IsBigOTVS.fun_symm, Submodule.mem_singleton_set_smul, Orientation.map_eq_det_inv_smul, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, Seminorm.continuousAt_zero', ContinuousLinearMap.coe_restrict_scalarsL', fderivWithin_fderivWithin_eq_of_eventuallyEq, StandardSubspace.IsCyclic, IsSMulRegular.submodule, Real.fourierIntegral_real_eq_integral_exp_smul, Matrix.toLinearMapₛₗ₂'_toMatrix', ConvexCone.mem_map, CochainComplex.HomComplex.Cochain.leftUnshift_smul, InnerProductSpace.laplacianWithin_smul, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2, StrongDual.polarSubmodule_eq_polar, HasDerivWithinAt.Ici_of_Ioi, Algebra.IsInvariant.orbit_eq_primesOver, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, StrictConvex.affinity, algebraMap_smul, finsuppTensorFinsupp_single, Real.deriv_fourierIntegral, PiTensorProduct.liftEquiv_symm_apply, PiToModule.fromMatrix_apply_single_one, Algebra.Extension.CotangentSpace.map_sub_map, TestFunction.coe_ofSupportedInLM, HasStrictDerivAt.cexp, QuadraticMap.associated_toQuadraticMap, RingHom.applyFaithfulSMul, Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, extDerivWithin_fun_smul, inner_smul_real_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Asymptotics.isLittleOTVS_fun_neg_right, ftaylorSeries_fun_zero, SchauderBasis.proj_apply, TensorProduct.CompatibleSMul.smul_tmul, IsLocalizedModule.mem_ker_iff, ConvexCone.strictlyPositive_le_positive, ContDiffWithinAt.smul, HasDerivAt.add_const, CovariantDerivative.affine_combination_toFun, Asymptotics.IsLittleOTVS.triangle, Seminorm.closedBall_finset_sup, AddSubmonoid.smul_mem_pointwise_smul, Antivary.sum_smul_le_sum_smul_comp_perm, MeasureTheory.SignedMeasure.re_toComplexMeasure, TemperedDistribution.smulLeftCLM_sub, fromTangentSpace_mfderiv_smul', HasDerivAt.of_isLittleO, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, Module.reflection_mul_reflection_pow, ZMod.algebraOfModule.proof, Seminorm.uniformSpace_eq_of_hasBasis, eq_pos_convex_span_of_mem_convexHull, BilinearForm.toMatrixAux_eq, QuadraticMap.two_nsmul_associated, SchwartzMap.postcompCLM_postcompCLM, OreLocalization.oreDiv_add_oreDiv, TensorProduct.lid_tmul, PolynomialModule.isScalarTower', IsBoundedLinearMap.smul, DualNumber.exists_mul_left_or_mul_right, iteratedDerivWithin_scomp_eq_sum_orderedFinpartition, SModEq.smul', intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, fourierCoeff.const_smul, Matrix.SeparatingLeft.toBilin, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, BddBelow.smul_of_nonpos, monovary_iff_forall_smul_nonneg, Submodule.smul_le_smul, closure_openSegment, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', HasDerivAt.sub_const, LinearMap.toMatrixOrthonormal_symm_apply, biUnion_associatedPrimes_eq_zero_divisors, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, IsLocalizedModule.map_linearCombination, hasSum_cauchyPowerSeries_integral, Convex.combo_interior_self_subset_interior, ContinuousLinearMap.aestronglyMeasurable_comp₂, MeasureTheory.Lp.instFourierSMul, SchwartzMap.smulLeftCLM_const, MeasureTheory.integral_fintype, smul_top_inf_eq_smul_of_isSMulRegular_on_quot, LinearEquiv.piRing_symm_apply, MDifferentiableAt.smul_section, toModuleEnd_apply, ConvexCone.disjoint_hull_left_of_convex, Set.OrdConnected.convex, Asymptotics.IsBigOTVS.congr_left, Mathlib.Tactic.LinearCombination.smul_le_const, strictConvexSpace_iff, intervalIntegral.smul_integral_comp_sub_mul, QuadraticMap.associated_left_inverse', HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, Asymptotics.IsLittleOTVS.smul_left, Ideal.inertiaEquiv_apply_smul, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, LieModule.Cohomology.mem_twoCochain_iff, hasDerivAt_of_tendstoUniformlyOn, Asymptotics.isLittleO_const_smul_right, smul_right_injective, Asymptotics.IsBigOTVS.proj, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, StarConvex.linear_image, Orientation.inner_rotation_pi_div_two_left_smul, sameRay_smul_left_iff_of_ne, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, smul_sphere, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, strictConvex_Iio, MeasureTheory.Measure.toSignedMeasure_smul, star_inv_intCast_smul, HVertexOperator.compHahnSeries_smul, Matrix.nondegenerate_toBilin_iff, HasStrictDerivAt.scomp_of_eq, DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap, AffineSubspace.smul_top, HasStrictDerivAt.fun_finset_prod, ConvexCone.toPointedCone_top, fourierIntegral_eq_half_sub_half_period_translate, LinearMap.range_toContinuousLinearMap, Bornology.IsVonNBounded.of_sub_right, linearDepOn_iff, Ideal.exact_mulQuot_quotOfMul, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, fderiv_const_smul_of_invertible, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, Matrix.inner_toEuclideanCLM, Ideal.Cotangent.smul_eq_zero_of_mem, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, Subring.mem_smul_pointwise_iff_exists, hasFDerivWithinAt_pow', IsGaloisGroup.mulEquivAlgEquiv_apply_apply, hasStrictDerivAt_finCons', Submodule.mem_colon_iff_le, LinearMap.transvection.apply, AffineSubspace.smul_mem_smul_iff_of_isUnit, hasDerivWithinAt_taylorWithinEval_at_Icc, ContinuousLinearMap.isBoundedLinearMap_comp_right, Matrix.PosSemidef.toLinearMap₂'_zero_iff, LinearMap.BilinForm.toMatrix'_compLeft, Matrix.toLinearMapₛₗ₂_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, HasFPowerSeriesWithinAt.pi, Module.Basis.isUnitSMul_apply, NormedSpace.isVonNBounded_iff', VonNeumannAlgebra.mem_carrier, TestFunction.lineDerivCLM_add, hasStrictDerivAt_finCons, PiTensorProduct.liftEquiv_apply, intervalIntegral.integral_deriv_comp_smul_deriv, Asymptotics.IsLittleOTVS.trans_isBigOTVS, WeakDual.isBounded_iff_isVonNBounded, StarAlgEquiv.ofBijective_apply, HasDerivWithinAt.congr_of_eventuallyEq_of_mem, has_antideriv_at_fourier_neg, hasFTaylorSeriesUpTo_top_iff', MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, Set.neg_smul, groupHomology.isBoundary₂_of_mem_boundaries₂, fderivWithin_iteratedFDerivWithin, fromTangentSpace_mfderiv_smul_apply', Convex.isLittleO_alternate_sum_square, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, HahnModule.instIsScalarTowerHahnSeries_1, rescale_to_shell, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, Polynomial.smul_X, mem_openSegment_add_sub, ConvexOn.map_sum_le, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, Submodule.mem_span_set, GradedMonoid.smulCommClass_right, Subspace.flip_quotDualCoannihilatorToDual_bijective, PiTensorProduct.liftAux_tprodCoeff, closure_convexHull_extremePoints, ContinuousLinearMap.deriv_of_bilinear, balanced_neg, Orientation.areaForm'_apply, HasStrictDerivAt.comp_of_eq, segment_inter_eq_endpoint_of_linearIndependent_of_ne, openSegment_eq_image, ContinuousLinearMap.nnnorm_holder_apply_apply_le, LinearMap.toSpanSingleton_smul, TrivSqZeroExt.mul_inv_cancel, Submodule.set_smul_eq_map, Polynomial.coe_smul, AffineMap.isCentralScalar, Asymptotics.isTheta_const_smul_left, intervalIntegral.integral_smul_measure, upperBounds_smul_of_neg, signedDist_smul_of_pos, Distribution.mapCLM_apply, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange, HasDerivAtFilter.star, isSMulRegular_of_isSMulRegular_on_submodule_on_quotient, Matrix.Nondegenerate.toBilin, WeakDual.CharacterSpace.toAlgHom_apply, TensorProduct.finsuppScalarRight_apply_tmul_apply, LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, Derivation.coe_comp, DFinsupp.instPosSMulStrictMono, ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule, infEdist_smul₀, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, Unitization.inrRangeEquiv_apply_coe_snd, Bornology.isVonNBounded_iff_smul_tendsto_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, Monotone.convex_lt, Ideal.Quotient.stabilizerHom_apply, Module.Basis.repr_symm_single, RingEquiv.moduleEndSelf_apply, apply_eq_dotProduct_toMatrix₂_mulVec, Module.reflection_reflection_iterate, TrivSqZeroExt.inv_mul_cancel, Polynomial.smul_eq_map, Submodule.smul_toAddSubmonoid, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, Convex.smul, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, lp.instSMulCommClassSubtypePreLpMemAddSubgroup, Subsemiring.smul_mem_pointwise_smul_iff₀, LinearMap.BilinForm.separatingRight_toMatrix_iff, HasDerivAtFilter.scomp, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, AffineMap.lineMap_apply_module', LinearMap.flip_apply, TensorProduct.finsuppLeft_apply, Submodule.orthogonal_orthogonal_eq_closure, Pi.single_smul, LieRinehartRing.leibniz_smul_right', AnalyticOn.const_smul, StrictConvex.linear_preimage, LinearMap.BilinForm.SeparatingLeft.toMatrix', isSMulRegular_iff_torsionBy_eq_bot, AffineSubspace.convex, TensorProduct.mapBilinear_apply, Submodule.smul_starProjection_singleton, finsuppTensorFinsuppRid_symm_single_smul, ContinuousLinearMap.map_smulₛₗ, SMulCommClass.complexToReal, contMDiff_smul, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonpos, smul_add_one_sub_smul, PointedCone.convex, UniformFun.continuousSMul_induced_of_range_bounded, ConvexOn.neg, intervalIntegral.integral_hasStrictFDerivAt, with_gaugeSeminormFamily, CStarAlgebra.linear_combination_nonneg, fderivWithin_mul_const', Submodule.mem_span_finset', ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, NonUnitalStarSubalgebra.unitization_injective, intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right, HasDerivWithinAt.fun_smul, IsBilinearMap.toContinuousBilinearMap_apply, smul_left_injective, SkewMonoidAlgebra.domCongr_refl, right_mem_openSegment_iff, inv_natCast_smul_comm, NonUnitalSubalgebra.smul_mem', ZMod.invDFT_def', TestFunction.lineDerivOp_eq_lineDerivCLM, ConvexCone.blunt_strictlyPositive, Module.toCentroidHom_apply_toFun, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, NonUnitalStarSubalgebra.unitization_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, aestronglyMeasurable_smul_const_iff, absConvexHull_add_subset, MvPowerSeries.le_weightedOrder_smul, HasStrictDerivAt.fun_div, PartitionOfUnity.finsum_smul_mem_convex, CliffordAlgebra.foldr'_algebraMap, differentiableAt_complex_iff_differentiableAt_real, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, IsRegular.isSMulRegular, Convex.exists_forall_hasDerivWithinAt, intervalIntegral.inv_smul_integral_comp_sub_div, ConvexCone.IsGenerating.top_le_span, TensorProduct.AlgebraTensorModule.dualDistrib_apply, hasDerivWithinAt_taylor_coeff_within, UniformConvexOn.convexOn, Seminorm.iSup_apply, HasFPowerSeriesAt.hasStrictDerivAt, SchwartzMap.fourierMultiplierCLM_apply, AnalyticOn.smul, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable, DFinsupp.sigmaCurry_smul, ClosedSubmodule.mem_symplComp_iff, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, WithSeminorms.tendsto_nhds, hasFDerivAt_list_prod_finRange', ContDiff.smulRight, Fintype.linearIndependent_iff'ₛ, not_linearIndependent_iffₒₛ, ContinuousMultilinearMap.flipLinear_apply_apply, Asymptotics.IsBigOTVS.trans_isLittleOTVS, ConvexOn.translate_right, Representation.instIsScalarTowerMonoidAlgebraAsModule, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, Module.FinitePresentation.linearEquivMap_apply, ContinuousMap.coe_smul', CochainComplex.HomComplex.δ_smul, LinearMap.hasDerivWithinAt, WithSeminorms.isOpen_iff_mem_balls, CStarMatrix.toCLM_apply_single, hasSum_two_pi_I_cauchyPowerSeries_integral, Real.fourier_fderiv, convexHull_pair, Set.Subsingleton.strictConvex, rescale_to_shell_semi_normed, MvPolynomial.rTensorAlgHom_toLinearMap, FormalMultilinearSeries.comp_id, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousMap.nnnorm_smul_const, smul_eq_zero_iff_left, ContinuousMap.adjoin_id_eq_span_one_union, CategoryTheory.Linear.comp_units_smul, MeasureTheory.condExp_smul, AlgebraicGeometry.StructureSheaf.smul_const, TrivSqZeroExt.invOf_eq_inv, LinearMap.llcomp_apply', Seminorm.const_isBounded, hasFTaylorSeriesUpTo_succ_nat_iff_right, IsCovariantDerivativeOn.leibniz, Seminorm.preimage_metric_closedBall, tangentConeAt_of_mem_nhds, SchwartzMap.compSubConstCLM_zero, ContDiffMapSupportedIn.seminorm_top_le_iff, neg_concaveOn_iff, convexOn_of_convex_epigraph, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, NonUnitalSubalgebra.instSMulCommClass, Algebra.Extension.CotangentSpace.map_cotangentComplex, LocalizedModule.mk_cancel_common_right, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, RCLike.wInner_smul_right, Complex.restrictScalars_one_smulRight, QuotSMulTop.equivQuotTensor_naturality, LinearMap.smulRightₗ_apply, LinearMap.IsNonneg.smul, IsModuleTopology.isoₛₗ, ClosedSubmodule.iInf_orthogonal, Polynomial.smul_eval_smul, Asymptotics.isLittleOTVS_iff_smallSets, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, smul_add_smul_lt_smul_add_smul', MeasureTheory.smul_extend, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity', HahnEmbedding.Partial.eval_smul, HasDerivAt.clm_comp, MeasureTheory.Measure.Regular.domSMul, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, iteratedDerivWithin_scomp_three, ProperCone.dual_singleton, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, LinearPMap.coe_smul, StrongDual.extendRCLikeₗ_apply, LinearMap.mapMatrix_smul, HasFDerivWithinAt.smul_const, AntivaryOn.card_smul_sum_le_sum_smul_sum, Seminorm.sSup_empty, KaehlerDifferential.derivationQuotKerTotal_apply, AdicCompletion.transitionMap_comp_reduceModIdeal, MeasureTheory.integral_posConvolution, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, TensorProduct.AlgebraTensorModule.uncurry_apply, Algebra.Extension.tensorCotangentSpace_tmul, MeasureTheory.LocallyIntegrableOn.smul_continuousOn, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, IsOpen.smul_sphere, EuclideanGeometry.Sphere.secondInter_smul, Subring.smul_closure, monovary_iff_smul_rearrangement, Module.AEval.X_pow_smul_of, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, strongConcaveOn_iff_convex, iteratedFDeriv_eq_equiv_comp, Real.smul_iInf_of_nonpos, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, MeasureTheory.condExpIndL1_smul, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, Matrix.conjTranspose_ratCast_smul, Differentiable.continuousMultilinearMapCompContinuousLinearMap, Unitization.norm_eq_sup, MonovaryOn.sum_smul_sum_le_card_smul_sum, LinearEquiv.toSpanNonzeroSingleton_apply, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Submodule.mem_span_insert', Matrix.ofLp_toEuclideanCLM, Ideal.coe_restrictScalars, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Fourier.fourierIntegral_const_smul, TrivSqZeroExt.inl_mul, HasDerivWithinAt.comp_hasDerivAt_of_eq, QuadraticMap.smul_apply, hasDerivAtFilter_iff_isLittleO, Absorbent.eventually_nhdsNE_zero, HasDerivAt.fun_const_smul, HasDerivAt.fun_sub, CStarMatrix.toCLM_apply_eq_sum, Set.Subsingleton.convex, Submodule.span_algebraMap_image_of_tower, HasStrictFDerivAt.restrictScalars, LinearMap.exact_smul_id_smul_top_mkQ, MeasureTheory.Measure.ae_smul_measure_iff, StarAlgEquiv.coe_ofBijective, balancedHull_add_subset, Projectivization.mk_eq_mk_iff, StarConvex.preimage_smul, MeasureTheory.Measure.instSMulCommClassDomMulActNNReal, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ConvexOn.quasiconvexOn, strictConvex_Ici, hasDerivAt_exp_smul_const, AddMonoidAlgebra.instIsPushout, HasDerivAtFilter.add_const, Meromorphic.fun_smul, HasSum.smul, Asymptotics.isBigOTVS_neg_left, MeasureTheory.Measure.NullMeasurableSet.const_smul, Balanced.closure, MeasureTheory.eLpNormEssSup_smul_measure, affineIndependent_smul, ContDiffMapSupportedIn.locallyConvexSpace, hasFDerivWithinAt_comp_smul_smul_iff, fourierCoeff_toLp, IsLocalizedModule.mk'_cancel', ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Algebra.Generators.H1Cotangent.δAux_ofComp, Algebra.Extension.CotangentSpace.map_tmul_eq_tmul_map, ContinuousMultilinearMap.smul_prod_smul, CategoryTheory.Functor.mapExactFunctor_smul, smul_unitBall_of_pos, smul_lt_smul_iff_of_neg_left, HasStrictDerivAt.congr_deriv, ProbabilityTheory.hasDerivAt_complexMGF, TensorProduct.AlgebraTensorModule.homTensorHomMap_apply, AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff, map_real_smul, RootPairing.reflectionPerm_root, DifferentiableWithinAt.isBigOTVS_sub, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, LinearOrder.concaveOn_of_lt, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', LinearIsometryEquiv.toSpanUnitSingleton_apply, Asymptotics.IsBigOWith.smul, Asymptotics.IsLittleOTVS.congr', IsScalarTower.rat, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', Convex.translate, LinearEquiv.apply_smulCommClass, StrictConvexOn.map_sum_lt, map_inv_natCast_smul, iteratedDeriv_comp_const_smul, norm_inner_eq_norm_tfae, Real.circleAverage_def, Submodule.map₂_span_singleton_eq_map_flip, LinearPMap.mkSpanSingleton'_apply, CategoryTheory.ShortComplex.smul_τ₃, LinearMap.pi_apply_eq_sum_univ, DilationEquiv.smulTorsor_apply, FormalMultilinearSeries.changeOrigin_eval_of_finite, Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite, Module.sum_smul_eq_zero_of_isTrivialRelation, intervalIntegral.integral_smul, ZMod.dft_apply, Seminorm.map_eq_zero_of_norm_eq_zero, Algebra.TensorProduct.distribBaseChange_comp_includeLeftSubRight, sigmaFinsuppEquivDFinsupp_smul, Rep.ofDistribMulAction_ρ_apply_apply, Quaternion.fst_imJ_dualNumberEquiv_symm, exists_nonneg_right_iff_sameRay, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, iteratedFDerivWithin_two_apply', HasDerivAt.const_smul, LinearMap.mul_toMatrix', UniqueDiffWithinAt.smul_iff, Convex.add_smul_mem, Balanced.interior, deriv.scomp, balancedCoreAux_balanced, HasStrictDerivAt.add, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, StarConvex.add_left, ContinuousMultilinearMap.instContinuousConstSMul, concaveOn_univ_piecewise_Ici_of_antitoneOn_Ici_monotoneOn_Iic, hasDerivAt_taylorWithinEval_succ, Convex.closure, Bornology.IsBounded.smul₀, MemHolder.smul, HVertexOperator.of_coeff_coeff, Module.Basis.mem_submodule_iff', skewAdjoint.negISMul_apply_coe, Submodule.smithNormalFormBotBasis_def, insert_endpoints_openSegment, PMF.integral_eq_tsum, not_linearIndependent_iffₛ, DiffContOnCl.circleAverage_smul_div, groupHomology.isCycle₁_of_mem_cycles₁, IsLocalFrameOn.eventually_eq_sum_coeff_smul, LinearMap.toMatrix_smulBasis_right, AddMonoidAlgebra.instIsPushout', lp.infty_smulCommClass, Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, intervalIntegral.integral_comp_div, Submodule.instCovariantClassHSMulLe, TensorProduct.lid'_apply_tmul, HasSum.exists_hasSum_smul_of_apply_eq_zero, KaehlerDifferential.instSMulCommClassTensorProduct_1, Algebra.Extension.Cotangent.val_smul', Finsupp.weight_single_index, DiscreteConvolution.ConvolutionExistsAt.smul_convolution, TensorProduct.map_smul_right, HVertexOperator.coeff_inj_iff, HasFPowerSeriesAt.fderiv_eq, CategoryTheory.endomorphism_simple_eq_smul_id, Orientation.oangle_sign_smul_left, Finset.sum_Ico_by_parts, HasDerivAtFilter.scomp_of_eq, ContinuousLinearMap.coe_restrictScalarsIsometry, MeasureTheory.Integrable.bdd_smul, Finsupp.linearCombination_apply, rank_eq_one_iff, Representation.IntertwiningMap.toLinearMap_smul, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, Submodule.mem_set_smul_of_mem_mem, MatrixModCat.mem_toModuleCatObj, HasDerivAt.scomp_hasDerivWithinAt_of_eq, GradedAlgHom.restrictScalars_coe_linearMap, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, ConvexBody.isBounded, VectorField.mlieBracketWithin_smul_left, Convex.combo_self, Unitization.inrRangeEquiv_apply_coe_fst, CStarMatrix.reindexₐ_apply, WeakBilin.instContinuousSMul, ContinuousLinearMap.isometry_iff_adjoint_comp_self, continuousMultilinearCurryFin0_apply, smul_le_smul_iff_of_neg_left, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, IsUnit.smul_eq_zero, LocalizedModule.smul'_mk, PiTensorProduct.dualSeminorms_bounded, FormalMultilinearSeries.radius_neg, Module.Flat.isSMulRegular_of_isRegular, HasFDerivWithinAt.mul_const', InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, extDeriv_smul, LinearMap.mul_toMatrix₂, homeomorphUnitSphereProd_symm_apply_coe, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, Module.algebraMap_end_eq_smul_id, Algebra.Extension.Cotangent.map_comp, HasDerivAt.comp_const_sub, taylorWithinEval_succ, convex_Ioo, Submodule.mulRightMap_eq_mulMap_comp, HasDerivAt.norm_sq, StarConvex.smul, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, HasDerivWithinAt.add, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, StrictConvexSpace.strictConvex_closedBall, Real.fourier_eq, Algebra.trace_comp_trace_of_basis, AffineMap.lineMap_vadd_apply, Mathlib.Tactic.LinearCombination.smul_lt_const_weak, differentialIdeal_le_fractionalIdeal_iff, Submodule.span_set_smul, HasStrictFDerivAt.continuousMultilinear_apply_const, LinearMap.lsmul_eq_DistribMulAction_toLinearMap, Asymptotics.IsLittleOTVS.sup, AddMonoid.End.isCentralScalar, ContDiffMapSupportedIn.monoLM_eq_zero, SMulPosReflectLT.toSMulPosReflectLE, sameRay_neg_smul_left_iff_of_ne, Set.OrdConnected.convex_of_chain, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, MultilinearMap.freeFinsuppEquiv_def, ConvexOn.convex_lt, Prod.openSegment_subset, WeakBilin.instIsScalarTower, Orientation.oangle_sign_smul_add_smul_smul_add_smul, DoubleCentralizer.algebraMap_snd, Finset.expect_dite_eq', Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, Convex.add, Polynomial.aeval_smul, MeasureTheory.Measure.integral_comp_mul_left, lp.instStarModuleSubtypePreLpMemAddSubgroup, AnalyticAt.analyticOrderNatAt_eq_iff, groupHomology.isBoundary₀_of_mem_coinvariantsKer, MeasureTheory.integrable_smul_const, SchauderBasis.RankOneDecomposition.basisCoeff_spec, hasFiniteFPowerSeriesOnBall_const, Module.End.smulLeft_apply, HahnModule.SMulCommClass, ZMod.invDFT_apply', iteratedFDerivWithin_succ_apply_left, HasFDerivAtFilter.fun_const_smul, Submodule.starProjection_unit_singleton, Matrix.dualNumberEquiv_symm_apply, Finset.weightedVSub_const_smul, SchwartzMap.fourier_evalCLM_eq, IsBaseChange.end, ContinuousWithinAt.integral_sub_linear_isLittleO_ae, convex_convexHull, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, DualNumber.exp_eps, Submodule.mul_smul_mul_eq_smul_mul_smul, Asymptotics.IsBigOTVS.prodMk, KaehlerDifferential.tensorKaehlerEquiv_left_inv, DifferentiableAt.fun_const_smul, AdicCompletion.pow_smul_top_eq_ker_eval, hasDerivWithinAt_natCast, IsTopologicalSemiring.toOppositeIsModuleTopology, CliffordAlgebra.foldl_algebraMap, Orientation.oangle_sign_smul_sub_left, RatFunc.div_smul, fderiv_pow_ring', LinearMap.toSpanSingleton_apply, MeasureTheory.memL1_smul_of_L1_withDensity, ContinuousLinearMap.bilinearComp_apply, analyticAt_iff_analytic_fun_smul, Module.End.restrict_eigenspace, imaginaryPart_eq_neg_I_smul_skewAdjointPart, AddSubmonoid.mem_inv_pointwise_smul_iff₀, midpoint_vsub_left, MeasureTheory.Measure.toSphere_apply', DiscreteConvolution.ConvolutionExistsAt.convolution_smul, TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, RatFunc.minpolyX_aeval_X, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOn, LinearMap.BilinForm.congr_refl, Submodule.range_lsum_smul, LieAlgebra.smulCommClass, SchwartzMap.evalCLM_apply_apply, Matrix.Module.instIsScalarTowerForall, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, Polynomial.smeval_C_mul, Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule, LinearMap.SeparatingRight.toMatrix₂, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, DiffContOnCl.smul_const, RootPairing.InvariantForm.apply_weylGroup_smul, Convex.linear_image, ContMDiffWithinAt.clm_bundle_apply₂, MeasureTheory.condExpIndL1_smul', Submodule.singleton_smul, LinearMap.conjugate_apply, TopologicalGroup.IsSES.integrate_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, HasDerivAt.fun_div, Submodule.toConvexCone_le_toConvexCone, tsum_const_smul'', vadd_segment, Matrix.Module.scalar_smul, mem_parallelepiped_iff, Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy, contDiff_smul_const, MeasureTheory.integral_biUnion_eq_sum_powerset, HasFTaylorSeriesUpToOn.fderivWithin, Prod.image_mk_openSegment_right, CStarMatrix.toCLM_apply, KaehlerDifferential.kerTotal_map, AddSubmonoid.smul_closure, Module.End.mem_genEigenspace_top, LieModule.lie_smul, DoubleCentralizer.algebraMap_toProd, continuousMultilinearCurryFin0_symm_apply_apply, HasDerivWithinAt.fun_const_smul, ConcaveOn.le_map_sum, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ContinuousLinearMap.ker_self_comp_adjoint, Quaternion.fst_imI_dualNumberEquiv_symm, LinearMap.BilinForm.toMatrix_symm, differentiableAt_norm_smul, exists_nontrivial_relation_sum_zero_of_not_affine_ind, FormalMultilinearSeries.id_comp, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, LinearMap.BilinMap.toQuadraticMap_smul, invOf_two_smul_add_invOf_two_smul, Real.circleAverage_eq_integral_add, Matrix.toLinearMap₂'_toMatrix', isSMulRegular_algebraMap_iff, HasFPowerSeriesAt.restrictScalars, hasDerivAt_integral_of_dominated_loc_of_deriv_le, intervalIntegral.inv_smul_integral_comp_div_sub, ConcaveOn.convex_hypograph, rank_dual_eq_card_dual_of_aleph0_le_rank', ContinuousLinearMap.instStarModuleId, ContDiff.smul_const, RCLike.wInner_smul_left, Matrix.toLinearMapₛₗ₂'_apply, edist_smul₀, Absorbs.sub, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right, Seminorm.convex_ball, VectorField.mlieBracketWithin_smul_right, Convex.combo_closure_interior_subset_interior, CategoryTheory.ShiftedHom.comp_smul, PolynomialModule.eval_lsingle, MultilinearMap.map_nonempty, DoubleCentralizer.instIsCentralScalar, Subsemiring.mem_inv_pointwise_smul_iff₀, groupHomology.single_isCycle₁_iff, HasDerivWithinAt.const_mul, Module.End.genEigenspace_one, ContinuousLinearMapWOT.instContinuousSMul, HasFDerivAt.continuousAlternatingMap_apply_const, CochainComplex.HomComplex.Cochain.smul_comp, Submodule.span_eq_closure, AddSubgroup.mem_smul_pointwise_iff_exists, Finset.smul_finset_neg, PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, PartitionOfUnity.sum_finsupport_smul_eq_finsum, LieModule.Cohomology.mem_twoCocycle_iff, norm_fderiv_iteratedFDeriv, IsCompact.extremePoints_nonempty, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1, TestFunction.lineDerivCLM_eq_fderivCLM, TopologicalAddGroup.IsSES.integrate_mono, HasDerivWithinAt.div, LinearMap.BilinForm.SeparatingLeft.toMatrix, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, Bornology.IsVonNBounded.sub, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, Path.range_segment, instIsStrictOrderedModuleOfIsCancelAdd, segment_subset_Icc, TensorProduct.AlgebraTensorModule.mapBilinear_apply, LinearMap.BilinMap.toQuadraticMapLinearMap_apply, convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic, TemperedDistribution.fourier_lineDerivOp_eq, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, groupHomology.inhomogeneousChains.d_single, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', Matrix.l2_opNNNorm_def, ContinuousLinearEquiv.strictConvex_image, ContinuousMultilinearMap.instIsBoundedSMul, hasDerivAtFilter_sub_const_iff, SmoothPartitionOfUnity.finsum_smul_mem_convex, spectrum.hasDerivAt_resolvent, Module.Basis.sum_toMatrix_smul_self, AdicCompletion.val_apply_mem_smul_top_iff, ContinuousLinearMap.adjointAux_adjointAux, apply_eq_star_dotProduct_toMatrix₂_mulVec, MvPolynomial.mkDerivation_monomial, smul_nonpos_iff_neg_imp_nonneg, Finsupp.linearCombination_single, HasStrictDerivAt.const_add, realPart_I_smul, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, Submodule.exists_smul_notMem_of_rank_lt, Convex.add_smul, LinearMap.toMatrix₂_compl₁₂, LinearMap.BilinForm.IsSymm.smul, Ideal.coe_smul_primesOver_mk, linearIndependent_smul, Seminorm.exists_apply_eq_finset_sup, PolynomialModule.smul_apply, ContMDiffAt.clm_precomp, NonUnitalAlgHom.coe_mulHom_mk, gauge_def, Complex.hasDerivAt_logTaylor, TestFunction.lineDerivCLM_apply, Multiset.sum_smul, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem, Mathlib.Tactic.Module.NF.zero_sub_eq_eval, deriv_smul, Prod.image_mk_segment_right, VectorField.mpullbackWithin_smul_apply, PositiveLinearMap.gnsStarAlgHom_apply, BilinForm.toMatrix_compRight, Real.fourier_iteratedDeriv, MeasureTheory.Integrable.smul_of_top_left, LinearMap.BilinForm.nondegenerate_toMatrix'_iff, MeasureTheory.integral_comp_rpow_Ioi, Asymptotics.IsBigOTVS.symm, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, Polynomial.wronskianBilin_apply, convex_closedEBall, hasDerivAt_iff_tendsto_slope_zero, LinearMap.toMatrix₂_toLinearMap₂, StrictConvex.affine_preimage, ConvexOn.convex_re_epigraph, IsExposed.convex, LinearMap.norm_extendTo𝕜'_apply_sq, Asymptotics.isLittleOTVS_iff_isLittleO, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, AffineSubspace.wSameSide_smul_vsub_vadd_left, TrivSqZeroExt.inv_inv, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, HasFTaylorSeriesUpToOn.hasFDerivAt, WeakFEPair.hf_zero, convex_ball, prodXSubSMul.coeff, real_inner_smul_right, LinearMap.BilinForm.congr_congr, groupHomology.isBoundary₂_iff, scalarSMulCLE_apply, ContinuousLinearMap.flip_add, QuadraticMap.polar_smul_left, exists_pos_left_iff_sameRay, hasFiniteFPowerSeriesAt_const, MeasureTheory.Integrable.toL1_smul', Seminorm.uniformContinuous, infDist_smul₀, Submodule.smul_mem_iff_of_isUnit, ContinuousAlternatingMap.hasBasis_nhds_zero, Orientation.oangle_sub_right_smul_rotation_pi_div_two, MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport, Bornology.isBounded_iff_isVonNBounded, Antivary.sum_smul_lt_sum_smul_comp_perm_iff, Convex.min_le_combo, monovaryOn_iff_smul_rearrangement, VectorFourier.fourierSMulRight_apply, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, ConcaveOn.translate_right, Derivation.leibniz, ContinuousLinearMap.isSelfAdjoint_iff', HasFDerivWithinAt.restrictScalars, LinearIsometry.map_smulₛₗ, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, OrthonormalBasis.equiv_apply_euclideanSpace, RootPairing.PolarizationIn_apply, LinearMap.BilinForm.toMatrixAux_apply, Convex.interior, StrongConcaveOn.strictConcaveOn, CochainComplex.HomComplex.Cochain.rightShift_smul, RatFunc.instIsScalarTowerPolynomial, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, LinearMap.liftQ₂_mk, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Seminorm.coe_sSup_eq', ContinuousMultilinearMap.uncurryRight_apply, HasDerivAt.comp_const_add, ContinuousLinearMap.isVonNBounded_iff, SchwartzMap.fourierMultiplierCLM_ofReal, InnerProductSpace.Core.inner_smul_ofReal_left, Real.isScalarTower, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, differentiableWithinAt_iff_restrictScalars, IsModuleTopology.iso, NormedSpace.normalize_smul_of_neg, TrivSqZeroExt.exp_def, derivWithin_comp_mul_left, Seminorm.coe_bot, hasDerivAt_circleMap, Submodule.smul_top_eq_range_lsum, vectorSpan_segment, ProperCone.smul_mem, derivWithin_fun_smul, ContinuousLinearMap.bilinearComp_zero, MeasureTheory.integral_fun_norm_addHaar, LinearMap.toMatrix₂Aux_eq, HasFDerivAt.fun_pow', LocalizedModule.subsingleton_iff, Convex.mem_toCone, MeasureTheory.setIntegral_ge_of_const_le, HasDerivWithinAt.scomp_hasDerivAt_of_eq, imaginaryPart_apply_coe, ContinuousLinearMap.isVonNBounded_image2_apply, segment_same, MulSemiringActionHom.map_one', Module.End.natCast_def, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, pinGroup.conjAct_smul_range_ι, LinearMap.lsmul_apply, HasMFDerivWithinAt.mul', intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, segment_subset_closedBall_left, UnitAddTorus.hasSum_mFourier_series_L2, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, Submodule.smul_closure_subset, HasFTaylorSeriesUpToOn.shift_of_succ, CentroidHom.instSMulCommClass_1, isAdjointPair_toLinearMap₂', ConvexCone.mem_add, SemimoduleCat.Algebra.instSMulCommClassCarrier, QuotSMulTop.map_exact, Representation.asModuleEquiv_symm_map_rho, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, LinearMap.toMatrix₂_symm, Module.End.commute_exp_left_of_commute, HasDerivWithinAt.neg, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, ContinuousLinearMap.norm_extendTo𝕜'_bound, sum_mem_ball_of_strictConvexSpace, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, le_egauge_smul_right, ContinuousMultilinearMap.integral_apply, NonUnitalSubalgebra.unitization_apply, SeminormFamily.basisSets_smul, DualNumber.lift_apply_apply, HasStrictDerivAt.smul_const, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LocalizedModule.smul_def, LinearMap.SeparatingLeft.toMatrix₂, Submodule.span_eq_iUnion_nat, HasStrictDerivAt.sub, groupHomology.single_isCycle₂_iff, LinearMap.toMatrix'_toLinearMap₂', SameRay.sameRay_nonneg_smul_right, HasFiniteFPowerSeriesOnBall.neg, ModuleTopology.eq_coinduced_of_surjectiveₛₗ, CentroidHom.instIsScalarTower_1, Basis.multilinearMap_apply_apply, HasDerivWithinAt.Ioo_of_Ioi, LinearMap.BilinForm.toLin'Flip_apply, Finset.weightedVSubOfPoint_smul, MeasureTheory.average_union_mem_segment, lineDifferentiableWithinAt_smul_iff, Fintype.expect_ite_mem, BilinForm.toMatrix_mul_basis_toMatrix, LinearMap.convexOn, DifferentiableWithinAt.smul_const, SMulCommClass.rat', MultilinearMap.dfinsuppFamilyₗ_apply, Submodule.le_span_singleton_iff, hasDerivAt_fourier, HahnSeries.SummableFamily.coeff_smul, Asymptotics.IsBigOTVS.congr_right, ContinuousLinearEquiv.smulLeft_apply_apply, DiffContOnCl.circleAverage_poissonKernel_smul, QuadraticMap.half_moduleEnd_apply_eq_half_smul, smul_lie, Seminorm.neg_closedBall, LinearMap.BilinForm.mul_toMatrix', EuclideanGeometry.Sphere.direction_orthRadius_le_iff, AffineMap.lineMap_apply, Finsupp.linearCombination_unique, toLinearEquiv_apply, TrivSqZeroExt.inr_mul_inl, smul_eq_zero_iff_right, AntivaryOn.sum_smul_comp_perm_eq_sum_smul_iff, StrongDual.extendRCLikeₗᵢ_symm_apply, Asymptotics.IsThetaTVS.isBigOTVS, MultilinearMap.map_update_smul', Real.fourier_bilin_convolution_eq, BoxIntegral.BoxAdditiveMap.toSMul_apply, RatFunc.irreducible_minpolyX, IsLocalizedModule.mk'_cancel_right, AntitoneOn.quasiconcaveOn, segment_eq_image', CStarMatrix.mul_entry_mul_eq_inner_toCLM, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Module.supportDim_quotSMulTop_succ_eq_supportDim, ConvexOn.smul_concaveOn, Matrix.toLinearMap₂_symm, homeomorphSphereProd_symm_apply_coe, Subring.smul_mem_pointwise_smul_iff₀, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Submodule.convex, ExteriorAlgebra.toTrivSqZeroExt_ι, FormalMultilinearSeries.le_comp_radius_of_summable, ContinuousLinearMap.le_opNorm₂, ContinuousLinearMap.lpPairing_eq_integral, TrivSqZeroExt.snd_invOf, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, slope_fun_def, Seminorm.continuous_iff, HasFDerivAt.smul_const, MeasureTheory.integrable_tilted_iff, Submodule.mem_smul_pointwise_iff_exists, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀, ContinuousLinearMap.norm_uncurryMid, Submodule.torsionBy.mk_ideal_smul, TopologicalGroup.IsSES.pushforward_apply_apply, isIntegralCurveOn_comp_mul_ne_zero, Submodule.mem_span_iff_of_fintype, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, ContinuousLinearMap.uncurryLeft_norm, DualNumber.ringHom_ext_iff, star_inv_natCast_smul, TestFunction.instLineDerivLeftSMulRealTopENat, mellin_eq_fourierIntegral, mem_vectorSpan_pair_rev, PiTensorProduct.smul_tprodCoeff_aux, hasStrictDerivAt_abs_neg, HasFDerivAt.comp_hasDerivWithinAt, ContinuousLinearMap.holder_smul_right, WithSeminorms.continuous_seminorm, HasFPowerSeriesOnBall.tendstoUniformlyOn', extremePoints_closedBall_subset_sphere, HasFPowerSeriesWithinOnBall.const_smul, HVertexOperator.coeff_inj, PolynomialModule.smul_single_apply, TensorProduct.rid_tmul, Submodule.coe_torsionBySet, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, Asymptotics.IsLittleOTVS.comp_tendsto, TrivSqZeroExt.inl_mul_inl, Subalgebra.smul_mem_pointwise_smul, Mathlib.Tactic.Module.NF.neg_eq_eval, Representation.TensorProduct.rid_apply, SchwartzMap.fourierMultiplierCLM_const, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, fderivWithin_const_smul_of_invertible, Real.fourierIntegral_eq', Real.circleAverage_fun_smul, RootPairing.coroot_root_two, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, TestFunction.monoCLM_eq_of_scalars, Ideal.inertiaEquiv_symm_apply_smul, UniformConvergenceCLM.isVonNBounded_image2_apply, CategoryTheory.ShortComplex.cyclesMap'_smul, PiTensorProduct.piTensorHomMapFun₂_smul, LieModule.Cohomology.add_apply_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', intervalIntegral.integral_comp_smul_deriv', Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Complex.hasSum_taylorSeries_on_emetric_ball, LinearEquiv.smulOfNeZero_apply, HasStrictDerivAt.of_notMem_tsupport, fderiv_continuousMultilinear_apply_const_apply, MeasureTheory.integrable_withDensity_iff_integrable_smul, Asymptotics.IsLittleOTVS.congr, MeasureTheory.Integrable.convolution_integrand, LieModule.exists_forall_lie_eq_smul, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Projectivization.exists_smul_eq_mk_rep, Module.reflection_mul_reflection_pow_apply_self, LinearMap.toMatrixOrthonormal_apply, DivisibleHull.qsmul_def, hasFPowerSeriesOn_cauchy_integral, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, MvPolynomial.coeff_rTensorAlgHom_tmul, antitone_smul_left, LinearEquiv.fixedReduce_eq_smul_iff, concaveOn_of_convex_hypograph, StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, EuclideanGeometry.inversion_def, LinearMap.IsPositive.smul_of_nonneg, NormedSpace.vonNBornology_eq, KaehlerDifferential.isBaseChange, Function.Periodic.const_smul₀, ConvexBody.smul_le_of_le, ConvexOn.lt_right_of_left_lt', SchwartzMap.integral_bilinear_laplacian_right_eq_left, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, KaehlerDifferential.instSMulCommClassTensorProduct, iteratedDeriv_fun_const_smul_field, HasFDerivAt.lim, RatFunc.Luroth.algEquiv_X, Seminorm.comp_apply, hasDerivWithinAt_const, openSegment_eq_image_lineMap, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', intervalIntegral.integral_comp_sub_mul, multiple_mem_span_of_mem_localization_span, OrthonormalBasis.sum_repr_symm, homeomorphUnitSphereProd_apply_fst_coe, CFC.posPart_smul_of_nonneg, MultilinearMap.cons_smul, Pi.single_smul₀, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, DifferentiableWithinAt.restrictScalars_fderivWithin, Module.End.eigenspace_def, isCompact_closedAbsConvexHull_of_totallyBounded, HasStrictFDerivAt.continuousAlternatingMap_apply, Orthonormal.inner_left_sum, NonUnitalSubalgebra.instSMulMemClass, Orientation.inner_smul_rotation_pi_div_two_right, UniformConcaveOn.concaveOn, DiscreteConvolution.AddConvolutionExistsAt.convolution_vadd, StrongDual.extendRCLikeₗ_symm_apply, HasDerivAtFilter.congr_of_eventuallyEq, HasStrictDerivAt.complexToReal_fderiv', Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric, constFormalMultilinearSeries_apply_of_nonzero, RootPairing.CoPolarization_apply, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', Matrix.linftyOpNormSMulClass, finsuppTensorFinsuppRid_single_tmul_single, Real.circleAverage_smul, LieModule.shiftedGenWeightSpace.coe_lie_shiftedGenWeightSpace_apply, star_qsmul, Subalgebra.inclusion.isScalarTower_right, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, WithLp.normSMulClassSeminormedAddCommGroupToProd, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, VectorField.lieBracket_const_smul_right, Module.preReflection_apply, Asymptotics.isBigOTVS_pi, DFinsupp.instPosSMulReflectLE, Derivation.smul_apply, PiLp.smul_apply, TrivSqZeroExt.hasSum_expSeries_of_smul_comm, DifferentiableWithinAt.clm_comp, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, MDifferentiableOn.cle_arrowCongr, PiLp.normSMulClassSeminormedAddCommGroupToPi, MeasureTheory.uniformIntegrable_average, LinearIsometryEquiv.strictConvex_image, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', CochainComplex.HomComplex.Cochain.shift_units_smul, AffineMap.homothety_linear, Algebra.Extension.contangentEquiv_tmul, Unitization.norm_def, convex_uIcc, ContMDiff.clm_bundle_apply₂, RatFunc.natDegree_minpolyX, ModuleTopology.eq_coinduced_of_surjective, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, Ideal.quotOfMul_surjective, Real.iteratedDeriv_fourier, map_natCast_smul, SchwartzMap.eLpNorm_le_seminorm, MDifferentiableAt.smul, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, HasStrictDerivAt.const_smul, StrictConvex.add, HasDerivAt.fun_sum, hasFDerivAtFilter_iff_isLittleOTVS, MeasureTheory.setIntegral_rnDeriv_smul', FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, TensorProduct.finsuppScalarLeft_apply_tmul_apply, TrivSqZeroExt.snd_pow_of_smul_comm, second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonneg, ContinuousMultilinearMap.curryRight_apply, CategoryTheory.Abelian.Ext.comp_smul, Ideal.pointwise_smul_eq_comap, Distribution.dsupport_smulLeftCLM_subset, ArithmeticFunction.mul_smul', DFinsupp.instPosSMulMono, Balanced.absorbs_self, CategoryTheory.Linear.comp_smul, star_nnqsmul, Module.End.mem_iInf_maxGenEigenspace_iff, HasFPowerSeriesOnBall.uniform_geometric_approx', image_segment, intervalIntegral.smul_integral_comp_mul_left, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul, Function.support_const_smul_of_ne_zero, ContinuousLinearMap.extendTo𝕜_apply, Submodule.starConvex, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, PowerSeries.coeff_smul, Module.AEval.of_symm_X_smul, MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct, HasFDerivAt.comp_hasDerivWithinAt_of_eq, Convex.gauge_le, convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Ici, Derivation.leibniz_of_mul_eq_one, uniformConcaveOn_zero, AffineSubspace.mem_affineSpan_insert_iff, ConvexCone.pointed_zero, LieModule.traceForm_eq_sum_finrank_nsmul, LieAlgebra.Basis.baseSupp_apply_smul_e, Matrix.toBilin'_apply, Seminorm.closedBall_eq_emptyset, Convex.strictConvex', egauge_le_of_smul_mem, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, LinearMap.det_restrictScalars, hasStrictFDerivAt_pow', convex_Icc, IsBoundedSMul.of_enorm_smul_le, ContinuousLinearMap.applySMulCommClass, strictConvex_Ioc, LinearMap.flip_injective_iff₂, RestrictScalars.ringEquiv_map_smul, AddSubmonoid.smul_mem_pointwise_smul_iff₀, ContinuousLinearMap.norm_extendTo𝕜', InnerProductGeometry.angle_smul_smul, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, RestrictScalars.lsmul_apply_apply, IsIntegralClosure.range_le_span_dualBasis, Matrix.toLin_apply, IsStarProjection.inr, Asymptotics.IsLittleOTVS.fun_symm, HasDerivAtFilter.const_add, HasDerivWithinAt.of_notMem_tsupport, StrictConvex.preimage_smul, not_linearIndependent_iff_finsupp, MDifferentiableAt.clm_precomp, ModelWithCorners.convex_range, ContDiffMapSupportedIn.postcompCLM_apply, SchwartzMap.compSubConstCLM_comp, HasDerivWithinAt.mono_of_mem_nhdsWithin, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, ContinuousAlternatingMap.curryLeft_zero, RootPairing.reflection_dualMap_eq_coreflection, Matrix.Module.smul_apply, DualNumber.coe_lift_symm_apply, ContDiffBump.integral_normed_smul, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, Orientation.oangle_sign_smul_right, Module.Basis.constr_apply_fintype, fwdDiff_smul, Asymptotics.IsTheta.isThetaTVS, LieSubmodule.Quotient.isCentralScalar, AddMonoidAlgebra.liftMagma_apply_apply, TensorProduct.LieModule.lift_apply, ContinuousAlternatingMap.cons_smul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, inhomogeneousCochains.d_hom_apply, ZMod.dft_dft, SmoothBumpFunction.contMDiff_smul, Quaternion.imJ_snd_dualNumberEquiv, HasDerivWithinAt.Ioi_of_Ioo, HasDerivWithinAt.fun_mul, DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap, AbsConvex.closure, Filter.Tendsto.zero_smul_isBoundedUnder_le, fderiv_fun_mul', TrivSqZeroExt.liftEquivOfComm_apply, Finset.centerMass_segment', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFDerivAt.const_smul, AdicCompletion.pow_smul_top_le_ker_eval, NormedSpace.expSeries_sum_eq_rat, Submodule.top_le_span_range_iff_forall_exists_fun, HasFPowerSeriesWithinAt.prod, HasDerivWithinAt.pow', LinearPMap.map_smul, ContMDiffMap.coe_smul, Set.neg_smul_set, LinearMap.concaveOn, MulSemiringActionHom.map_mul', Derivation.instIsCentralScalar, IsLocalizedModule.exists_integer_multiple, ContinuousLinearMap.adjoint_comp_self_injective_iff, Convex.is_linear_image, FormalMultilinearSeries.leftInv_coeff_one, LinearMap.IsSymmetric.smul, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul', Module.Basis.smul_eq_map, MultilinearMap.smulRight_apply, Submodule.singleton_set_smul, PosSMulReflectLT.toPosSMulReflectLE, SkewMonoidAlgebra.support_mul_single_subset, sameRay_iff_inv_norm_smul_eq, mdifferentiableOn_continuousLinearMapCoordChange, instIsPushoutPolynomial, hasDerivAtFilter_intCast, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, MonoidAlgebra.instIsPushout', Asymptotics.IsThetaTVS.symm, Polynomial.aeval_apply_smul_mem_of_le_comap', BoxIntegral.integral_smul, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH, Submodule.exists_smith_normal_form_of_rank_eq, MeasureTheory.L1.setToL1_smul, hasFPowerSeriesAt_pi_iff, MeasureTheory.eLpNorm'_const_smul, IsBaseChange.iff_lift_unique, QuadraticMap.canLift', ProbabilityTheory.integral_tilted_mul_eq_mgf, MeasureTheory.integral_simpleFunc_larger_space, Antitone.convex_gt, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, finrank_eq_one_iff', ContDiffBump.apply, TrivSqZeroExt.isUnit_inv_iff, CStarMatrix.smul_mul, Seminorm.ball_zero_absorbs_ball_zero, Module.Basis.smulTower'_apply, ModuleCat.smulShortComplex_f, Submodule.pointed_toConvexCone, Orientation.oangle_sign_add_smul_left, Submodule.span_range_update_sub_smul, Submodule.topologicalClosure_mem_invtSubmodule, HasFDerivAt.lim_real, OrderDual.instSMulPosMono, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, exists_open_convex_of_notMem, lp.coeFn_smul, smul_upperBounds_subset_lowerBounds_smul, InnerProductSpace.isStarProjection_rankOne_self, MulSemiringAction.charpoly_eq, StrictConvex.smul, ProperCone.relative_hyperplane_separation, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, affineSegment_eq_segment, DomMulAct.mk_smul_linearMap_apply, ContinuousAffineMap.coe_smul, Submodule.coe_torsionBy, Quaternion.snd_imK_dualNumberEquiv_symm, strictConvex_Ico, HasFPowerSeriesAt.hasFDerivAt, StrictConvex.linearIsometry_preimage, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, ConcaveOn.openSegment_subset_strict_hypograph, ConvexCone.coe_positive, Bornology.IsVonNBounded.extend_scalars, analyticAt_iff_analytic_smul, Asymptotics.IsBigOTVS.congr, LinearEquiv.smul_apply, instInvertibleReprₛ, Submodule.range_powSMulQuotInclusion, StrongDual.extendRCLikeₗᵢ_apply, UniformConcaveOn.strictConcaveOn, Subalgebra.inclusion.faithfulSMul, HasDerivAt.ofReal_comp, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, DFinsupp.sigmaUncurry_smul, DivisibleHull.qsmul_of_nonneg, LinearMap.BilinForm.nondegenerate_congr_iff, LinearMap.mkContinuous₂_norm_le, CochainComplex.HomComplex.Cochain.units_smul_v, IsBilinearMap.smul_left, MvPowerSeries.le_order_smul, SkewMonoidAlgebra.coeff_mul_single, HomologicalComplex.smul_f_apply, IsLocalizedModule.smul_inj, FormalMultilinearSeries.zero_radius, smul_unitBall, IsLocalization.linearMap_compatibleSMul, IsCompactOperator.smul_unit_iff, intervalIntegral.integral_const_of_cdf, Algebra.Extension.H1Cotangent.val_smul, LinearMap.BilinForm.flip_apply, DifferentiableWithinAt.const_smul, PolynomialModule.instIsScalarTower, AlternatingMap.curryLeft_smul, NonUnitalAlgHom.toFun_eq_coe, WithSeminorms.congr_equiv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, intervalIntegral.integral_const', TrivSqZeroExt.inv_neg, MeasureTheory.condExp_smul_of_aestronglyMeasurable_left, VertexOperator.ext_iff, StrictConcaveOn.map_sum_eq_iff', Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral, hasStrictDerivAt_const, Set.smul_mem_center, SkewMonoidAlgebra.support_mul, toAddEquiv_apply, ContinuousLinearMap.continuousConstSMul, PosSMulMono.toSMulPosMono, Derivation.coe_smul, intervalIntegral.integral_smul_deriv_eq_deriv_smul, ContinuousLinearMap.self_comp_adjoint_injective_iff, Module.algebraMap_end_apply, hasStrictFDerivAt_list_prod_attach', Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsLocalizedModule.iso_symm_apply_aux, HasStrictDerivAt.scomp, Orientation.oangle_sub_left_smul_rotation_pi_div_two, HasFPowerSeriesWithinAt.restrictScalars, tangentConeAt_real_subset_isRCLikeNormedField, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, integral_withDensity_eq_integral_toReal_smul, LinearEquiv.toLinearMap_smul, ZLattice.covolume.tendsto_card_div_pow', MvPolynomial.ker_eval₂Hom_universalFactorizationMap, WithCStarModule.instContinuousSMul, MeasureTheory.Lp.instIsCentralScalar, ContinuousLinearMap.restrictScalars_smul, fderiv_continuousAlternatingMap_apply_apply, Matrix.scalar_comm_iff, SchwartzMap.hasDerivAt, HasDerivWithinAt.fun_sub, Module.End.mem_eigenspace_iff, lp.single_smul, Seminorm.inf_apply, TrivSqZeroExt.sndHom_comp_map, PiTensorProduct.mapLMultilinear_apply_apply, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, RatFunc.minpolyX_eq_zero_iff, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, Units.neg_smul, HasFDerivWithinAt.clm_comp, AddMonoid.End.smulCommClass, ContinuousLinearMap.evalL_apply, LinearPMap.supSpanSingleton_apply_smul_self, CategoryTheory.Functor.map_units_smul, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, ContinuousLinearEquiv.map_smulₛₗ, Submodule.mem_span_range_iff_exists_fun, Unitization.nnreal_cfcₙ_eq_cfc_inr, exteriorPower.presentation_relation, StarConvex.add_smul_sub_mem, hasDerivAtFilter_iff_tendsto, AddMonoid.End.applyFaithfulSMul, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, convex_hyperplane, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, CStarModule.inner_smul_left_real, HasStrictDerivAt.comp, HVertexOperator.ext_iff, Finset.weightedVSubOfPoint_apply_const, PosSMulMono.toPosSMulStrictMono, InnerProductSpace.HarmonicOnNhd.const_smul, hasStrictFDerivAt_ringInverse, KaehlerDifferential.map_compDer, OrderDual.instSMulPosReflectLT, MeasureTheory.setIntegral_indicatorConstLp, InnerProductSpace.HarmonicContOnCl.fun_const_smul, LinearMap.liftBaseChange_tmul, ContinuousLinearMap.mul_apply', starConvex_singleton, AffineSubspace.wOppSide_smul_vsub_vadd_right, Algebra.traceMatrix_of_basis, fromTangentSpace_mfderiv_smul, TrivSqZeroExt.map_comp_map, CStarMatrix.reindexₐ_symm, ContDiff.smul, ConcaveOn.add, LinearMap.instStarModuleId, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, signedDist_smul, LieModule.Cohomology.smul_apply_apply, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_pos, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, smulAddHom_apply, MeasureTheory.convolution_lsmul_swap, Orientation.oangle_add_right_smul_rotation_pi_div_two, TestFunction.mkCLM_apply, FixedPoints.smul_polynomial, PolyEquivTensor.toFunBilinear_apply_apply, Ideal.IsPrime.smul, LinearEquiv.apply_smulCommClass', HasDerivAtFilter.comp_of_eq, Module.End.instSMulCommClass', Orientation.inner_smul_rotation_pi_div_two_left, lp.instIsCentralScalarSubtypePreLpMemAddSubgroup, Matrix.toBilin_toMatrix, hasDerivAtFilter_finCons', Asymptotics.IsBigOTVS.eventually_smallSets, MeasureTheory.Supermartingale.smul_nonpos, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, PolyEquivTensor.toFunLinear_tmul_apply, TensorProduct.smul_tmul', ContinuousMap.toLp_injective, StrictConcaveOn.map_sum_eq_iff, TestFunction.fderivCLM_eq_of_scalars, midpoint_vsub_right, ContinuousLinearMap.comp_smulₛₗ, setIntegral_withDensity_eq_setIntegral_smul, IsLocalizedModule.mk'_smul_mk', ConcaveOn.translate_left, Matrix.nondegenerate_toLinearMap₂_iff, Function.Antiperiodic.const_smul₀, Module.End.instIsScalarTower, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, StrictConvexOn.convex_lt, LinearMap.BilinForm.comp_congr, hasDerivWithinAt_finCons', AffineMap.coe_lineMap, Matrix.toBilin'_comp, mellin_comp_rpow, ProbabilityTheory.integral_poissonMeasure, TrivSqZeroExt.instL1IsBoundedSMul, LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain, VectorField.mpullbackWithin_const_smul_apply, Finsupp.toDFinsupp_smul, MeasureTheory.Submartingale.sum_smul_sub', Asymptotics.Filter.Tendsto.isBigOTVS_one, StarConvex.preimage_add_left, antivaryOn_iff_smul_rearrangement, TestFunction.lineDerivCLM_eq_of_scalars, convex_RCLike_iff_convex_real, PointedCone.mem_span_set, Representation.norm_ofDistribMulAction_eq, Module.End.HasUnifEigenvector.apply_eq_smul, IsFractionRing.stabilizerHom_apply_apply_mk, intervalIntegral.smul_integral_comp_mul_add, IsIntegralCurveAt.comp_mul_ne_zero, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Module.AEval.X_smul_of, Convex.combo_closure_interior_mem_interior, InnerProductSpace.rankOne_comp, CochainComplex.HomComplex.Cochain.rightShift_units_smul, Module.End.apply_smulCommClass, Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Finset.sum_range_by_parts, Asymptotics.IsTheta.const_smul_left, CliffordAlgebra.invOf_ι, DifferentiableWithinAt.fun_smul, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, Rep.leftRegularHom_hom_single, HasDerivWithinAt.scomp, lp.instIsScalarTowerPreLp, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, TrivSqZeroExt.snd_pow_of_smul_comm', Asymptotics.IsLittleOTVS.snd, hasFPowerSeriesWithinAt_pi_iff, IsLocalizedModule.exists_of_eq, MeasureTheory.eLpNorm_const_smul, hasDerivWithinAt_comp_mul_left_smul_iff, Ideal.restrictScalars_mul, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, hasDerivAt_iff_isLittleO_nhds_zero, inner_smul_right, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, QuadraticMap.toFun_smul, SchwartzMap.tsupport_smulLeftCLM_subset, DFinsupp.instSMulPosReflectLT, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, HasFDerivWithinAt.continuousMultilinear_apply_const, Bornology.IsVonNBounded.vadd, LinearMap.equivariantProjection_apply, cfcₙHom_real_eq_restrict, MvPolynomial.rTensor_symm_apply_single, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, LinearMap.polar_AbsConvex, vadd_openSegment, MeasureTheory.ComplexMeasure.im_apply, LinearMap.IsPerfPair.bijective_right, PiTensorProduct.liftIsometry_comp_mapL, iteratedFDeriv_smul_const_apply, FractionalIdeal.den_mul_self_eq_num, HasStrictDerivAt.fun_const_smul, MeasureTheory.Measure.addHaar_smul_of_nonneg, add_smul, HasDerivWithinAt.congr_deriv, CochainComplex.HomComplex.Cochain.rightUnshift_smul, Seminorm.continuous_iSup, LinearMap.mul_toMatrix₂_mul, Submodule.map_smul', RootPairing.pairingIn_one_four_iff, MeasureTheory.Lp.instIsBoundedSMul, RootPairing.Equiv.instSMulCommClassAut, InnerProductSpace.isSymmetric_rankOne_self, AddSubgroup.smul_mem_pointwise_smul, Orientation.oangle_smul_right_of_neg, ContinuousLinearMap.toSpanSingleton_comp_toSpanSingleton, Seminorm.ball_smul_ball, IsSMulRegular.of_flat_of_isBaseChange, ContinuousMap.coe_toLp, Real.fourierIntegral_convergent_iff, skewAdjointPart_apply_coe, continuousMultilinearCurryLeftEquiv_apply, SkewMonoidAlgebra.coeff_mul_single_one, LinearMap.BilinForm.tensorDistribEquiv_tmul, IsIntegralCurveAt.hasDerivAt, linearIndependent_add_smul_iff, MonoidAlgebra.GroupSMul.linearMap_apply, MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff, Seminorm.coe_sSup_eq, Ideal.smul_mem_pointwise_smul, ConvexBody.nonempty, MeasureTheory.integral_rnDeriv_smul, Asymptotics.IsBigOTVS.rfl, fourierCoeff_eq_intervalIntegral, Seminorm.bddBelow_range_add, NonUnitalSubalgebra.instSMulCommClass', CStarAlgebra.conjugate_le_norm_smul', Asymptotics.IsLittleOTVS.bot, IsSemisimpleModule.exists_end_algEquiv, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, RootPairing.weylGroup.ofIdx_smul, ContinuousLinearMap.isBigOTVS_comp, ContDiffAt.smul_const, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, Module.supportDim_le_supportDim_quotSMulTop_succ, AnalyticAt.exists_eq_sum_add_pow_mul, QuotSMulTop.equivQuotTensor_naturality_mk, inner_sum_smul_sum_smul_of_sum_eq_zero, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, WithLp.smul_fst, iteratedDerivWithin_comp_const_smul, StrictConvexSpace.extremePoints_closedBall_eq_sphere, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap, Complex.taylorSeries_eq_on_eball, MeasureTheory.Measure.map_addHaar_smul, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, ContinuousLinearMap.intervalIntegral_apply, LinearMap.range_smul', Function.noZeroSMulDivisors, span_fourierLp_closure_eq_top, selfAdjointPartL_apply_coe, HasFDerivWithinAt.comp_hasDerivWithinAt, PMF.integral_eq_sum, MeasureTheory.average_add_measure, hasDerivAt_intCast, Seminorm.absorbent_ball_zero, IsRegular.smul_eq_zero_iff_right, PiTensorProduct.liftIsometry_symm_apply, Derivation.tensorProductTo_mul, IsCompactOperator.smul_iff₀, fderivWithin_continuousAlternatingMap_apply_apply, Matrix.toLinearMapₛₗ₂_symm, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, RootPairing.pairingIn_neg_one_neg_four_iff, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonpos, LinearMap.BilinMap.tensorDistrib_tmul, Polynomial.smeval_at_zero, RestrictScalars.addEquiv_symm_map_smul_smul, IsBilinearMap.smul_right, LinearMap.BilinForm.mul_toMatrix_mul, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, PowerSeries.constantCoeff_smul, FormalMultilinearSeries.leftInv_comp, LieModule.smul_lie, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Submodule.span_range_update_add_smul, ValuationSubring.ofPrime_scalar_tower, IsLocalization.smul_mem_iff, Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson, HasFPowerSeriesAt.const_smul, iteratedFDeriv_succ_eq_comp_right, ContinuousMultilinearMap.changeOriginSeries_support, WeakFEPair.functional_equation₀, DiscreteConvolution.AddConvolutionExistsAt.vadd_convolution, Finsupp.linearCombination_comp_addSingleEquiv, convex_multiset_sum, Real.tendsto_integral_cexp_sq_smul, Asymptotics.isBigOTVS_fun_comm, TrivSqZeroExt.algebraMap_eq_inl, ContDiffMapSupportedIn.seminorm_apply, LinearMap.BilinForm.toMatrix_mul_basis_toMatrix, AffineSubspace.sSameSide_smul_vsub_vadd_right, Matrix.toLinAlgEquiv_apply, WithSeminorms.tendsto_nhds_atTop, Submodule.mem_smul_top_iff, aemeasurable_withDensity_iff, derivWithin_const_smul, HasFDerivAt.isThetaTVS_sub, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, DifferentiableAt.clm_comp, SubmodulesRingBasis.leftMul, Fintype.not_linearIndependent_iff, DistribMulActionHom.map_zero', LinearMap.nondegenerate_toMatrix₂'_iff, Monovary.sum_smul_comp_perm_lt_sum_smul_iff, MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff, QuadraticMap.weightedSumSquares_apply, CochainComplex.HomComplex.Cochain.smul_v, ODE.hasDerivWithinAt_picard_Icc, Module.support_quotSMulTop, signedDist_smul_of_neg, LinearMap.BilinForm.toMatrix'_comp, MeasureTheory.lpNorm_const_smul, VectorField.lieBracket_smul_left, DualNumber.range_inlAlgHom_sup_adjoin_eps, Submodule.smul_one_eq_span, ContinuousLinearMap.rotation_apply, Real.iteratedFDeriv_fourier, Seminorm.smul_closedBall_subset, Submodule.span_singleton_smul_eq, circleAverage_sub_sub_inv_smul_of_differentiable_on, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, TopologicalAddGroup.IsSES.pushforward_def, DoubleCentralizer.algebraMap_fst, LinearMap.smul_compAlternatingMap, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, Submodule.mem_span_image_finset_iff_exists_fun, deriv_clm_comp, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, Submodule.mem_annihilator_span, Bornology.IsVonNBounded.of_topologicalSpace_le, DifferentiableAt.fun_smul, circleIntegral.integral_smul_const, ContDiffMapSupportedIn.structureMapCLM_top_apply, inner_smul_real_left, Submodule.span_smul, Balanced.zero_insert_interior, DistribMulActionHom.map_add', Submodule.map_pointwise_smul, Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card, IsLocalization.map_eq_toLinearMap_mapₐ, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, QuadraticMap.coe_associatedHom, LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplitting, Real.hasDerivAt_Gamma_one_half, IsClosed.balancedCore, toSpanSingleton_derivWithin, Asymptotics.IsBigOTVS.triangle, fderiv_norm_smul, IsOrderedModule.of_smul_nonneg, isMIntegralCurveAt_comp_mul_ne_zero, ContinuousLinearMap.isEmbedding_restrictScalars, lowerBounds_smul_of_neg, spectrum.hasFDerivAt_resolvent, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, HasFDerivAt.hasFDerivAt_norm_smul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, HasFiniteFPowerSeriesOnBall.eq_partialSum', VectorField.mlieBracket_const_smul_left, exists_lt_of_gauge_lt, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, CategoryTheory.ShortComplex.homologyMap'_smul, StarModule.complexToReal, Module.End.eigenspace_div, AffineSubspace.smul_mem_smul_iff, IsScalarTower.to_smulCommClass, HasDerivAt.comp_hasDerivWithinAt, Complex.wedgeIntegral_add_wedgeIntegral_eq, IsMIntegralCurve.comp_mul, IsBoundedBilinearMap.toContinuousLinearMap_apply, Module.annihilator_eq_bot, isSMulRegular_of_ker_lsmul_eq_bot, Bornology.isVonNBounded_sub, ModuleFilterBasis.smul', LinearMap.BilinForm.toMatrix_mul, MatrixModCat.isScalarTower_toModuleCat, HasFDerivWithinAt.curveIntegral_segment_source, ModuleCat.restrictScalars.smul_def, LinearIndependent.sum_smul_of_nondegenerate, Subsemiring.coe_pointwise_smul, HasFPowerSeriesOnBall.pi, Submodule.toSubMulAction_strictMono, HasFPowerSeriesWithinOnBall.fderivWithin_eq, jacobson_density, nhds_basis_closed_balanced, ContinuousMultilinearMap.piₗᵢ_symm_apply, ray_pos_smul, Matrix.instIsScalarTowerForall, convex_parallelepiped, HasDerivAt.scomp, Module.End.genEigenrange_nat, ContDiffMapSupportedIn.structureMapLM_top_apply, ContinuousLinearMap.ker_adjoint_comp_self, AnalyticAt.analyticOrderAt_ne_top, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, CochainComplex.HomComplex.Cochain.comp_units_smul, ContinuousLinearMap.smulRight_comp_smulRight, balancedCoreAux_subset, Submodule.mem_span_pair, Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable, Matrix.toLinearMap₂_apply, Filter.Tendsto.isVonNBounded_range, HasDerivAt.const_mul, Real.hasFDerivAt_fourierIntegral, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, HasDerivWithinAt.congr, SchwartzMap.integralCLM_apply, IsCovariantDerivativeOn.add_one_form, Submodule.set_smul_eq_iSup, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, PolynormableSpace.withSeminorms', ConvexBody.isClosed, hasDerivAt_one, HasDerivAtFilter.fun_neg, SameRay.exists_nonneg_left, CliffordAlgebra.forall_mul_self_eq_iff, LinearMap.IsSymmetric.apply_eigenvectorBasis, IsOpen.strictConvex_iff, RootPairing.coroot_root_eq_pairing, Matrix.Module.single_smul, hasFDerivAt_iff_isLittleOTVS, Representation.smul_tprod_one_asModule, IsBoundedSMul.of_nnnorm_smul_le, LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, AnalyticAt.const_smul, smul_nonneg_iff, KaehlerDifferential.kerTotal_mkQ_single_smul, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero, MvPolynomial.rTensor_apply_monomial_tmul, ContinuousAt.clm_bundle_apply₂, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, HahnSeries.SummableFamily.binomialFamily_apply, PiTensorProduct.piTensorHomMapFun₂_add, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, ZMod.map_smul, Algebra.Generators.repr_CotangentSpaceMap, ContinuousMultilinearMap.isVonNBounded_image2_apply, DividedPowerAlgebra.dp_sum_smul, hasLineDerivAt_iff_tendsto_slope_zero, MultilinearMap.piFamily_smul, AlternatingMap.uncurryFin_smul, Ideal.mem_iInf_smul_pow_eq_bot_iff, HasFDerivAt.list_prod', MeasureTheory.SignedMeasure.singularPart_smul_nnreal, Function.Even.smul_odd, ProbabilityTheory.strong_law_Lp, separatingDual_iff_injective, fderivWithin_const_smul_field, Pi.openSegment_subset, fderiv_continuousMultilinearMapCompContinuousLinearMap, deriv_fun_const_smul, MeasureTheory.integral_const, LinearEquiv.isSMulRegular_congr', Module.Basis.smulTower_apply, Function.Antiperiodic.const_smul, LinearMap.map_smul₂, IsLocalizedModule.isScalarTower_module, AffineMap.homothety_apply, HasDerivWithinAt.smul_const, CStarAlgebra.star_left_conjugate_le_norm_smul, LinearMap.intrinsicStarModule, DifferentiableOn.smul, contDiff_nat_iff_continuous_differentiable, hasFDerivAt_pow', ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, sameRay_smul_right_iff_of_ne, absorbent_ball, MeasureTheory.Lp.simpleFunc.coe_smul, Seminorm.zero_or_exists_apply_eq_finset_sup, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, LinearMap.comp_smul, Submodule.topologicalClosure_eq_top_iff, Module.End.span_orbit_mem_invtSubmodule, StarConvex.affinity, hasDerivAt_abs, LinearMap.IsContPerfPair.bijective_right, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, iteratedDeriv_comp_const_sub, LinearMap.det_smul, Submodule.coe_smul, ContinuousLinearMap.opNorm_lsmul_le, LinearMapClass.map_smul, Seminorm.ball_comp, FixedBy.intermediateField_mem_iff, ContinuousMultilinearMap.instUniformContinuousConstSMul, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.mkContinuousMultilinear_norm_le, LinearMap.BilinForm.toMatrix_compLeft, WithLp.instProdNormSMulClass, RootPairing.polarizationEquiv_symm_apply_coroot, BilinForm.toMatrix_apply, ContDiffMapSupportedIn.monoCLM_eq_zero, StrictConvex.sum_mem_interior, DualNumber.commute_eps_left, KaehlerDifferential.isLocalizedModule, MulSemiringAction.toAlgEquiv_apply, hasDerivAt_natCast, IsMprojection.Mnorm, smul_vsub_rev_mem_vectorSpan_pair, HasDerivAtFilter.fun_sub, TrivSqZeroExt.kerIdeal_sq, RingHom.smul_def, ContinuousMap.coeFn_toLp, Seminorm.rescale_to_shell, AffineSubspace.direction_affineSpan_pair_le_iff_exists_smul, Matrix.toBilin'_apply', HasDerivWithinAt.union, gaugeRescale_def, Matrix.smul_mul, ConvexBody.isCompact, Real.hasDerivAt_Gamma_one, Convex.toCone_isLeast, segment_translate_image, ArithmeticFunction.smul_map, Real.fourier_bilin_convolution_eq_integral, Derivation.map_aeval, Matrix.toLinearMap₂'_single, closedBall_normSeminorm, Complex.coe_smul, SchauderBasis.RankOneDecomposition.exists_coeff, ContinuousWithinAt.clm_bundle_apply₂, Matrix.smul_eq_mulVec, ContinuousLinearMap.coe_restrictScalarsL, LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero', ModuleFilterBasis.smul_left, MemHolder.nnHolderNorm_smul, Convex.combo_interior_self_mem_interior, HasDerivWithinAt.add_const, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, MeasureTheory.Integrable.integral_smul, lp.mem_lp_const_smul, Matrix.star_dotProduct_gram_mulVec, Bornology.IsVonNBounded.of_add_left, OpenPartialHomeomorph.univUnitBall_apply, LocalizedModule.instIsScalarTower, LinearMap.BilinForm.mul_toMatrix, ContinuousLinearMap.norm_compL_le, Seminorm.continuousAt_zero_of_forall, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, EulerSine.antideriv_cos_comp_const_mul, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, Module.isTorsionBySet_quotient_iff, fderivWithin_clm_comp, integralClosure.coe_smul, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, sameRay_neg_smul_right_iff_of_ne, meromorphicOrderAt_smul_of_ne_zero, HasDerivWithinAt.congr_set, Submodule.mem_smul_span, Matrix.normSMulClass, Bornology.isVonNBounded_add, DualNumber.algHom_ext_iff, HasFPowerSeriesAt.sub, MvPolynomial.support_smul_eq, QuadraticMap.associated_linMulLin, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, MeasureTheory.Lp.instSMulCommClass, BoxIntegral.integralSum_smul, taylor_integral_remainder_aux, OrderDual.instIsOrderedModule, Finset.centerMass_segment, Finsupp.sum_option_index_smul, OrthogonalFamily.range_linearIsometry, QuadraticForm.associated_isSymm, IsBaseChange.dual, isIntegralCurve_comp_mul_ne_zero, TensorProduct.finsuppScalarLeft_apply_tmul, Real.tendsto_integral_exp_smul_cocompact, mellin_convergent_iff_norm, RestrictScalars.isScalarTower, MeasureTheory.setIntegral_tilted', fderiv_continuousMultilinear_apply_const, HasDerivWithinAt.smul, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq, Mathlib.Tactic.LinearCombination.smul_const_lt, ContinuousOn.integral_sub_linear_isLittleO_ae, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, MvPolynomial.tensorEquivSum_X_tmul_X, MeasureTheory.L1.SimpleFunc.integral_smul, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one, iteratedDerivWithin_smul, NonUnitalStarSubalgebra.instSMulCommClass', ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, ContinuousLinearMap.opNNNorm_mul_flip_apply, HasDerivWithinAt.fun_pow, PiTensorProduct.smul_tprodCoeff', HasDerivWithinAt.finset_prod, LinearMap.mul_toMatrix₂'_mul, smul_le_smul_of_nonpos_left, IsNilpotent.exp_eq_sum, LinearMap.toMatrix₂'_mul, ConvexOn.sub_strictConcaveOn, HasFPowerSeriesOnBall.hasFDerivAt, egauge_eq_zero_iff, HasDerivWithinAt.mono, Orientation.oangle_smul_smul_self_of_nonneg, Algebra.Extension.Cotangent.val_smul, MeromorphicNFAt.smul_analytic, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, zero_mem_absConvexHull, LinearMap.BilinForm.flip_flip, Submodule.powSMulQuotInclusion_mk, ContinuousMultilinearMap.curryMid_apply, AntitoneOn.quasilinearOn, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, inv_smul_lt_iff_of_neg, HasFDerivWithinAt.comp_hasDerivAt, SchwartzMap.compCLM_apply, AddSubgroup.smul_mem_pointwise_smul_iff₀, convex_Ici, Finset.weightedVSub_eq_linear_combination, TemperedDistribution.fourierMultiplierCLM_apply_apply, Module.Basis.map_orientation_eq_det_inv_smul, ClosedSubmodule.sInf_orthogonal, AlternatingMap.coeFn_smul, intervalIntegral.fderivWithin_integral_of_tendsto_ae, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, concaveOn_iff_pairwise_pos, HasDerivAt.mul, ContinuousMap.toLp_comp_toContinuousMap, Function.HasTemperateGrowth.smul, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, HasStrictFDerivAt.isBigOTVS_sub, Matrix.separatingLeft_toLinearMap₂'_iff, TensorProduct.AlgebraTensorModule.map_smul_right, rescale_to_shell_zpow, ConvexCone.mem_zero, ContMDiff.clm_postcomp, Asymptotics.IsLittleOTVS.tendsto_inv_smul, PolynomialModule.eval_apply, LieAlgebra.isScalarTower, LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero', balanced_closedBall_zero, integrableOn_peak_smul_of_integrableOn_of_tendsto, TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent, Finset.neg_smul_finset, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, ModelWithCorners.convex_range', MeasureTheory.Lp.smul_comm, Submodule.smul_mem_iff, Module.End.baseChangeHom_apply_apply, isBoundedBilinearMap_smul, fderivWithin_continuousAlternatingMap_apply_const, ConcaveOn.map_add_sum_le, NonUnitalAlgHom.map_mul', BilinForm.toMatrix_mul, EulerSine.antideriv_sin_comp_const_mul, LinearMap.map_smul, Module.End.instSMulCommClass, mapsTo_tangentConeAt_pi, Finset.sum_smul_sum_eq_sum_perm, strictConvex_singleton, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, ContinuousLinearMap.norm_restrictScalars, Asymptotics.IsLittleOTVS.isBigOTVS, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, coe_normSeminorm, MvPolynomial.tensorEquivSum_C_tmul_one, Submodule.restrictScalars.isScalarTower, Module.reflection_mul_reflection_zpow_apply_self, ConvexCone.coe_add, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, parallelepiped_eq_sum_segment, MDifferentiableWithinAt.clm_postcomp, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, WeakDual.instContinuousSMul, convex_Iio, Matrix.toLinAlgEquiv_self, RootPairing.coreflection_apply, convex_halfSpace_gt, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, HasDerivWithinAt.const_sub, Algebra.Extension.tensorCotangentInvFun_smul_mk, ContDiffBump.convolution_eq_right, ContinuousMultilinearMap.map_update_smul, TemperedDistribution.instFourierInvSMul, sameRay_neg_smul_right_iff, MeasureTheory.AEEqFun.Integrable.smul, ExistsContDiffBumpBase.w_def, HasDerivWithinAt.const_smul, MeasureTheory.Measure.setIntegral_comp_smul, Matrix.separatingLeft_toBilin'_iff, ContDiffOn.smul, mem_vectorSpan_pair, WeakFEPair.hf_modif_FE, HasDerivWithinAt.hasDerivAt, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, ContinuousLinearMap.opNorm_mul_apply_le, deriv_smul_const, intervalIntegral.integral_hasFDerivWithinAt, HasFPowerSeriesAt.tendsto_partialSum, TopologicalGroup.IsSES.pushforward_mono, ContinuousLinearMap.smul_def, LinearMap.toMatrix₂_mul_basis_toMatrix, ContinuousLinearMap.orthogonal_range, Antitone.quasilinearOn, HasFiniteFPowerSeriesAt.add, Matrix.conjTranspose_intCast_smul, HasFPowerSeriesAt.hasDerivAt, TensorProduct.AlgebraTensorModule.lift_apply, RatFunc.natDegree_num_le_natDegree_minpolyX, hasDerivWithinAt_congr_set', Module.End.IsSemisimple_smul, Finsupp.mem_span_range_iff_exists_finsupp, Module.Basis.toMatrix_eq_toMatrix_constr, Module.Finite.toModuleEnd_moduleEnd_surjective, ContinuousLinearMap.isThetaTVS_comp, DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul, StrictConcaveOn.neg, fourierIntegral_half_period_translate, ediam_smul₀, CategoryTheory.ShiftedHom.map_smul, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, AddCommMonoid.nat_isScalarTower, tendsto_smul_congr_of_tendsto_left_cobounded_of_isBoundedUnder, StrictConvexSpace.sphere_subset_extremePoints_closedBall, TestFunction.fderivCLM_apply_of_gt, MeasureTheory.withDensitySMulLI_apply, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivWithinAt_const_add_iff, convexHull_toCone_isLeast, ConvexCone.IsGenerating.span_eq_top, MeasureTheory.Measure.addHaar_nnreal_smul, ContinuousLinearMap.spectralRadius_eq_nnnorm, Complex.taylorSeries_eq_on_emetric_ball, finsuppTensorFinsuppLid_apply_apply, EuclideanGeometry.hasFDerivAt_inversion, MeasureTheory.convolutionExistsAt_iff_integrable_swap, Module.toModuleEnd_apply, dist_div_norm_sq_smul, mem_segment_iff_wbtw, torusIntegral_smul, PolyEquivTensor.toFunBilinear_apply_eq_smul, WithConv.symm_matrixToLin'StarAlgEquiv_apply, ConcaveOn.neg, VectorField.mpullback_smul, hasDerivAt_ofReal_cpow_const, Monovary.sum_comp_perm_smul_eq_sum_smul_iff, Monovary.sum_comp_perm_smul_le_sum_smul, Submodule.factorPow_comp_powSMulQuotInclusion, CliffordAlgebraDualNumber.equiv_ι, Derivation.leibniz_pow, convex_iff_div, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType, hasDerivAt_norm_rpow, ContinuousLinearMap.spectrum_eq, HasStrictFDerivAt.fun_const_smul, TensorProduct.lcurry_apply, IsLocalizedModule.smul_injective, TrivSqZeroExt.snd_map, Ideal.mem_torsionOf_iff, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem, smul_algebra_smul_comm, fderivWithin_const_smul, concaveOn_univ_piecewise_Iic_of_monotoneOn_Iic_antitoneOn_Ici, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, Submodule.mem_span_triple, QuadraticMap.radical_eq_ker_associated, Matrix.instSMulCommClassForall, HasStrictDerivAt.fun_sub, HasDerivWithinAt.star, Submodule.mem_torsionBy_iff, Matrix.kroneckerTMul_smul, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, Ideal.smul_bot, TensorProduct.smul_tmul_smul, Module.Invertible.instFaithfulSMul, Seminorm.smul_closedBall_preimage, HasFDerivWithinAt.unique_on, MeromorphicOn.extract_zeros_poles, CategoryTheory.Free.lift_map_single, ProbabilityTheory.IsGaussianProcess.smul, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, ContinuousLinearMap.norm_bilinearRestrictScalars, ContinuousLinearMap.nhds_zero_eq, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, DistribSMul.toAddMonoidHom_eq_zsmulAddGroupHom, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HasDerivAt.sum, ProbabilityTheory.covarianceBilin_map, zero_mem_tangentConeAt, SchwartzMap.instFourierSMul, CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, Orientation.two_zsmul_oangle_smul_right_self, Finsupp.sum_smul_index_semilinearMap', MvPowerSeries.instIsScalarTower, SchwartzMap.fourierTransformCLM_apply, HasFDerivAt.curveIntegral_segment_source', LinearEquiv.isSMulRegular_congr, HasFPowerSeriesWithinOnBall.neg, selfAdjointPart_apply_coe, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, Seminorm.bound_of_shell_sup, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Finset.expect_univ, WeakSpace.instContinuousSMul, intervalIntegral.integral_deriv_smul_deriv_comp, AlgEquiv.moduleEndSelfOp_symm_apply, TensorProduct.directSumRight'_restrict, ConcaveOn.mul, skewAdjointPartL_apply_coe, Finset.weightedVSub_apply, ContinuousLinearMap.bilinearComp_zero_left, HasStrictDerivAt.finCons, ContinuousLinearMap.nnnorm_smulRight_apply, mem_tangentConeAt_of_openSegment_subset, RootPairing.pairing_neg_one_neg_four_iff', hasFPowerSeriesWithinOnBall_pi_iff, HasDerivAt.fun_smul, hasDerivAt_zero, Convex.add_smul_sub_mem_interior', Matrix.toBilin'Aux_eq, SchwartzMap.fderivCLM_fourier_eq, TensorProduct.lift.equiv_symm_apply, ContinuousMultilinearMap.instContinuousSMul, IsLocalizedModule.mk'_smul, CStarModule.inner_mul_inner_swap_le, HasFDerivWithinAt.isLittleOTVS, ConvexOn.sup, addMonoidHomLequivNat_apply, Multiset.pow_smul_esymm, mellin_const_smul, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, ContMDiffOn.const_smul_section, LinearIndependent.units_smul, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, IsBaseChange.linearMapLeftRight, Seminorm.gauge_ball, FreeLieAlgebra.Rel.smulOfTower, Module.End.IsSemisimple_smul_iff, NormedSpace.exp_smul, Fintype.sum_smul_sum, MeasureTheory.integral_fun_fst, SmoothPartitionOfUnity.contMDiff_finsum_smul, hasDerivWithinAt_inter', MeasureTheory.pdf.integrable_pdf_smul_iff, Seminorm.coe_comp, LinearMap.map_smulₛₗ, DirectSum.GAlgebra.smul_def, HasDerivWithinAt.scomp_hasDerivAt, MDifferentiableOn.clm_precomp, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, VectorField.lieBracketWithin_smul_right, AddSubmonoid.mem_inv_pointwise_smul_iff, DualNumber.commute_eps_right, ConvexOn.mul_concaveOn, StrictConvexOn.sup, fderiv_fun_const_smul, hasDerivAt_exp_smul_const_of_mem_ball', extremePoints_convexHull_subset, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, LinearEquiv.isScalarTower, instIsPushoutFractionRingPolynomial, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, StarConvex.is_linear_preimage, gauge_lt_eq', deriv_comp_mul_left, Submodule.mem_span_image_finset_iff_exists_fun', hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, Module.End.mem_genEigenspace_one, intervalIntegral.integral_hasDerivAt_right, hasFTaylorSeriesUpToOn_succ_iff_left, HasDerivWithinAt.mul_const, mem_segment_iff_div, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Absorbs.neg_neg, MonotoneOn.quasiconcaveOn, HasCompactSupport.hasDerivAt_convolution_left, SkewMonoidAlgebra.isScalarTower_self, AlgebraicClosure.instIsScalarTower, HasDerivWithinAt.cexp, Balanced.starConvex, MvPolynomial.aevalTower_comp_toAlgHom, DualNumber.instIsLocalRing, VectorFourier.integral_bilin_fourierIntegral_eq_flip, LinearMap.charpoly_sub_smul, smul_inv_le_iff_of_neg, Ideal.pointwise_smul_le_pointwise_smul_iff, LinearEquiv.congrRight₂_trans, deriv_clm_apply, Module.End.apply_faithfulSMul, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, exposedPoints_subset_extremePoints, Module.isTorsionBy_quotient_iff, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK, Finset.centerMass_pair, contDiff_smul, exists_maximal_linearIndepOn, AffineMap.hasStrictDerivAt, ConvexBody.iInter_smul_eq_self, InnerProductSpace.toLinearMap_rankOne, openSegment_translate_preimage, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, HasDerivWithinAt.Ioi_of_Ici, Module.reflection_mul_reflection_zpow_apply, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, VectorField.mpullback_mfderivWithin_apply_smul, VectorField.mpullbackWithin_const_smul, MeromorphicOn.smul, Seminorm.finset_sup_smul, Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real, Complex.taylorSeries_eq_on_ball, TemperedDistribution.instLineDerivSMulComplex, StrictConcaveOn.translate_left, LinearMap.restrict_smul_one, CStarAlgebra.conjugate_le_norm_smul, HasStrictFDerivAt.clm_apply, ContMDiffAt.clm_bundle_apply₂, Nat.cast_smul_eq_nsmul, ContDiffMapSupportedIn.fderivLM_apply, finsuppTensorFinsupp_symm_single, smul_lowerBounds_subset_upperBounds_smul, addMonoidHomLequivInt_symm_apply, Seminorm.isBounded_sup, norm_midpoint_lt_iff, LinearMap.prodMap_smul, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LinearMap.trace_tensorProduct, continuousMultilinearCurryRightEquiv_symm_apply', AntitoneOn.convex_ge, comp_dualTensorHom, MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', NormedSpace.expSeries_sum_eq_div, Summable.tsum_smul_const, Homotopy.smul_hom, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, Convex.add_smul_mem_interior', LinearEquiv.mem_stabilizer_fixedSubmodule, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, measurable_smul_const, AffineSubspace.wSameSide_smul_vsub_vadd_right, WeakFEPair.functional_equation, MeasureTheory.Submartingale.sum_smul_sub, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, LinearEquiv.map_smul, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, convex_Ioc, LinearEquiv.smul_id_of_finrank_eq_one_apply, MvPolynomial.pderiv_inr_universalFactorizationMap_X, LinearMap.toMatrix'_toLinearMapₛₗ₂', Submodule.smul_torsionBy, intervalIntegral.integral_comp_smul_deriv''', TrivSqZeroExt.fst_map, HasDerivWithinAt.fun_add, LinearMap.BilinForm.smul_right, LinearMap.isStarProjection_toContinuousLinearMap_iff, CategoryTheory.Limits.IsColimit.ι_smul, Matrix.Semiring.isScalarTower, MeromorphicOn.divisor_smul, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, IsLinearMap.isLinearMap_smul, LocalizedModule.mk'_smul_mk, Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, HasFDerivAtFilter.isLittleOTVS, Representation.ofModule_asAlgebraHom_apply_apply, Submodule.smul_le, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, iteratedDerivWithin_eq_equiv_comp, MvPowerSeries.coeff_smul, HasDerivAt.const_add, slope_sub_smul, iteratedFDerivWithin_two_apply, Matrix.conjTranspose_ofNat_smul, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, extDerivWithin_smul, AddAction.automorphize_smul_left, Derivation.compAEval_eq, ContDiffMapSupportedIn.seminorm_postcompLM_le, Matrix.separatingLeft_toLinearMap₂_iff, CategoryTheory.MonoidalLinear.smul_whiskerRight, Derivation.tensorProductTo_tmul, Module.End.mem_maxGenEigenspace, IsExtreme.convex_diff, MeasureTheory.integral_countable, DoubleCentralizer.coe_fst, HasStrictFDerivAt.fun_smul, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul, Polynomial.aeval_endomorphism, MvPolynomial.instIsPushout_1, Module.End.genEigenspace_div, smul_inv_lt_iff_of_neg, CompactlySupportedContinuousMap.toReal_smul, Derivation.map_smul, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, Seminorm.closedBall_bot, LocallyConvexSpace.convex_open_basis_zero, Submodule.adjoint_orthogonalProjection, CategoryTheory.MonoidalLinear.whiskerLeft_smul, Filter.HasBasis.isBigOTVS_iff, Real.sInf_smul_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, HasFDerivAt.pow', IsCompactOperator.smul, Function.Odd.smul_even, HasStrictFDerivAt.pow', LinearMap.toMatrix₂_apply, ContDiffWithinAt.smul_const, surjOn_extremePoints_image, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, Convex.smul_mem_of_zero_mem, Real.fourierIntegral_continuousLinearMap_apply', CurveIntegrable.smul, BoxIntegral.Integrable.smul, RootPairing.rootFormIn_self_smul_coroot, LinearEquiv.smul_def, Finset.centroid_pair, TopModuleCat.hom_smul, isMIntegralCurveOn_comp_mul_ne_zero, ContinuousLinearMap.hasFDerivAt_of_bilinear, starConvex_iff_forall_pos, Submodule.tensorToSpan_apply_tmul, lp.infty_isScalarTower, FormalMultilinearSeries.min_radius_le_radius_add, hasStrictDerivAt_one, FormalMultilinearSeries.ofScalars_comp_neg_id, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, RootPairing.corootForm_self_smul_root, HasDerivWithinAt.of_isLittleO, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_apply_tmul, StrongDual.extendRCLike_apply, ContinuousLinearMap.closed_range_of_antilipschitz, LinearPMap.smul_graph, tendsto_integral_comp_smul_smul_of_integrable, Matrix.frobeniusNormSMulClass, HasDerivAt.div_const, strictConvex_iff_div, HasDerivAt.scomp_of_eq, VonNeumannAlgebra.coe_toStarSubalgebra, LieAlgebra.SemiDirectSum.smul_eq_mk, BddAbove.smul_of_nonpos, lie_eq_smul, SeminormFamily.basisSets_singleton_mem, Ideal.ofList_cons_smul, Module.AEval.of_aeval_smul, Finset.centerMass_eq_of_sum_1, Pi.single_smul', Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, LieModule.Cohomology.twoCochain_val_apply, ContDiffMapSupportedIn.continuous_iff_comp_order_le, Mathlib.Tactic.Module.NF.sub_eq_eval₂, TensorialAt.mkHom₂_apply, ConvexCone.disjoint_hull_right_of_convex, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, TopologicalAddGroup.IsSES.integral_inducedMeasure, IsScalarTower.complexToReal, HasFPowerSeriesAt.pi, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, StrictConcaveOn.add_concaveOn, smul_ball, Subalgebra.instIsScalarTowerSubtypeMem, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', map_intCast_smul, AddAut.mulLeft_apply_apply, IntervalIntegrable.continuousOn_smul, Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, SameRay.exists_pos, VectorFourier.fourierPowSMulRight_apply, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, finsuppTensorFinsuppRid_apply_apply, Module.Basis.repr_sum_self, SameRay.smul, inner_eq_norm_mul_iff_real, HasDerivAt.cexp, ContinuousAlternatingMap.prodLIE_apply, Finsupp.linearCombination_option, MeasureTheory.Submartingale.smul_nonpos, SkewMonoidAlgebra.support_single_mul_subset, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, QuadraticMap.associated_sq, LinearMap.dualMap_def, iSupIndep_iff_dfinsupp_lsum_injective, image_extremePoints, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, Summable.smul_const, QuadraticMap.associated_comp, MeasureTheory.Lp.simpleFunc.toLp_smul, LieAlgebra.IsKilling.chainLength_smul, segment_eq_image_lineMap, sub_smul_slope, dist_smul₀, convexCombination_eq_sum, concaveOn_iff_forall_pos, ftaylorSeries_zero, PadicInt.mahlerEquiv_apply, Module.Basis.toMatrix_smul_left, Submodule.span_singleton_eq_range, CentroidHom.instIsCentralScalar, SchwartzMap.convolution_flip, Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul, QuadraticMap.associated_isOrtho, HasDerivWithinAt.isLittleO, ContinuousLinearMap.opNorm_flip, LieRinehartAlgebra.Hom.map_smul_apply, Module.Basis.parallelepiped_map, Seminorm.bound_of_shell_smul, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, Filter.Tendsto.integral_sub_linear_isLittleO_ae, FormalMultilinearSeries.radius_compContinuousLinearMap_le, MeasureTheory.distribHaarChar_eq_div, hasDerivWithinAt_derivWithin_iff, IsCompactOperator.smul_isUnit_iff, hasDerivAt_sub_const_iff, midpoint_mem_segment, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, LinearMap.smulRightₗ_apply_apply, HasDerivAt.div, Complex.isometryOfOrthonormal_apply, IsConformalMap.smul, AddSubgroup.coe_pointwise_smul, intervalIntegral.smul_integral_comp_mul_right, HasDerivWithinAt.pow, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity, Matrix.dualNumberEquiv_apply, intervalIntegral.integral_comp_div_add, ConvexCone.isGenerating_top, ConvexBody.zero_mem_of_symmetric, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, CategoryTheory.Pretriangulated.Triangle.smul_hom₃, Matrix.separatingRight_toBilin'_iff, Complex.hasDerivAt_Gamma_one, TemperedDistribution.fourierMultiplierCLM_sum, LinearMap.restrictScalars_extendScalarsOfIsLocalization, intervalIntegral.integral_smul_const, FormalMultilinearSeries.derivSeries_eq_zero, InnerProductSpace.laplacianWithin_smul_nhds, AntitoneOn.quasiconvexOn, QuotientGroup.automorphize_smul_left, TestFunction.lineDerivCLM_smul, Unitization.instStarModule, Algebra.Generators.H1Cotangent.δ_eq_δAux, ContDiffWithinAt.smulRight, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, HasDerivWithinAt.congr_of_eventuallyEq, HasDerivAtFilter.isEquivalent_sub, Derivation.coe_smul_linearMap, AddSubmonoid.coe_pointwise_smul, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ContinuousLinearMap.star_eq_adjoint, SchwartzMap.integral_fourier_smul_eq, Real.dimH_segment, FormalMultilinearSeries.comp_rightInv, IsSMulRegular.skewMonoidAlgebra_iff, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable, IsBaseChange.equiv_tmul, ContinuousMultilinearMap.curryLeft_apply, Finset.centerMass_smul, LinearMap.tensorProduct_apply, Monotone.quasiconvexOn, Submodule.mem_toConvexCone, AffineSpace.asymptoticNhds_eq_smul, smul_max_of_nonpos, HasStrictDerivAt.fun_neg, AffineSubspace.direction_smul, ContDiffAt.fun_smul, HasFPowerSeriesWithinAt.neg, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, RootPairing.pairing_smul_coroot_eq, Function.Antiperiodic.smul, Bornology.IsVonNBounded.closure, HasFDerivAt.hasFDerivAt_norm_smul_neg, QuotSMulTop.map_comp, finsuppTensorFinsuppLid_single_tmul_single, Asymptotics.isThetaTVS_comm, Ideal.pointwise_central_scalar, fderivWithin_list_prod', AlternatingMap.mkContinuousLinear_norm_le, FreeLieAlgebra.instIsCentralScalar, ProperCone.hyperplane_separation_of_notMem, ConvexOn.mul', Module.End.genEigenspace_nat, MeasureTheory.charFun_map_smul_comp, fderiv_clm_apply, DualNumber.eps_pow_two, ContinuousAlternatingMap.curryLeftLI_apply, smul_pos_iff_of_neg_left, ContMDiffWithinAt.const_smul_section, ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasis, ContinuousLinearEquiv.smul_apply, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, HasFDerivWithinAt.fun_mul', ContinuousLinearMap.norm_compSL_le, TestFunction.monoCLM_apply, QuadraticMap.Ring.associated_pi, ContinuousAlternatingMap.instIsCentralScalar, fderivWithin_smul_const, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, Balanced.neg, LinearMap.nondegenerate_toMatrix₂_iff, ContDiffMapSupportedIn.withSeminorms, Polynomial.rootSet.coe_smul, ConvexCone.mem_strictlyPositive, AnalyticOn.fun_const_smul, MeasureTheory.withDensityᵥ_smul, wbtw_or_wbtw_smul_vadd_of_nonneg, ContDiffAt.exists_eventually_eq_hasDerivAt, MvPolynomial.instIsPushout, ContinuousLinearEquiv.continuousSMul, DivisibleHull.qsmul_of_nonpos, TopologicalAddGroup.IsSES.pushforward_mono, Bornology.isVonNBounded_vadd, star_mul_self_sub_self_mul_star, MeasureTheory.integrable_comp_smul_iff, MeasureTheory.distribHaarChar_mul, derivWithin_fun_const_smul', convex_halfSpace_le, Convex.openSegment_closure_interior_subset_interior, mem_openSegment_of_gauge_lt_one, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, ConvexOn.convex_strict_epigraph, HasFDerivWithinAt.isBigOTVS_sub, DirectSum.support_smul, convexHull_isClosed, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, iteratedDeriv_const_smul_field, Seminorm.absorbent_closedBall, SemilinearEquivClass.map_smulₛₗ, IsMIntegralCurveAt.comp_mul_ne_zero, CategoryTheory.NatTrans.app_smul, inf_eq_half_smul_add_sub_abs_sub, InnerProductSpace.isIdempotentElem_rankOne_self_iff, HasDerivAt.tendsto_slope_zero, fderivWithin_continuousLinearEquiv_comp, ContinuousMultilinearMap.toUniformOnFun_toFun, Quaternion.re_snd_dualNumberEquiv, Matrix.toLin_transpose, Ideal.pointwise_smul_toAddSubgroup, sub_mem_posTangentConeAt_of_openSegment_subset, MulSemiringAction.toAlgHom_apply, IsLocalization.instCompatibleSMulLocalizationOfIsScalarTower, Submodule.span_singleton_mul, div_le_egauge_ball, TrivSqZeroExt.algebraMap_eq_inlHom, hasDerivAtFilter_pi, stereographic_apply, Asymptotics.IsThetaTVS.trans, Submodule.mem_stabilizer_submodule_iff_map_eq, Orientation.rotation_apply, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, ContinuousSMul.of_basis_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, SameRay.norm_smul_eq, Representation.leftRegular_norm_apply, segment_subset_uIcc, BilinForm.mul_toMatrix, TensorProduct.liftAux.smul, inner_map_polarization, not_linearIndepOn_finset_iff, UniformConvergenceCLM.instContinuousConstSMul, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, AddMonoid.End.isScalarTower, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Real.iteratedFDeriv_fourierIntegral, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonneg, SMulPosMono.toSMulPosStrictMono, Mathlib.Tactic.Module.NF.eval_smul, StieltjesFunction.measure_smul, MeasureTheory.Lp.coe_LpSubmodule, Submodule.exists_of_finrank_lt, Bornology.isVonNBounded_insert, Algebra.Generators.CotangentSpace.map_toComp_injective, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, HahnSeries.instIsScalarTower, StieltjesFunction.ae_hasDerivAt, InnerProductSpaceable.innerProp, Continuous.clm_bundle_apply₂, MeasureTheory.withDensityᵥ_rnDeriv_smul, Matrix.toLinearMapₛₗ₂_apply_basis, FormalMultilinearSeries.ofScalars_series_eq_zero, CochainComplex.HomComplex.Cochain.leftShift_units_smul, differentiableWithinAt_smul_iff, Antivary.sum_smul_comp_perm_eq_sum_smul_iff, Asymptotics.IsLittleOTVS.mono, fderivWithin_pow_ring', ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, LocalizedModule.mk_smul_mk, TensorProduct.finsuppLeft_apply_tmul, ConvexCone.mem_hull_of_convex, LinearEquiv.coord_apply_smul, FormalMultilinearSeries.changeOrigin_eval, VertexOperator.ncoeff_of_coeff, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, LinearMap.toSeminorm_ball_zero, Polynomial.smul_mem_rootSet_iff_of_isUnit, AffineMap.homothety_def, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ExteriorAlgebra.liftAlternating_algebraMap, StrictConvex.add_smul_sub_mem, inner_smul_left_eq_smul, Finset.expect_dite_eq, StrongConvexOn.strictConvexOn, DifferentiableOn.const_smul, Convex.sum_mem, CategoryTheory.Free.lift_map, midpoint_sub_left, Submodule.mem_span_set', ContinuousLinearMap.reApplyInnerSelf_smul, ConcaveOn.smul', MeasureTheory.integral_indicator_const, Asymptotics.IsThetaTVS.trans_isLittleOTVS, ConcaveOn.smul, VertexOperator.ncoeff_eq_zero_of_lt_order, IsSelfAdjoint.adjoint_conj, Asymptotics.IsBigOTVS.trans_isThetaTVS, Bornology.IsVonNBounded.image, not_linearIndependent_iff, closedAbsConvexHull_eq_closure_absConvexHull, LinearMap.toMatrix₂_symm', MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff, RootPairing.pairing_smul_root_eq, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasDerivAt.inner, HasFPowerSeriesAt.prod, TensorProduct.lidOfCompatibleSMul_tmul, midpoint_vsub, LinearMap.toSeminorm_apply, LinearIndependent.units_smul_iff, linearDepOn_iffₛ, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, convex_sum, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonneg, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ZMod.invDFT_def, skewAdjoint.smul_mem, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, lineDeriv_smul, ContinuousMap.smul_apply', MeasureTheory.integrable_rnDeriv_smul_iff, AlternatingMap.mkContinuousAlternating_norm_le_max, LinearMap.map_smul', OrthonormalBasis.sum_rankOne_eq_id, Module.End.mem_genEigenspace_nat, ProbabilityTheory.strong_law_ae_simpleFunc_comp, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, hasDerivAt_finCons', HasStrictDerivAt.hasDerivAt, segment.lift, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Asymptotics.IsLittleOTVS.trans, absorbs_iff_eventually_nhds_zero, LinearMap.Nondegenerate.toMatrix₂', Finsupp.support_smul_eq, RootPairing.Equiv.reflection_smul, StrictConvex.add_smul_mem, TensorProduct.equivFinsuppOfBasisRight_symm, TensorProduct.AlgebraTensorModule.ker_mapOfCompatibleSMul, GradedMonoid.isScalarTower_right, HasFPowerSeriesWithinAt.add, Antivary.card_smul_sum_le_sum_smul_sum, ContDiffMapSupportedIn.fderivCLM_apply_of_le, inf_eq_half_smul_add_sub_abs_sub', ContinuousLinearMap.adjoint_inner_right, Real.tendsto_integral_gaussian_smul, map_nnratCast_smul, HVertexOperator.compHahnSeries_coeff, LinearMap.liftBaseChange_comp, HahnSeries.map_smul, IsSMulRegular.subsingleton_linearMap_iff, LieDerivation.smul_apply, HasFDerivWithinAt.fun_pow', StarAlgEquiv.ofInjective'_apply, Module.Basis.orientation_unitsSMul, ConvexOn.comp_affineMap, IntervalIntegrable.integral_smul, Matrix.Nondegenerate.toBilin', HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, groupHomology.isBoundary₀_iff, StrictConvex.convex, HasStrictFDerivAt.continuousAlternatingMap_apply_const, VectorFourier.fourierIntegral_comp_add_right, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, ContDiffMapSupportedIn.postcompLM_apply, LinearMap.BilinForm.congr_trans, DFinsupp.instSMulPosReflectLE, LinearMap.BilinForm.toMatrix'_mul, Submodule.mem_colon_singleton, UnitAddTorus.span_mFourier_closure_eq_top, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, Convex.combo_le_max, MeasureTheory.withDensityᵥ_smul', AlgEquiv.apply_faithfulSMul, differentiableAt_iff_restrictScalars, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, smul_mem_asymptoticCone_iff, Mathlib.Tactic.Module.NF.add_eq_eval, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, DirectSum.smul_apply, intervalIntegral.integral_deriv_smul_comp''', Filter.Tendsto.cesaro_smul, Algebra.Extension.Hom.sub_tmul, StrictConvex.preimage_add_right, LinearEquiv.reduce_mk, deriv_fun_const_smul_field, Convex.combo_self_interior_mem_interior, SubMulAction.val_neg, tendsto_integral_exp_inner_smul_cocompact, QuadraticMap.polar_smul_right_of_tower, CategoryTheory.Linear.instEpiHSMulHomOfInvertible, StrictConvex.linear_image, Finset.centroid_pair_fin, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, MeasureTheory.Measure.addHaarScalarFactor_domSMul, inner_smul_right_eq_smul, LieModule.mem_genWeightSpaceOf, NonUnitalAlgHom.coe_mk, ProperCone.pointed_toConvexCone, ConvexCone.Pointed.of_nonempty_of_isClosed, StarConvex.is_linear_image, QuadraticMap.apply_linearCombination, LinearMap.toMatrix₂'_compl₂, RingAut.apply_faithfulSMul, IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul, MulAction.automorphize_smul_left, DualNumber.exp_smul_eps, AddSubmonoid.smul_mem_pointwise_smul_iff, SchwartzMap.integral_smul_laplacian_right_eq_left, StrictConvexOn.convexOn, ContinuousMultilinearMap.smulRight_apply, StrictConcaveOn.add_const, tsum_smul_tsum, Set.OrdConnected.strictConvex, TrivSqZeroExt.map_inl, FormalMultilinearSeries.radius_prod_eq_min, imaginaryPart_smul, CliffordAlgebra.foldr_algebraMap, Quaternion.snd_imI_dualNumberEquiv_symm, OrthonormalBasis.coe_equiv_euclideanSpace, StrongDual.im_extendRCLike_apply, VectorFourier.fourierIntegral_probChar, ModuleCat.restrictScalars.smul_def', SkewMonoidAlgebra.coeff_mul_left, Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass, Mathlib.Tactic.Module.NF.eq_const_cons, openSegment_same, QuaternionAlgebra.star_smul, Seminorm.preimage_metric_ball, LocallyConvexSpace.convex_basis, Submodule.smul_mem_span_smul', HasFDerivAt.mul_const', Set.smul_neg, MvPolynomial.derivation_C_mul, essSup_smul_measure, RatFunc.C_minpolyX, mem_segment_add_sub, IsCyclic.mulAutMulEquiv_symm_apply_apply, Module.toAddMonoidEnd_apply_apply, Orientation.two_zsmul_oangle_smul_left_self, ContinuousLinearMap.le_of_opNorm₂_le_of_le, AddSubgroup.mem_inv_pointwise_smul_iff₀, Fourier.fourierIntegral_def, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, NonUnitalStarSubalgebra.instIsScalarTower, Complex.IsExactOn.with_val_at, LinearMap.rid_comp_lTensor, ContinuousMultilinearMap.currySum_apply, exists_convex_convex_compl_subset, Submodule.mem_colon, NormSMulClass.toIsBoundedSMul, Matrix.Module.diagonal_const_smul, MeasureTheory.ComplexMeasure.re_apply, FormalMultilinearSeries.ofScalars_comp_neg, MvPolynomial.tensorEquivSum_one_tmul_X, SeminormedSpace.Core.norm_smul, Matrix.nondegenerate_toLinearMap₂'_iff, Seminorm.comp_mono, HasDerivAt.pow', Unitization.norm_splitMul_snd_sq, LinearMap.separatingRight_toMatrix₂_iff, SameRay.sameRay_pos_smul_right, HasStrictFDerivAt.fun_pow', CentroidHom.coe_smul, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, le_egauge_ball_one, ConcaveOn.left_lt_of_lt_right', Coalgebra.lTensor_counit_comp_comul, TestFunction.instLineDerivSMulTopENat, rank_eq_zero_iff, NonUnitalSubalgebra.instIsScalarTowerSubtypeMem, TemperedDistribution.lineDerivOp_fourierInv_eq, QuotientAddGroup.automorphize_smul_left, fourierCoeffOn_eq_integral, CliffordAlgebra.changeForm.associated_neg_proof, MeasureTheory.SimpleFunc.integral_const, Submodule.smul_span, CompactConvergenceCLM.continuousSMul, mfderiv_smul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, LinearMap.BilinForm.IsNonneg.smul, hasStrictDerivAt_zero, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousLinearMap.isBigOTVS_fun_comp, Orientation.oangle_sign_smul_add_smul_right, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, Coalgebra.TensorProduct.rid_tmul, Pi.image_update_segment, HasDerivAtFilter.finCons, Finset.sum_smul_vsub_const_eq_weightedVSub, MeasureTheory.integral_deriv_smul_comp_Ioi, le_egauge_of_forall_ne_zero, IsBoundedSMul.of_norm_smul_le, Finset.sum_smul_vsub_const_eq_affineCombination_vsub, realPart_apply_coe, convex_of_nonneg_surjective_algebraMap, FormalMultilinearSeries.coeff_iterate_fslope, QuotSMulTop.map_apply_mk, HasFPowerSeriesAt.eq_zero, AbsolutelyContinuousOnInterval.fun_smul, Matrix.represents_iff', ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, deriv_const_smul', ContDiffMapSupportedIn.fderivCLM_apply, DualNumber.lift_apply_inl, intervalIntegral.integral_comp_mul_right, hasStrictDerivAt_exp_smul_const_of_mem_ball', tangentConeAt_subset_zero, ContinuousLinearMap.extendTo𝕜'_apply, LocalizedModule.smul_eq_iff_of_mem, TestFunction.fderivCLM_apply, Matrix.conjTranspose_rat_smul, MeasureTheory.integral_concaveOn_of_integrand_ae, ContinuousLinearMap.isAdjointPair_inner, LinearMap.coe_smulRight, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, EuclideanGeometry.dist_smul_vadd_eq_dist, PolynomialModule.monomial_smul_apply, posSMulMono_iff_posSMulStrictMono, MeasureTheory.integral_singleton, intervalIntegral.integral_comp_div_sub, SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply, isSelfAdjoint_smul_of_mem_skewAdjoint, Submodule.setSemiring_smul_def, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, Module.End.isNilpotent_restrict_genEigenspace_top, complexOfReal_hasDerivAt, ConvexBody.hausdorffDist_coe, LieSubmodule.exists_smul_add_of_span_sup_eq_top, MeasureTheory.integral_comp_smul_deriv_Ioi, not_linearIndepOn_finset_iffₛ, Convex.starConvex_iff, openSegment_subset_Ioo, Convex.add_smul_sub_mem, IsLocalRing.ResidueField.residue_smul, HVertexOperator.coeff_comp, DifferentiableAt.smul_const, StrictConvexOn.add_const, convexHull_smul, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, Finset.sum_Ioc_by_parts, Real.fourier_continuousMultilinearMap_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h, Unitization.splitMul_injective, WeakFEPair.f_modif_aux1, MDifferentiableAt.smul_const_section, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, collinear_iff_exists_forall_eq_smul_vadd, MeasureTheory.Lp.smul_assoc, ContDiffMapSupportedIn.continuous_iff_comp, Asymptotics.IsTheta.const_smul_right, ContinuousLinearMap.smulRight_comp, Algebra.normalizedTrace_trans, DualNumber.lift_op_smul, ContMDiffOn.smul_section_of_tsupport, Seminorm.uniformContinuous', HasStrictDerivAt.div_const, HasStrictDerivAt.fun_mul, autEquivRootsOfUnity_apply_rootOfSplit, ContMDiffWithinAt.smul_section, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, TrivSqZeroExt.mul_right_eq_one, UniformConvergenceCLM.instUniformContinuousConstSMul, fderivWithin_continuousAlternatingMap_apply, ContinuousMultilinearMap.instIsCentralScalar, IsBaseChange.comp, smul_mem_asymptoticCone, absConvexHull_eq_convexHull_balancedHull, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, ProbabilityTheory.hasDerivAt_mgf, HasFPowerSeriesAt.eq_zero_of_eventually, LinearMap.separatingLeft_toMatrix₂_iff, SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply, NormedSpace.norm_smul_normalize, Set.OrdConnected.starConvex, Derivation.apply_aeval_eq', smul_add_smul_le_smul_add_smul', HVertexOperator.coeff_apply_apply, div_le_egauge_closedBall, StrictConcaveOn.add, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, hasStrictFDerivAt_inv', MeasureTheory.Integrable.smul_prod, LinearMap.mem_span_iff_bound, Representation.asModuleEquiv_map_smul, homeomorphSphereProd_apply_fst_coe, WithSeminorms.partial_sups, Convex.lift, ConcaveOn.sub, SameRay.exists_pos_left, HasDerivAt.scomp_hasDerivWithinAt, MeasureTheory.Lp.toTemperedDistribution_apply, SchwartzMap.smulLeftCLM_sub, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, HasStrictDerivAt.add_const, wbtw_or_wbtw_smul_vadd_of_nonpos, Subring.smul_mem_pointwise_smul, Module.Basis.smul_apply, ConvexCone.salient_positive, Bornology.IsVonNBounded.smul_tendsto_zero, intervalIntegral.integral_hasStrictDerivAt_right, strongConvexOn_zero, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, DistribSMul.toAddMonoidHom_eq_nsmulAddMonoidHom, Asymptotics.isBigO_const_smul_left, ConvexBody.hausdorffEDist_coe, LinearMap.BilinForm.toMatrix'_toBilin', Fintype.linearCombination_apply_single, LinearEquiv.symm_smul_apply, HVertexOperator.of_coeff_apply, MDifferentiableOn.smul_section, MeasureTheory.SimpleFunc.integral_eq, integral_withDensity_eq_integral_toReal_smul₀, SchwartzMap.fourier_convolution_apply, Seminorm.smul_ball_zero, Fintype.linearCombination_apply, mem_openSegment_iff_div, MvPolynomial.totalDegree_smul_le, Real.iteratedDeriv_fourierIntegral, Asymptotics.isBigOTVS_map, Projectivization.generalLinearGroup_smul_def, iteratedFDeriv_two_apply, starConvex_compl_Iic, PointedCone.mem_toConvexCone, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, PiTensorProduct.map_update_smul, MeasureTheory.setIntegral_finset, real_inner_smul_left, ContDiffAt.smul, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, TemperedDistribution.smulLeftCLM_sum, intervalIntegral.integral_hasStrictDerivAt_left, StrictConvex.sub, TensorProduct.map_smul_left, Asymptotics.IsBigOTVS.neg_left, ModuleCat.Algebra.instSMulCommClassCarrier, antivaryOn_iff_forall_smul_nonpos, Matrix.separatingLeft_toBilin_iff, Module.End.apply_isScalarTower, gauge_smul, ConvexCone.isGenerating_bot_iff, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, MDifferentiable.clm_precomp, InnerProductSpace.laplacian_smul_nhds, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, ConvexBody.hausdorffEdist_coe, ContDiffMapSupportedIn.fderivLM_apply_of_le, sameRay_smul_right_iff, LinearMap.Nondegenerate.toMatrix₂, Pi.segment_subset, MultilinearMap.mkPiRing_apply, IsLocalizedModule.eq_iff_exists, fderiv_norm_smul_pos, Fintype.expect_ite_eq', Convex.strictConvex_of_isOpen, FormalMultilinearSeries.le_radius_pi, Polynomial.smul_eval, AffineSpace.asymptoticNhds_eq_smul_vadd, continuousMultilinearCurryLeftEquiv_symm_apply, MultilinearMap.map_smul_univ, WithLp.unitization_mul, UnitAddTorus.mFourierCoeff_eq_integral, FixedPoints.smul, hasDerivAt_exp_smul_const', CategoryTheory.ShortComplex.smul_τ₁, TrivSqZeroExt.exp_def_of_smul_comm, DoubleCentralizer.instStarModule, HasStrictDerivAt.finset_prod, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, LinearMap.existsUnique_eq_smul_id_of_finrank_eq_one, ContinuousMultilinearMap.smulRightL_apply, NNReal.instIsStrictOrderedModule, StrictConcaveOn.concaveOn, Representation.smul_one_tprod_asModule, CStarAlgebra.star_right_conjugate_le_norm_smul, smul_nonneg_iff_pos_imp_nonneg, Convex.second_derivative_within_at_symmetric_of_mem_interior, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, iteratedDerivWithin_scomp_two, exists_pos_left_iff_sameRay_and_ne_zero, CochainComplex.HomComplex.Cochain.comp_smul, sameRay_neg_smul_left_iff, LieSubalgebra.instIsScalarTowerSubtypeMem, lp.norm_const_smul_le, TestFunction.instContinuousSMulReal, MeasureTheory.integral_comp_mul_left_Ioi, Asymptotics.IsLittleOTVS.congr_right, ContinuousMap.norm_smul_const, iteratedFDeriv_succ_eq_comp_left, ContinuousMapZero.toNNReal_neg_smul, LinearMap.BilinForm.Nondegenerate.toMatrix', Submodule.smul_mem_smul, antivary_iff_forall_smul_nonpos, ContinuousLinearMap.smul_compLpL, MeasureTheory.Measure.addHaarScalarFactor_smul_congr', VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, Submodule.instSMulCommClass_1, MeasureTheory.SimpleFunc.map_integral, infinite_range_add_smul_iff, ContDiffMapSupportedIn.fderivLM_apply_of_gt, IsLocalizedModule.smul_mem_finsetIntegerMultiple_span, HasDerivAt.hasDerivAtFilter, Convex.sub, cfcₙ_const_mul, AffineMap.homothety_add, SkewPolynomial.instSMulCommClass, CategoryTheory.ShortComplex.smul_τ₂, AddMonoid.End.coe_smul, HasDerivAt.comp_hasDerivWithinAt_of_eq, ContinuousLinearMap.opNorm_mulLeftRight_le, ConvexOn.mul, gauge_smul_left, Finset.sum_smul_vsub_eq_affineCombination_vsub, MeasureTheory.measure_smul_setAverage, ClosedSubmodule.orthogonal_closure, DualNumber.lift_comp_inlHom, ModuleFilterBasis.smul, AntivaryOn.sum_smul_le_sum_smul_comp_perm, AlgHom.linearMapMk_toAddHom, MeasureTheory.Integrable.comp_smul, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, ContDiffMapSupportedIn.structureMapCLM_zero_injective, Seminorm.ball_finset_sup_eq_iInter, Matrix.SeparatingRight.toBilin', LinearMap.lflip_symm, HasFDerivWithinAt.curveIntegral_segment_source', ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, Module.Basis.opNNNorm_le, Derivation.leibniz_div_const, Module.End.smulLeft_eq, TrivSqZeroExt.inl_mul_eq_smul, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, ContMDiffWithinAt.clm_precomp, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Convex.exists_mem_add_smul_eq, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, HasDerivAtFilter.comp, DualNumber.algHom_ext'_iff, MeasureTheory.Integrable.fourier_smul, LinearMap.coe_toContinuousLinearMap_symm, IsCompactOperator.smul_iff, hasStrictFDerivAt_list_prod', finsum_smul', right_sub_midpoint, balancedHull.balanced, Submodule.torsionBySet.mk_smul, continuousMultilinearCurryFin1_symm_apply, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, HasStrictDerivAt.fun_add, Convex.toCone_eq_sInf, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, FixedPoints.smulCommClass', balancedCore_zero_mem, intervalIntegral.integral_comp_mul_add, HasSum.smul_const, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, Set.smul_mem_centralizer, FormalMultilinearSeries.radius_pi_le, DualNumber.ideal_trichotomy, NonUnitalStarAlgHom.coe_mk, HasDerivAt.comp_of_eq, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, VectorFourier.integral_fourierIntegral_smul_eq_flip, AffineSubspace.sOppSide_smul_vsub_vadd_left, Complex.integral_boundary_rect_of_differentiableOn_real, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, smul_vsub_mem_vectorSpan_pair, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Orientation.inner_smul_rotation_pi_div_two_smul_left, Submodule.mem_annihilator_span_singleton, Module.reflection_apply, CategoryTheory.Functor.linear_iff, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, ConvexCone.coe_hull_of_convex, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, HasStrictFDerivAt.smul_const, SchwartzMap.coe_apply, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, IsInvariantSubfield.smul_mem, sub_smul_dslope, ConvexOn.smul', PointedCone.dual_eq_comap_dual_eval, UniformOnFun.continuousSMul_submodule_of_image_bounded, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, LinearMap.trace_comp_comm, MeasureTheory.condExp_bot', WeakSpace.instIsScalarTower, Subbimodule.smul_mem, SchwartzMap.smulLeftCLM_ofReal, StarConvex.sub', Orientation.oangle_smul_right_of_pos, norm_iteratedFDeriv_smul_le, KaehlerDifferential.instIsScalarTowerTensorProduct_1, Function.Periodic.const_smul, realPart_smul, exists_eq_smul_of_parallel, ContDiffAt.differentiableAt_iteratedFDeriv, BilinForm.toMatrix_compLeft, TrivSqZeroExt.inv_zero, SMulCommClass.nnrat, abs_real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivAt.hasFDerivAt_norm_smul_pos, MeasureTheory.Integrable.smul_const, Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, Monotone.convex_le, ContinuousMultilinearMap.nnnorm_smulRight, HasDerivAt.finset_prod, Ring.uniformContinuousConstSMul_op, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, zero_mem_tangentConeAt_iff, ContDiffOn.smulRight, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, Convex.subset_toCone, LinearIsometryEquiv.map_smul, DualNumber.eps_mul_eps, MeasureTheory.lpMeasToLpTrim_smul, RootPairing.pairing_one_four_iff, LinearMap.toMatrix₂'_comp, MvPolynomial.rTensor_apply, disjoint_interior_extremePoints, Matrix.toLinearMap₂_apply_basis, MDifferentiableOn.smul_section_of_tsupport, MeasureTheory.integral_finset, ConcaveOn.mul_convexOn, ContinuousLinearMap.norm_adjoint_comp_self, LinearMap.commute_transvections_iff_of_basis, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, Pi.evalStarAlgHom_apply, Orientation.inner_smul_rotation_pi_div_two_smul_right, hasDerivWithinAt_intCast, MeasureTheory.integral_bilinear_hasDerivAt_eq_sub, Convex.add_smul_sub_mem_interior, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, Asymptotics.IsBigO.const_smul_self, ContinuousAt.integral_sub_linear_isLittleO_ae, CircleIntegrable.out, PolynomialModule.monomial_smul_lsingle, ContMDiff.clm_precomp, birkhoffAverage_apply_sub_birkhoffAverage, IsLinearTopology.tendsto_smul_zero, locallyConvexSpace_iff_zero, TensorProduct.Algebra.moduleAux_apply, ContinuousLinearMap.continuousConstSMul_apply, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousLinearMap.isCentralScalar, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, ConcaveOn.lt_right_of_left_lt', Real.hasDerivAt_fourierIntegral, fderivWithin_fun_const_smul, Antivary.sum_smul_le_sum_comp_perm_smul, SameRay.sameRay_pos_smul_left, Antitone.quasiconcaveOn, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearEquiv.strictConvex_preimage, DividedPowerAlgebra.dp_smul, CategoryTheory.ShortComplex.rightHomologyMap'_smul, LinearMap.BilinMap.polarBilin_toQuadraticMap, Mathlib.Tactic.LinearCombination.smul_const_le, ContinuousLinearMap.hasDerivWithinAt, Submodule.Convex.semilinear_range, Antivary.sub_smul_sub_nonpos, Mathlib.Tactic.Module.NF.sub_eq_eval, LinearPMap.smul_apply, HasDerivWithinAt.comp_of_eq, FormalMultilinearSeries.derivSeries_apply_diag, CFC.negPart_smul, MultilinearMap.currySum_smul, Seminorm.coe_iSup_eq, LinearMap.BilinForm.toMatrix_comp, StrictConvex.preimage_add_left, SameRay.exists_nonneg_right, lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup, ClosedSubmodule.symplComp_sup, DistribMulActionSemiHomClass.toMulActionSemiHomClass, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, groupCohomology.isCocycle₂_of_mem_cocycles₂, LinearMap.map_smul_inv, Asymptotics.IsLittleOTVS.add, convex_vadd, ContinuousLinearMap.opNorm_lsmul, IsLocalizedModule.map_integerMultiple, Submodule.comap_smul', Seminorm.zero_comp, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, Submodule.mem_set_smul, FormalMultilinearSeries.norm_changeOriginSeriesTerm, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Seminorm.continuous_of_continuousAt_zero, left_mem_openSegment_iff, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, finsum_smul, TrivSqZeroExt.instIsScalarTower, Subsemiring.smul_closure, ContinuousAlternatingMap.toContinuousMultilinearMap_smul, VectorField.lieBracketWithin_const_smul_right, HasGradientAt.hasDerivAt, ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, StrictConvexOn.add_convexOn, Algebra.FormallyUnramified.comp_sec, HasFTaylorSeriesUpTo.zero_eq', AffineSubspace.setOf_sOppSide_eq_image2, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, Representation.dual_apply, Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, ConvexBody.coe_add, ContinuousAlternatingMap.map_smul_univ, map_rat_smul, Finsupp.linearCombination_comapDomain, fourierCoeffOn.const_smul, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, Function.Odd.smul_odd, ModuleCat.smulShortComplex_X₃_isModule, inv_smul_le_iff_of_neg, MeasureTheory.convolution_eq_swap, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Real.fourierInv_eq, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, mulInvariantVectorField_smul, hasDerivAt_const_add_iff, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonpos, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', Convex.translate_preimage_left, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, Projectivization.mk_eq_mk_iff', InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, MeasureTheory.Measure.euclideanHausdorffMeasure_smul₀, WithSeminorms.continuous_iff_continuous_comp, WeakDual.seminormFamily_apply, MeasureTheory.condExpIndSMul_ae_eq_smul, HasFTaylorSeriesUpTo.fderiv, concaveOn_iff_convex_hypograph, Seminorm.ball_finset_sup, DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul, ConvexOn.add, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, mem_tangentConeAt_of_add_smul_mem, neg_strictConcaveOn_iff, StarAlgEquiv.ofLeftInverse'_symm_apply, IsRegular.smul_right_inj, IsModuleTopology.instPi, Submodule.span_smul_span, AlternatingMap.alternatizeUncurryFin_smul, LinearMap.toMatrixₛₗ₂'_apply, ContinuousLinearMap.norm_holderL_le, SmoothPartitionOfUnity.contMDiff_smul, gaugeSeminorm_lt_one_of_isOpen, Asymptotics.IsLittleOTVS.fun_add, PolynormableSpace.withSeminorms, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, interval_average_eq, Submodule.mem_biSup_iff_exists_dfinsupp, hasFDerivWithinAt_iff_isLittleOTVS, TensorProduct.AlgebraTensorModule.range_lTensor_idealMap, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, segment_subset_closure_openSegment, gaugeSeminormFamily_ball, Mathlib.Tactic.Module.NF.add_eq_eval₂, ConvexOn.add_const, HahnModule.instIsTorsionFree, mdifferentiable_smul_section, isSMulRegular_iff_ker_lsmul_eq_bot, SubMulAction.neg_mem_iff, HasFDerivWithinAt.mul', LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, PresheafOfModules.germ_ringCat_smul, rank_le_one_iff, QuadraticForm.associated_tmul, QuadraticMap.polarSym2_map_smul, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, SchwartzMap.instFourierInvSMul, Seminorm.comp_smul_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, TemperedDistribution.derivCLM_apply_apply, gauge_lt_eq, groupCohomology.isCoboundary₂_of_mem_coboundaries₂, AffineBasis.linear_combination_coord_eq_self, TorusIntegrable.function_integrable, RootPairing.smul_coroot_eq_of_root_eq_smul, AffineSubspace.setOf_wSameSide_eq_image2, Submodule.coe_toSubMulAction, MeasureTheory.Supermartingale.smul_nonneg, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, hasDerivWithinAt_Ici_of_tendsto_deriv, spectrum.hasDerivAt_resolvent_const_left, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson, LinearMap.hasDerivAt, Submodule.smulMemClass, CategoryTheory.ShortComplex.rightHomologyMap_smul, MDifferentiableWithinAt.smul, Module.Basis.sum_equivFun, IsCovariantDerivativeOn.affine_combination, Module.End.mem_genEigenspace, egauge_smul_right, MeasureTheory.weightedSMul_smul_measure, VectorField.lieBracket_smul_right, midpoint_vsub_midpoint_same_left, TensorProduct.piScalarRightHom_tmul, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, HasFDerivAtFilter.restrictScalars, Balanced.smul_eq, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, convex_halfSpace_lt, intervalIntegral.integral_hasFDerivAt, LinearMap.flip_surjective_iff₂, Subalgebra.pointwise_smul_toSubmodule, HasFiniteFPowerSeriesOnBall.fderiv_eq, ConvexOn.pow, Bialgebra.mul_compr₂_comul, smul_closedBall, PointedCone.to_isOrderedModule, ContMDiffOn.smul, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, IsLocalFrameOn.coeff_sum_eq, IsBaseChange.linearMapRight, Complex.hasDerivAt_log_sub_logTaylor, PointedCone.mem_hull_set, TestFunction.lineDerivCLM_apply_of_gt, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real, WithSeminorms.isVonNBounded_iff_seminorm_bounded, DualNumber.snd_mul, ContinuousLinearMap.smulRight_apply, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, intervalIntegral.fderiv_integral, right_vsub_midpoint, MeasureTheory.IntegrableOn.continuousOn_smul_of_subset, intervalIntegral.integral_unitInterval_deriv_eq_sub, RootPairing.reflection_apply, ContinuousLinearMap.analyticAt_bilinear, integral_withDensity_eq_integral_smul₀, IsModuleFiltration.toGradedSMul, HasFDerivWithinAt.comp_hasDerivAt_of_eq, HasFPowerSeriesAt.hasStrictFDerivAt, Polynomial.aevalTower_comp_toAlgHom, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, HasDerivWithinAt.comp_hasDerivAt, AnalyticOnNhd.fun_const_smul, QuadraticMap.coeFn_smul, MeasureTheory.integral_prod_smul, Set.add_smul_subset, QuotSMulTop.map_id, convex_closed_sInter, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Submodule.map_dualCoannihilator_linearEquiv_flip, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, Module.Basis.constr_apply, fderivWithin_mul', AffineSubspace.sSameSide_smul_vsub_vadd_left, Derivation.leibniz_invOf, hasStrictDerivAt_exp_smul_const_of_mem_ball, Module.Baer.ExtensionOfMaxAdjoin.eqn, smul_neg_iff_of_neg_left, ContMDiff.const_smul_section, HasDerivWithinAt.fun_sum, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, Ideal.map_pointwise_smul, lp.instSMulCommClassPreLp, Ideal.smul_mem_pointwise_smul_iff, Real.hasDerivAt_Gamma_nat, LinearMap.rTensor_smul, Orientation.oangle_smul_right_self_of_nonneg, Convex.affinity, TopologicalGroup.IsSES.integrate_mono, LinearMap.BilinForm.SeparatingRight.toMatrix', LinearPMap.supSpanSingleton_apply_mk, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, NormedAddGroupHom.coe_smul, TensorProduct.toLinearMap_symm_rid, hasDerivAt_pi, strictConvex_uIoc, MeasureTheory.ContinuousMap.inner_toLp, convexOn_const, HasDerivAt.of_notMem_tsupport, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, RestrictScalars.isCentralScalar, MeasureTheory.integrable_fun_norm_addHaar, integral_bilinear_fderiv_right_eq_neg_left_of_integrable, CategoryTheory.Linear.toCatCenter_apply_app, skewAdjoint.I_smul_neg_I, Derivation.linearEquiv_coe_comp, hasFDerivAt_inv', ModuleCat.sMulCommClass_mk, PowerSeries.smul_eq_C_mul, SeminormFamily.basisSets_mem, LinearMap.flip_flip, MvPolynomial.tensorEquivSum_X_tmul_one, Submodule.powSMulQuotInclusion_injective, HasDerivAt.fun_mul, Finset.zero_mem_smul_iff, HasStrictDerivAt.const_sub, hasDerivWithinAt_finCons, TensorProduct.AlgebraTensorModule.coe_rTensor, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, PresheafOfModules.germ_smul, CFC.abs_smul, exists_continuousLinearEquiv_fderiv_symm_eq, HasDerivAt.smul, FormalMultilinearSeries.rightInv_coeff, Seminorm.absorbent_ball, Meromorphic.smul, Convex.mem_toCone', LieAlgebra.Extension.twoCocycleOf_coe_coe, LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero, TensorialAt.mkHom₂_apply_eq_extend, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Module.Basis.dvd_coord_smul, Orientation.oangle_sign_smul_add_smul_left, Matrix.Module.smul_def', tendsto_integral_comp_smul_smul_of_integrable', IsLinearMap.map_smul, LinearMap.map_smulₛₗ₂, SModEq.smul, LinearMap.BilinForm.Nondegenerate.toMatrix, Convex.affine_preimage, not_linearIndepOn_finset_iffₒₛ, isClosedMap_smul_left, Asymptotics.IsBigOTVS.mono, Asymptotics.IsLittleOTVS.proj, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, LinearMap.dualCoannihilator_range_eq_ker_flip, ContDiffOn.differentiableOn_iteratedFDerivWithin, QuadraticMap.associated_flip, MeasureTheory.average_union_mem_openSegment, PosSMulStrictMono.toSMulPosStrictMono, ConcaveOn.add_strictConcaveOn, LinearMap.BilinForm.congr_symm, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, ZMod.instIsScalarTower, Real.fourierInv_eq', RestrictScalars.addEquiv_symm_map_algebraMap_smul, Asymptotics.IsBigOTVS.trans, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div', ConvexBody.coe_nsmul, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, ConvexCone.mem_toPointedCone, ModuleCat.isScalarTower_of_algebra_moduleCat, mem_segment_translate, TensorProduct.lift_mk_compr₂, Convex.convexJoin, RootPairing.CoPolarizationIn_apply, HasStrictDerivAt.neg, MellinConvergent.cpow_smul, ContDiffOn.fun_smul, Real.fourierIntegral_deriv, Seminorm.closedBall_comp, ContinuousLinearMap.holderL_apply_apply, FormalMultilinearSeries.comp_rightInv_aux2, CFC.negPart_smul_of_nonneg, TrivSqZeroExt.mul_inv_rev, Algebra.Extension.CotangentSpace.map_comp, Module.Basis.units_smul_span_eq_top, MeasureTheory.integral_fun_snd, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, fwdDiff_smul_const, ZLattice.covolume.tendsto_card_div_pow'', Asymptotics.isLittleOTVS_insert, IsScalarTower.restrictScalars, AdicCompletion.ofPowSMul_val_apply, Polynomial.sylveserMap_comp_adjSylvester, isClosedEmbedding_smul_left, ModuleCat.Algebra.instIsScalarTowerCarrier, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, real_inner_smul_self_right, Submodule.smul_mem_iff'', hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, dist_smul_add_one_sub_smul_le, ConvexOn.comp_linearMap, MeromorphicAt.smul, SeminormFamily.basisSets_iff, VectorFourier.hasFDerivAt_fourierChar_smul, Ideal.coe_smul_primesOver, MeasureTheory.LocallyIntegrableOn.continuousOn_smul, Finset.neg_smul, ConvexCone.IsReproducing.sub_eq_univ, LinearMap.IsAdjointPair.smul, NonUnitalStarAlgHom.map_star', Real.fourierIntegral_real_eq, ContMDiffWithinAt.cle_arrowCongr, Matrix.scalar_commute_iff, fderiv_const_smul_of_field, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, groupHomology.single_isCycle₁_of_mem_fixedPoints, HasLineDerivAt.smul, OrthonormalBasis.sum_repr', Finset.expect_ite_eq, continuousMultilinearCurryRightEquiv_apply, Seminorm.convex_closedBall, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, HasDerivAt.comp_add_const, Algebra.traceForm_toMatrix_powerBasis, Bornology.isVonNBounded_of_smul_tendsto_zero, Module.Presentation.tautologicalRelations_relation, Module.End.HasEigenvector.pow_apply, ContDiffMapSupportedIn.structureMapLM_zero_apply, FixedPoints.mem_intermediateField_iff, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, MeasureTheory.average_union, Ideal.exists_map_eq_of_isGalois, OpenPartialHomeomorph.univUnitBall_symm_apply, Module.p_pow_smul_lift, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countable, convex_zero, Subring.smul_mem_pointwise_smul_iff, concaveOn_const, AnalyticOnNhd.const_smul, DifferentiableOn.hasDerivAt, Seminorm.continuous_of_forall, Bornology.sUnion_isVonNBounded_eq_univ, StarConvex.add_right, LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmodule, finrank_eq_one_iff_of_nonzero', SchwartzMap.integral_smul_deriv_right_eq_neg_left, QuadraticMap.polar_smul_right, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left', smul_inv'', intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Orientation.two_zsmul_oangle_smul_smul_self, ContMDiffAt.smul_section, fderiv_list_prod', SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, Module.Basis.unitsSMul_apply, intervalIntegral.integral_deriv_smul_comp'', SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, UnitAddTorus.span_mFourierLp_closure_eq_top, fderivWithin_comp_smul, Orientation.rotation_symm_apply, nnratCast_smul_eq, strictConvex_Ioi, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero', Orthonormal.inner_right_fintype, MultilinearMap.snoc_smul, NonUnitalStarSubalgebra.instSMulCommClass, LinearEquiv.smul_refl, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, HasFPowerSeriesAt.compContinuousLinearMap, MvPolynomial.scalarRTensor_apply_tmul_apply, Asymptotics.IsBigOTVS.refl, LieSubalgebra.instSMulMemClass, convex_closedConvexHull, WeakFEPair.f_modif_aux2, cfcₙ_comp_const_mul, Asymptotics.isTheta_const_smul_right, Prod.smul_zero_mk, fderivWithin_clm_apply, IsLocalizedModule.mk'_cancel, Algebra.trace_comp_trace, QuadraticMap.associated_isSymm, exists_continuousLinearEquiv_fderivWithin_symm_eq, eHolderNorm_smul, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', mellin_cpow_smul, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, LinearMap.SeparatingLeft.toMatrix₂', QuotSMulTop.mem_annihilator, Module.Basis.sum_repr, fderiv_continuousAlternatingMap_apply_const_apply, Differentiable.smul_const, WithLp.instProdIsBoundedSMul, RootPairing.coreflection_apply_coroot, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, LinearMap.toMatrix₂'_apply, LieDerivation.ofGrading_apply_apply, Submodule.toSubMulAction_one, absorbs_neg_neg, Submodule.image_smul_top_eq_range_lsum, ContinuousLinearMap.isBigOTVS_id, PointedCone.instCanLiftConvexConeToConvexConePointed, Module.End.genEigenspace_le_smul, MeasureTheory.condExpIndL1Fin_smul', RatFunc.natDegree_denom_le_natDegree_minpolyX, ContinuousLinearMap.norm_holder_apply_apply_le, SemimoduleCat.hom_smul, LieModule.Cohomology.d₂₃_comp_d₁₂, ClosedSubmodule.symplComp_inf, intervalIntegral.integral_deriv_smul_comp, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, UniformConvergenceCLM.isVonNBounded_iff, DualNumber.instIsPrincipalIdealRing, Algebra.Generators.CotangentSpace.map_ofComp_surjective, absorbent_ball_zero, Asymptotics.IsBigOTVS.fst, SMulCommClass.nnrat', LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent_of_basis, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, RootPairing.Equiv.instSMulCommClassMulOppositeAut, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, LinearMap.BilinForm.separatingLeft_toMatrix_iff, MvPolynomial.tensorEquivSum_C_tmul_C, constFormalMultilinearSeries_apply_succ, StrictConvex.vadd, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, StrictConvexOn.sub, FormalMultilinearSeries.continuousOn, ZMod.smul_mem, Mathlib.Tactic.Module.NF.smul_eq_eval, HasStrictFDerivAt.clm_comp, ZMod.dft_smul_const, ProbabilityTheory.Kernel.integral_withDensity, Orientation.oangle_sign_smul_sub_right, AlgebraicGeometry.structureSheafInType.smul_apply, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, LieAlgebra.of_symm_smul, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, Submodule.basis_of_pid_aux, Submodule.span_singleton_eq_span_singleton, QuadraticForm.associated_baseChange, Projectivization.smul_mk, Representation.IntertwiningMap.coe_smul, Function.Odd.const_smul, VectorFourier.fourierIntegral_fderiv, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, Convex.finsum_mem, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, KaehlerDifferential.map_liftBaseChange_smul, WeakFEPair.Λ_residue_zero, LinearMap.range_smul, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', Matrix.toBilin'_toMatrix', LieSubalgebra.instIsCentralScalarSubtypeMem, Seminorm.continuous_iff_continuous_comp, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, gaugeRescale_smul, constFormalMultilinearSeries_zero, StarConvex.add, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, Asymptotics.IsBigOTVS.of_egauge_le_mul, Asymptotics.IsLittleOTVS.symm, Real.fourierIntegralInv_eq, Convex.thickening, HasStrictFDerivAt.continuousMultilinearMap_apply, Submodule.instSMulCommClassSubtypeMemTorsion', cfcₙ_const_mul_id, Asymptotics.IsBigO.isBigOTVS, Int.cast_smul_eq_zsmul, IsScalarTower.nnrat, CliffordAlgebra.contractLeftAux_apply_apply, taylor_within_apply, Asymptotics.isLittleOTVS_neg_left, Matrix.toLinearMapₛₗ₂_toMatrix₂, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top, LinearIsometryEquiv.toContinuousLinearEquiv_smul, Function.Antiperiodic.const_inv_smul, LinearMap.BilinForm.IsAlt.smul, ContinuousLinearMap.opNNNorm_mul_apply, le_comap_range_rTensor, LaurentPolynomial.instIsScalarTowerPolynomial, ContinuousMultilinearMap.curryFinFinset_apply, LieRinehartAlgebra.LieRinehartRing.lie_smul_eq_mul, ContDiffAt.smulRight, Unitization.inrRangeEquiv_symm_apply, Affine.Simplex.ninePointCircle_center, Convex.add_smul_mem_interior, TestFunction.injective_toBoundedContinuousFunctionCLM, Submodule.le_traceDual_iff_map_le_one, VertexOperator.coeff_eq_ncoeff, derivWithin_smul_const, FormalMultilinearSeries.changeOriginSeriesTerm_bound, Matrix.SeparatingLeft.toLinearMap₂, MultilinearMap.uncurrySum_smul, HasDerivWithinAt.sum, MeasureTheory.integral_smul_measure, Fintype.not_linearIndependent_iffₒₛ, KaehlerDifferential.kerTotal_map', convex_Ioi, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, Asymptotics.IsLittleOTVS.of_tendsto_div, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, smul_pos_of_neg_of_neg, ContinuousLinearMap.norm_precompL_le, HasFTaylorSeriesUpToOn.restrictScalars, Differentiable.smul, isConformalMap_iff_is_complex_or_conj_linear, ZMod.dft_def, starConvex_iff_div, ProbabilityTheory.integral_poissonMeasure', HasDerivAtFilter.neg, IsArithFrobAt.conj, ContinuousLinearMap.apply_apply, ConcaveOn.sub_strictConvexOn, AbsolutelyContinuousOnInterval.smul, egauge_zero_right, dotProduct_toMatrix₂_mulVec, Module.Presentation.tautological_relation, Asymptotics.isThetaTVS_iff_isTheta, Algebra.Extension.CotangentSpace.map_comp_apply, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, GroupWithZero.toNoZeroSMulDivisors, HVertexOperator.comp_apply, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, PiTensorProduct.mapLMultilinear_opNorm, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, hasDerivWithinAt_inter, fderivWithin_restrictScalars_comp, isSMulRegular_of_range_eq_ker, Seminorm.uniformContinuous_of_forall', PiLp.instIsBoundedSMul, hasFPowerSeriesAt_iff', StarConvex.neg, CategoryTheory.ShiftedHom.smul_comp, StrictConvex.smul_mem_of_zero_mem, Real.fourier_eq', CompactlySupportedContinuousMap.instIsScalarTower, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, hasDerivAt_exp_smul_const_of_mem_ball, Module.IsTorsionBy.mk_smul, Polynomial.eval_smul', LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, RingTheory.Sequence.isRegular_cons_iff', Real.fourierIntegral_iteratedFDeriv, hasMellin_const_smul, Algebra.Extension.CotangentSpace.map_comp_cotangentComplex, star_rat_smul, deriv_const_smul_field, mem_convexJoin, HasFDerivAt.mul', DirectSum.instIsScalarTower, WeakFEPair.Λ_residue_k, convex_iff_forall_pos, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, WithSeminorms.hasBasis_ball, ContDiff.fun_smul, Convex.openSegment_interior_closure_subset_interior, Monovary.sum_smul_sum_le_card_smul_sum, exteriorPower.presentation.relations_relation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, Orientation.rotationAux_apply, Fourier.fourierIntegral_comp_add_right, derivWithin_clm_apply, Finset.sum_smul_sum, smul_finsum, Quaternion.fst_re_dualNumberEquiv_symm, TrivSqZeroExt.mem_kerIdeal_iff_inr, SchwartzMap.fourierMultiplierCLM_smul, MeasureTheory.MemLp.toLp_const_smul, QuadraticMap.basisRepr_apply, Set.Finite.isVonNBounded, slope_def_module, fwdDiff_iter_const_smul, openSegment_subset_union, smul_right_inj, IsBaseChange.endHom_comp, HasStrictDerivAt.congr_of_eventuallyEq, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_div, IsSMulRegular.of_isLocalizedModule, Quaternion.imI_snd_dualNumberEquiv, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, MeasureTheory.IntegrableOn.smul_continuousOn_of_subset, Algebra.forall_mem_adjoin_smul_eq_self_iff, HasCompactSupport.convolution_integrand_bound_right, bddAbove_smul_iff_of_neg, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, MonovaryOn.smul_add_smul_le_smul_add_smul, integral_comp_pi_polarCoord_symm, CategoryTheory.ShiftedHom.mk₀_smul, SkewPolynomial.smul_monomial, Submodule.mem_span_insert, DirectSum.decompose_smul, Asymptotics.isBigOTVS_comm, Submodule.toConvexCone_bot, Seminorm.finset_sup_le_sum, HasDerivAt.comp_semilinear, IsLocalizedModule.isInteger_smul, convexJoin_singleton_right, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, IsSMulRegular.of_ne_zero, InnerProductSpace.symm_toEuclideanLin_rankOne, LinearMap.BilinForm.toMatrix'_compRight, isBoundedBilinearMap_smulRight, HasDerivAt.clog_real, HasDerivAt.comp_sub_const, ModuleFilterBasis.smul_right', MeasureTheory.charFun_map_smul, convexHull_eq_self, convex_closedBall, intervalIntegral.integral_deriv_smul_deriv_comp', Algebra.Extension.Cotangent.ker_mk, ContMDiffAt.cle_arrowCongr, VertexOperator.coeff_eq_zero_of_lt_order, groupHomology.isBoundary₁_iff, IsLocalizedModule.mk'_cancel_left, Matrix.op_smul_eq_vecMul, convexOn_iff_convex_epigraph, HasFDerivAt.clm_comp, ContinuousLinearMap.adjoint_innerSL_apply, IsGaloisGroup.commutes, SameRay.pos_smul_right, StrictConvexOn.map_sum_eq_iff', sameRay_iff_norm_smul_eq, LSeries.hasDerivAt_term, TrivSqZeroExt.mul_inl_eq_op_smul, gaugeSeminorm_toFun, Ideal.pointwise_smul_toAddSubmonoid, Finset.expect_ite_eq', IsBoundedBilinearMap.smul_right, Asymptotics.isLittleOTVS_pi, Module.finrank_eq_zero_iff, Bundle.Pretrivialization.continuousLinearMapCoordChange_apply, DifferentiableWithinAt.smul, ContDiffMapSupportedIn.structureMapLM_apply, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, TensorProduct.AlgebraTensorModule.lcurry_apply, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, LieDerivation.instSMulBase, derivWithin_const_smul', Convex.mem_smul_of_zero_mem, isBoundedLinearMap_prod_multilinear, Matrix.SeparatingRight.toBilin, Module.reflection_mul_reflection_mul_reflection_pow_apply_self, LinearEquiv.reduce_mkQ, Orthonormal.inner_sum, Module.End.algebraMap_isUnit_inv_apply_eq_iff, HasCompactSupport.convolution_integrand_bound_right_of_subset, hasStrictDerivAt_of_hasDerivAt_of_continuousAt, Finsupp.weight_apply, HasStrictDerivAt_ofNat, Function.Periodic.const_inv_smul₀, Real.fourier_smul_convolution_eq, Module.reflection_mul_reflection_mul_reflection_zpow_apply_self, PointedCone.smul_mem, Module.reflection_mul_reflection_zpow, DoubleCentralizer.smul_snd, lipschitzGroup.conjAct_smul_range_ι, balancedCore_eq_iInter, ConcaveOn.convex_gt, AntitoneOn.convex_lt, HasFiniteFPowerSeriesAt.comp, Submodule.exists_smith_normal_form_of_le, Subring.mem_inv_pointwise_smul_iff₀, second_derivative_symmetric_of_eventually_of_real, hasDerivWithinAt_iff_tendsto, lp.instIsScalarTowerSubtypePreLpMemAddSubgroup, Convex.convexIndependent_extremePoints, balancedHull_convexHull_subseteq_absConvexHull, ContDiffAt.hasStrictDerivAt', StrictConvex.mem_smul_of_zero_mem, MeasureTheory.integral_countable', finrank_le_one_iff, TemperedDistribution.laplacianCLM_apply, isBigO_rpow_zero_log_smul, Seminorm.finset_sup_apply_le, ConvexBody.coe_smul', IsLocalization.mem_span_iff, Monovary.sub_smul_sub_nonneg, PresheafOfModules.Sheafify.SMulCandidate.h, HasDerivAt.star_conj, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, Wbtw.mem_segment, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, Bornology.IsVonNBounded.insert, groupCohomology.isCoboundary₁_of_mem_coboundaries₁, Subsemiring.mem_inv_pointwise_smul_iff, segment_inter_eq_endpoint_of_linearIndependent_sub, IsLocalizedModule.mk'_eq_iff, NonUnitalStarSubalgebra.instIsScalarTower', Seminorm.continuousAt_zero, ftaylorSeriesWithin_fun_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, Submodule.torsionBy.mk_smul, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, Submodule.mem_torsion'_iff, HasFDerivAt.smul, Real.deriv_fourier, CStarAlgebra.exists_sum_four_nonneg, RootPairing.EmbeddedG2.threeShortAddLongRoot_eq, CategoryTheory.Linear.smul_comp, Mathlib.Tactic.LinearCombination.smul_const_lt_weak, Submodule.toSubMulAction_injective, CategoryTheory.Pretriangulated.Triangle.smul_hom₁, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, LinearIndependent.pair_add_smul_add_smul_iff, KaehlerDifferential.instIsScalarTowerTensorProduct_2, DoubleCentralizer.coe_snd, MemHolder.smul_iff, ContinuousLinearMap.opNorm_le_bound₂, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, MeasureTheory.integral_convolution, Seminorm.closedBall_finset_sup_eq_iInter, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, PosSMulMono.of_smul_nonneg, CategoryTheory.ShortComplex.leftHomologyMap_smul, IsLocalRing.spanFinrank_eq_finrank_quotient, Seminorm.comp_add_le, DivisibleHull.nnqsmul_mk, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, Polynomial.mkDerivation_apply, Ideal.mem_inv_pointwise_smul_iff, RightDerivMeasurableAux.le_of_mem_A, Representation.TensorProduct.lid_apply, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, TrivSqZeroExt.snd_expSeries_of_smul_comm, ContinuousMultilinearMap.norm_curryMid, Submodule.smul_mem, zero_mem_tangentCone, ContinuousAffineMap.instIsCentralScalar, CategoryTheory.ShortComplex.opcyclesMap'_smul, TopologicalAddGroup.IsSES.integrate_apply, aestronglyMeasurable_withDensity_iff, Affine.Simplex.points_vsub_eulerPoint, hasDerivAt_of_tendstoUniformlyOnFilter, Ideal.pointwise_smul_def, Submodule.starProjection_tendsto_closure_iSup, LieSubalgebra.smul_mem, InnerProductGeometry.angle_smul_left_of_pos, AddMonoidHom.mapMatrix_smul, SMulCommClass.rat, domain_mvt, TrivSqZeroExt.inv_inr, MeasureTheory.Lp.toTemperedDistribution_smul_eq, SchwartzMap.laplacian_eq_fourierMultiplierCLM, Asymptotics.IsBigOTVS.pi, egauge_le_of_smul_mem_of_ne, HasFDerivAt.isLittleOTVS, HVertexOperator.coeff_of_coeff, IsAddUnit.smul_right, MeasureTheory.Lp_toLp_restrict_smul, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, const_smul_mfderiv, Filter.EventuallyEq.hasDerivAtFilter_iff, Seminorm.smul_le_smul, HasMFDerivAt.const_smul, HasDerivAtFilter.fun_sum, IsCovariantDerivativeOn.finite_affine_combination, Matrix.toBilin_comp, MeasureTheory.condExp_bot_ae_eq, map_inv_intCast_smul, FormalMultilinearSeries.hasFPowerSeriesOnBall, KaehlerDifferential.mulActionBaseChange_smul_tmul, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, ModuleFilterBasis.continuousSMul, ContinuousLinearMap.coe_mulₗᵢ, deriv_fun_const_smul', LinearMap.BilinForm.apply_smul_sub_smul_sub_eq, lsum_comp_mapRange_toSpanSingleton, TensorProduct.instIsCentralScalar, balancedCoreAux_empty, Function.Periodic.const_inv_smul, MDifferentiableOn.clm_bundle_apply₂, Seminorm.sSup_apply, Module.isTorsionBy_quotient_element_smul, Seminorm.ball_bot, SkewMonoidAlgebra.coeff_single_mul, egauge_pi', Asymptotics.IsBigO.smul_isLittleO, left_sub_midpoint, HasFDerivWithinAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.innerSL_apply_comp, Module.Finite.of_isComplemented_codomain, Balanced.smul_mono, CategoryTheory.ShortComplex.leftHomologyMap'_smul, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, mem_convexAddSubmonoid, midpoint_vsub_midpoint_same_right, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, QuadraticMap.nondegenerate_associated_iff, Algebra.lsmul_coe, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Affine.Simplex.centroid_vsub_eq, Orientation.oangle_smul_left_of_pos, openSegment.lift, HilbertBasis.hasSum_repr_symm, ContinuousLinearMap.map_smul, CStarMatrix.norm_def, ContinuousAlternatingMap.smulRight_apply, AlternatingMap.instIsCentralScalar, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_deriv₂, IsMIntegralCurveAt.eventually_hasDerivAt, openSegment_subset_iff_segment_subset, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, RestrictScalars.smul_def, ModuleCat.ihom_ev_app, ContMDiffOn.clm_bundle_apply₂, inner_smul_left, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', TrivSqZeroExt.eq_smul_exp_of_invertible, TensorProduct.finsuppLeft'_apply, balanced_iff_neg_mem, DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, Seminorm.continuous_of_le, mem_segment_sub_add, AddSubmonoid.mem_smul_pointwise_iff_exists, ContinuousLinearMap.adjoint_adjoint, StrictConvexOn.sub_concaveOn, HasCompactSupport.hasFDerivAt_convolution_left, TrivSqZeroExt.map_id, Submodule.flip_quotDualCoannihilatorToDual_injective, Algebra.Extension.H1Cotangent.map_comp, LinearMap.lflip_apply, HolderWith.smul_iff, MeasureTheory.Integrable.smul_of_top_right, Bundle.ContinuousRiemannianMetric.isVonNBounded, TensorProduct.lift.equiv_apply, MonovaryOn.sub_smul_sub_nonneg, IsBaseChange.linearMapLeftRightHom_comp, HasDerivWithinAt.finCons, HasStrictDerivAt.clm_apply, IsLocalizedModule.fromLocalizedModule'_smul, TemperedDistribution.smulLeftCLM_apply_apply, HasDerivAt.congr_deriv, HasDerivAt.tendsto_slope_zero_right, Submodule.toSubMulAction_mono, Matrix.Nondegenerate.toLinearMap₂', WithSeminorms.hasBasis_zero_ball, Finset.sum_smul_vsub_eq_weightedVSub_sub, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, DFinsupp.instSMulPosStrictMono, ContinuousLinearMap.hasDerivAt_of_bilinear, Circle.norm_smul, ConvexOn.map_add_sum_le, instIsPushoutFractionRingMvPolynomial_1, locallyConvexSpace_iff_exists_convex_subset_zero, second_derivative_symmetric_of_eventually, uniformConvexOn_zero, Convex.mem_extremePoints_iff_convex_diff, HasFDerivAt.comp_hasDerivAt_of_eq, Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂, VectorField.lieBracketWithin_const_smul_left, mellin_comp_mul_left, DifferentiableOn.fun_smul, Submodule.map_smul, convexOn_iff_pairwise_pos, Convex.combo_affine_apply, convex_segment, vadd_left_mem_affineSpan_pair, Finsupp.linearCombination_onFinset, MeasureTheory.SignedMeasure.im_toComplexMeasure, HasDerivAtFilter.const_sub, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, left_vsub_midpoint, Module.Basis.groupSMul_apply, LinearMap.IsRefl.ker_flip, AnalyticAt.hasStrictDerivAt, LinearMap.ker_smul, BoxIntegral.unitPartition.tag_mem_smul_span, Asymptotics.IsThetaTVS.refl, Asymptotics.IsLittleO.const_smul_left, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, AffineMap.coe_homothety, ContMDiff.smul_section, Filter.EventuallyEq.hasDerivWithinAt_iff, Seminorm.neg_mem_closedBall_zero, LinearMap.toMatrix₂Aux_apply, NonUnitalStarAlgHom.mk_coe, intervalIntegral.inv_smul_integral_comp_add_div, AlgebraicGeometry.Scheme.Modules.map_smul, SeminormFamily.basisSets_smul_left, InnerProductSpace.norm_rankOne, MeasureTheory.Measure.ae_smul_measure_eq, Ideal.stabilizerEquiv_apply_smul, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, Complex.hasDerivAt_Gamma_nat, Pi.noZeroSMulDivisors, RestrictScalars.addEquiv_map_smul, hasFDerivAt_integral_of_dominated_loc_of_lip, smul_eq_zero, tendsto_smul_comp_nat_floor_of_tendsto_nsmul, ArchimedeanClass.mk_smul, TensorProduct.uncurry_apply, Submodule.pointwiseCentralScalar, Antivary.sum_comp_perm_smul_eq_sum_smul_iff, Submodule.smul_coe, PiTensorProduct.mapLMultilinear_toFun_apply, IsLocalizedModule.eq_zero_iff, VectorField.mlieBracket_smul_right, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, CStarMatrix.inner_toCLM_conjTranspose_right, FixedBy.subfield_mem_iff, HasDerivAtFilter.fun_const_smul, instSMulMemClassHomogeneousSubmodule, LinearIsometryEquiv.map_smulₛₗ, MeasureTheory.integral_sum_dirac, real_inner_I_smul_self, AnalyticWithinAt.smul, Seminorm.closedBall_smul_closedBall, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, balancedCore_subset_balancedCoreAux, Orthonormal.inner_right_sum, mellin_comp_mul_right, IsLocalizedModule.surj, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, PointedCone.dual_singleton, RingFilterBasis.SubmodulesBasis.smul, convexOn_norm, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, bernsteinApproximation.apply, LinearMap.sum_repr_mul_repr_mul, fderiv_eq_smul_deriv, StrictConvex.add_right, CStarMatrix.toCLM_apply_single_apply, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Submodule.instIsScalarTower, LinearMap.ker_toContinuousLinearMap, groupCohomology.isCocycle₁_of_mem_cocycles₁, PointedCone.salient_iff_inter_neg_eq_singleton, MeasureTheory.integral_sum_dirac_eq_tsum, Submodule.span_smul_of_span_eq_top, ContinuousLinearMap.comp_smul, Polynomial.C_smul_derivation_apply, exists_pos_right_iff_sameRay_and_ne_zero, closedConvexHull_isClosed, LinearMap.toLinearMap₂'Aux_toMatrix₂Aux, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, ContinuousSMul.induced, PointedCone.toConvexCone_injective, HasDerivAt.mul_const, LinearMap.isSymm_iff_isHermitian_toMatrix, HasStrictDerivAt.fun_smul, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀, Monotone.convex_gt, ContinuousLinearMap.algebraMap_apply, LinearEquiv.apply_faithfulSMul, Representation.leftRegularMapEquiv_symm_apply_toFun, Seminorm.uniformity_eq_of_hasBasis, LinearMap.lsmul_eq_distribSMultoLinearMap, AlgEquiv.apply_smulCommClass, MeasureTheory.average_eq, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, MDifferentiableWithinAt.smul_section, Matrix.toBilin'_single, ContMDiffOn.smul_section, StarConvex.linear_preimage, TensorProduct.liftAux.smulₛₗ, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, WithSeminorms.finset_sups, LinearEquiv.conjAlgEquiv_ext_iff, MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOn, Submodule.restrictScalars_map, hasDerivWithinAt_sub_const_iff, Convex.linear_preimage, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, TensorProduct.restrictScalar_directSumRight, intervalIntegral.smul_integral_comp_add_mul, Complex.restrictScalars_toSpanSingleton', AffineSubspace.sOppSide_smul_vsub_vadd_right, HasFDerivWithinAt.list_prod', HasFDerivAt.continuousMultilinearMap_apply, Complex.hasSum_taylorSeries_on_eball, ofMul_uzpow, exists_smul_eq_of_finrank_eq_one, Quaternion.imK_snd_dualNumberEquiv, Module.Flat.isSMulRegular_of_nonZeroDivisors, fderiv_inv', MeasureTheory.Measure.integral_comp_inv_mul_right, TensorProduct.finsuppLeft_apply_tmul_apply, ContinuousLinearMapWOT.ext_inner_iff, Besicovitch.SatelliteConfig.exists_normalized_aux3, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, NormedSpace.exp_eq_expSeries_sum, TwoSidedIdeal.coe_mop_smul, Convex.asymptoticCone, Monovary.sum_smul_comp_perm_eq_sum_smul_iff, instIsPushoutFractionRingMvPolynomial, PolynomialModule.eval_single, VectorField.mlieBracket_const_smul_right, norm_inner_div_norm_mul_norm_eq_one_iff, Valuation.HasExtension.instIsScalarTowerInteger, Submodule.disjoint_span_singleton'', HasStrictDerivAt.star, ProbabilityTheory.integral_tilted_mul_eq_cgf, FormalMultilinearSeries.comp_assoc, egauge_smul_left, MeasureTheory.Measure.addHaar_smul, HasFPowerSeriesWithinAt.comp, IsLocalizedModule.mk'_sub_mk', ContinuousSMul.of_nhds_zero, MeasureTheory.hasSum_integral_sum_dirac, MeasureTheory.L1.SimpleFunc.setToL1S_smul, MvPolynomial.pderiv_inl_universalFactorizationMap_X, autEquivRootsOfUnity_smul, fderivWithin_pow', Algebra.Extension.Cotangent.val_smul'', balanced_zero, continuousMultilinearCurryFin1_apply, locallyConvexSpace_iff_exists_convex_subset, RootPairing.reflection_apply_root, LineDifferentiableAt.smul, StarConvex.mem_smul, IsLocalizedModule.injective_iff_isRegular, star_intCast_smul, RootPairing.reflectionPerm_eq_iff_smul_coroot, LinearMap.dualAnnihilator_ker_eq_range_flip, TensorialAt.smul, HilbertBasis.finite_spans_dense, Derivation.apply_aeval_eq, Module.notMem_support_iff', MeasureTheory.setIntegral_const, HasStrictDerivAt.fun_pow, norm_combo_lt_of_ne, Matrix.GeneralLinearGroup.fin_two_smul_prod, Ideal.mulQuot_injective, LinearIsometry.adjoint_comp_self, Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun, ConvexCone.mem_comap, MvPolynomial.rTensorAlgHom_apply_eq bridge: BoxIntegral.hasIntegralIndicatorConst
toMulAction 📖	CompOp	4113 math math: AdicCompletion.of_surjective_iff, range_cfcₙ_nnreal, Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, LinearMap.det_toContinuousLinearMap, LinearEquiv.multilinearMapCongrLeft_symm_apply, OreLocalization.left_distrib, units_inv_smul, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, LeftPreLieAlgebra.toSMulCommClass, ContMDiffAt.coordChangeL, LinearMap.IsSymmetric.clm_adjoint_eq, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, KaehlerDifferential.kerCotangentToTensor_toCotangent, TemperedDistribution.lineDerivOpCLM_eq, IsLocalizedModule.iso_symm_apply', CliffordAlgebra.contractRight_algebraMap_mul, LinearMap.restrictScalars_toMatrix, MeasureTheory.Lp.toTemperedDistributionCLM_apply, fderiv_iteratedFDeriv, Orientation.kahler_map_complex, MDifferentiable.coordChangeL, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, Seminorm.isBounded_const, TensorAlgebra.ofDirectSum_of_tprod, LinearMap.mkContinuous₂_norm_le', FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_changeOrigin, KaehlerDifferential.mvPolynomialBasis_apply, Matrix.toLinAlgEquiv_one, ContinuousLinearMap.derivWithin_of_bilinear, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, SemimoduleCat.Hom.hom₂_apply, HasDerivWithinAt.clm_comp, SchwartzMap.lineDerivOpCLM_eq, LinearMap.charpoly_def, LinearEquiv.congrRight₂_refl, Field.Emb.Cardinal.equivLim_coherence, InfiniteGalois.normal_iff_isGalois, SymmetricAlgebra.lift_ι_apply, LinearMap.mkContinuous₂_apply, PiTensorProduct.lift_reindex, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, dot_self_cross, CliffordAlgebra.contractRight_algebraMap, InnerProductSpace.isPositive_rankOne_self, LieDerivation.instNoetherian, Matrix.toLin_kronecker, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, IntermediateField.exists_algHom_adjoin_of_splits, Matrix.toLin'_symm, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right, LinearMap.detAux_def'', ContinuousLinearMap.mulLeftRight_isBoundedBilinear, Ideal.Filtration.submodule_eq_span_le_iff_stable_ge, TensorProduct.LieModule.liftLie_apply, HasFDerivWithinAt.continuousMultilinearMap_apply, PiTensorProduct.lift.tprod, IntermediateField.aeval_gen_minpoly, MDifferentiableOn.clm_postcomp, CliffordAlgebra.contractRight_eq, OrthonormalBasis.orthogonalProjection_eq_sum, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', LinearMap.toMatrixAlgEquiv'_mul, SymmetricAlgebra.rank_eq, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, Module.Basis.end_repr_apply, AdicCompletion.algebraMap_apply, OreLocalization.cardinalMk, AdicCompletion.mk_zero_of, SchwartzMap.instLineDerivLeftSMulReal, LinearMap.adjoint_adjoint, Matrix.SeparatingRight.toLinearMap₂, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, Rep.MonoidalClosed.linearHomEquiv_symm_hom, IntermediateField.algHomEquivAlgHomOfSplits_symm_apply, SchwartzMap.integral_sesq_fourier_fourier, MultilinearMap.fromDFinsuppEquiv_apply, OreLocalization.oreDiv_add_char, Submodule.isScalarTower, Module.support_quotient, LinearMap.exists_monic_and_aeval_eq_zero, Ideal.Quotient.map_ker_stabilizer_subtype, Subspace.dualAnnihilator_dualAnnihilator_eq_map, AnalyticOn.exists_hasFTaylorSeriesUpToOn, Real.hasFDerivAt_fourierChar_neg_bilinear_left, LinearMap.toLinearMap_tracePositiveLinearMap, isSMulRegular_iff_mem_nonZeroSMulDivisors, MeasureTheory.convolution_eq_right', TensorProduct.AlgebraTensorModule.leftComm_eq, UniformConvergenceCLM.continuous_of_continuous_uncurry, Quaternion.snd_imJ_dualNumberEquiv_symm, CFC.monotoneOn_one_sub_one_add_inv, Real.fderiv_fourierIntegral, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, Ideal.IsTwoSided.pow_succ, InnerProductSpace.rankOne_one_left_eq_innerSL, Submodule.le_annihilator_iff, ContDiff.fderiv_succ, IntermediateField.adjoin.finrank, AlternatingMap.constLinearEquivOfIsEmpty_symm_apply, LinearMap.Nondegenerate.congr, NonUnitalCStarAlgebra.toStarModule, Submodule.mem_ideal_smul_span_iff_exists_sum, nnnorm_cfcₙ_nnreal_le_iff, LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, Matrix.separatingRight_toLinearMap₂'_iff, LinearMap.baseChange_smul, LinearMap.BilinForm.isSkewAdjoint_bracket, ContinuousLinearMap.smulRight_one_eq_toSpanSingleton, AffineMap.lineMap_linear, Complex.kahler, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, AlgCat.hom_inv_associator, ContinuousLinearMap.map_add_add, CliffordAlgebra.foldl_prod_map_ι, TrivSqZeroExt.lift_inlAlgHom_inrHom, Module.Finite.multilinearMap, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, IntermediateField.algHomEquivAlgHomOfSplits_apply_apply, AdicCompletion.AdicCauchySequence.mk_eq_mk, CStarModule.innerₛₗ_apply, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, Module.End.HasEigenvalue.mem_spectrum, LieModule.toEnd_pow_apply_map, Polynomial.toMatrix_sylvesterMap', IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, Matrix.toLinearMapRight'_mul, ContinuousLinearMap.toLinearMap₁₂_injective, Submodule.smul_eq_map₂, LinearMap.restrictScalarsRange₂_apply, Polynomial.disjoint_ker_aeval_of_isCoprime, LinearMap.IsRefl.domRestrict, Ideal.iInf_pow_smul_eq_bot_of_isLocalRing, MvPolynomial.universalFactorizationMap_comp_map, MDifferentiableAt.cle_arrowCongr, LinearMap.isPositive_adjoint_comp_self, PolynomialModule.smul_def, ContinuousLinearMap.continuousSMul, LinearMap.isAdjointPair_iff_comp_eq_compl₂, hasFTaylorSeriesUpToOn_top_iff_right, Module.End.isNilpotent_restrict_genEigenspace_nat, Submodule.map_dualCoannihilator_le, Matrix.separatingRight_toLinearMap₂_iff, RatFunc.algEquivOfTranscendental_X, CliffordAlgebra.foldr'_ι, AdicCompletion.map_val_apply, Ideal.mul_le_right, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, Matrix.spectrum_toEuclideanLin, ContDiff.iteratedFDeriv_right, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, SchwartzMap.pairing_apply_apply, MeasureTheory.integral_domSMul, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, SymmetricAlgebra.isSymmetricAlgebra_ι, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, Ideal.smul_top_eq_map, Differentiable.clm_comp, Module.Basis.toDual_linearCombination_left, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Commute.cfcₙ_nnreal, IntermediateField.isScalarTower_mid', LinearEquiv.congrRight_symm, LinearMap.mapMatrixLinear_apply, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', LieModule.trace_toEnd_eq_zero_of_mem_lcs, Algebra.Generators.cotangentSpaceBasis_apply, Matrix.toLinearMap₂'_comp, FormalMultilinearSeries.changeOriginSeriesTerm_apply, PiTensorProduct.lift_reindex_symm, kroneckerTMulAlgEquiv_symm_single_tmul, LinearMap.toMatrix_apply', IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, LinearMap.llcomp_apply, LinearMap.toMatrix₂_mul, HasDerivWithinAt.complexToReal_fderiv', Orientation.kahler_comp_rightAngleRotation', Algebra.Extension.H1Cotangent.map_id, mdifferentiableAt_iff_localFrame_coeff, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, IsCovariantDerivativeOn.difference_apply, Module.Basis.dualBasis_coord_toDualEquiv_apply, Matrix.repr_toLin, AdicCompletion.of_ofAlgEquiv_symm, IntermediateField.isPurelyInseparable_iSup, WeierstrassCurve.Projective.nonsingularLift_some, LocalizedModule.restrictScalars_map_eq, ContinuousLinearMap.precompUniformConvergenceCLM_apply, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, KaehlerDifferential.mvPolynomialBasis_repr_D_X, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, AlternatingMap.constLinearEquivOfIsEmpty_apply, LinearMap.tensorKer_tmul, ContMDiffCovariantDerivativeOn.affine_combination, LinearMap.orthogonal_ker, LinearMap.toMatrixAlgEquiv_comp, LinearMap.IsSymmetric.diagonalization_apply_self_apply, TensorProduct.sum_tmul_basis_right_injective, Submodule.mem_colon', Real.fourier_continuousLinearMap_apply, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, Unitization.real_cfcₙ_eq_cfc_inr, intervalIntegral.fderiv_integral_of_tendsto_ae, ContDiffAt.fderiv_right_succ, Representation.asAlgebraHom_single, AffineIsometryEquiv.ofTop_apply, HasFDerivWithinAt.clm_apply, LieAlgebra.finrank_engel, skewAdjointLieSubalgebraEquiv_apply, AnalyticOnNhd.iteratedFDeriv_of_isOpen, Continuous.convolution_integrand_fst, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, Module.Ray.neg_units_smul, iteratedFDerivWithin_succ_eq_comp_right, OrthonormalBasis.toBasis_tensorProduct, SchwartzMap.lineDerivOp_fourier_eq, Subspace.dualRestrict_comp_dualLift, LinearEquiv.conj_trans, TensorAlgebra.toTrivSqZeroExt_ι, LinearMap.mul_apply_apply, LinearMap.BilinForm.toMatrix_compRight, LinearMap.rTensor_smul_action, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerₛₗ_apply, Algebra.lmul_algebraMap, HasFTaylorSeriesUpTo.hasFDerivAt, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, norm_iteratedFDerivWithin_clm_apply, ContMDiffWithinAt.mfderivWithin_const, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Submodule.dualQuotEquivDualAnnihilator_apply, Unitization.splitMul_apply, ContMDiffOn.clm_postcomp, TensorAlgebra.ι_comp_lift, LinearEquiv.congrQuadraticMap_symm, LinearEquiv.conj_apply_apply, LinearMap.adjoint_eq_toCLM_adjoint, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, TensorAlgebra.adjoin_range_ι, LeftInvariantDerivation.left_invariant', TemperedDistribution.fourierMultiplierCLM_smul, FormalMultilinearSeries.le_changeOriginSeries_radius, Matrix.toLinearMap₂_toMatrix₂, LinearMap.toMatrix_one, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, Module.isTorsionBySet_quotient_ideal_smul, MultilinearMap.currySum_add, DualNumber.range_lift, Unitization.algHom_ext'_iff, QuotSMulTop.equivTensorQuot_naturality, LieAlgebra.IsKilling.rootSystem_coroot_apply, MultilinearMap.mkContinuousMultilinear_apply, TensorAlgebra.toDirectSum_tensorPower_tprod, TemperedDistribution.lineDerivOp_fourier_eq, Module.End.spectrum_intrinsicStar, Module.Flat.ker_lTensor_eq, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, SpecialLinearGroup.mem_center_iff_spec, cross_cross, FormalMultilinearSeries.derivSeries_coeff_one, Matrix.spectrum_toLpLin, mdifferentiableOn_symm_coordChangeL, AdicCompletion.instIsScalarTower_1, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, Submodule.ideal_span_singleton_smul, LinearMap.ofIsCompl_smul, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, fderiv_clm_comp, IsSymmetricAlgebra.equiv_apply, LinearMap.surjective_compr₂ₛₗ_of_exists_rightInverse, Submodule.top_eq_ofList_cons_smul_iff, SchwartzMap.bilinLeftCLM_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, Module.Dual.eval_comp_comp_evalEquiv_eq, fderiv_continuousAlternatingMap_apply_const, LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank, OreLocalization.universalHom_apply, OreLocalization.nsmul_eq_nsmul, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, CategoryTheory.Linear.comp_apply, LinearEquiv.map_mem_invtSubmodule_conj_iff, Module.End.isFinitelySemisimple_sub_algebraMap_iff, InfiniteGalois.normalAutEquivQuotient_apply, LinearMap.mem_isPairSelfAdjointSubmodule, Submodule.dualPairing_apply, IsGaloisGroup.fixingSubgroup_top, NonUnitalAlgHom.coe_lmul_eq_mul, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_symm_apply_mk_tmul, Matrix.toLin_mul_apply, ContDiffMapSupportedIn.seminorm_fderivLM_le, LinearMap.tensorEqLocusEquiv_apply, toMatrix_distrib_mul_action_toLinearMap, LinearMap.IsRefl.ker_flip_eq_bot, LinearMap.domRestrict'_apply, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContDiffMapSupportedIn.seminorm_fderivLM_top, Module.dualMap_dualMap_eq_iff, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, ModuleCat.Iso.homCongr_eq_arrowCongr, AlgEquiv.linearEquivConj_mulLeft, LieIdeal.reflectionPerm_mem_rootSet_iff, PiToModule.fromEnd_apply, IntermediateField.isAlgebraic_tower_bot, Submodule.sup_eq_sup_smul_of_le_smul_of_le_jacobson, LieAlgebra.Basis.borelLower_le_biSup, IsGaloisGroup.fixedPoints_top, TensorPower.gMul_eq_coe_linearMap, AnalyticOn.iteratedFDerivWithin, LieSubalgebra.toEnd_eq, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, ContinuousAlternatingMap.compContinuousLinearMapₗ_apply, Module.FinitePresentation.exists_notMem_bijective, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, Submodule.mem_smul_span_singleton, WittVector.factorPowSucc_comp_fontaineThetaModPPow, ContinuousAlternatingMap.piLIE_apply_apply, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, AdicCompletion.incl_apply, IntermediateField.algHomEquivAlgHomOfSplits_apply, AdicCompletion.map_ext'_iff, IntermediateField.botEquiv_symm, AlgCat.hom_inv_rightUnitor, Unitization.starAlgHom_ext_iff, LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero', LinearEquiv.congrRight₂_apply, cross_self, Rep.to_Module_monoidAlgebra_map_aux, CliffordAlgebra.contractRight_mul_ι, SpecialLinearGroup.mem_center_iff, Ideal.iInf_pow_smul_eq_bot_of_le_jacobson, AdicCompletion.val_smul_eq_evalₐ_smul, Matrix.Nondegenerate.toLinearMap₂, rTensor_injective_iff_lcomp_surjective, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, TensorProduct.gradedMul_assoc, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, ContinuousLinearMap.isometry_mul_flip, Quaternion.snd_re_dualNumberEquiv_symm, LinearMap.injective_compr₂_of_injective, Module.Basis.flag_le_ker_dual, Module.Ray.units_smul_of_neg, Matrix.intrinsicStar_toLin', LieModule.isNilpotent_toEnd_genWeightSpace_zero, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Ideal.Filtration.smul_le, InnerProductSpace.smul_left, LinearMap.coe_toContinuousLinearMap', HasFDerivWithinAt.linear_multilinear_comp, KaehlerDifferential.polynomialEquiv_D, AdicCompletion.exists_smodEq_pow_smul_top_and_smodEq_pow_add_one_smul_top, SemimoduleCat.Iso.homCongr_eq_arrowCongr, iteratedFDerivWithin_succ_eq_comp_left, Module.supportDim_add_length_eq_supportDim_of_isRegular, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, contDiffOn_iff_continuousOn_differentiableOn, CommRing.Pic.mul_eq_tensor, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, LinearEquiv.dualMap_trans, Module.Basis.coe_dualBasis, Submodule.comap_le_comap_smul, CStarModule.innerSL_apply, IsLocalizedModule.iso_symm_apply, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, ExteriorAlgebra.liftAlternating_ι_mul, LinearMap.tensorKer_coe, LinearIsometryEquiv.conjStarAlgEquiv_apply, Bundle.ContinuousLinearMap.vectorBundle, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, Module.Baer.iff_surjective, Algebra.Extension.CotangentSpace.map_id, LinearMap.toMatrixOrthonormal_reindex, LinearMap.toMatrixAlgEquiv_toLinAlgEquiv, MeasureTheory.ConvolutionExistsAt.integrable, LinearMap.ker_self_comp_adjoint, Fintype.linearIndependent_iff', CliffordAlgebra.foldr_mul, QuadraticMap.toMatrix'_comp, LinearMap.trace_mul_cycle, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, ExteriorAlgebra.toTrivSqZeroExt_comp_map, IsAdicComplete.mkQ_comp_lift, TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensor, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, LinearMap.lTensor_smul, LinearMap.ker_localizedMap_eq_localized'_ker, Distribution.IsVanishingOn.smulLeftCLM, exteriorPower.alternatingMapLinearEquiv_ιMulti, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, IsLocalizedModule.iso_apply_mk, IntermediateField.exists_algHom_of_adjoin_splits, Quaternion.imJ_fst_dualNumberEquiv, InnerProductSpace.inner_left_rankOne_apply, cfcₙHom_nnreal_eq_restrict, star_dotProduct_toMatrix₂_mulVec, norm_iteratedFDeriv_clm_apply, IsBaseChange.linearMapLeftRightHom_comp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange, SchwartzMap.fderivCLM_apply, IntermediateField.normal_iff_forall_map_eq, Subspace.dualAnnihilator_dualAnnihilator_eq, MultilinearMap.currySumEquiv_apply, LocalizedModule.divBy_apply, TensorProduct.AlgebraTensorModule.lTensor_id, LocalizedModule.lift'_smul, skewAdjointLieSubalgebraEquiv_symm_apply, TrivSqZeroExt.fstHom_comp_map, ContinuousAlternatingMap.curryLeft_smul, zero_prodMap_dualTensorHom, Ideal.mul_sup_eq_of_coprime_right, Matrix.Represents.smul, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, ContMDiffAt.clm_postcomp, Algebra.lmul_injective, RightPreLieAlgebra.toIsScalarTower, ContMDiffWithinAt.clm_postcomp, LinearMap.spectrum_toMatrix', LieModule.trace_toEnd_genWeightSpace, Real.integrable_prod_sub, Real.smul_map_diagonal_volume_pi, LinearMap.smulRight_id, ContinuousLinearMap.eq_adjoint_iff, ContDiffAt.fderiv_succ, toMatrix_rotation, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, LinearMap.separatingRight_congr_iff, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic, KaehlerDifferential.isScalarTower', Module.eval_apply_injective, LinearEquiv.congrQuadraticMap_refl, AlgHom.mulLeftRightMatrix.inv_comp, Submodule.dualAnnihilator_map_dualMap_le, Derivation.linearEquiv_coe_to_linearMap_comp, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, le_comap_range_lTensor, HasFDerivAt.continuousMultilinear_apply_const, Submodule.dualCopairing_eq, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousLinearMap.IsPositive.smul_of_nonneg, InnerProductSpace.rankOne_apply, LieModule.shiftedGenWeightSpace.toEnd_eq, MeasureTheory.convolution_tendsto_right, IntermediateField.restrictScalars_normal, WittVector.factorPowSucc_fontaineThetaModPPow_eq, IntermediateField.isScalarTower, HasFTaylorSeriesUpToOn.zero_eq', KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, TensorProduct.liftAux_tmul, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, LieAlgebra.ad_isSemisimple_of_isSemisimple, QuotSMulTop.equivTensorQuot_naturality_mk, LieDerivation.inner_apply_apply, IsLocalRing.map_mkQ_eq, dot_cross_self, HasStrictDerivAt.clm_comp, LieModule.Cohomology.twoCochain_alt, WeierstrassCurve.Projective.Point.zero_point, Module.endTensorEndAlgHom_apply, Matrix.toLpLin_mul_same, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, LinearMap.mem_skewAdjointSubmodule, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, Ideal.bot_pow, RootPairing.Hom.weight_coweight_transpose, contMDiffOn_localFrame_coeff, ContinuousMultilinearMap.norm_smulRightL_le, TensorProduct.coe_directSumRight', Algebra.TensorProduct.comm_comp_map_apply, AnalyticOnNhd.iteratedFDeriv, smul_add, IsArithFrobAt.mul_inv_mem_inertia, derivWithin_clm_comp, Module.DualBases.coe_dualBasis, ContinuousLinearMap.precompL_apply, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom, IsSelfAdjoint.adjoint_eq, Submodule.mem_dualAnnihilator, isPurelyInseparable_iff_fd_isPurelyInseparable, Submodule.mem_ideal_smul_span_iff_exists_sum', LinearMap.isHermitian_toMatrix_iff, LinearMap.toMatrix_baseChange, TrivSqZeroExt.fst_exp, Ideal.FG.pow, IntermediateField.LinearDisjoint.of_isField', Representation.asAlgebraHom_def, RKHS.kernel_apply, Submodule.dualAnnihilator_eq_top_iff, TensorProduct.adjoint_map, LinearEquiv.conj_comp, VectorBundleCore.contMDiffOn_coordChange, PowerBasis.equivAdjoinSimple_symm_aeval, CliffordAlgebra.contractRight_comm, MDifferentiable.clm_postcomp, Ideal.pow_sup_eq_top, Ring.jacobson_smul_top_le, TrivSqZeroExt.map_inr, Unitization.starLift_symm_apply_apply, NonUnitalSubalgebra.prod_inf_prod, LinearMap.ker_adjoint_comp_self, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, Module.End.instLieModule, CStarMatrix.toCLM_injective, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, ContinuousLinearMap.isPositive_self_comp_adjoint, LinearMap.trace_eq_matrix_trace_of_finset, Unitization.starLift_apply_apply, LinearMap.adjoint_toContinuousLinearMap, Matrix.SeparatingLeft.toLinearMap₂', MeasureTheory.Measure.IsAddHaarMeasure.domSMul, IntermediateField.lift_adjoin_simple, LinearMap.rTensor_comp_flip_mk, Submodule.coe_dualCoannihilator_span, Unitization.sqrt_inr, ExteriorAlgebra.liftAlternating_comp, algebraicClosure.normalClosure_eq_self, contMDiffOn_baseSet_iff_localFrame_coeff, LinearEquiv.conj_refl, CharacterModule.curry_apply_apply, IntermediateField.AdjoinDouble.normal_algebraicClosure, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, Subalgebra.inclusion.isScalarTower_left, ContinuousLinearMap.toSesqForm_apply_coe, Submodule.comap_smul_top_of_surjective, Module.Basis.toDualEquiv_apply, CliffordAlgebra.changeFormAux_changeFormAux, Submodule.pow_smul_top_le, HasFPowerSeriesWithinOnBall.fderivWithin, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, Ideal.range_mul', SchwartzMap.integral_bilin_fourierIntegral_eq, Real.fourierIntegral_continuousMultilinearMap_apply, LinearMap.rank_diagonal, LinearMap.ker_localizedMap_eq_localized₀_ker, QuotSMulTop.map_comp_mkQ, RootPairing.injOn_dualMap_subtype_span_root_coroot, LinearIsometryEquiv.adjoint_eq_symm, extDeriv_fun_smul, ContinuousAlternatingMap.toAlternatingMap_curryLeft, TensorProduct.flip_mk_surjective, Ideal.pow_sup_pow_eq_top, Matrix.toEuclideanLin_apply, LieSubmodule.Quotient.toEnd_comp_mk', LinearMap.injective_compr₂ₛₗ_of_injective, Quaternion.imI_fst_dualNumberEquiv, ContinuousLinearMap.toLinearMap₁₂_apply, LinearMap.IsPositive.isPositive_smul_iff, Algebra.toMatrix_lmul_eq, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousLinearMap.finiteDimensional, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, TensorProduct.tensorQuotEquivQuotSMul_comp_mkQ_lTensor, LinearMap.toMatrixAlgEquiv'_id, isAdjointPair_toLinearMap₂, ContinuousLinearMap.opNorm_mul, LieModule.Cohomology.d₂₃_apply, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_iInf, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, LieModule.instIsTriangularizableSubtypeEndMemLieSubalgebraRangeToEnd, WeierstrassCurve.Projective.Point.toAffineLift_of_Z_ne_zero, exteriorPower.alternatingMapLinearEquiv_symm_map, LieIdeal.toInvtRootSubmodule_mono, TemperedDistribution.smulLeftCLM_neg, Orthonormal.basisTensorProduct, algebraicClosure.isAlgebraic, MDifferentiable.cle_arrowCongr, QuadraticForm.tmul_tensorMap_apply, PointwiseConvergenceCLM.postcomp_apply, Submodule.stabilizer_coe, HasFTaylorSeriesUpTo.fderiv_eq, IsGalois.normalClosure, Unitization.nnnorm_def, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Matrix.liftLinear_singleLinearMap, LieModule.Cohomology.d₁₂_apply_apply, TestFunction.fderivCLM_ofSupportedIn, NonUnitalSubalgebra.prod_top, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, LinearMap.IsSymmetric.conj_adjoint, LieModule.mem_posFittingCompOf, fderiv_continuousAlternatingMapCompContinuousLinearMap, LinearMap.ofIsComplProd_apply, LinearMap.mul_apply', compactOperator_topologicalClosure, LocalizedModule.divBy_mul_by, LinearMap.toMatrix_symm, IntermediateField.isAlgebraic_iff, LinearMap.toMatrix₂'_compl₁₂, PiTensorProduct.mapL_smul, Module.End.maxGenEigenspace_eq_maxGenEigenspace_zero, SchwartzMap.integral_sesq_fourier_eq, DualNumber.lift_apply_eps, Real.fderiv_fourier, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, ContinuousLinearMap.adjointAux_norm, MeasureTheory.L1.setToL1_smul_left, LinearMap.prodEquiv_apply, CStarMatrix.norm_def', MDifferentiable.clm_bundle_apply₂, OreLocalization.add_zero, Ideal.map_mul, Module.Basis.toLin_toMatrix, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, Submodule.map_smul'', Finsupp.linearCombination_one_tmul, WeierstrassCurve.Projective.addMap_of_Z_eq_zero_left, OreLocalization.neg_add_cancel, Ideal.mul_bot, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, ContinuousAlternatingMap.instContinuousSMul, LinearMap.ker_smul', LinearMap.toMatrixOrthonormal_apply_apply, LocalizedModule.map_surjective, IsLocalizedModule.map_linearMap_of_isLocalization, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, Matrix.toLin'_mul_apply, MultilinearMap.fromDirectSumEquiv_symm_apply, LieModule.isNilpotent_range_toEnd_iff, IntermediateField.coe_inclusion, LieAlgebra.bracket_ofTwoCocycle, Matrix.toLin'_hadamard, VectorFourier.fourierIntegral_continuousLinearMap_apply, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, AffineSubspace.coe_subtypeₐᵢ, Ideal.smul_eq_mul, Ideal.Quotient.stabilizerHom_surjective, TensorProduct.AlgebraTensorModule.restrictScalars_curry, IntermediateField.finiteDimensional_iSup_of_finset, LieAlgebra.rank_le_natTrailingDegree_charpoly_ad, LinearMap.trace_eq_contract_of_basis', TensorProduct.AlgebraTensorModule.rightComm_eq, CliffordAlgebra.foldl_one, QuadraticForm.tmul_comp_tensorComm, LinearMap.toMatrixAlgEquiv_apply, IntermediateField.LinearDisjoint.of_le, LocalizedModule.lift'_mk, RingTheory.Sequence.isWeaklyRegular_iff_Fin, IsGaloisGroup.quotientMap, CliffordAlgebra.foldr'Aux_foldr'Aux, SchwartzMap.fourier_lineDerivOp_eq, CliffordAlgebra.foldl_mul, LieAdmissibleAlgebra.toSMulCommClass, LinearMap.toContinuousBilinearMap_apply, TemperedDistribution.instLineDerivLeftSMulReal, norm_iteratedFDerivWithin_clm_apply_const, CStarMatrix.inner_toCLM_conjTranspose_left, LinearMap.toMatrix'_toLin', MultilinearMap.curryRight_apply, IntermediateField.LinearDisjoint.trace_algebraMap, isBoundedBilinearMap_comp, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Module.mapEvalEquiv_apply, LinearMap.bijective_compr₂_of_equiv, TensorProduct.toMatrix_assoc, Subspace.finrank_dualCoannihilator_eq, AdicCompletion.ofPowSMul_ofValEqZero, Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap, TemperedDistribution.fourierInv_lineDerivOp_eq, LieSubmodule.lie_top_eq_of_span_sup_eq_top, TrivSqZeroExt.lift_comp_inrHom, LeftInvariantDerivation.lift_smul, TensorProduct.quotTensorEquivQuotSMul_mk_one_tmul, Algebra.SubmersivePresentation.basisKaehlerOfIsCompl_apply, Algebra.Extension.instIsScalarTowerRingTensorProductBaseChange, PiToModule.fromEnd_injective, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, instIsPushoutFractionRingPolynomial_1, LinearMap.coe_lTensorHom, KaehlerDifferential.mapBaseChange_tmul, OrderIso.smulRightDual_apply, LinearMap.toMatrix_id, Real.fourier_iteratedFDeriv, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, SchwartzMap.smulLeftCLM_real_smul, MultilinearMap.currySum_apply', OreLocalization.neg_def, HasMFDerivAt.smul, Orientation.kahler_eq_zero_iff, KaehlerDifferential.kerTotal_eq, LinearMap.eq_adjoint_iff_basis_left, contDiff_succ_iff_fderiv, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, OreLocalization.zero_smul, MDifferentiableAt.clm_prodMap, Matrix.toAlgEquiv_kroneckerStarAlgEquiv, Algebra.Generators.H1Cotangent.δAux_C, ContinuousLinearMap.one_smulRight_eq_toSpanSingleton, Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply, QuadraticMap.associated_prod, SemimoduleCat.ofHom₂_hom_apply_hom, Module.add_smul, IntermediateField.minpoly_gen, NonUnitalSubalgebra.unitization_injective, LinearMap.toMatrix_transpose, LinearMap.toMatrix₂_toLinearMapₛₗ₂, Ideal.adic_module_basis, TensorAlgebra.toDirectSum_ofDirectSum, ContinuousLinearMap.mulLeftRight_apply, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, ContinuousLinearMap.holderₗ_apply_apply, LinearMap.trace_smulRight, ContinuousMultilinearMap.curryRight_norm, AdicCompletion.factor_eval_eq_evalₐ, ContinuousLinearMap.analyticOn_bilinear, iteratedFDeriv_comp_const_smul, LocalizedModule.mem_ker_mkLinearMap_iff, Matrix.det_kroneckerMapBilinear, ContinuousLinearMap.continuous_of_continuous_uncurry, LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, MeasureTheory.convolution_lsmul, Matrix.toLinAlgEquiv_mul, MDifferentiableAt.clm_postcomp, fderiv_continuousAlternatingMap_apply, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, Localization.algHom_ext_iff, Bornology.isVonNBounded_iff_absorbing_le, LinearMap.BilinMap.apply_apply_mem_of_mem_span, IsLocalizedModule.fromLocalizedModule.bij, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, Algebra.Extension.CotangentSpace.map_tmul, Orientation.kahler_swap, Matrix.vecMulBilin_apply, element_smul_restrictScalars, Unitization.lift_symm_apply_apply, cross_anticomm, LinearMap.range_smulRight_apply_of_surjective, RegularNormedAlgebra.isometry_mul', KaehlerDifferential.polynomialEquiv_comp_D, ContDiffWithinAt.hasFDerivWithinAt_nhds, KaehlerDifferential.span_range_map_derivation_of_isLocalization, LinearMap.dualMap_surjective_of_injective, Rep.ihom_ev_app_hom, IsBaseChange.endHom_toMatrix, IsCovariantDerivativeOn.torsion_self, Module.Free.multilinearMap, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, Ideal.range_mul, CommRing.Pic.mk_tensor, IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eq', toLinearEquiv_symm_apply, Field.Emb.Cardinal.succEquiv_coherence, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, MDifferentiableWithinAt.clm_bundle_apply₂, TrivSqZeroExt.algHom_ext'_iff, Submodule.dualAnnihilator_anti, IsAdicComplete.of_liftRingHom, GradedTensorProduct.mul_def, Algebra.TensorProduct.linearMap_comp_rid, HasFDerivAt.clm_apply, LieModule.isNilpotent_toEnd_of_isNilpotent, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, MultilinearMap.curryFinFinset_apply, LocalizedModule.map_injective, NonUnitalStarSubalgebra.unitization_range, CliffordAlgebra.foldr_prod_map_ι, Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv, Algebra.Extension.tensorCotangentSpace_tmul_tmul, VectorFourier.hasFDerivAt_fourierIntegral, TensorProduct.equivFinsuppOfBasisLeft_symm, SymmetricAlgebra.instModuleFree, Submodule.comap_smul, LinearMap.IsProj.eq_conj_prodMap, LinearMap.tensorEqLocus_coe, TensorAlgebra.toExterior_ι, AlternatingMap.alternatizeUncurryFin_apply, hasFDerivAt_ringInverse, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, TensorProduct.curry_injective, HasFDerivAt.continuousAlternatingMap_apply, MeasureTheory.convolution_precompR_apply, lTensorHomEquivHomLTensor_apply, VectorFourier.fourierIntegral_iteratedFDeriv, LinearMap.extendScalarsOfIsLocalizationEquiv_apply, rank_lt_rank_dual', coeSubmodule_differentIdeal_fractionRing, LieAlgebra.Basis.borelUpper_eq, QuotSMulTop.map_surjective, Ideal.Fiber.lift_residueField_surjective, InnerProductSpace.nnnorm_rankOne, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, IsGaloisGroup.fixedPoints_of_isGaloisGroup, LinearMap.trace_mul_comm, LinearMap.trace_eq_contract, OrthonormalBasis.orthogonalProjection_apply_eq_sum, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, Orientation.kahler_comp_rightAngleRotation, LinearMap.toKerLocalized_isLocalizedModule, Seminorm.ball_smul, LieAlgebra.Basis.linearIndepOn_root_baseSupp, ContinuousLinearEquiv.arrowCongr_apply, NonUnitalSubalgebra.unitization_range, CliffordAlgebra.changeFormAux_apply_apply, LocalizedModule.equivTensorProduct_symm_apply_tmul, LinearMap.isSymmetric_self_comp_adjoint, LinearEquiv.arrowCongr_symm_apply, LinearMap.trace_eq_sum_inner, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, ContinuousLinearMap.toUniformConvergenceCLM_apply, ContinuousAlternatingMap.curryLeft_apply_apply, ContinuousLinearMap.flip_smul, LieSubmodule.coe_map_toEnd_le, Module.FinitePresentation.linearEquivMap_symm_apply, IntermediateField.linearDisjoint_comm, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, Submodule.annihilator_mul, Subspace.dualPairing_nondegenerate, OreLocalization.oreDiv_add_char', Matrix.isNilpotent_toLin'_iff, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, Orientation.volumeForm_zero_pos, LinearMap.trace_one, TensorAlgebra.equivFreeAlgebra_symm_ι, homTensorHomEquiv_apply, LieModule.mem_genWeightSpace, MeasureTheory.ConvolutionExistsAt.integrable_swap, SchwartzMap.laplacianCLM_eq', IsModuleTopology.continuous_bilinear_of_pi_fintype, TensorProduct.mk_apply, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, AlternatingMap.alternatizeUncurryFin_add, ContMDiffCovariantDerivativeOn.finite_affine_combination, Matrix.toLinearEquiv'_symm_apply, IntermediateField.equivOfEq_symm, nnnorm_cfcₙ_nnreal_lt, WeierstrassCurve.Projective.Point.toAffineLift_of_Z_eq_zero, LinearMap.BilinForm.mul_toMatrix'_mul, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, Matrix.toLin_symm, LieIdeal.rootSpan_mem_invtRootSubmodule, LinearMap.toMatrixAlgEquiv_id, fderivWithin_continuousAlternatingMap_apply_const_apply, LieAlgebra.Basis.coroot_eq_h', ContinuousMultilinearMap.curryFinFinset_symm_apply_const, IntermediateField.restrictRestrictAlgEquivMapHom_apply, instIsPushoutPolynomial_1, SeparatingDual.dualMap_surjective_iff, InnerProductGeometry.norm_toLp_symm_crossProduct, IsDecompositionField.toIsGaloisGroup, dualTensorHom_apply, BilinForm.mul_toMatrix_mul, isNoetherian_linearMap_pi, TrivSqZeroExt.map_comp_inlAlgHom, QuadraticForm.tensorRId_symm_apply, HasFPowerSeriesOnBall.fderiv_eq, Module.Invertible.rTensorEquiv_apply_apply, LinearMap.localized'_range_eq_range_localizedMap, lTensorHomEquivHomLTensor_toLinearMap, Ideal.bot_mul, Quaternion.fst_imK_dualNumberEquiv_symm, LinearMap.trace_comp_eq_mul_of_commute_of_isNilpotent, IsCovariantDerivativeOn.smul_const, Module.Basis.linearMap_apply, Submodule.dualCoannihilator_iSup_eq, Subalgebra.centralizer_coe_image_includeRight_eq_center_tensorProduct, LinearMap.det_toLpLin, Module.comap_eval_surjective, Module.FinitePresentation.exists_lift_of_isLocalizedModule, IntermediateField.fieldRange_comp_val, Matrix.toLinearMap₂_compl₁₂, LinearMap.dualMap_id, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, LinearAlgebra.FreeProduct.ι_apply, CFC.sqrt_map_prod, IntermediateField.adjoin.powerBasis_gen, ContinuousLinearMap.fderiv_of_bilinear, ExteriorAlgebra.liftAlternating_ιMulti, AlgCat.hom_hom_associator, Algebra.Extension.Hom.comp_id, linearIndependent_algHom_toLinearMap', Ideal.map_mk_comap_factorPow, IntermediateField.equivOfEq_rfl, Seminorm.gaugeSeminorm_ball, MeasureTheory.Measure.addHaarScalarFactor_smul_congr, iteratedFDerivWithin_succ_apply_right, ContinuousAlternatingMap.alternatizeUncurryFin_smul, CliffordAlgebra.changeForm_ι_mul, IsLocalizedModule.iso_symm_comp, contDiffAt_map_inverse, QuadraticForm.tensorAssoc_toLinearEquiv, TensorProduct.AlgebraTensorModule.rTensor_tensor, LinearMap.localized'_ker_eq_ker_localizedMap, Module.Ray.linearEquiv_smul_eq_map, Submodule.mem_annihilator', IntermediateField.normal_iff_normalClosure_le, DualNumber.fst_eq_zero_iff_eps_dvd, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, TrivSqZeroExt.eq_smul_exp_of_ne_zero, CovariantDerivative.torsion_apply, Real.fourierIntegral_continuousLinearMap_apply, LinearMap.mk₂_apply, AdicCompletion.isAdicCauchy_iff, LinearMap.polyCharpoly_baseChange, Submodule.adjoint_subtypeL, IsCovariantDerivativeOn.torsion_antisymm, MatrixEquivTensor.toFunBilinear_apply, AnalyticOn.fderivWithin, LinearMap.isSymmetric_adjoint_mul_self, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, ContinuousLinearMap.opNorm_mul_apply, ContinuousLinearMap.norm_smulRightL, Submodule.dualRestrict_ker_eq_dualAnnihilator, IsBaseChange.transvection, LieSubalgebra.toEnd_mk, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, LinearMap.piApply_apply, Ideal.mul_left_self_sup, MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize, LieAlgebra.Basis.symm_baseSupp, IsLocalRing.map_tensorProduct_mk_eq_top, Bialgebra.TensorProduct.comulAlgHom_def, Module.Dual.eval_apply, ContDiffAt.fderiv_right, MeasureTheory.convolution_def, LinearMap.toMatrix₂_compl₂, ContMDiffFiberwiseLinear.locality_aux₂, ContinuousMultilinearMap.curryLeft_norm, ContinuousLinearMap.compContinuousMultilinearMapL_apply, InnerProductSpace.trace_rankOne, rTensorHomEquivHomRTensor_apply, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, LinearMap.trace_eq_contract_apply, ExteriorAlgebra.liftAlternatingEquiv_apply, MDifferentiableWithinAt.cle_arrowCongr, dualTensorHomEquivOfBasis_symm_cancel_right, units_smul_eq_self_iff, MDifferentiableWithinAt.clm_precomp, ContMDiffVectorBundle.continuousLinearMap, Matrix.toLpLin_symm_pow, Ideal.card_stabilizer_eq, Polynomial.mkDerivation_one_eq_derivative', TensorProduct.prodLeft_tmul, IsGaloisGroup.quotient, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, IsAdicComplete.of_lift, IsLocalization.tensorProduct_isLocalizedModule, ContDiffOn.fderiv_of_isOpen, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', TensorAlgebra.lift_symm_apply, isBoundedBilinearMap_compMultilinear, IsBaseChange.det_endHom, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, LinearMap.polyCharpolyAux_map_eval, AlternatingMap.curryLeft_apply_apply, IsLocalizedModule.mapExtendScalars_apply_apply, units_smul_eq_neg_iff, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, KaehlerDifferential.linearMapEquivDerivation_apply_apply, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, IntermediateField.relfinrank_dvd_finrank_bot, NormedSpace.toLinearMap_inclusionInDoubleDualWeak, TensorProduct.directSumRight_comp_rTensor, Module.preReflection_preReflection, Ideal.stabilizerEquiv_symm_apply_smul, ContDiffAt.iteratedFDeriv_right, HasFPowerSeriesWithinAt.fderivWithin_eq, TensorAlgebra.equivDirectSum_apply, ContDiffBump.convolution_tendsto_right, Matrix.linfty_opNNNorm_toMatrix, inCoordinates_apply_eq₂, Module.Basis.end_apply_apply, AnalyticOnNhd.fderiv_of_isOpen, Module.Basis.coe_constrL, Matrix.isRepresentation.toEnd_represents, mdifferentiableOn_localFrame_coeff, IsHausdorff.iInf_pow_smul, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, MeasureTheory.distribHaarChar_apply, contDiffOn_infty_iff_fderivWithin, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, IsLocalizedModule.fromLocalizedModule.inj, Matrix.toEuclideanCLM_toLp, Module.Invertible.bijective_curry, LinearMap.trace_eq_zero_of_mapsTo_ne, KaehlerDifferential.isLocalizedModule_map, DualNumber.lift_inlAlgHom_eps, isSMulRegular_submodule_iff_right_eq_zero_of_smul, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, CPolynomialOn.iteratedFDeriv, IntermediateField.adjoin_simple_adjoin_simple, Module.End.hasUnifEigenvalue_iff_mem_spectrum, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, cross_anticomm', IsCompactOperator.antilipschitz_of_not_hasEigenvalue, Matrix.toLin_scalar, IntermediateField.normal_iSup, LeftInvariantDerivation.evalAt_coe, fderiv_inverse, HasFPowerSeriesOnBall.fderiv, LinearMap.adjoint_rTensor, WeierstrassCurve.Projective.Point.toAffineLift_some, MeasureTheory.FiniteMeasure.map_fst_prod, ContMDiffOn.clm_precomp, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousMultilinearMap.restrictScalarsLinear_apply, contDiffOn_nat_iff_continuousOn_differentiableOn, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, Ideal.FG.mul, Submodule.LinearDisjoint.linearIndependent_right_of_flat, IsGaloisGroup.instSMulCommClassQuotientSubgroupSubtypeMemIntermediateField, Subalgebra.isScalarTower_right, IntermediateField.AdjoinSimple.norm_gen_eq_one, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, LieModule.coe_genWeightSpaceOf_zero, LinearMap.adjoint_inner_right, TensorAlgebra.equivFreeAlgebra_ι_apply, InnerProductSpace.adjoint_rankOne, IntermediateField.range_val, IntermediateField.instFiniteSubtypeMemBot, MultilinearMap.coe_currySumEquiv_symm, IntermediateField.isCyclotomicExtension_lcm_sup, LinearMap.trace_transpose', LieAlgebra.Basis.baseSupp_apply_smul_f, InnerProductSpace.rankOne_eq_zero, fderivWithin_continuousMultilinear_apply_const_apply, LinearMap.IntrinsicStar.starLinearEquiv_eq_arrowCongr, IsTensorProduct.equiv_symm_apply, Projectivization.cross_mk_of_cross_ne_zero, Unitization.splitMul_injective_of_clm_mul_injective, Matrix.toLpLin_one, ContinuousAlternatingMap.norm_curryLeft, Algebra.Extension.instIsScalarTowerRing, IntermediateField.linearDisjoint_iff', MultilinearMap.curryFinFinset_symm_apply_piecewise_const, ContMDiffOn.coordChangeL, IsGaloisGroup.fixedPoints_fixingSubgroup, InnerProductSpace.inner_right_rankOne_apply, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, Module.Dual.transpose_apply, IntermediateField.splits_iff_mem, LinearMap.isPosSemidef_iff_posSemidef_toMatrix, ContinuousAlternatingMap.apply_apply, mdifferentiableAt_hom_bundle, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, AffineIsometryEquiv.coe_ofEq_apply, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, TrivSqZeroExt.snd_exp, fderivWithin_inv', Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, TensorProduct.prodLeft_symm_tmul, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, IsLocalizedModule.map_comp', MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, ContinuousLinearMap.fderivWithin_of_bilinear, AffineSubspace.isometryEquivMap.toAffineMap_eq, Submodule.comap_dualAnnihilator, TensorAlgebra.lift_ι_apply, KaehlerDifferential.linearMapEquivDerivation_symm_apply, Algebra.normalizedTrace_intermediateField, TensorAlgebra.instModuleFree, LinearMap.BilinForm.tensorDistribEquiv_apply, ContDiffMapSupportedIn.uniformSpace_eq_iInf, KaehlerDifferential.span_range_derivation, WeierstrassCurve.Projective.smul_eq, Matrix.piLp_ofLp_toEuclideanLin, Algebra.Generators.H1Cotangent.δAux_monomial, PiTensorProduct.liftIsometry_tprodL, Submodule.eq_smul_of_le_smul_of_le_jacobson, DualNumber.isNilpotent_iff_eps_dvd, TrivSqZeroExt.map_comp_inrHom, contDiffWithinAt_iff_of_ne_infty, TensorProduct.map₂_apply_tmul, LieSubmodule.traceForm_eq_zero_of_isTrivial, PowerBasis.constr_pow_algebraMap, UniformConvergenceCLM.continuousSMul, lieEquivMatrix'_apply, TensorAlgebra.rank_eq, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, TensorProduct.AlgebraTensorModule.congr_eq, DualNumber.isMaximal_span_singleton_eps, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, Convex.second_derivative_within_at_symmetric, LieModule.weight_vector_multiplication, isNormalClosure_normalClosure, VectorFourier.iteratedFDeriv_fourierIntegral, Unitization.starMap_injective, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, ContDiffBump.normed_convolution_eq_right, LinearMap.norm_mkContinuous₂_aux, AdicCompletion.range_eval, InnerProductSpace.rankOne_eq_rankOne_iff_comm, MulSemiringAction.toAlgEquiv_symm_apply, Ideal.Quotient.smul_top, Algebra.Generators.cotangentSpaceBasis_repr_tmul, IntermediateField.finrank_eq_one_iff, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, IntermediateField.lift_top, ContinuousLinearMap.precompR_apply, RingHom.SurjectiveOnStalks.tensorProductMap, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, IsGaloisGroup.fixingSubgroup_le_of_le, NonUnitalAlgHom.toAlgHom_zero, LinearMap.minpoly_toMatrix', LieSubalgebra.coe_ad_pow, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, Seminorm.comp_smul, IsGreatest.nnnorm_cfcₙ_nnreal, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', MeasureTheory.hasFDerivAt_convolution_right_with_param, LinearMap.trace_prodMap, Submodule.iSup_dualAnnihilator_le_iInf, ContMDiffAt.mfderiv_const, Algebra.Generators.Hom.comp_id, LinearMap.liftBaseChangeEquiv_symm_apply, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, CommAlgCat.lift_unop_hom, iteratedFDerivWithin_eq_equiv_comp, LinearMap.toMatrix₂_comp, Module.Quotient.mk_smul_mk, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, VonNeumannAlgebra.centralizer_centralizer', CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, IntermediateField.exists_algHom_adjoin_of_splits_of_aeval, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, RightPreLieAlgebra.toSMulCommClass, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, Unitization.starMap_id, Ideal.sup_pow_eq_top', LinearMap.lsmul_flip_apply, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, DistribMulActionHom.coe_fn_coe', isLocalizedModule_iff, AlgebraicIndependent.lift_reprField, Matrix.SeparatingRight.toLinearMap₂', Algebra.Extension.Hom.sub_one_tmul, Module.Basis.toDual_ker, DualNumber.lift_smul, Module.Basis.dualBasis_apply_self, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, IntermediateField.isAlgebraic_adjoin, TensorProduct.lift.tmul', Submodule.map₂_map_left, Quaternion.imK_fst_dualNumberEquiv, QuadraticForm.tensorRId_apply, LinearMap.exists_eq_smul_id_of_forall_notLinearIndependent, Bundle.Pretrivialization.continuousLinearMap.isLinear, LinearMap.IsSymmetric.adjoint_conj, instIsLiouvilleSubtypeMemIntermediateField, isInertiaField_iff, LinearMap.pow_eq_aeval_mod_charpoly, LinearMap.prodEquiv_symm_apply, AffineIsometryEquiv.ofTop_symm_apply_coe, LinearMap.tensorProductEnd_apply, ContinuousLinearMap.adjoint_inner_left, Bialgebra.TensorProduct.assoc_tmul, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, lift_rank_lt_rank_dual', PointwiseConvergenceCLM.isInducing_inducingFn, Matrix.toLpLin_pow, Module.ext_iff, LinearMap.trace_eq_contract', Algebra.Generators.H1Cotangent.δAux_toAlgHom, ContinuousLinearEquiv.arrowCongr_symm, ContinuousLinearMap.isBoundedBilinearMap, LinearEquiv.symm_flip, LinearMap.restrictScalars_self, isDecompositionField_iff, KaehlerDifferential.D_apply, IsSymmetricAlgebra.equiv_symm_comp, InnerProductSpace.AlgebraOfCoalgebra.mul_def, Matrix.isUnit_toLin'_iff, Module.piEquiv_apply_apply, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, LinearMap.range_dualMap_eq_dualAnnihilator_ker, Polynomial.adjSylvester_comp_sylveserMap, fderivWithin_continuousMultilinear_apply_const, Ideal.ResidueField.liftₐ_comp_toAlgHom, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, TensorAlgebra.toClifford_ι, RootPairing.GeckConstruction.trace_toEnd_eq_zero, Matrix.toLin'_mul, IsArtinian.range_smul_pow_stabilizes, LieModule.lie_mem_maxGenEigenspace_toEnd, Unitary.conjStarAlgAut_ext_iff', Matrix.isSymmetric_toEuclideanLin_iff, LinearMap.isNilpotent_toMatrix_iff, LieModule.Cohomology.twoCochain_skew, MDifferentiableOn.coordChangeL, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, Quaternion.re_fst_dualNumberEquiv, ContinuousAlternatingMap.ofSubsingletonLIE_apply, Module.End.rTensorAlgHom_apply_apply, LinearMap.det_eq_det_toMatrix_of_finset, LieSubmodule.trace_eq_trace_restrict_of_le_idealizer, continuousMultilinearCurryRightEquiv_symm_apply, LinearMap.toMatrix_reindexRange, TemperedDistribution.fourierMultiplierCLM_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, ExteriorAlgebra.liftAlternating_apply_ιMulti, Seminorm.bound_of_continuous, PowerBasis.equivAdjoinSimple_aeval, IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, LieModule.isFaithful_iff, hasFTaylorSeriesUpToOn_top_iff', IsTensorProduct.assocOfMapSMul_symm_tmul, ContinuousLinearMap.lsmul_apply, AdicCompletion.transitionMap_comp_eval, LinearIsometryEquiv.conjStarAlgEquiv_trans, AffineIsometryEquiv.ofEq_symm, Matrix.ofLp_toLpLin, Module.range_piEquiv, ContinuousLinearMap.bilinearComp_zero_right, DivisibleHull.instIsStrictOrderedModuleNNRat, LinearMap.adjoint_comp_self_injective_iff, ContDiffWithinAt.fderivWithin'', Module.Basis.dualBasis_equivFun, Submodule.restrictScalars_map_smul_eq, PiTensorProduct.piTensorHomMap_tprod_tprod, RatFunc.algEquivOfTranscendental_symm_gen, Unitization.starLift_range, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, LinearMap.toMatrix_smulBasis_left, Ideal.mul_sup, CFC.nnrpow_def, VertexOperator.ncoeff_apply, Module.Dual.transpose_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, IsAzumaya.mulLeftRight_comp_congr, Convex.taylor_approx_two_segment, MDifferentiableOn.clm_prodMap, contMDiffAt_coordChangeL, IntermediateField.LinearDisjoint.of_le_right, Polynomial.sup_aeval_range_eq_top_of_isCoprime, WithConv.matrixToLin'StarAlgEquiv_apply, Ideal.Quotient.stabilizerHom_surjective_of_profinite, ContinuousLinearMap.adjointAux_apply, MultilinearMap.fromDFinsuppEquiv_single, eq_separableClosure_iff, Algebra.Generators.Hom.toExtensionHom_id, LinearMap.range_dualMap_dual_eq_span_singleton, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, LinearMap.det_toLin', IsCompactOperator.hasEigenvalue_or_mem_resolventSet, VonNeumannAlgebra.coe_mk, TensorAlgebra.lift_comp_ι, LieSubmodule.toEnd_comp_subtype_mem, TemperedDistribution.fourierMultiplierCLM_const, Submodule.map₂_map_right, Matrix.kroneckerMapBilinear_apply_apply, LinearMap.minpoly_dvd_charpoly, Ideal.mul_mono, LinearMap.SeparatingRight.congr, Ideal.pi_tensorProductMk_quotient_surjective, Matrix.rank_eq_finrank_range_toLin, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, Matrix.toLinearMapRight'_mul_apply, Submodule.annihilator_smul, InnerProductSpace.rankOne_def, Submodule.jacobson_smul_lt_top, MDifferentiableWithinAt.coordChangeL, BilinForm.toMatrix_comp, Ideal.inertia_le_stabilizer, LieAlgebra.ad_nilpotent_of_nilpotent, OreLocalization.numeratorRingHom_apply, CliffordAlgebra.EvenHom.contract, ContinuousLinearMap.coe_flipₗᵢ', MDifferentiableAt.clm_bundle_apply₂, AlgHom.mulLeftRight_apply, Module.Basis.linearCombination_dualBasis, PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, IntermediateField.normal_iff_forall_fieldRange_le, contDiffOn_succ_iff_fderiv_of_isOpen, fderivWithin_fderivWithin_eq_of_mem_nhds, LinearMap.lTensor_smul_action, transpose_dualTensorHom, ContinuousLinearMap.norm_smulRight_apply, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, Matrix.toLin_mul, contDiff_iff_continuous_differentiable, TensorAlgebra.ι_range_disjoint_one, LieModule.rank_eq_natTrailingDegree, Matrix.toLin_pow, Algebra.TensorProduct.lmul'_comp_map, LieSubmodule.mem_baseChange_iff, Module.End.aeval_apply_of_hasEigenvector, AdicCompletion.instIsHausdorff, QuadraticMap.associated_tmul, LinearMap.smulRight_eq_comp, IsAzumaya.bij, IsGalois.normalAutEquivQuotient_apply, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_comp_inl, Derivation.liftKaehlerDifferential_comp, Matrix.toLin_self, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, kroneckerTMulLinearEquiv_one, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, Submodule.dualCoannihilator_bot, SchwartzMap.integral_bilin_fourier_eq, KaehlerDifferential.ker_map, DifferentiableOn.clm_comp, ContinuousMultilinearMap.prodL_apply, Orientation.kahler_neg_orientation, AdicCompletion.coe_eval, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousOn.clm_bundle_apply₂, ContinuousLinearMap.coe_flipMultilinearEquiv, LieAlgebra.trace_toEnd_eq_zero, IntermediateField.LinearDisjoint.finrank_right_eq_finrank, NonUnitalAlgHom.coe_Lmul, ContinuousLinearMap.toSpanSingleton_comp, ContinuousMultilinearMap.norm_map_init_le, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, LeftInvariantDerivation.left_invariant'', CliffordAlgebra.contractLeft_contractLeft, TensorProduct.algebraMap_gradedMul, Subalgebra.centralizer_coe_map_includeRight_eq_center_tensorProduct, SchwartzMap.smulRightCLM_apply_apply, hasEigenvector_toLin'_diagonal, LinearIsometryEquiv.conjStarAlgEquiv_refl, IntermediateField.rank_adjoin_eq_one_iff, MeasureTheory.setToFun_smul_left, HasDerivAt.complexToReal_fderiv', LinearMap.separatingRight_iff_flip_ker_eq_bot, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, LinearMap.toMatrixAlgEquiv'_apply, LieAlgebra.ad_pow_lie, SubMulAction.algebraMap_mem, Module.Dual.instIsReflecive, Module.Ray.units_smul_of_pos, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, SchwartzMap.toTemperedDistributionCLM_apply_apply, fderivWithin_fderivWithin_eq_of_eventuallyEq, CliffordAlgebra.foldr'_ι_mul, IsSMulRegular.submodule, LinearMap.toMatrix'_algebraMap, isNoetherian_linearMap, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, AlgCat.hom_hom_rightUnitor, PiTensorProduct.liftEquiv_symm_apply, PiToModule.fromMatrix_apply_single_one, LocalizedModule.coe_map_eq, Representation.linHom_apply, LinearMap.dualMap_injective_of_surjective, extDerivWithin_fun_smul, Unitization.starMap_inl, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, LinearMap.dualMap_injective_iff, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, ContMDiffOn.clm_comp, AlternatingMap.curryLeft_apply_toMultilinearMap, LieModule.isNilpotent_toEnd_of_isNilpotent₂, Module.Basis.eval_range, TemperedDistribution.smulLeftCLM_sub, fromTangentSpace_mfderiv_smul', HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, Module.reflection_mul_reflection_pow, CliffordAlgebra.contractLeft_ι_mul, OreLocalization.oreDiv_add_oreDiv, Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux, IntermediateField.finrank_eq_fixingSubgroup_index, LinearMap.dualPairing_nondegenerate, PointedCone.basis_coord_mem_dual, Submodule.localized₀_smul, RootPairing.GeckConstruction.span_range_h'_eq_top, Submodule.norm_subtypeL, SModEq.smul', intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, Matrix.charpoly_toLin, LinearMap.toMatrixOrthonormal_symm_apply, Derivation.compAlgebraMapL_apply_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, IsTensorProduct.assoc_symm_tmul, IsLocalizedModule.map_linearCombination, ContinuousLinearMap.aestronglyMeasurable_comp₂, Module.Flat.eqLocus_lTensor_eq, Subspace.dualRestrict_leftInverse, QuadraticForm.tmul_tensorAssoc_apply, SchwartzMap.smulLeftCLM_const, smul_top_inf_eq_smul_of_isSMulRegular_on_quot, trace_eq_trace_adjoin, Ideal.Filtration.Stable.exists_pow_smul_eq_of_ge, CliffordAlgebra.even.lift_ι, LinearMap.toMatrix_mulVec_repr, OreLocalization.zsmul_eq_zsmul, LinearMap.toMatrix_innerₛₗ_apply, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, Ideal.inertiaEquiv_apply_smul, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, LieModule.Cohomology.mem_twoCochain_iff, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, Unitization.starMap_inr, TensorProduct.lift.tmul, Ideal.sup_mul_right_self, Matrix.toLin_apply_eq_zero_iff, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Algebra.Extension.Hom.toRingHom_algebraMap, TensorProduct.lTensorHomToHomLTensor_apply, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap, LinearMap.range_toContinuousLinearMap, IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eq, Submodule.traceDual_le_span_map_traceDual, Polynomial.mkDerivationEquiv_symm_apply, AdicCompletion.mk_smul_mk, Matrix.inner_toEuclideanCLM, ContinuousLinearMap.norm_precompR_le, IsGaloisGroup.fixingSubgroup_fixedPoints, Matrix.toLin'_reindex, Ideal.mul_le, IsFractionRing.stabilizerHom_surjective, Submodule.mem_colon_iff_le, LocalizedModule.subsingleton_iff_ker_eq_top, InfiniteGalois.proj_adjoin_singleton_val, contMDiffOn_baseSet_localFrame_coeff, CliffordAlgebra.contractRight_mul_algebraMap, IntermediateField.lift_inf, IsSemiprimaryRing.isNilpotent, ContinuousLinearMap.isBoundedLinearMap_comp_right, IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank, LinearMap.BilinForm.toMatrix'_compLeft, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂, Matrix.toLinearMapₛₗ₂_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, IsLocalizedModule.fromLocalizedModule_mk, VonNeumannAlgebra.mem_carrier, PiTensorProduct.liftEquiv_apply, LinearMap.lsmul_injective, Ideal.quotientMulEquivQuotientProd_snd, hasFTaylorSeriesUpTo_top_iff', Module.IsReflexive.bijective_dual_eval', fderivWithin_iteratedFDerivWithin, ContDiffWithinAt.clm_comp, Unitization.algebraMap_eq_inl, Convex.isLittleO_alternate_sum_square, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, MultilinearMap.mkContinuousLinear_norm_le, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, ExteriorAlgebra.liftAlternating_one, AffineEquiv.arrowCongrₗ_symm_apply, LinearMap.isSelfAdjoint_iff', Derivation.commutator_coe_linear_map, ContinuousLinearMap.deriv_of_bilinear, Submodule.apply_mem_map₂, Orientation.areaForm'_apply, IntermediateField.exists_finset_of_mem_supr'', Module.Basis.end_apply, Continuous.cfcₙ_nnreal, ContinuousLinearMap.nnnorm_holder_apply_apply_le, IntermediateField.exists_algHom_of_splits, MultilinearMap.curryMid_apply_apply, Distribution.mapCLM_apply, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Module.End.isSemisimple_sub_algebraMap_iff, PowerBasis.equivAdjoinSimple_gen, Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange, Polynomial.aeval_apply_smul_mem_of_le_comap, Derivation.coe_comp, LinearMap.IsRefl.eq_zero, Field.Emb.Cardinal.equivSucc_coherence, ContinuousLinearMap.bilinear_hasTemperateGrowth, LinearMap.toMatrix'_apply, IsBoundedBilinearMap.isBoundedLinearMap_deriv, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, Ideal.Quotient.stabilizerHom_apply, QuadraticForm.tmul_tensorComm_apply, Matrix.toLpLin_toLp, apply_eq_dotProduct_toMatrix₂_mulVec, ContinuousLinearMap.postcomp_apply, Ideal.fst_comp_quotientMulEquivQuotientProd, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, Ideal.span_mul_span', ContinuousLinearMap.uncurryLeft_apply, IsLocalizedModule.map_injective, MultilinearMap.freeDFinsuppEquiv_def, map_equiv_traceDual, LieAlgebra.Basis.iSupIndep_rootSpace, IntermediateField.restrictScalars_adjoin_eq_sup, TensorProduct.mapBilinear_apply, FiniteGaloisIntermediateField.isGalois, MeasureTheory.dist_convolution_le, LinearEquiv.conj_apply, Module.Basis.toDual_range, PiTensorProduct.dualDistribInvOfBasis_apply, Matrix.isRepresentation.toEnd_exists_mem_ideal, intervalIntegral.integral_hasStrictFDerivAt, Representation.asAlgebraHom_single_one, MeasureTheory.FiniteMeasure.instContinuousSMulNNReal, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, NonUnitalStarSubalgebra.unitization_injective, IsBilinearMap.toContinuousBilinearMap_apply, contMDiffOn_continuousLinearMapCoordChange, Submodule.map₂_eq_span_image2, NonUnitalStarSubalgebra.unitization_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Rep.ihom_obj_ρ_apply, Matrix.ker_toLin_eq_bot, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, cfcHom_real_eq_restrict, IntermediateField.LinearDisjoint.finrank_left_eq_finrank, IntermediateField.Lifts.lt_iff, WeierstrassCurve.Projective.addMap_eq, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, LieSubalgebra.coe_incl', IntermediateField.extendScalars_le_iff, Algebra.TensorProduct.toLinearEquiv_tensorTensorTensorComm, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, Submodule.dualAnnihilator_sup_eq, ContinuousAt.cfcₙ_nnreal, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, GradedTensorProduct.auxEquiv_mul, ContinuousMultilinearMap.apply_apply, ContDiff.smulRight, Fintype.linearIndependent_iff'ₛ, QuadraticForm.tmul_tensorRId_apply, LinearMap.IsSymmetric.adjoint_eq, ContinuousMultilinearMap.flipLinear_apply_apply, SymmetricAlgebra.algebraMap_eq_zero_iff, Submodule.lTensorOne'_tmul, RingTheory.Sequence.IsWeaklyRegular.regular_mod_prev, Module.FinitePresentation.linearEquivMap_apply, CStarMatrix.toCLM_apply_single, Real.fourier_fderiv, IsGaloisGroup.fixedPoints_bot, FormalMultilinearSeries.cpolynomialAt_changeOrigin_of_finite, LinearMap.llcomp_apply', Submodule.dualCoannihilator_sup_eq, Seminorm.const_isBounded, Splits.algebraicClosure, hasFTaylorSeriesUpTo_succ_nat_iff_right, PowerBasis.equivAdjoinSimple_symm_gen, LieModule.exists_forall_pow_toEnd_eq_zero, IsCovariantDerivativeOn.leibniz, Unitization.starMap_surjective, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, IntermediateField.coe_val, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Ideal.pow_le_self, QuotSMulTop.equivQuotTensor_naturality, LinearMap.smulRightₗ_apply, Submodule.rTensorOne'_tmul, JacobsonNoether.exist_pow_eq_zero_of_le, LinearMap.tracePositiveLinearMap_apply, MDifferentiableAt.clm_comp, LinearMap.toMatrix'_symm, Module.End.IsSemisimple.aeval, HasDerivAt.clm_comp, Module.symm_dualMap_evalEquiv, LinearMap.flip_mul, MeasureTheory.Measure.Regular.domSMul, VectorFourier.fderiv_fourierIntegral, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, AdicCompletion.of_bijective_iff, LinearMap.mapMatrix_smul, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, LieAlgebra.IsKilling.isSimple_iff_isIrreducible, InnerProductGeometry.norm_ofLp_crossProduct, AdicCompletion.transitionMap_comp_reduceModIdeal, MeasureTheory.integral_posConvolution, Algebra.Extension.tensorCotangentSpace_tmul, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, AlternatingMap.domCoprod'_apply, LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule, iteratedFDeriv_eq_equiv_comp, LinearMap.polyCharpolyAux_map_eq_charpoly, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Submodule.baseChange_eq_span, linearMap_toMatrix_mul_basis_toMatrix, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, Differentiable.continuousMultilinearMapCompContinuousLinearMap, Unitization.norm_eq_sup, Submodule.dualCopairing_apply, Matrix.kroneckerTMulAlgEquiv_symm_apply, Module.dualPairing_apply, Matrix.ofLp_toEuclideanCLM, Polynomial.mkDerivationEquiv_apply, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Derivation.liftKaehlerDifferential_comp_D, LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, CStarMatrix.toCLM_apply_eq_sum, TensorProduct.AlgebraTensorModule.coe_lTensor, LinearMap.exact_smul_id_smul_top_mkQ, Coalgebra.rTensor_counit_comp_comul, LinearMap.toMatrix_transpose_apply, IntermediateField.finrank_eq_finrank_subalgebra, Matrix.kroneckerTMulStarAlgEquiv_apply, LieSubmodule.toEnd_restrict_eq_toEnd, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', toMatrix_dualTensorHom, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_eq, AdicCompletion.ofPowSMul_injective, LinearEquiv.arrowCongr_apply, ContDiffMapSupportedIn.locallyConvexSpace, hasFDerivWithinAt_comp_smul_smul_iff, IntermediateField.restrictRestrictAlgEquivMapHom_injective, AdicCompletion.isAdicComplete, exteriorPower.alternatingMapLinearEquiv_apply_ιMulti, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Algebra.Generators.H1Cotangent.δAux_ofComp, Algebra.Extension.CotangentSpace.map_tmul_eq_tmul_map, Ideal.pow_right_mono, ContinuousMultilinearMap.smul_prod_smul, IsAdicComplete.of_comp_lift, TensorProduct.AlgebraTensorModule.homTensorHomMap_apply, LinearMap.isPositive_toContinuousLinearMap_iff, Matrix.range_toLin', LinearMap.prodMapLinear_apply, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', LieModule.IsFaithful.injective_toEnd, Submodule.map₂_span_singleton_eq_map_flip, Ideal.iSup_mul, PiTensorProduct.piTensorHomMap_tprod_eq_map, Quaternion.fst_imJ_dualNumberEquiv_symm, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, Representation.linHom.invariantsEquivRepHom_apply, LinearMap.dualMap_apply', iteratedFDerivWithin_two_apply', LinearMap.mul_toMatrix', LinearMap.toMatrix₂_basisFun, Algebra.Presentation.differentials.comm₂₃', cfcₙ_tsub, OreLocalization.zero_add, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, inr_comp_cfcₙHom_eq_cfcₙAux, Submodule.finite_quotient_smul, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, FGModuleCat.ihom_obj, IntermediateField.LinearDisjoint.finrank_sup, PiTensorProduct.lift_comp_reindex, IsLocalizedModule.lift_comp_iso, IsMIntegralCurveAt.hasMFDerivAt, LinearMap.dualMap_bijective_iff, HVertexOperator.of_coeff_coeff, PiTensorProduct.map₂_tprod_tprod, LinearMap.star_eq_adjoint, LinearMap.instLieModule, Module.Basis.sum_dual_apply_smul_coord, Ideal.Filtration.Stable.exists_pow_smul_eq, contDiffWithinAt_succ_iff_hasFDerivWithinAt', ContinuousLinearMap.range_smulRight_apply, LinearMap.toMatrix_smulBasis_right, Matrix.toLpLin_symm_id, contDiffOn_succ_iff_hasFDerivWithinAt, OreLocalization.right_distrib, Module.Basis.toDual_eq_repr, Matrix.range_toLin_eq_top, AdicCompletion.smul_mk, AlternatingMap.curryLeft_zero, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm, Module.Basis.baseChange_end, IntermediateField.finrank_adjoin_eq_one_iff, Matrix.toLin_finTwoProd_apply, AdicCompletion.exists_smodEq_pow_add_one_smul, FDRep.char_linHom, FormalMultilinearSeries.radius_unshift, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, TensorProduct.map_smul_right, HVertexOperator.coeff_inj_iff, HasFPowerSeriesAt.fderiv_eq, IntermediateField.normal_iff_forall_map_le', Matrix.isPositive_toEuclideanLin_iff, ContinuousWithinAt.cfcₙ_nnreal, Representation.IntertwiningMap.toLinearMap_smul, ContinuousLinearMap.memLp_of_bilin, TensorAlgebra.ofDirectSum_toDirectSum, IntermediateField.normal_iff_forall_fieldRange_eq, FreeAlgebra.toTensor_ι, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent, ContinuousLinearMap.isometry_iff_adjoint_comp_self, continuousMultilinearCurryFin0_apply, LocalizedModule.smul'_mk, IsLocalizedModule.map_mk', PiTensorProduct.dualSeminorms_bounded, extDeriv_smul, LinearMap.mul_toMatrix₂, PointwiseConvergenceCLM.coeLMₛₗ_apply, ContinuousLinearMap.postcompCompactConvergenceCLM_apply, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, Submodule.mulRightMap_eq_mulMap_comp, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, IsSelfAdjoint.conj_adjoint, Ideal.mul_mem_mul, LinearMap.surjective_compr₂_of_equiv, ContinuousMultilinearMap.curryMidEquiv_apply, TensorProduct.AlgebraTensorModule.rid_eq_rid, IsBaseChange.prodMap, kroneckerTMulLinearEquiv_mul, QuadraticMap.discr_comp, Module.Basis.linearMap_repr_apply, exteriorPower.alternatingMapLinearEquiv_comp_ιMulti, HasStrictFDerivAt.continuousMultilinear_apply_const, LinearMap.lsmul_eq_DistribMulAction_toLinearMap, Module.eval_apply_eq_zero_iff, IntermediateField.finrank_bot, kroneckerTMulLinearEquiv_symm_kroneckerTMul, MultilinearMap.curryFinFinset_apply_const, AdicCompletion.map_mk, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, MultilinearMap.freeFinsuppEquiv_def, localizedModuleIsLocalizedModule, TensorProduct.AlgebraTensorModule.map_eq, IsModuleTopology.continuous_bilinear_of_finite_left, DoubleCentralizer.algebraMap_snd, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, LieModule.trace_comp_toEnd_genWeightSpace_eq, LinearMap.nondegenerate_congr_iff, TensorProduct.gradedMul_one, QuadraticForm.tensorComm_toLinearEquiv, CliffordAlgebra.contractLeft_comm, InfiniteGalois.restrict_fixedField, Ideal.mul_sup_eq_of_coprime_left, iteratedFDerivWithin_succ_apply_left, instIsDecompositionFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupStabilizerIdealOfIsGalois, Matrix.dualNumberEquiv_symm_apply, LinearMap.toMatrix'_mul, Algebra.TensorProduct.productMap_eq_comp_map, SchwartzMap.fourier_evalCLM_eq, IsBaseChange.end, LinearMap.adjoint_toSpanSingleton, mul_basis_toMatrix, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, Module.Basis.toDual_toDual, Submodule.mul_smul_mul_eq_smul_mul_smul, IntermediateField.sepDegree_bot, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, AdicCompletion.pow_smul_top_eq_ker_eval, contDiffOn_infty_iff_fderiv_of_isOpen, CliffordAlgebra.foldl_algebraMap, Submodule.rTensorOne_tmul, LinearEquiv.conj_symm_conj, ContinuousLinearMap.map_sub₂, ContinuousLinearMap.bilinearComp_apply, killingForm_apply_apply, Module.End.restrict_eigenspace, LinearMap.trace_id, LinearMap.toMatrix_algebraMap, QuadraticModuleCat.toIsometry_hom_rightUnitor, TemperedDistribution.instLineDerivSMulReal, LinearMap.spectrum_toMatrix, AdicCompletion.ofAlgEquiv_apply, PowerBasis.constr_pow_gen, Submodule.range_lsum_smul, RatFunc.algEquivOfTranscendental_symm_aeval, range_cfcₙ_nnreal_eq_image_cfcₙ_real, SchwartzMap.evalCLM_apply_apply, LieSubalgebra.mem_engel_iff, Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule, Algebra.norm_eq_norm_adjoin, LieAlgebra.lie_smul, LinearMap.SeparatingRight.toMatrix₂, Matrix.isUnit_toLin_iff, analyticOn_taylorComp, ContMDiffWithinAt.clm_bundle_apply₂, Subspace.quotAnnihilatorEquiv_apply, Unitization.mem_spectrum_inr_of_not_isUnit, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, Filter.Tendsto.cfcₙ_nnreal, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, Matrix.diagonal_toLin', LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, Module.isTorsionBySet_iff_subseteq_ker_lsmul, IntermediateField.LinearDisjoint.norm_algebraMap, HasFTaylorSeriesUpToOn.fderivWithin, CStarMatrix.toCLM_apply, IntermediateField.restrictScalars_bot_eq_self, Module.End.mem_genEigenspace_top, DoubleCentralizer.algebraMap_toProd, continuousMultilinearCurryFin0_symm_apply_apply, LinearMap.isPositive_self_comp_adjoint, Algebra.TensorProduct.mul_one, RingTheory.Sequence.isWeaklyRegular_append_iff', ContinuousLinearMap.ker_self_comp_adjoint, Matrix.charpoly_toLin', Quaternion.fst_imI_dualNumberEquiv_symm, ContinuousLinearMap.norm_map_tail_le, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient, contMDiffOn_symm_coordChangeL, rank_dual_eq_card_dual_of_aleph0_le_rank', ContinuousLinearMap.instStarModuleId, contMDiffAt_hom_bundle, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply, IsLocalizedModule.map_apply, sectionOfRetractionKerToTensorAux_prop, Module.End.genEigenspace_one, HasFDerivAt.continuousAlternatingMap_apply_const, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, Submodule.smul_le_right, LinearIsometry.adjoint_comp_self', Matrix.toLin'_pow, PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, LieAdmissibleAlgebra.toIsScalarTower, IsSymmetricAlgebra.equiv_symm_apply, LinearIsometryEquiv.toLinearEquiv_smul, LieModule.Cohomology.mem_twoCocycle_iff, Ideal.ker_tensorProductMk_quotient, norm_fderiv_iteratedFDeriv, Unitization.lift_range, CommAlgCat.tensorHom_hom, TestFunction.lineDerivCLM_eq_fderivCLM, instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient, Derivation.liftKaehlerDifferential_unique_iff, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, Derivation.liftKaehlerDifferential_D, TensorProduct.AlgebraTensorModule.mapBilinear_apply, Ideal.span_mul_span, TemperedDistribution.fourier_lineDerivOp_eq, Matrix.toLinAlgEquiv'_apply, Matrix.l2_opNNNorm_def, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, Module.Basis.dualBasis_apply, AdicCompletion.val_apply_mem_smul_top_iff, ContinuousLinearMap.adjointAux_adjointAux, apply_eq_star_dotProduct_toMatrix₂_mulVec, mdifferentiableOn_baseSet_localFrame_coeff, tensorKaehlerQuotKerSqEquiv_tmul_D, LinearMap.aeval_eq_aeval_mod_charpoly, LinearMap.toMatrix_mul, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, LinearMap.toMatrix₂_compl₁₂, ContDiffOn.clm_comp, LinearMap.restrictScalarsRange₂_apply_eq_zero_iff, LinearMap.hasEigenvalue_zero_tfae, Matrix.minpoly_toLin', WeierstrassCurve.Projective.Point.fromAffine_some, ContMDiffAt.clm_precomp, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left, MeasureTheory.FiniteMeasure.smul_testAgainstNN_apply, LinearMap.eq_adjoint_iff, nnnorm_cfcₙ_nnreal_lt_iff, GradedTensorProduct.mulHom_apply, PositiveLinearMap.gnsStarAlgHom_apply, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, LieModule.toEnd_eq_iff, BilinForm.toMatrix_compRight, CliffordAlgebra.foldr_ι, MulSemiringAction.toRingEquiv_symm_apply, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, LinearMap.toMatrix₂_toLinearMap₂, IntermediateField.finrank_sup_le, LinearMap.detAux_def', TensorAlgebra.algebraMap_eq_one_iff, MultilinearMap.fromDirectSumEquiv_lof, LinearMap.toMatrix_transpose_apply', AlgCat.hom_whiskerLeft, HasFTaylorSeriesUpToOn.hasFDerivAt, LinearMap.toMatrix'_intrinsicStar, MultilinearMap.domCoprod'_apply, ContinuousLinearMap.flip_add, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, IntermediateField.adjoinRootEquivAdjoin_apply_root, LinearMap.finiteDimensional, MDifferentiable.clm_prodMap, Algebra.Extension.Cotangent.map_id, QuadraticForm.tensorComm_apply, AffineSubspace.isometryEquivMap.coe_apply, cross_apply, LinearEquiv.lieConj_apply, LieModule.isNilpotent_toEnd_of_mem_rootSpace, IsBaseChange.linearMapLeftRightHom_toMatrix, ContinuousLinearMap.isSelfAdjoint_iff', CliffordAlgebra.foldl_ι, PiTensorProduct.mapMultilinear_apply, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, ContinuousMultilinearMap.uncurryRight_apply, Seminorm.closedBall_smul, IntermediateField.rank_bot, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, LinearEquiv.dualMap_symm, SchwartzMap.fourierMultiplierCLM_ofReal, Module.Invertible.toModuleEnd_bijective, WeierstrassCurve.Projective.nonsingularLift_iff, Module.End.isNilpotent_restrict_maxGenEigenspace_sub_algebraMap, AdicCompletion.of_surjective, TrivSqZeroExt.exp_def, Algebra.Generators.Cotangent.exact, LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv', Submodule.smul_top_eq_range_lsum, LinearMap.toMatrix_smulRight, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, contMDiffAt_localFrame_coeff, kroneckerTMulLinearEquiv_tmul, Module.stabilizer_units_eq_bot_of_ne_zero, LinearEquiv.alternatingMapCongrRight_apply_apply, ContinuousLinearMap.bilinearComp_zero, LinearMap.toMatrix₂Aux_eq, le_restrictScalars_separableClosure, MultilinearMap.curryLeft_apply, Representation.IntertwiningMap.comp_def, iteratedDeriv_eq_equiv_comp, LinearMap.lsmul_apply, LieDerivation.toLinearMapLieHom_injective, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, vecMulVecBilin_apply_apply, CliffordAlgebra.foldl_reverse, QuadraticForm.tmul_comp_tensorMap, isAdjointPair_toLinearMap₂', Matrix.toLin'_apply', QuotSMulTop.map_exact, LinearMap.isPairSelfAdjoint_equiv, LinearMap.toMatrix₂_symm, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, IntermediateField.instIsScalarTowerSubtypeMem_1, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, TensorPower.toTensorAlgebra_gMul, Matrix.ker_toLin'_eq_bot_iff, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, NonUnitalSubalgebra.unitization_apply, LinearMap.vecCons₂_apply, IsAzumaya.coe_tensorEquivEnd, DualNumber.lift_apply_apply, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LinearMap.eval_charpoly, LinearMap.SeparatingLeft.toMatrix₂, TensorProduct.lift_comp_map, TensorPower.toTensorAlgebra_gOne, Derivation.llcomp_apply, LinearMap.trace_comp_eq_zero_of_commute_of_trace_restrict_eq_zero, Basis.multilinearMap_apply_apply, MulSemiringAction.smul_mul, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, LinearMap.reduceModIdeal_apply, RingTheory.Sequence.isWeaklyRegular_append_iff, LocalizedModule.lift_comp, MultilinearMap.dfinsuppFamilyₗ_apply, cfcₙ_real_eq_nnreal, Ideal.IsTwoSided.instHPowNat, Unitization.lift_symm_apply, LinearMap.toMatrix_map_left, LinearMap.BilinForm.mul_toMatrix', IntermediateField.finrank_bot_mul_relfinrank, LieModule.toEnd_lie, cfcₙ_map_prod, QuadraticForm.tensorAssoc_symm_apply, LinearMap.map_mul_iff, Real.fourier_bilin_convolution_eq, SymmetricAlgebra.algHom_ext_iff, CStarMatrix.mul_entry_mul_eq_inner_toCLM, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, Matrix.toLinearMap₂_symm, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, CliffordAlgebra.foldr_one, Module.End.isRoot_of_hasEigenvalue, ExteriorAlgebra.toTrivSqZeroExt_ι, ContinuousLinearMap.le_opNorm₂, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ContinuousLinearMap.norm_uncurryMid, Submodule.torsionBy.mk_ideal_smul, SymmetricAlgebra.equivMvPolynomial_symm_X, IntermediateField.LinearDisjoint.of_basis_right, InnerProductSpace.rankOne_def', ContDiff.clm_comp, ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.uncurryLeft_norm, LeftPreLieAlgebra.ext_iff, LinearMap.toMatrixAlgEquiv_symm, ContDiffWithinAt.fderivWithin', TestFunction.instLineDerivLeftSMulRealTopENat, LinearMap.toMatrixRight'_id, leibniz_cross, AdicCompletion.ofPowSMul_val_apply_eq_zero, HVertexOperator.coeff_inj, LinearMap.minpoly_toMatrix, LinearMap.det_dualMap, Submodule.instFiniteQuotientIdealHSMulTop, PiToModule.fromEnd_apply_single_one, Ideal.pow_le_pow_right, SchwartzMap.fourierMultiplierCLM_const, SchwartzMap.integral_sesq_fourierIntegral_eq, CharacterModule.homEquiv_symm_apply_apply_apply, IntermediateField.finiteDimensional_adjoin, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, Ideal.inertiaEquiv_symm_apply_smul, QuadraticModuleCat.toIsometry_inv_rightUnitor, PiTensorProduct.piTensorHomMapFun₂_smul, LinearMap.adjoint_lTensor, LieModule.Cohomology.add_apply_apply, Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, fderiv_continuousMultilinear_apply_const_apply, IntermediateField.lift_injective, multilinearCurryLeftEquiv_apply, MeasureTheory.Integrable.convolution_integrand, IsCyclotomicExtension.Rat.galEquivZMod_stabilizer, CliffordAlgebra.evenToNeg_ι, LinearMap.toMatrixOrthonormal_apply, Representation.asAlgebraHom_of, LinearMap.IsPositive.smul_of_nonneg, SchwartzMap.integral_bilinear_laplacian_right_eq_left, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, LinearMap.lTensor_comp_mk, Module.Basis.toDual_injective, Ideal.Filtration.stable_iff_exists_pow_smul_eq_of_ge, ContinuousLinearMap.isometry_mul, LieSubalgebra.isNilpotent_ad_of_isNilpotent_ad, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', NonUnitalCommCStarAlgebra.toStarModule, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, Orientation.kahler_apply_self, Module.Invertible.rTensorInv_leftInverse, Ideal.span_singleton_mul_span_singleton, RootPairing.Hom.weight_coweight_transpose_apply, MultilinearMap.curryFinFinset_symm_apply_const, SchwartzMap.norm_toBoundedContinuousFunction_le, KaehlerDifferential.mvPolynomialBasis_repr_apply, LinearMap.prodMapAlgHom_apply_apply, Module.End.eigenspace_def, IntermediateField.AdjoinSimple.trace_gen_eq_zero, HasStrictFDerivAt.continuousAlternatingMap_apply, MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero, ContinuousLinearMap.continuous_uncurry_of_multilinear, HasStrictDerivAt.complexToReal_fderiv', SymmetricAlgebra.lift_comp_ι, MeasureTheory.dist_convolution_le', AlternatingMap.curryLeftLinearMap_apply, LinearMap.flip_separatingRight, SymmetricAlgebra.lift_ι, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, Algebra.toMatrix_lmul', LinearMap.singularValues_fin, LinearMap.sq_singularValues_of_lt, LieAlgebra.ad_apply, CovariantDerivative.torsion_eq_zero_iff, LieAlgebra.toEnd_pow_apply_mem, DifferentiableWithinAt.clm_comp, MDifferentiableOn.cle_arrowCongr, CommAlgCat.whiskerLeft_hom, MultilinearMap.mkContinuousMultilinear_norm_le', AffineMap.homothety_linear, Unitization.norm_def, ContMDiff.clm_bundle_apply₂, Subalgebra.coe_smul, Submodule.map₂_span_span, WeierstrassCurve.Projective.addMap_of_Y_eq, IsLocalizedModule.map_id, Orientation.kahler_rotation_left', Representation.linHom.invariantsEquivRepHom_symm_apply_coe, IntermediateField.finSepDegree_adjoin_simple_le_finrank, Matrix.ker_diagonal_toLin', second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, ContDiff.fourierPowSMulRight, Distribution.dsupport_smulLeftCLM_subset, ContMDiffWithinAt.mfderivWithin, LinearMap.polyCharpolyAux_baseChange, Module.End.mem_iInf_maxGenEigenspace_iff, LinearMap.coe_rTensorHom, Ideal.snd_comp_quotientMulEquivQuotientProd, Module.Basis.symmetricAlgebra_repr_apply, LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective, Coalgebra.lift_lsmul_comp_counit_comp_comul, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, IntermediateField.card_algHom_adjoin_integral, FGModuleCat.Iso.conj_eq_conj, AffineSubspace.subtypeₐᵢ_linear, LieAlgebra.Basis.baseSupp_apply_smul_e, IntermediateField.relrank_dvd_rank_bot, LieAlgebra.conj_ad_apply, QuadraticForm.tensorRId_toLinearEquiv, RestrictScalars.lsmul_apply_apply, LinearMap.toMatrix_prodMap, Matrix.toLin_apply, Matrix.toLin'_one, CliffordAlgebra.foldr_reverse, AdicCompletion.mk_surjective, MDifferentiableAt.clm_precomp, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, ContinuousAlternatingMap.curryLeft_zero, RootPairing.reflection_dualMap_eq_coreflection, DualNumber.coe_lift_symm_apply, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Orientation.normSq_kahler, AlgEquiv.linearEquivConj_mulLeftRight, LinearMap.IsRefl.flip_isRefl_iff, LinearEquiv.symm_conj_apply, TensorProduct.LieModule.lift_apply, Ideal.Filtration.pow_smul_le_pow_smul, LinearMap.finrank_range_adjoint, LinearMap.isOrtho_flip, Algebra.Generators.toKaehler_tmul_D, LieDerivation.IsKilling.rangeAdOrthogonal_carrier, Quaternion.imJ_snd_dualNumberEquiv, Module.Basis.linearIndependent_coord, DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap, CoalgCat.MonoidalCategoryAux.counit_tensorObj, MultilinearMap.piFamilyₗ_apply, MultilinearMap.fromDirectSumEquiv_apply, TrivSqZeroExt.liftEquivOfComm_apply, TensorProduct.isBaseChange, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, AdicCompletion.pow_smul_top_le_ker_eval, Module.isTorsionBy_iff_mem_ker_lsmul, LinearMap.sq_singularValues_fin, LinearPMap.map_smul, ext_iff, Module.injOn_dualMap_subtype_span_range_range, Module.End.finite_spectrum, Submodule.map₂_le, WeierstrassCurve.Projective.negMap_eq, Ideal.mul_assoc, ContinuousLinearMap.adjoint_comp_self_injective_iff, iteratedFDeriv_succ_apply_right, NonUnitalStarSubalgebra.prod_inf_prod, FormalMultilinearSeries.leftInv_coeff_one, LinearMap.IsSymmetric.smul, Module.Basis.smul_eq_map, Matrix.toLin_conjTranspose, mdifferentiableOn_continuousLinearMapCoordChange, CommAlgCat.whiskerRight_hom, instIsPushoutPolynomial, AdicCompletion.map_ext''_iff, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, cfcHom_nnreal_eq_restrict, LinearMap.range_adjoint_comp_self, LinearEquiv.conj_conj_symm, IntermediateField.LinearDisjoint.of_inf_eq_bot, Algebra.Extension.Cotangent.map_toInfinitesimal_bijective, Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_pow, PointwiseConvergenceCLM.precomp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, homTensorHomEquiv_toLinearMap, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, endVecAlgEquivMatrixEnd_apply_apply, Quaternion.snd_imK_dualNumberEquiv_symm, contDiff_clm_apply_iff, HasFPowerSeriesAt.hasFDerivAt, Submodule.dualAnnihilator_gc, SpecialLinearGroup.centerEquivRootsOfUnity_apply, TensorAlgebra.toDirectSum_comp_ofDirectSum, spec_cfcₙAux, Submodule.range_powSMulQuotInclusion, AlgebraicIndependent.liftAlgHom_comp_reprField, sectionOfRetractionKerToTensor_algebraMap, ContinuousOn.cfcₙ_nnreal', LinearMap.IsPositive.trace_nonneg, Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply, Algebra.TensorProduct.map_range, IntermediateField.finrank_top', LinearMap.mkContinuous₂_norm_le, LinearMap.aeval_self_charpoly, exteriorPower.alternatingMapLinearEquiv_comp, Matrix.trace_toLin'_eq, Orientation.rotation_eq_matrix_toLin, Subalgebra.isScalarTower_mid, AlternatingMap.curryLeft_smul, IntermediateField.inclusion_self, OreLocalization.zero_oreDiv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Module.eval_ker, IntermediateField.lift_bot, LinearMap.isNilpotent_trace_of_isNilpotent, SymmetricAlgebra.equivMvPolynomial_ι_apply, ContinuousLinearMap.self_comp_adjoint_injective_iff, LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank, Submodule.sup_dualAnnihilator_le_inf, Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsLocalizedModule.iso_symm_apply_aux, IsBaseChange.endHom_apply, LinearMap.isSkewAdjoint_iff_neg_self_adjoint, IntermediateField.normalClosure_of_normal, LinearMap.polyCharpoly_eq_of_basis, LieAlgebra.rootSpace_comap_eq_genWeightSpace, Module.Invertible.rTensorInv_injective, TensorProduct.AlgebraTensorModule.lTensor_mul, Algebra.TensorProduct.map_comp_includeRight, contDiffOn_clm_apply, fderiv_continuousAlternatingMap_apply_apply, stabilizer_isOpen_of_isIntegral, Algebra.TensorProduct.one_mul, Ideal.constr_basisSpanSingleton, TrivSqZeroExt.sndHom_comp_map, PiTensorProduct.mapLMultilinear_apply_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, HasFDerivWithinAt.clm_comp, LinearEquiv.isUnit_det, ContinuousLinearMap.evalL_apply, RootPairing.range_polarizationIn, isBoundedBilinearMap_apply, InfiniteGalois.isOpen_iff_finite, Ideal.pow_sup_eq_top', Unitization.nnreal_cfcₙ_eq_cfc_inr, CliffordAlgebra.contractLeft_ι, LinearMap.polyCharpolyAux_map_aeval, ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse, hasStrictFDerivAt_ringInverse, KaehlerDifferential.map_compDer, Subspace.dualAnnihilator_iInf_eq, ContinuousLinearMap.mul_apply', IntermediateField.isSplittingField_iSup, fromTangentSpace_mfderiv_smul, TrivSqZeroExt.map_comp_map, TensorProduct.quotTensorEquivQuotSMul_symm_mk, AdicCompletion.of_ofLinearEquiv_symm, AdicCompletion.kerProj_of, LinearMap.instStarModuleId, LieDerivation.commutator_coe_linear_map, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LieModule.Cohomology.smul_apply_apply, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, MeasureTheory.convolution_lsmul_swap, Matrix.spectrum_toLin, TensorAlgebra.ι_leftInverse, IntermediateField.relfinrank_bot_left, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem, Module.Basis.eval_injective, Unitization.starLift_apply, LinearMap.toMatrix'_comp, Matrix.toLinearEquiv'_apply, LinearMap.isUnit_toMatrix'_iff, CommAlgCat.associator_inv_hom, ModuleCat.ihom_coev_app, Ideal.span_singleton_mul_left_mono, Module.AEval.mem_mapSubmodule_symm_apply, TestFunction.fderivCLM_eq_of_scalars, Matrix.nondegenerate_toLinearMap₂_iff, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, Matrix.toBilin'_comp, Matrix.isHermitian_iff_isSymmetric, LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain, Subspace.dualRestrict_surjective, LieModule.toEnd_pow_lie, IsBaseChange.endHom_one, LinearMap.toMatrix_directSum_collectedBasis_eq_blockDiagonal', AdicCompletion.evalOneₐ_of, IsFractionRing.stabilizerHom_apply_apply_mk, IntermediateField.LinearDisjoint.rank_sup, IntermediateField.le_extendScalars_iff, Submodule.map₂_span_singleton_eq_map, InnerProductSpace.rankOne_comp, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, Unitization.starMap_comp, Submodule.map₂_flip, LocalizedModule.lift_mk, Orientation.kahler_rightAngleRotation_left, Ideal.IsTwoSided.mul_one, IsAdicComplete.StrictMono.of_comp_lift, LinearMap.separatingLeft_congr_iff, Module.Basis.end_repr_symm_apply, IntermediateField.rank_sup_le_of_isAlgebraic, TensorAlgebra.GradedAlgebra.ι_apply, LieSubmodule.coe_toEnd, Ideal.restrictScalars_mul, Module.evalEquiv_apply, Orientation.kahler_comp_linearIsometryEquiv, Real.fourierIntegral_fderiv, Ideal.sup_mul_eq_of_coprime_right, CliffordAlgebra.contractRight_contractRight, InnerProductSpace.toMatrix_rankOne, MDifferentiableWithinAt.clm_comp, HasFDerivWithinAt.continuousMultilinear_apply_const, cfcₙHom_real_eq_restrict, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, LieModule.toEnd_apply_apply, PiTensorProduct.liftIsometry_comp_mapL, FractionalIdeal.den_mul_self_eq_num, MDifferentiableOn.clm_comp, Ideal.pow_sup_pow_eq_top', LinearMap.mul_toMatrix₂_mul, Submodule.map_smul', InnerProductSpace.isSymmetric_rankOne_self, TensorAlgebra.hom_ext_iff, WeierstrassCurve.Projective.addMap_of_Z_eq_zero_right, IsTensorProduct.assoc_tmul, continuousMultilinearCurryLeftEquiv_apply, LinearMap.trace_tensorProduct', LocalizedModule.eq_zero_of_smul_eq_zero, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, SchwartzMap.norm_toLp_top_le, precomp_compactConvergenceCLM_apply, LieModule.commute_toEnd_of_mem_center_right, ContMDiffAt.clm_prodMap, KaehlerDifferential.D_tensorProductTo, OreLocalization.add_assoc, IntermediateField.inclusion_injective, Ideal.mul_le_left, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, ContinuousAlternatingMap.restrictScalarsCLM_apply, IsGaloisGroup.subgroup_iff, IsSemisimpleModule.exists_end_algEquiv, SchwartzMap.tsupport_fderivCLM_subset, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, IntermediateField.LinearDisjoint.bot_right, TensorAlgebra.range_lift, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, QuotSMulTop.equivQuotTensor_naturality_mk, Ideal.ResidueField.algHom_ext_iff, SymmetricAlgebra.algebraMap_eq_one_iff, Matrix.isSymmetric_toLin_iff, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, LinearMap.toMatrix'_id, Algebra.TensorProduct.algEquivIncludeRange_toAlgHom, LinearMap.polyCharpolyAux_coeff_eval, AnalyticOnNhd.fderiv, LinearMap.range_smul', LieModule.toEnd_baseChange, LocalizedModule.mul_by_divBy, Orientation.kahler_rotation_left, PiTensorProduct.liftIsometry_symm_apply, fderivWithin_continuousAlternatingMap_apply_apply, Matrix.toLinearMapₛₗ₂_symm, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, SemimoduleCat.Iso.conj_eq_conj, IntermediateField.normal_iff_forall_map_le, LinearMap.BilinMap.tensorDistrib_tmul, Projectivization.cross_mk, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, LinearMap.BilinForm.mul_toMatrix_mul, LinearMap.trace_transpose, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Polynomial.mkDerivation_X, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, iteratedFDeriv_succ_eq_comp_right, ContinuousMultilinearMap.changeOriginSeries_support, separableClosure.isAlgebraic, QuadraticForm.comp_tensorRId_eq, TrivSqZeroExt.algebraMap_eq_inl, IsBaseChange.endHom_comp_apply, LinearAlgebra.FreeProduct.rel_id, Matrix.toLinAlgEquiv_apply, Submodule.mem_smul_top_iff, DifferentiableAt.clm_comp, LinearMap.BilinForm.toMatrix'_comp, Submodule.map_map₂, DualNumber.range_inlAlgHom_sup_adjoin_eps, Real.iteratedFDeriv_fourier, Algebra.Generators.CotangentSpace.exact, DoubleCentralizer.algebraMap_fst, LinearMap.ker_dualMap_eq_dualCoannihilator_range, fderiv_continuousLinearEquiv_comp, ContinuousLinearMap.intrinsicStar_smulRight, Submodule.exists_injOn_mkQ_image_span_eq_of_span_eq_map_mkQ_of_le_jacobson_bot, deriv_clm_comp, CharacterModule.dual_rTensor_conj_homEquiv, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, quasispectrumRestricts_iff_spectrumRestricts_inr, IsArtinianRing.isNilpotent_jacobson_bot, mulLinearMap_apply_apply, Submodule.mulLeftMap_eq_mulMap_comp, CliffordAlgebra.changeForm_contractLeft, ContDiffOn.fderivWithin, Submodule.map_pointwise_smul, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, IsLocalization.map_eq_toLinearMap_mapₐ, IntermediateField.rank_eq_one_iff, triple_product_eq_det, LinearEquiv.dualMap_apply, IsGaloisGroup.intermediateField, Matrix.toLinearMap₂_basisFun, TensorAlgebra.algebraMap_inj, AdicCompletion.factor_eval_liftRingHom, QuadraticMap.coe_associatedHom, LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplitting, LinearMap.mem_selfAdjointSubmodule, LinearMap.finrank_range_dualMap_eq_finrank_range, LocalizedModule.map_exact, spectrum.hasFDerivAt_resolvent, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, Module.bijective_dual_eval, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_ite, Module.End.eigenspace_div, Algebra.Extension.Hom.subToKer_apply_coe, IsBoundedBilinearMap.toContinuousLinearMap_apply, Matrix.toLinearMapRight'_apply, IsTensorProduct.assocOfMapSMul_tmul, LinearMap.BilinForm.toMatrix_mul, spectralNorm.eq_of_normalClosure, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, HasFPowerSeriesWithinOnBall.fderivWithin_eq, Module.FaithfullyFlat.tensorProduct_mk_injective, Polynomial.span_minpoly_eq_annihilator, ContinuousMultilinearMap.piₗᵢ_symm_apply, IntermediateField.LinearDisjoint.linearIndependent_right, Unitization.fstHom_apply, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, ContDiff.iteratedFDeriv_right', Module.End.genEigenrange_nat, ContinuousLinearMap.ker_adjoint_comp_self, SchwartzMap.pairing_continuous_left, LieAlgebra.SpecialLinear.val_single, Matrix.ofLp_toEuclideanLin_apply, ContinuousLinearMap.smulRight_comp_smulRight, spectralNorm.eq_of_normalClosure', AffineEquiv.arrowCongrₗ_apply, Matrix.toLinearMap₂_apply, AdicCompletion.of_inj, Real.hasFDerivAt_fourierIntegral, LieModule.isNilpotent_iff_forall, IsCovariantDerivativeOn.add_one_form, Polynomial.mkDerivation_one_eq_derivative, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, Ideal.quotientMulEquivQuotientProd_fst, CliffordAlgebra.forall_mul_self_eq_iff, FormalMultilinearSeries.radius_shift, LieModule.isNilpotent_toEnd_sub_algebraMap, rTensorHomEquivHomRTensor_toLinearMap, IsBaseChange.ofEquiv, AdicCompletion.ofTensorProduct_tmul, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, MultilinearMap.uncurryRight_apply, LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero, ContinuousAt.clm_bundle_apply₂, NonUnitalStarSubalgebra.coe_smul, PiTensorProduct.piTensorHomMapFun₂_add, Matrix.mulVecBilin_apply, nat_smul_eq_nsmul, LinearEquiv.congrQuadraticMap_symm_apply, Module.Basis.dualBasis_repr, CategoryTheory.Abelian.Ext.bilinearCompOfLinear_apply_apply, AlternatingMap.uncurryFin_smul, Ideal.mem_iInf_smul_pow_eq_bot_iff, lieEquivMatrix'_symm_apply, separableClosure.isSepClosure, LieSubalgebra.instIsNoetherianSubtypeMem, InfiniteGalois.toAlgEquivAux_eq_liftNormal, Matrix.proj_diagonal, TensorProduct.dualDistribInvOfBasis_apply, fderiv_continuousMultilinearMapCompContinuousLinearMap, Ideal.Filtration.pow_smul_le, isNilpotent_tensor_residueField_iff, LinearMap.trace_eq_sum_trace_restrict, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, BialgHomClass.map_comp_comulAlgHom, LinearMap.disjoint_ker_of_nondegenerate_restrict, Polynomial.sup_ker_aeval_le_ker_aeval_mul, IntermediateField.normalClosure_def'', contDiff_nat_iff_continuous_differentiable, dualTensorHom_prodMap_zero, Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint, Unitization.starMap_apply, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, mdifferentiableOn_coordChangeL, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, Ideal.card_inertia_eq_ramificationIdxIn, LinearMap.isUnit_toMatrix_iff, LinearMap.det_smul, Subfield.relrank_eq_rank_of_le, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, Submodule.coe_smul, ContinuousLinearMap.opNorm_lsmul_le, LieAlgebra.Basis.cartanMatrix_base_eq, LocalizedModule.map_id, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, MultilinearMap.curryMidLinearEquiv_apply, MultilinearMap.mkContinuousMultilinear_norm_le, LinearMap.BilinForm.toMatrix_compLeft, LinearMap.trace_eq_matrix_trace, IntermediateField.isSeparable_tower_bot, Matrix.linfty_opNorm_toMatrix, IntermediateField.minpoly_eq, TrivSqZeroExt.kerIdeal_sq, Module.Basis.linearCombination_coord, Real.fourier_bilin_convolution_eq_integral, Ideal.smul_restrictScalars, ExteriorAlgebra.liftAlternating_comp_ιMulti, ContinuousWithinAt.clm_bundle_apply₂, range_cfcₙ_nnreal_subset, LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero', Algebra.TensorProduct.mul_assoc, LinearMap.adjoint_inner_left, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, IntermediateField.isSplittingField_iff, Module.IsTorsionBySet.isScalarTower, Module.Basis.toDual_apply, LocalizedModule.instIsScalarTower, LinearMap.BilinForm.mul_toMatrix, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, Module.Basis.tensorAlgebra_repr_apply, ContMDiffVectorBundle.contMDiffOn_coordChangeL, Algebra.Generators.toKaehler_cotangentSpaceBasis, fderivWithin_clm_comp, Submodule.mem_smul_span, Subspace.dualLift_rightInverse, IntermediateField.topEquiv_symm_apply_coe, QuadraticMap.associated_linMulLin, FiniteGaloisIntermediateField.adjoin_val, LieAlgebra.rank_le_finrank_engel, dualTensorHomEquivOfBasis_toLinearMap, Module.apply_evalEquiv_symm_apply, Submodule.coe_dualAnnihilator_span, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, TensorAlgebra.tprod_apply, fderiv_continuousMultilinear_apply_const, FixedPoints.linearIndependent_smul_of_linearIndependent, Orientation.kahler_mul, LinearMap.trace_conj', Matrix.SpecialLinearGroup.toLin'_to_linearMap, ContinuousLinearMap.opNNNorm_mul_flip_apply, LinearMap.mul_toMatrix₂'_mul, Rep.coinvariantsTensor_hom_ext_iff, LinearMap.toMatrix₂'_mul, Nonneg.instNonUnitalContinuousFunctionalCalculus, HasFPowerSeriesOnBall.hasFDerivAt, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, SchwartzMap.instLocallyConvexSpace, CovariantDerivative.torsion_antisymm, AdicCompletion.transitionMap_map_pow, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, IsTensorProduct.lift_eq, Submodule.powSMulQuotInclusion_mk, ContinuousMultilinearMap.curryMid_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, IntermediateField.AdjoinSimple.normal_algebraicClosure, Algebra.toMatrix_lsmul, toMatrix_innerSL_apply, TemperedDistribution.fourierMultiplierCLM_apply_apply, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, Algebra.SubmersivePresentation.basisKaehler_apply, LinearMap.flip_nondegenerate, intervalIntegral.fderivWithin_integral_of_tendsto_ae, Ideal.Quotient.ker_stabilizerHom, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, IntermediateField.normal_iff_forall_map_eq', Matrix.separatingLeft_toLinearMap₂'_iff, TensorProduct.AlgebraTensorModule.map_smul_right, Representation.Equiv.dualTensorHom_toFun, ContMDiff.clm_postcomp, triple_product_permutation, LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero', TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent, IntermediateField.intermediateFieldMap_apply_coe, IntermediateField.topEquiv_apply, LinearMap.intrinsicStar_smulRight, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, MDifferentiableAt.coordChangeL, Module.End.baseChangeHom_apply_apply, fderivWithin_continuousAlternatingMap_apply_const, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, Matrix.isRepresentation.toEnd_surjective, ContDiffAt.clm_comp, IntermediateField.LinearDisjoint.symm, BilinForm.toMatrix_mul, IntermediateField.exists_algHom_adjoin_of_splits', Subspace.dualCopairing_nondegenerate, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, LinearMap.toMatrix_comp, Submodule.restrictScalars.isScalarTower, ContinuousLinearEquiv.arrowCongrSL_apply, Algebra.normalizedTrace_def, MDifferentiableWithinAt.clm_postcomp, Matrix.toLinAlgEquiv_self, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, Module.Basis.coe_toDual_self, ContDiffBump.convolution_eq_right, Matrix.kroneckerMapBilinear_mul_mul, TemperedDistribution.instFourierInvSMul, Submodule.mul_smul, FiniteField.minpoly_frobeniusAlgHom, ContMDiff.clm_prodMap, Submodule.dualAnnihilator_top, Matrix.trace_toLin_eq, Module.AEval'_def, FormalMultilinearSeries.analyticAt_changeOrigin, ContinuousLinearMap.opNorm_mul_apply_le, Coalgebra.TensorProduct.assoc_tmul, intervalIntegral.integral_hasFDerivWithinAt, IntermediateField.AdjoinSimple.isIntegral_gen, LinearMap.toMatrix₂_mul_basis_toMatrix, ContinuousLinearMap.orthogonal_range, TensorProduct.AlgebraTensorModule.lift_apply, AffineMap.coe_homothetyAffine, Module.End.IsSemisimple_smul, LieAlgebra.IsKilling.rootSystem_pairing_apply, Module.Basis.toMatrix_eq_toMatrix_constr, Module.Finite.toModuleEnd_moduleEnd_surjective, TensorProduct.comul_tmul, NormedSpace.norm_smul_le, LinearMap.polyCharpoly_map_eq_charpoly, HasFDerivAt.linear_multilinear_comp, Ideal.pi_mkQ_rTensor, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, TestFunction.fderivCLM_apply_of_gt, IntermediateField.exists_lt_finrank_of_infinite_dimensional, IntermediateField.adjoin_rank_le_of_isAlgebraic, ContinuousLinearMap.spectralRadius_eq_nnnorm, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, MeasureTheory.convolutionExistsAt_iff_integrable_swap, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, AdicCompletion.of_injective, CliffordAlgebra.contractRight_one, WithConv.symm_matrixToLin'StarAlgEquiv_apply, LinearEquiv.smulOfNeZero_symm_apply, IntermediateField.normal_iInf, LinearMap.isOrthoᵢ_def, Submodule.factorPow_comp_powSMulQuotInclusion, WeierstrassCurve.Projective.Point.zero_def, PiTensorProduct.lift_tprod, Algebra.IsAlgebraic.isNormalClosure_normalClosure, ContinuousLinearMap.spectrum_eq, AffineEquiv.linear_arrowCongr, TensorProduct.lcurry_apply, TrivSqZeroExt.snd_map, TensorProduct.curry_apply, IntermediateField.isPurelyInseparable_bot, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, toAddEquiv_symm_apply, IsHausdorff.eq_iff_smodEq, QuadraticMap.radical_eq_ker_associated, dualTensorHomEquivOfBasis_symm_cancel_left, Module.End.hasEigenvalue_iff_isRoot, AdicCompletion.restrictScalars_range_ofPowSMul_eq_ker_eval, ContinuousMultilinearMap.compContinuousLinearMapL_apply, Module.Invertible.rTensorEquiv_symm_apply_apply, LinearMap.surjective_compr₂_of_exists_rightInverse, TensorProduct.comul_def, HasDerivAtFilter.prodMk, ContinuousLinearMap.norm_bilinearRestrictScalars, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin, Module.Flat.iff_lift_lsmul_comp_subtype_injective, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, Ideal.range_finsuppTotal, AlgebraicIndependent.aevalEquivField_apply_coe, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, CliffordAlgebra.foldr'Aux_apply_apply, ProbabilityTheory.covarianceBilin_map, NonUnitalAlgHom.toAlgHom_apply, LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent, Unitization.nnnorm_eq_sup, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, IntermediateField.LinearDisjoint.exists_field_of_isDomain, Seminorm.bound_of_shell_sup, LinearEquiv.conj_id, MultilinearMap.uncurrySum_add, Module.End.isNilpotent_restrict_sub_algebraMap, minpoly_algEquiv_toLinearMap, ContinuousLinearMap.bilinearComp_zero_left, ContinuousLinearMap.nnnorm_smulRight_apply, RingTheory.Sequence.IsRegular.quot_ofList_smul_nontrivial, RingHom.Finite.tensorProductMap, SchwartzMap.fderivCLM_fourier_eq, TensorProduct.lift.equiv_symm_apply, ContinuousMultilinearMap.instContinuousSMul, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct, FormalMultilinearSeries.ofScalars_smul, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, IsBaseChange.linearMapLeftRight, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, Module.End.IsSemisimple_smul_iff, Ideal.top_mul, AlternatingMap.curryLeft_compAlternatingMap, Orientation.volumeForm_zero_neg, IntermediateField.finiteDimensional_left, AffineSubspace.subtypeₐᵢ_linearIsometry, Matrix.isSymm_iff_intrinsicStar_toLin', LinearMap.toMatrixAlgEquiv'_symm, IntermediateField.finiteDimensional_iSup_of_finite, ContDiffBump.dist_normed_convolution_le, instIsPushout_1, MeasureTheory.FiniteMeasure.map_smul, MDifferentiableOn.clm_precomp, IsPrecomplete.prec, Algebra.Extension.Hom.sub_aux, instIsPushoutFractionRingPolynomial, OreLocalization.smul_add, ContinuousLinearMap.adjoint_comp, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, HasStrictDerivAt.prodMk, LieModule.toEnd_eq_zero_iff, hasFTaylorSeriesUpToOn_succ_iff_left, LinearMap.surjective_compr₂ₛₗ_of_equiv, KaehlerDifferential.derivationTensorProduct_algebraMap, isConjRoot_iff_orbitRel, le_perfectClosure_iff, perfectClosure.isAlgebraic, LinearMap.IsProj.trace, Submodule.smul_comap_le_comap_smul, DualNumber.instIsLocalRing, VectorFourier.integral_bilin_fourierIntegral_eq_flip, LinearMap.charpoly_sub_smul, LinearEquiv.congrRight₂_trans, deriv_clm_apply, Subspace.map_le_dualAnnihilator_dualAnnihilator, IntermediateField.isSeparable_sup, contDiffOn_succ_iff_fderivWithin, Algebra.TensorProduct.lTensor_ker, FiniteGaloisIntermediateField.finiteDimensional, Matrix.kroneckerTMulBilinear_apply, InnerProductSpace.toLinearMap_rankOne, KaehlerDifferential.tensorProductTo_surjective, ContinuousLinearMap.adjointAux_inner_right, Seminorm.finset_sup_smul, ContDiffWithinAt.iteratedFDerivWithin_right, TemperedDistribution.instLineDerivSMulComplex, LinearMap.restrict_smul_one, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, HasStrictFDerivAt.clm_apply, Algebra.norm_apply, Submodule.image2_subset_map₂, RingHom.smulOneHom_apply, Algebra.norm_eq_zero_iff', Module.Basis.linearMap_apply_apply, IntermediateField.coe_smul, IsGaloisGroup.fixingSubgroup_bot, ContMDiffAt.clm_bundle_apply₂, ContDiffMapSupportedIn.fderivLM_apply, Seminorm.isBounded_sup, LinearMap.prodMap_smul, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LinearMap.trace_tensorProduct, continuousMultilinearCurryRightEquiv_symm_apply', comp_dualTensorHom, LocalizedModule.lift_mk_one, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, LinearEquiv.mem_stabilizer_fixedSubmodule, ContDiffWithinAt.fderivWithin, hasEigenvalue_toLin'_diagonal_iff, ContinuousLinearMap.prodL_apply, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, IsLocalizedModule.mk_eq_mk', IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, Coalgebra.TensorProduct.assoc_symm_tmul, LinearEquiv.smul_id_of_finrank_eq_one_apply, Submodule.smul_torsionBy, TrivSqZeroExt.fst_map, AdicCompletion.transitionMap_ideal_mk, LinearMap.isStarProjection_toContinuousLinearMap_iff, Rep.MonoidalClosed.linearHomEquiv_hom, Representation.ofModule_asAlgebraHom_apply_apply, Ideal.mul_le_inf, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, Matrix.toLpLin_mul, iteratedDerivWithin_eq_equiv_comp, TensorProduct.map_convMul_map, TensorAlgebra.equivDirectSum_symm_apply, InfiniteGalois.restrictNormalHom_continuous, Matrix.toLin'_submatrix, TensorProduct.gradedMul_algebraMap, IntermediateField.isAlgebraic_iSup, iteratedFDerivWithin_two_apply, extDerivWithin_smul, Module.End.isIntegral, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, IsGaloisGroup.subgroup, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, MulSemiringAction.smul_one, Matrix.separatingLeft_toLinearMap₂_iff, Module.End.mem_maxGenEigenspace, DoubleCentralizer.coe_fst, HasDerivAt.prodMk, Ideal.card_stabilizer_eq_card_inertia_mul_finrank, AdicCompletion.transitionMap_map_mul, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, Polynomial.aeval_endomorphism, Module.End.genEigenspace_div, ContDiffPointwiseHolderAt.fderiv, IsGalois.of_separable_splitting_field_aux, WeierstrassCurve.Projective.negMap_of_Z_eq_zero, IntermediateField.coe_equivMap_apply, norm_cfcₙ_one_sub_one_add_inv_lt_one, Matrix.toLin_toMatrix, PiTensorProduct.lift_comp_map, Submodule.adjoint_orthogonalProjection, TensorProduct.homTensorHomMap_apply, LinearMap.tensorEqLocus_tmul, Matrix.isRepresentation.eq_toEnd_of_represents, continuousOn_cfcₙ_nnreal, LieModule.traceForm_apply_apply, cross_dot_cross, LinearMap.toMatrix₂_apply, ModuleCat.Hom.hom₂_apply, Real.fourierIntegral_continuousLinearMap_apply', sectionOfRetractionKerToTensorAux_algebraMap, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, TopModuleCat.hom_smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, LinearMap.adjoint_comp, krullTopology_mem_nhds_one_iff, IsPrecomplete.prec', PiToModule.fromMatrix_apply, SymmetricAlgebra.algHom_surjective, contMDiffAt_iff_localFrame_coeff, Algebra.baseChange_lmul, KaehlerDifferential.mvPolynomialBasis_repr_D, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_apply_tmul, QuadraticForm.tensorAssoc_apply, LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective, LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, Ideal.ofList_cons_smul, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, LinearMap.dualMap_apply, LieModule.Cohomology.twoCochain_val_apply, ContDiffMapSupportedIn.continuous_iff_comp_order_le, LieAlgebra.ext_iff, WeierstrassCurve.Projective.addMap_of_Z_ne_zero, TensorialAt.mkHom₂_apply, ContinuousAlternatingMap.curryLeft_add, Ideal.sup_mul_eq_of_coprime_left, TensorAlgebra.ι_inj, LinearMap.dualMap_surjective_iff, multilinearCurryLeftEquiv_symm_apply, LinearIsometry.strictConvexSpace_range_iff, MultilinearMap.piLinearMap_apply_apply_apply, TensorProduct.toLinearMap_symm_lid, TensorAlgebra.ι_eq_zero_iff, NonUnitalSubalgebra.coe_smul, CoalgCat.MonoidalCategoryAux.comul_tensorObj, ContinuousAlternatingMap.prodLIE_apply, Ideal.mul_iSup, PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal, QuadraticMap.associated_sq, LinearMap.dualMap_def, MultilinearMap.coe_currySumEquiv, MultilinearMap.uncurrySum_apply, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, RootPairing.toPerfPair_conj_reflection, KaehlerDifferential.ker_map_of_surjective, TensorProduct.tmul_of_gradedMul_of_tmul, smul_zero, CPolynomialOn.fderiv, Module.zero_smul, IsLocalizedModule.map_exact, SchwartzMap.convolution_flip, QuadraticMap.associated_isOrtho, ContinuousLinearMap.opNorm_flip, Algebra.H1Cotangent.isLocalizedModule, Algebra.TensorProduct.lift_comp_includeRight', Seminorm.bound_of_shell_smul, HasDerivWithinAt.prodMk, CliffordAlgebra.contractLeft_mul_algebraMap, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, ContinuousLinearMap.precompCompactConvergenceCLM_apply, map_dualTensorHom, Submodule.range_dualMap_mkQ_eq, ContinuousLinearMap.IsPositive.adjoint_conj, IntermediateField.isSeparable_iSup, MultilinearMap.curryMidLinearEquiv_symm_apply, Polynomial.toMatrix_sylvesterMap, LinearMap.smulRightₗ_apply_apply, krullTopology_mem_nhds_one_iff_of_normal, IsConformalMap.smul, LinearMap.IsRefl.eq_iff, AlternatingMap.uncurryFin_add, TensorProduct.AlgebraTensorModule.lTensor_one, Matrix.dualNumberEquiv_apply, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, LieModule.maxGenEigenSpace_toEnd_eq_top, TemperedDistribution.fourierMultiplierCLM_sum, Submodule.smul_le_of_le_smul_of_le_jacobson_bot, LinearMap.vecEmpty₂_apply, ContMDiffCovariantDerivativeOn.contMDiff, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, Matrix.toLin_finTwoProd, FormalMultilinearSeries.derivSeries_eq_zero, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, TestFunction.lineDerivCLM_smul, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, ContDiffWithinAt.smulRight, Module.Basis.linearMap_repr_symm_apply, Matrix.toLinAlgEquiv'_toMatrixAlgEquiv', LinearEquiv.lieConj_symm, ContinuousLinearMap.star_eq_adjoint, CliffordAlgebra.even.lift.aux_ι, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, LieAlgebra.rank_eq_natTrailingDegree, ContinuousMultilinearMap.curryLeft_apply, Module.End.ker_aeval_ring_hom'_unit_polynomial, Algebra.lmul_isUnit_iff, LinearEquiv.charpoly_conj, LinearMap.tensorProduct_apply, AffineSubspace.direction_smul, AlternatingMap.uncurryFin_uncurryFinLM_comp_of_symmetric, Rep.coinvariantsTensorMk_apply, ContMDiffWithinAt.coordChangeL, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, QuotSMulTop.map_comp, LinearMap.isSymmetric_adjoint_comp_self, Projectivization.cross_mk_of_ne, Algebra.tensorH1CotangentOfIsLocalization_toLinearMap, AlternatingMap.mkContinuousLinear_norm_le, Matrix.kroneckerTMulAlgEquiv_apply, LinearMap.not_separatingLeft_zero, ProperCone.hyperplane_separation_of_notMem, Module.End.trace_eq_sum_roots_charpoly_of_splits, LieAlgebra.Basis.borelUpper_le_biSup, Module.End.mem_invtSubmodule_adjoint_iff, Module.End.genEigenspace_nat, Unitization.complex_cfcₙ_eq_cfc_inr, Module.ker_algebraMap_end, fderiv_clm_apply, separableClosure.isSeparable, LieAdmissibleAlgebra.ext_iff, DualNumber.eps_pow_two, FormalMultilinearSeries.radius_le_radius_derivSeries, ContinuousAlternatingMap.curryLeftLI_apply, endVecAlgEquivMatrixEnd_symm_apply_apply, CharacterModule.uncurry_apply, LinearMap.restrictScalarsField_apply_apply, AdicCompletion.of_bijective, Bialgebra.TensorProduct.assoc_toCoalgEquiv, iteratedFDerivWithin_zero_eq_comp, Ideal.span_singleton_mul_left_inj, ContinuousLinearMap.norm_compSL_le, QuadraticMap.Ring.associated_pi, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, LinearMap.nondegenerate_toMatrix₂_iff, Matrix.trace_kroneckerMapBilinear, Module.dualMap_dualMap_eq_iff_of_injective, AlgEquiv.linearEquivConj_mulRight, ContMDiffFiberwiseLinear.locality_aux₁, IsAdicComplete.StrictMono.factorPow_comp_extend, LinearMap.range_self_comp_adjoint, ModuleCat.Iso.conj_eq_conj, LieAlgebra.mem_corootSpace', cfcₙ_nnreal_eq_real, Matrix.toLinAlgEquiv'_one, Matrix.toLin_one, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, CliffordAlgebra.contractLeft_algebraMap_mul, IntermediateField.adjoin.finiteDimensional, IntermediateField.botEquiv_def, Submodule.FG.jacobson_smul_lt, InnerProductSpace.isIdempotentElem_rankOne_self_iff, le_algebraicClosure_iff, fderivWithin_continuousLinearEquiv_comp, Quaternion.re_snd_dualNumberEquiv, LinearMap.trace_eq_contract_of_basis, LinearMap.range_dualMap_le_dualAnnihilator_ker, Matrix.toLin_transpose, IntermediateField.adjoin_adjoin_comm, TrivSqZeroExt.algebraMap_eq_inlHom, stereographic_apply, Complex.toMatrix_conjAe, Ideal.mem_mul_span_singleton, Submodule.mem_stabilizer_submodule_iff_map_eq, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, Submodule.finite_dualAnnihilator_iff, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, Representation.leftRegular_norm_apply, BilinForm.mul_toMatrix, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, Ideal.IsTwoSided.pow_add, ContMDiffAt.mfderiv, Module.End.IsSemisimple.minpoly_squarefree, IntermediateField.val_mk, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Real.iteratedFDeriv_fourierIntegral, Algebra.Generators.CotangentSpace.map_toComp_injective, TestFunction.instLocallyConvexSpaceReal, TensorProduct.mk_surjective, AdicCompletion.evalₐ_of, Module.End.lTensorAlgHom_apply_apply, Continuous.clm_bundle_apply₂, IntermediateField.rank_sup_le, Matrix.toLpLin_symm_comp, IntermediateField.LinearDisjoint.self_right, LinearIsometry.strictConvexSpace_range, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_toLinearMap, LieAlgebra.IsKilling.lieIdealOrderIso_right_inv, Module.Basis.toDual_linearCombination_right, Matrix.toLinearMapₛₗ₂_apply_basis, LieAlgebra.ad_lie, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, isPrecomplete_iff, LocalizedModule.mk_smul_mk, Unitization.lift_range_le, VertexOperator.ncoeff_of_coeff, AffineMap.homothety_def, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ExteriorAlgebra.liftAlternating_algebraMap, Orientation.kahler_apply_apply, NonUnitalCStarAlgebra.toIsScalarTower, LinearMap.toMatrix_toSpanSingleton, RootPairing.toPerfPair_flip_conj_coreflection, VertexOperator.ncoeff_eq_zero_of_lt_order, IsSelfAdjoint.adjoint_conj, LinearMap.toMatrix₂_symm', FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, AlgEquiv.restrictNormalHom_apply, LieModule.isNilpotent_iff_forall', InfiniteGalois.mk_toAlgEquivAux, IsLocalizedModule.fromLocalizedModule'_mk, VectorPrebundle.contMDiffOn_contMDiffCoordChange, instIsAbelianGaloisSubtypeMemIntermediateField, IsCovariantDerivativeOn.torsion_apply_eq_extend, AlternatingMap.mkContinuousAlternating_norm_le_max, IsInertiaField.toIsGaloisGroup, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, OrthonormalBasis.sum_rankOne_eq_id, Module.End.mem_genEigenspace_nat, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, mdifferentiableAt_coordChangeL, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, SymmetricAlgebra.algebraMap_leftInverse, TensorProduct.equivFinsuppOfBasisRight_symm, TensorProduct.AlgebraTensorModule.ker_mapOfCompatibleSMul, IntermediateField.inclusion_inclusion, ContDiffMapSupportedIn.fderivCLM_apply_of_le, ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, Subspace.dualAnnihilator_le_dualAnnihilator_iff, Representation.char_linHom, hasFDerivAt_integral_of_dominated_of_fderiv_le'', LieSubmodule.coe_toEnd_pow, DistribMulActionHom.map_smulₑ, Submodule.lTensorOne_tmul, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, FDRep.Iso.conj_ρ, IntermediateField.extendScalars_restrictScalars, HasStrictFDerivAt.continuousAlternatingMap_apply_const, LinearMap.IsAlt.eq_of_add_add_eq_zero, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, LinearMap.isIntegral, Ideal.mul_mono_left, DistribMulActionHom.toFun_eq_coe, LinearMap.toMatrix_singleton, CovariantDerivative.torsion_self, LinearMap.BilinForm.toMatrix'_mul, ContinuousLinearMap.norm_smulRightL_le, TensorAlgebra.algebraMap_leftInverse, LinearMap.trace_restrict_eq_of_forall_mem, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, Algebra.Extension.Hom.sub_tmul, LinearEquiv.reduce_mk, LieAlgebra.isNilpotent_range_ad_iff, exteriorPower.alternatingMapLinearEquiv_symm_apply, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, MeasureTheory.Measure.addHaarScalarFactor_domSMul, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, IsAdicComplete.mk_lift, LieModule.mem_genWeightSpaceOf, Rep.ihom_coev_app_hom, LieAlgebra.IsKilling.coe_invtSubmoduleToLieIdeal_eq_iSup, Submodule.top_smul, LinearMap.toMatrix₂'_compl₂, IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul, AdicCompletion.factor_evalₐ_eq_eval, Basis.multilinearMap_apply, Algebra.TensorProduct.comm_comp_map, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, TrivSqZeroExt.map_inl, Matrix.toLinAlgEquiv'_symm, CliffordAlgebra.foldr_algebraMap, Quaternion.snd_imI_dualNumberEquiv_symm, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, AffineEquiv.arrowCongr_symm_apply, Submodule.le_dualAnnihilator_iff_le_dualCoannihilator, NonUnitalCommCStarAlgebra.toSMulCommClass, LieDerivation.instLieModule, LieAlgebra.IsKilling.traceForm_coroot, InfiniteGalois.proj_of_le, HasFiniteFPowerSeriesOnBall.fderiv', ContinuousLinearMap.le_of_opNorm₂_le_of_le, Submodule.span_smul_eq, Orientation.kahler_rotation_right, LieAlgebra.Basis.borelLower_eq, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, iteratedFDerivWithin_clm_apply_const_apply, LinearMap.rid_comp_lTensor, ContinuousMultilinearMap.currySum_apply, PiTensorProduct.lift.unique', Matrix.nondegenerate_toLinearMap₂'_iff, Unitization.norm_splitMul_snd_sq, LinearMap.separatingRight_toMatrix₂_iff, CFC.nnrpow_eq_nnrpow_prod, ContinuousLinearMap.smulRight_id, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, Ideal.instNoZeroDivisors, Coalgebra.lTensor_counit_comp_comul, KaehlerDifferential.isBaseChange_of_formallyEtale, IsLocalizedModule.map_units, TemperedDistribution.lineDerivOp_fourierInv_eq, AlternatingMap.curryLeft_compLinearMap, LieAlgebra.nilpotent_ad_of_nilpotent_algebra, DivisibleHull.instIsStrictOrderedModuleRat, CliffordAlgebra.changeForm.associated_neg_proof, CompactConvergenceCLM.continuousSMul, mfderiv_smul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, CliffordAlgebra.ofEven_ι, IntermediateField.lift_adjoin, ContinuousAlternatingMap.alternatizeUncurryFin_add, LinearIsometryEquiv.toMatrix_mem_unitaryGroup, QuotSMulTop.map_apply_mk, LieModule.instIsFaithfulEnd, Matrix.cramer_smul, ContinuousLinearMap.flip_zero, ContMDiffWithinAt.clm_prodMap, IsGaloisGroup.fixedPoints_le_of_le, ContDiffMapSupportedIn.fderivCLM_apply, Submodule.dualAnnihilator_bot, DualNumber.lift_apply_inl, Representation.linHom.mem_invariants_iff_comm, LocalizedModule.smul_eq_iff_of_mem, LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdeal, TestFunction.fderivCLM_apply, ContinuousLinearMap.isAdjointPair_inner, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, AdicCompletion.eval_of, CommAlgCat.associator_hom_hom, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, Module.End.isNilpotent_restrict_genEigenspace_top, IsLocalizedModule.map_comp, Module.Dual.eval_naturality, HVertexOperator.coeff_comp, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, Real.fourier_continuousMultilinearMap_apply, Units.orbitRel_nonZero_iff, ModuleCat.ofHom₂_hom_apply_hom, Unitization.splitMul_injective, IntermediateField.rank_eq_rank_subalgebra, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousLinearMap.smulRight_comp, LieAlgebra.Basis.root_mem_or_mem_neg, DualNumber.lift_op_smul, LinearMap.trace_conj, Submodule.map_range_rTensor_subtype_lid, QuadraticMap.Isometry.tmul_apply, isSMulRegular_on_quot_iff_lsmul_comap_eq, ContinuousLinearEquiv.coord_norm', exists_bijective_map_powers, fderivWithin_continuousAlternatingMap_apply, OrderIso.smulRightDual_symm_apply, IsLocalizedModule.iso_localizedModule_eq_refl, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, jacobi_cross, IntermediateField.LinearDisjoint.of_finrank_sup, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, LinearMap.separatingLeft_toMatrix₂_iff, Module.map_eval_injective, HVertexOperator.coeff_apply_apply, ContinuousLinearMap.toUniformConvergenceCLM_continuous, SymmetricAlgebra.algebraMap_inj, hasStrictFDerivAt_inv', IntermediateField.lift_sup, basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix, AdicCompletion.evalₐ_mk, Module.Basis.toDualFlip_apply, LinearMap.mem_span_iff_bound, Representation.asModuleEquiv_map_smul, Set.Finite.convexHull_eq_image, ContinuousOn.cfcₙ_nnreal, Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct, AlternatingMap.uncurryFin_apply, TemperedDistribution.smulLeftCLM_const, normalClosure.normal, Algebra.IsStandardSmooth.iff_exists_basis_kaehlerDifferential, fromModuleCatToModuleCatLinearEquiv_apply, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, QuadraticMap.PosDef.smul, SchwartzMap.fourier_convolution_apply, OreLocalization.add_oreDiv, neg_cross, Projectivization.generalLinearGroup_smul_def, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, LocalizedModule.map_mk, PiTensorProduct.lift_comp_reindex_symm, AffineSubspace.isometryEquivMap.apply_symm_apply, PiTensorProduct.map_update_smul, IsAdicComplete.StrictMono.of_lift, LieModule.coe_lcs_range_toEnd_eq, ModuleCat.ofHom₂_compr₂, LinearMap.flip_separatingLeft, LieModule.toEnd_module_end, IntermediateField.adjoin_adjoin_left, LieAlgebra.mem_zeroRootSubalgebra, TemperedDistribution.smulLeftCLM_sum, PowerBasis.constr_pow_mul, TensorProduct.map_smul_left, Ideal.ncard_primesOver_mul_card_inertia_mul_finrank, SubMulAction.mem_one', LieAlgebra.IsKilling.restr_invtSubmoduleToLieIdeal_eq_iSup, AddAut.mulLeft_apply_symm_apply, LinearMap.det_toMatrix', LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, IntermediateField.AdjoinSimple.coe_aeval_gen_apply, LinearMap.eq_adjoint_iff_basis_right, MDifferentiable.clm_precomp, LinearEquiv.arrowCongr_trans, MDifferentiable.clm_comp, Unitization.starLift_range_le, LinearMap.bijective_compr₂ₛₗ_of_equiv, ContDiffMapSupportedIn.fderivLM_apply_of_le, LinearMap.Nondegenerate.toMatrix₂, LinearMap.toMatrixAlgEquiv_apply', ContMDiff.clm_comp, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, continuousMultilinearCurryLeftEquiv_symm_apply, isSemiprimaryRing_iff, Ideal.pow_mem_pow, IsModuleTopology.continuous_bilinear_of_finite_right, DoubleCentralizer.instStarModule, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, LinearMap.existsUnique_eq_smul_id_of_finrank_eq_one, ContinuousMultilinearMap.smulRightL_apply, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, Convex.second_derivative_within_at_symmetric_of_mem_interior, NNReal.instContinuousMapZero.UniqueHom, LieSubalgebra.instIsScalarTowerSubtypeMem, TestFunction.instContinuousSMulReal, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, LinearMap.orthogonal_range, iteratedFDeriv_succ_eq_comp_left, MeasureTheory.Measure.addHaarScalarFactor_smul_congr', VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, IntermediateField.insepDegree_bot, LinearMap.singularValues_of_lt, DivisibleHull.mk_zero, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl, CovariantDerivative.torsion_apply_eq_extend, ContDiffMapSupportedIn.fderivLM_apply_of_gt, LinearMap.toMatrix_basis_equiv, Ideal.top_pow, contMDiffOn_coordChangeL, IntermediateField.equivOfEq_apply, ContinuousLinearEquiv.arrowCongrSL_symm_apply, AffineMap.homothety_add, NormedSpace.ext_iff, Module.evalEquiv_toLinearMap, DivisibleHull.zero_qsmul, ContinuousLinearMap.opNorm_mulLeftRight_le, MultilinearMap.compLinearMapMultilinear_apply, PointwiseConvergenceCLM.evalCLM_apply, ContDiffPointwiseHolderAt.iteratedFDeriv, DualNumber.lift_comp_inlHom, LinearMap.trace_prodMap', Module.End.mem_spectrum_iff_isRoot_charpoly, IsLocalizedModule.fromLocalizedModule.surj, LinearMap.dualMap_comp_dualMap, LinearMap.piApply_apply_apply, LinearMap.separatingLeft_iff_ker_eq_bot, LieAlgebra.commute_ad_of_commute, LinearMap.compQuadraticMap_polarBilin, ContinuousMultilinearMap.piₗᵢ_apply, Module.End.smulLeft_eq, Algebra.injective_lift_lsmul, ContMDiffWithinAt.clm_precomp, AdicCompletion.ofLinearEquiv_apply, TensorProduct.lift_compr₂, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, Ideal.sup_pow_eq_top, Ideal.mul_top, norm_iteratedFDerivWithin_fderivWithin, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, LinearMap.lid_comp_rTensor, DualNumber.algHom_ext'_iff, Ideal.pow_eq_top_iff, LinearMap.coe_toContinuousLinearMap_symm, Matrix.range_diagonal, Unitization.lift_apply_apply, IntermediateField.LinearDisjoint.of_basis_mul, AdicCompletion.mk_apply_coe, Submodule.torsionBySet.mk_smul, continuousMultilinearCurryFin1_symm_apply, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, separableClosure_le_separableClosure_iff, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, DualNumber.ideal_trichotomy, LinearMap.toMatrix_map_right, IsSymmetricAlgebra.comp_equiv, LieModule.iterate_toEnd_mem_lowerCentralSeries, LinearMap.extendScalarsOfIsLocalizationEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, OreLocalization.add_comm, LinearMap.dualMap_eq_lcomp, UniformOnFun.continuousSMul_submodule_of_image_bounded, IsLocalRing.map_mkQ_eq_top, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, LinearMap.trace_comp_comm, KaehlerDifferential.map_D, LinearMap.range_smulRight_apply, LinearMap.trace_eq_sum_trace_restrict', ContDiffAt.differentiableAt_iteratedFDeriv, BilinForm.toMatrix_compLeft, LinearMap.IsPositive.adjoint_eq, Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace, Ideal.iInf_pow_smul_eq_bot_of_isTorsionFree, Algebra.coe_lmul_eq_mul, ContinuousLinearMap.prodₗ_apply, ContinuousLinearEquiv.coord_norm, Module.Basis.toDual_apply_left, LinearMap.nilRank_le_natTrailingDegree_charpoly, KaehlerDifferential.DLinearMap_apply, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, ContDiffOn.smulRight, MeasureTheory.lpMeasToLpTrim_smul, LinearMap.toMatrix₂'_comp, LinearEquiv.congrQuadraticMap_apply, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, Matrix.toLinearMap₂_apply_basis, ContinuousAlternatingMap.liftCLM_apply, LinearEquiv.conjAlgEquiv_surjective, ContinuousLinearMap.norm_adjoint_comp_self, LinearMap.commute_transvections_iff_of_basis, TensorProduct.lift_comp_comm_eq, ContinuousLinearMap.map_add₂, MeasureTheory.integral_bilinear_hasDerivAt_eq_sub, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, NonUnitalStarSubalgebra.prod_top, Module.End.hasEigenvalue_iff_mem_spectrum, ContMDiff.clm_precomp, TensorPower.toTensorAlgebra_galgebra_toFun, TensorProduct.Algebra.moduleAux_apply, RingTheory.Sequence.map_first_exact_on_four_term_right_exact_of_isSMulRegular_last, LinearMap.not_hasEigenvalue_zero_tfae, LinearMap.toMatrix_pow, TensorAlgebra.algebraMap_eq_zero_iff, LinearPMap.closure_inverse_graph, RingTheory.Sequence.isWeaklyRegular_iff, Module.FinitePresentation.isLocalizedModule_mapExtendScalars, IntermediateField.rank_bot_mul_relrank, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, LieDerivation.coe_ad_apply_eq_ad_apply, ContMDiffOn.clm_prodMap, IsBaseChange.linearMapLeftRightHom_apply, Algebra.trace_apply, TensorAlgebra.toDirectSum_ι, FormalMultilinearSeries.derivSeries_apply_diag, ContMDiffWithinAt.clm_comp, MultilinearMap.currySum_smul, Submodule.norm_orthogonalProjection, LinearMap.BilinForm.toMatrix_comp, LinearEquiv.map_mem_invtSubmodule_iff, AnalyticAt.fderiv, ExteriorAlgebra.ιMulti_succ_curryLeft, Matrix.SpecialLinearGroup.toLin'_symm_apply, fderiv_comp_smul, iteratedFDeriv_clm_apply_const_apply, ContinuousLinearMap.opNorm_lsmul, Submodule.comap_smul', Submodule.mem_set_smul, FormalMultilinearSeries.norm_changeOriginSeriesTerm, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, LeftPreLieAlgebra.toIsScalarTower, instIsInertiaFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupInertiaOfIsGalois, LinearMap.trace_comp_cycle, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, Algebra.FormallyUnramified.comp_sec, HasFTaylorSeriesUpTo.zero_eq', Module.Basis.toDual_apply_right, AlgCat.hom_tensorHom, LinearMap.trace_comp_cycle', integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, LinearMap.toMatrix'_one, Representation.dual_apply, LieAlgebra.SpecialLinear.val_singleSubSingle, Polynomial.contentIdeal_mul_le_mul_contentIdeal, AdicCompletion.transitionMap_comp_eval_apply, AdicCompletion.of_injective_iff, Submodule.comap_smul'', Matrix.cstar_norm_def, PointwiseConvergenceCLM.withSeminorms, Submodule.baseChange_span, MeasureTheory.convolution_eq_swap, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, ContinuousLinearMap.map_zero₂, Module.surjective_piEquiv_apply_iff, LinearMap.nondegenerate_restrict_of_disjoint_orthogonal, LinearMap.eq_restrictScalarsRange₂_iff, UniformCauchySeqOnFilter.one_smulRight, ContDiff.fderiv_right, Unitization.starLift_symm_apply, Submodule.dualAnnihilator_iSup_eq, ContinuousMultilinearMap.curryFinFinset_symm_apply, Submodule.map₂_map_map, LieAlgebra.isNilpotent_iff_forall, Module.Dual.eq_of_preReflection_mapsTo', Submodule.dualAnnihilator_eq_bot_iff, TensorAlgebra.lift_unique, IntermediateField.finiteDimensional_map, TensorProduct.quotTensorEquivQuotSMul_comp_mk, LieAlgebra.ad_ker_eq_bot_of_hasTrivialRadical, Orientation.kahler_rightAngleRotation_right, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, Coalgebra.TensorProduct.assoc_toLinearEquiv, RatFunc.algEquivOfTranscendental_algebraMap, LinearEquiv.dualMap_refl, HasFTaylorSeriesUpTo.fderiv, cross_cross_eq_smul_sub_smul', QuadraticForm.tmul_comp_tensorAssoc, TensorProduct.rTensorHomToHomRTensor_apply, LinearMap.tensorKerEquiv_apply, basis_toMatrix_mul_linearMap_toMatrix, LinearMap.IsAlt.self_eq_zero, Submodule.span_smul_span, AlternatingMap.alternatizeUncurryFin_smul, Representation.dualTensorHom_comm, ContinuousLinearMap.precomp_apply, LinearMap.exact_lcomp_of_exact_of_surjective, ContinuousLinearMap.norm_holderL_le, AdicCompletion.eval_lift_apply, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, Ideal.mul_mono_right, contDiff_infty_iff_fderiv, TensorProduct.AlgebraTensorModule.range_lTensor_idealMap, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Matrix.toLinearMapRight'_one, isSMulRegular_iff_ker_lsmul_eq_bot, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem_of_analyticOn, IntermediateField.normalClosure_le_iff_of_normal, IsLocalizedModule.map_surjective, QuadraticForm.associated_tmul, Seminorm.comp_smul_apply, LinearEquiv.alternatingMapCongrRight_symm_apply_apply, instIsPushout, TemperedDistribution.derivCLM_apply_apply, MultilinearMap.curryFinFinset_symm_apply, AlgHom.fieldRange_of_normal, LinearMap.toMatrixAlgEquiv_reindexRange, ContinuousLinearMap.precomp_uniformConvergenceCLM_apply, IntermediateField.Lifts.eq_iff, Orientation.norm_kahler, Submodule.dualRestrict_apply, TensorProduct.one_gradedMul, IsLocalizedModule.map_iso_commute, IsCovariantDerivativeOn.affine_combination, Module.End.mem_genEigenspace, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, ContinuousLinearMap.postcompUniformConvergenceCLM_apply, Submodule.index_smul_le, MeasureTheory.weightedSMul_smul_measure, Module.Basis.SmithNormalForm.toMatrix_restrict_eq_toMatrix, TensorAlgebra.ofDirectSum_comp_toDirectSum, QuadraticForm.tensorComm_symm, intervalIntegral.integral_hasFDerivAt, LinearMap.self_comp_adjoint_injective_iff, HasFiniteFPowerSeriesOnBall.fderiv_eq, Bialgebra.mul_compr₂_comul, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, IsBaseChange.linearMapRight, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IntermediateField.normalClosure_map_eq, Submodule.dualAnnihilator_eq_bot_iff', LinearMap.ker_lsmul, LocalizedModule.zero_mk, intervalIntegral.fderiv_integral, ContinuousLinearMap.analyticAt_bilinear, Matrix.toLpLin_apply, IntermediateField.relrank_bot_left, HasFPowerSeriesAt.hasStrictFDerivAt, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, Matrix.toLin'_apply, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, CliffordAlgebra.contractRight_ι, QuotSMulTop.map_id, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, Unitization.algebraMap_eq_inlRingHom, isBoundedLinearMap_continuousMultilinearMap_comp_linear, LinearEquiv.arrowCongr_comp, isSMulRegular_on_quot_iff_lsmul_comap_le, IsCovariantDerivativeOn.torsion_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, LieAlgebra.isNilpotent_ad_of_isNilpotent, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, AffineEquiv.arrowCongr_apply, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, mdifferentiableAt_localFrame_coeff, LinearMap.rTensor_smul, MeasureTheory.FiniteMeasure.map_snd_prod, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, TensorProduct.toLinearMap_symm_rid, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, Submodule.smul_top_le_comap_smul_top, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, IsSymmetricAlgebra.equiv_toAlgHom, integral_bilinear_fderiv_right_eq_neg_left_of_integrable, Ideal.sup_mul, Derivation.linearEquiv_coe_comp, Module.Dual.instLieModule, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, ModuleCat.sMulCommClass_mk, Submodule.powSMulQuotInclusion_injective, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, LinearMap.diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne, IntermediateField.le_normalClosure, exists_continuousLinearEquiv_fderiv_symm_eq, QuadraticMap.tensorDistrib_tmul, Subspace.map_dualCoannihilator, OpenPartialHomeomorph.unitBallBall_symm_apply, Representation.Equiv.dualTensorHom_invFun, LieAlgebra.Extension.twoCocycleOf_coe_coe, LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero, TensorialAt.mkHom₂_apply_eq_extend, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, MeasureTheory.AEStronglyMeasurable.convolution_integrand', CharacterModule.homEquiv_apply_apply, IntermediateField.equivOfEq_trans, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, Ideal.IsTwoSided.instHMul, ContinuousLinearMap.isPositive_adjoint_comp_self, IntermediateField.normalClosure_def', LinearMap.dualCoannihilator_range_eq_ker_flip, ContDiffOn.differentiableOn_iteratedFDerivWithin, LinearMap.im_inner_adjoint_mul_self_eq_zero, AlgCat.hom_whiskerRight, Algebra.TensorProduct.map_bijective, ContinuousLinearMap.map_neg₂, LinearMap.compr₂ₛₗ_apply, Matrix.l2_opNorm_def, LinearMap.toMatrixAlgEquiv_mul, Ideal.span_pair_mul_span_pair, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Matrix.toEuclideanLin_toLp, TensorProduct.lift_mk_compr₂, LinearMap.IsSymmetric.toMatrix_eigenvectorBasis, Algebra.Extension.Cotangent.map_mk, Submodule.LinearDisjoint.linearIndependent_left_of_flat, ContinuousLinearMap.holderL_apply_apply, AdicCompletion.eval_surjective, Unitization.quasispectrum_eq_spectrum_inr, AdicCompletion.ofPowSMul_val_apply, Polynomial.sylveserMap_comp_adjSylvester, isConformalMap_const_smul, MeasureTheory.AEStronglyMeasurable.convolution_integrand, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, PowerBasis.constr_pow_aeval, Submodule.FG.smul, AffineSubspace.subtypeₐᵢ_toAffineMap, VectorFourier.hasFDerivAt_fourierChar_smul, IntermediateField.mem_restrict, Ideal.iInf_pow_smul_eq_bot_of_noZeroSMulDivisors, ContMDiffWithinAt.cle_arrowCongr, PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal', FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, Real.exists_extension_norm_eq, CliffordAlgebra.EvenHom.contract_mid, continuousMultilinearCurryRightEquiv_apply, LinearMap.det_toMatrix, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, Matrix.minpoly_toLin, basis_toMatrix_mul, nnnorm_cfcₙ_nnreal_le, LieDerivation.maxTrivSubmodule_eq_bot_of_center_eq_bot, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, Matrix.toLin'_toMatrix', Ideal.sup_mul_left_self, ContinuousAlternatingMap.prodLIE_symm_apply, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, AlternatingMap.alternatizeUncurryFinLM_apply, LinearMap.det_toLin, LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmodule, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcₙ_nnreal, Representation.Equiv.conj_apply_self, IntermediateField.LinearDisjoint.isDomain, LinearMap.posSemidef_toMatrix_iff, ContDiff.fderiv, Submodule.localized'_smul, instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation, SchwartzMap.fourier_convolution, LinearMap.trace_mul_cycle', fderivWithin_comp_smul, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, IntermediateField.finrank_dvd_of_le_right, Module.Basis.coord_unitsSMul, ContinuousLinearMap.flipₗᵢ_symm, LinearMap.isOrthoᵢ_flip, Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia, Matrix.Represents.algebraMap, continuousOn_cfcₙ_nnreal_setProd, fderivWithin_clm_apply, ContinuousLinearMap.postcomp_uniformConvergenceCLM_apply, exists_continuousLinearEquiv_fderivWithin_symm_eq, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, FGModuleCat.Iso.conj_hom_eq_conj, AdicCompletion.transitionMap_map_one, Module.Basis.toDual_eq_equivFun, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, TensorProduct.toMatrix_comm, Bialgebra.mul_compr₂_counit, fderiv_continuousAlternatingMap_apply_const_apply, TensorAlgebra.ι_eq_algebraMap_iff, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, IntermediateField.finrank_le_of_le_right, dualTensorHomEquivOfBasis_apply, Ideal.mul_right_self_sup, RightPreLieAlgebra.ext_iff, Submodule.toSubMulAction_one, Submodule.image_smul_top_eq_range_lsum, OreLocalization.smul_zero, Module.End.genEigenspace_le_smul, LinearMap.isAdjointPair_inner, LinearMap.IsPositive.adjoint_conj, ContinuousLinearMap.norm_holder_apply_apply_le, LieModule.Cohomology.d₂₃_comp_d₁₂, LinearMap.ker_tensorProductMk, Unitization.lift_apply, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, DualNumber.instIsPrincipalIdealRing, LinearMap.ker_dualMap_eq_dualAnnihilator_range, Matrix.kroneckerStarAlgEquiv_apply, LieModule.commute_toEnd_of_mem_center_left, LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent_of_basis, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, Submodule.norm_subtypeL_le, LinearEquiv.trans_dualMap_symm_flip, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, isGalois_bot, LinearMap.trace_comp_comm', Submodule.sup_smul_eq_sup_smul_of_le_smul_of_le_jacobson, TensorProduct.sum_tmul_basis_left_injective, LieAlgebra.Basis.coe_baseSupportEquiv_apply, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, OreLocalization.add_smul, IntermediateField.intermediateFieldMap_symm_apply_coe, HasStrictFDerivAt.clm_comp, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, Module.AEval.mem_mapSubmodule_apply, AlgebraicGeometry.structureSheafInType.smul_apply, PiTensorProduct.lift.unique, TensorProduct.coe_directSumRight, QuadraticForm.associated_baseChange, MonotoneOn.nnnorm_cfcₙ, Real.volume_preserving_transvectionStruct, VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.fpowerSeries_apply_one, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Representation.asAlgebraHom_mem_of_forall_mem, LieAlgebra.Basis.linearIndependent_baseSupp, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, LinearMap.range_smul, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Matrix.toLpLinAlgEquiv_symm_apply, MDifferentiableWithinAt.clm_prodMap, ContMDiffAt.clm_comp, LieAlgebra.ad_ker_eq_self_module_ker, Algebra.Generators.Hom.id_comp, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, AdicCompletion.eval_apply, Ideal.mul_eq_bot, OpenPartialHomeomorph.unitBallBall_apply, LinearMap.trace_baseChange, HasStrictFDerivAt.continuousMultilinearMap_apply, LinearEquiv.multilinearMapCongrLeft_apply, Submodule.instSMulCommClassSubtypeMemTorsion', CliffordAlgebra.contractLeftAux_apply_apply, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, ContDiffBump.convolution_tendsto_right_of_continuous, Matrix.toLinearMapₛₗ₂_toMatrix₂, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, ContinuousLinearMap.opNNNorm_mul_apply, CliffordAlgebra.contractLeft_one, le_comap_range_rTensor, ContinuousMultilinearMap.curryFinFinset_apply, MultilinearMap.domCoprodDep'_apply, ContDiffAt.smulRight, LinearMap.toMatrix'_mulVec, LinearMap.trace_eq_sum_trace_restrict_of_eq_biSup, Subspace.dualAnnihilator_inf_eq, VertexOperator.coeff_eq_ncoeff, FormalMultilinearSeries.changeOriginSeriesTerm_bound, IsLocalizedModule.map_LocalizedModules, Matrix.SeparatingLeft.toLinearMap₂, MultilinearMap.uncurrySum_smul, IntermediateField.finiteDimensional_adjoin_pair, SchwartzMap.denseRange_toLpCLM, IntermediateField.normal_sup, IntermediateField.coe_algebraMap_apply, hasEigenvector_toLin_diagonal, LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero, LinearMap.codRestrict₂_apply, Bialgebra.TensorProduct.assoc_symm_tmul, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, mdifferentiableWithinAt_hom_bundle, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, ContinuousLinearMap.norm_precompL_le, ContinuousLinearMap.apply_apply, dotProduct_toMatrix₂_mulVec, ContinuousLinearMap.norm_map_removeNth_le, Module.End.exists_isNilpotent_isSemisimple, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, separableClosure.isGalois, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, TensorProduct.gradedComm_gradedMul, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, Module.End.HasUnifEigenvalue.mem_spectrum, PiTensorProduct.mapLMultilinear_opNorm, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, fderivWithin_restrictScalars_comp, Bialgebra.TensorProduct.assoc_toAlgEquiv, AdicCompletion.exists_smodEq_pow_smul_top_and_mkQ_eq, Matrix.diagonal_comp_single, FDRep.dualTensorIsoLinHom_hom_hom, ContinuousLinearMap.instModuleFinite, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_of_symmetric, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, TensorPower.toTensorAlgebra_tprod, Real.fourierIntegral_iteratedFDeriv, IntermediateField.restrictScalars_adjoin, LinearMap.toMatrixAlgEquiv_transpose_apply, NonUnitalCStarAlgebra.toSMulCommClass, IntermediateField.finiteDimensional_iSup_of_finset', Submodule.orthogonalProjection_norm_le, OreLocalization.universalHom_commutes, IntermediateField.finrank_adjoin_simple_eq_one_iff, MultilinearMap.compLinearMapₗ_apply, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, derivWithin_clm_apply, Quaternion.fst_re_dualNumberEquiv_symm, IntermediateField.LinearDisjoint.map, IsLocalizedModule.lift_iso, TrivSqZeroExt.mem_kerIdeal_iff_inr, SchwartzMap.fourierMultiplierCLM_smul, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, IsBaseChange.endHom_comp, Module.End.eigenspace_aeval_polynomial_degree_1, Quaternion.imI_snd_dualNumberEquiv, RatFunc.algEquivOfTranscendental_apply, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, MeasureTheory.norm_condExpL2_le_one, HasCompactSupport.convolution_integrand_bound_right, LinearMap.traceAux_def, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, MultilinearMap.fromDFinsuppEquiv_symm_apply, Algebra.leftMulMatrix_apply, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, AdicCompletion.ofLinearEquiv_symm_of, InnerProductSpace.symm_toEuclideanLin_rankOne, Subspace.isCompl_dualAnnihilator, LinearMap.BilinForm.toMatrix'_compRight, isBoundedBilinearMap_smulRight, LocalizedModule.mkLinearMap_apply, IntermediateField.finiteDimensional_sup, ContMDiffAt.cle_arrowCongr, VertexOperator.coeff_eq_zero_of_lt_order, IntermediateField.Lifts.le_iff, HasFDerivAt.clm_comp, ContinuousLinearMap.adjoint_innerSL_apply, LieAlgebra.Basis.baseSupp_apply_h', Module.Basis.eval_ker, LinearPMap.IsClosable.graph_closure_eq_closure_graph, Algebra.Extension.Hom.toAlgHom_id, Bundle.Pretrivialization.continuousLinearMapCoordChange_apply, WeierstrassCurve.Projective.nonsingularLift_zero, ExteriorAlgebra.liftAlternating_ι, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, trace_adjoinSimpleGen, isBoundedLinearMap_prod_multilinear, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', Ideal.span_singleton_pow, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, LinearEquiv.reduce_mkQ, AlgEquiv.eq_linearEquivConjAlgEquiv, Representation.IntertwiningMap.toLinearMapl_apply, IntermediateField.normal_iff_normalClosure_eq, HasCompactSupport.convolution_integrand_bound_right_of_subset, IntermediateField.rank_adjoin_simple_eq_one_iff, Real.fourier_smul_convolution_eq, CliffordAlgebra.contractLeftAux_contractLeftAux, Module.reflection_mul_reflection_zpow, postcomp_compactConvergenceCLM_apply, Subspace.comap_dualAnnihilator_dualAnnihilator, LinearMap.toMatrix_apply, AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective, second_derivative_symmetric_of_eventually_of_real, IsAdicComplete.StrictMono.mkQ_comp_lift, Module.erange_coe, TensorProduct.toMatrix_map, Matrix.toLinAlgEquiv_toMatrixAlgEquiv, Matrix.rank_vecMulVec, TemperedDistribution.laplacianCLM_apply, LieAlgebra.IsKilling.rootSystem_root_apply, AdicCompletion.map_of, ContinuousLinearMap.toWOT_apply, IntermediateField.isIntegral_iff, contMDiffWithinAt_hom_bundle, mem_contMDiffFiberwiseLinear_iff, Submodule.le_dualCoannihilator_dualAnnihilator, IntermediateField.LinearDisjoint.isField_of_isAlgebraic, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, Submodule.torsionBy.mk_smul, Algebra.Extension.Hom.toAlgHom_apply, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, Matrix.toLinAlgEquiv_symm, SchwartzMap.smulLeftCLM_smul, Module.FinitePresentation.exists_basis_localizedModule_powers, DoubleCentralizer.coe_snd, ContinuousLinearMap.opNorm_le_bound₂, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, MeasureTheory.integral_convolution, LinearMap.toMatrix_id_eq_basis_toMatrix, IsLocalRing.spanFinrank_eq_finrank_quotient, separableClosure.normalClosure_eq_self, LinearMap.toMatrixAlgEquiv_transpose_apply', Polynomial.mkDerivation_apply, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, CFC.nnrpow_map_prod, LinearMap.baseChangeHom_apply, LinearMap.toMatrixRight'_comp, Derivation.evalAt_apply, LinearMap.isOrtho_def, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, LieSubalgebra.instIsArtinianSubtypeMem, ContinuousMultilinearMap.norm_curryMid, Matrix.kroneckerStarAlgEquiv_symm_apply, Algebra.Generators.H1Cotangent.δ_map, AlternatingMap.curryLeft_add, LinearMap.uncurryLeft_apply, LinearMap.trace_map, IntermediateField.adjoin.powerBasis_dim, AdicCompletion.of_apply, TensorProduct.AlgebraTensorModule.assoc_eq, norm_iteratedFDeriv_fderiv, MeasureTheory.Lp.toTemperedDistribution_smul_eq, SchwartzMap.laplacian_eq_fourierMultiplierCLM, Module.FinitePresentation.isLocalizedModule_map, IsGalois.of_fixedField_normal_subgroup, HVertexOperator.coeff_of_coeff, const_smul_mfderiv, Seminorm.smul_le_smul, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, LinearMap.applyₗ_apply_apply, IntermediateField.essFiniteType_iff, LinearMap.IsAlt.neg, Field.Emb.cardinal_separableClosure, HasMFDerivAt.const_smul, IsCovariantDerivativeOn.finite_affine_combination, Subspace.finrank_add_finrank_dualAnnihilator_eq, Matrix.toBilin_comp, WeierstrassCurve.Projective.Point.toAffineLift_eq, IntermediateField.isPurelyInseparable_sup, NonUnitalCommCStarAlgebra.toIsScalarTower, AlternatingMap.curryLeft_same, LinearMap.polyCharpoly_coeff_eval, ContinuousLinearMap.coe_mulₗᵢ, LieModuleHom.map_lie₂, IntermediateField.splits_of_splits, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, MDifferentiableOn.clm_bundle_apply₂, IsAdicComplete.StrictMono.mk_lift, Module.isTorsionBy_quotient_element_smul, LocalizedModule.oreEqv_eq_r, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, LinearMap.det_toMatrix_eq_det_toMatrix, HasFDerivWithinAt.continuousAlternatingMap_apply_const, Algebra.TensorProduct.mul_apply, UniversalEnvelopingAlgebra.lift_ι_apply', ContinuousLinearMap.innerSL_apply_comp, Matrix.SpecialLinearGroup.toLin'_apply, Module.Finite.of_isComplemented_codomain, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Submodule.piQuotientLift_mk, QuadraticMap.nondegenerate_associated_iff, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, LinearMap.toKerIsLocalized_apply_coe, CStarMatrix.norm_def, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_deriv₂, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, ModuleCat.ihom_ev_app, ContMDiffOn.clm_bundle_apply₂, LinearMap.adjoint_id, contDiff_succ_iff_hasFDerivAt, TrivSqZeroExt.eq_smul_exp_of_invertible, Submodule.restrictScalars_self, MultilinearMap.currySumEquiv_symm_apply, LieModule.Weight.hasEigenvalueAt, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, Ideal.exists_pow_inf_eq_pow_smul, HasCompactSupport.hasFDerivAt_convolution_left, TrivSqZeroExt.map_id, TensorProduct.lift.equiv_apply, IsBaseChange.linearMapLeftRightHom_comp, Algebra.Extension.cotangentComplex_mk, IsLocalizedModule.fromLocalizedModule'_smul, TemperedDistribution.smulLeftCLM_apply_apply, Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct, Subspace.dualPairing_eq, LinearMap.SeparatingLeft.congr, Matrix.Nondegenerate.toLinearMap₂', AlgHom.mulLeftRightMatrix.comp_inv, AdicCompletion.eval_comp_of, retractionOfSectionOfKerSqZero_tmul_D, ContinuousLinearMap.hasDerivAt_of_bilinear, instIsPushoutFractionRingMvPolynomial_1, second_derivative_symmetric_of_eventually, KaehlerDifferential.linearCombination_surjective, IsLocalizedModule.map_lTensor, ContMDiff.coordChangeL, Submodule.restrictScalars_localized'_smul, Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂, Submodule.map_smul, Module.Basis.coord_toDualEquiv_symm_apply, Module.Basis.baseChange_linearMap, int_smul_eq_zsmul, ContinuousLinearMap.orthogonal_ker, LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul, ContDiffWithinAt.fderivWithin_right, LinearMap.IsRefl.ker_flip, LinearMap.toMatrixAlgEquiv'_comp, LinearMap.ker_smul, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, Continuous.cfcₙ_nnreal', LinearPMap.IsClosable.existsUnique, contDiffWithinAt_succ_iff_hasFDerivWithinAt, Module.mapEvalEquiv_symm_apply, LieModule.rank_le_natTrailingDegree_charpoly_ad, InnerProductSpace.norm_rankOne, Ideal.stabilizerEquiv_apply_smul, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, derivationQuotKerSq_mk, LieSubalgebra.coe_ad, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, TensorProduct.uncurry_apply, Submodule.map_le_smul_top, PiTensorProduct.mapLMultilinear_toFun_apply, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, CStarMatrix.inner_toCLM_conjTranspose_right, HasFiniteFPowerSeriesOnBall.fderiv, LieModule.toEnd_matrix, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, ContinuousMultilinearMap.curryMidEquiv_symm_apply, LinearMap.sum_repr_mul_repr_mul, CStarMatrix.toCLM_apply_single_apply, LinearMap.IsPositive.conj_adjoint, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, LinearMap.IsPerfPair.dualEval, LinearMap.ker_toContinuousLinearMap, TensorProduct.AlgebraTensorModule.lTensor_tmul, IntermediateField.adjoin_rootSet_isSplittingField, IsLocalizedModule.iso_mk_one, IntermediateField.nonempty_algHom_adjoin_of_splits, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, QuadraticModuleCat.hom_hom_associator, LinearMap.charpoly_toMatrix, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, LieModule.toEnd_pow_comp_lieHom, LinearMap.isSymm_iff_isHermitian_toMatrix, LinearMap.trace_lie, LinearMap.lsmul_eq_distribSMultoLinearMap, IsAzumaya.AlgHom.mulLeftRight_bij, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, IntermediateField.LinearDisjoint.linearIndependent_left, perfectClosure.isPurelyInseparable, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, contMDiffOn_iff_localFrame_coeff, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, iteratedFDeriv_succ_apply_left, LinearMap.separatingLeft_dualProd, IsSymmSndFDerivAt.eq, LinearMap.toMatrix_toLin, IntermediateField.isSeparable_adjoin_iff_isSeparable, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, TensorProduct.includeRight_lid, Complex.restrictScalars_toSpanSingleton', HasFDerivAt.continuousMultilinearMap_apply, Quaternion.imK_snd_dualNumberEquiv, LinearMap.range_localizedMap_eq_localized₀_range, prod_galRestrict_eq_norm, fderiv_inv', AdicCompletion.eval_lift, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, MultilinearMap.currySum_apply, instIsPushoutFractionRingMvPolynomial, IsTensorProduct.map_eq, DirectSum.gMulLHom_apply_apply, LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly, Algebra.Extension.H1Cotangent.map_toInfinitesimal_bijective, Algebra.Extension.Cotangent.val_smul'', QuadraticModuleCat.hom_inv_associator, hasEigenvalue_toLin_diagonal_iff, continuousMultilinearCurryFin1_apply, PiTensorProduct.lift_symm, CliffordAlgebra.contractLeft_algebraMap, Matrix.spectrum_toLin', AdicCompletion.ofAlgEquiv_symm_of, LieSubalgebra.ad_comp_incl_eq, norm_iteratedFDeriv_clm_apply_const, LinearIsometry.adjoint_comp_self

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	SemigroupAction.toSMul Monoid.toSemigroup MulAction.toSemigroupAction toMulAction	—	—	—
ext_iff 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MulAction.toSemigroupAction toMulAction	—	ext
smul_add 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MulAction.toSemigroupAction toMulAction AddSemigroup.toAdd AddMonoid.toAddSemigroup	—	—
smul_zero 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MulAction.toSemigroupAction toMulAction AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass	—	—
toAddMonoidEnd_apply 📖	mathematical	—	DFunLike.coe MonoidHom AddMonoid.End AddZeroClass.toAddZero AddMonoid.toAddZeroClass MulOneClass.toMulOne Monoid.toMulOneClass AddMonoid.End.instMonoid MonoidHom.instFunLike toAddMonoidEnd DistribSMul.toAddMonoidHom toDistribSMul	—	—
toAddMonoidHom_apply 📖	mathematical	—	DFunLike.coe AddMonoidHom AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoidHom.instFunLike toAddMonoidHom SMulZeroClass.toSMul AddZero.toZero DistribSMul.toSMulZeroClass toDistribSMul	—	—

DistribSMul

Definitions

Name	Category	Theorems
compFun 📖	CompOp	—
toAddMonoidHom 📖	CompOp	5 math math: AddMonoidHom.coe_smul', DistribMulAction.toAddMonoidEnd_apply, toAddMonoidHom_apply, toAddMonoidHom_eq_zsmulAddGroupHom, toAddMonoidHom_eq_nsmulAddMonoidHom
toSMulZeroClass 📖	CompOp	6651 math, 1 bridge math: AnalyticWithinAt.const_smul, MultilinearMap.map_piecewise_smul, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, range_cfcₙ_nnreal, Matrix.l2_opNorm_toEuclideanCLM, AffineIndependent.smul, LinearMap.det_toContinuousLinearMap, HasDerivAt.fun_neg, LieSubmodule.coe_smul, SubMulAction.zero_mem, units_inv_smul, TestFunction.lineDerivCLM_apply_of_le, absorbent_iff_eventually_nhdsNE_zero, LeftPreLieAlgebra.toSMulCommClass, MeasureTheory.Measure.integral_comp_inv_smul, SkewMonoidAlgebra.mapDomain_smul, CategoryTheory.ShortComplex.opcyclesMap_smul, StarConvex.preimage_add_right, iteratedDeriv_scomp_two, HasDerivAt.isLittleO, LinearMap.IsSymmetric.clm_adjoint_eq, Finset.expect_ite_mem, ContinuousLinearMap.rayleigh_smul, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, ContinuousMap.toLp_inj, Real.hasDerivAt_fourier, InnerProductSpace.Core.inner_smul_right, AffineSpace.asymptoticNhds_smul, Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe, ContinuousMultilinearMap.map_piecewise_smul, LinearIsometryEquiv.strictConvex_preimage, TemperedDistribution.lineDerivOpCLM_eq, IsIntegralCurve.comp_mul, vsub_midpoint, LinearMap.restrictScalars_toMatrix, Orientation.oangle_sign_smul_add_right, DiffContOnCl.smul, MeasureTheory.Lp.toTemperedDistributionCLM_apply, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Complex.im_qsmul, HasStrictDerivAt.fun_pow', ConvexCone.convex, Convex.translate_preimage_right, MeasureTheory.setIntegral_tilted, RootPairing.rootForm_self_smul_coroot, CochainComplex.HomComplex.δ_units_smul, FormalMultilinearSeries.comp_rightInv_aux1, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, Seminorm.isBounded_const, PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective, LinearMap.mkContinuous₂_norm_le', AffineMap.lineMap_apply_module, HasDerivWithinAt.clog_real, ContinuousMultilinearMap.norm_mkPiRing, taylor_integral_remainder, CFC.posPart_smul_of_nonpos, Finsupp.linearCombination_apply_of_mem_supported, ContinuousLinearMap.derivWithin_of_bilinear, Submodule.mem_colon_span_singleton, ConvexOn.smul'', EuclideanGeometry.dist_smul_vadd_sq, StrictConcaveOn.sub, Bundle.ContMDiffRiemannianMetric.isVonNBounded, HasDerivWithinAt.clm_comp, PointedCone.toConvexCone_closure_pointed, NonUnitalAlgHom.map_smul, real_inner_div_norm_mul_norm_eq_neg_one_iff, HasDerivWithinAt.congr_of_mem, Convex.neg, ConvexOn.mul_concaveOn', hasDerivWithinAt_Iio_iff_Iic, LinearMap.BilinForm.isOrtho_smul_right, HasStrictFDerivAt.fun_mul', Derivation.apply_eval_eq, LinearMap.mkContinuous₂_apply, LieDerivation.coe_smul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, Bundle.ContMDiffRiemannianMetric.contMDiff, HahnModule.smul_add, InnerProductSpace.isPositive_rankOne_self, AffineMap.lineMap_vsub_left, DFinsupp.lsum_lsingle, MonoidAlgebra.liftMagma_apply_apply, MeasureTheory.condExpL1_smul, Seminorm.absorbent_closedBall_zero, LinearMap.ortho_smul_right, ModuleCat.FilteredColimits.colimit_smul_mk_eq, ordinaryHypergeometric_sum_eq, AlgEquiv.moduleEndSelfOp_apply_apply, MeasureTheory.Lp.instIsScalarTower, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, CategoryTheory.ShortComplex.homologyMap_smul, Module.Basis.mem_submodule_iff, HasFDerivWithinAt.continuousMultilinearMap_apply, Polynomial.smeval_monomial_mul, RootPairing.pairing_smul_root_eq_of_not_linearIndependent, MDifferentiableOn.clm_postcomp, OrthonormalBasis.orthogonalProjection_eq_sum, hasDerivWithinAt_ofNat, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', Seminorm.bound_of_shell, Matrix.frobeniusIsBoundedSMul, HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, MeasureTheory.Martingale.smul, LinearMap.IsSymmetric.inner_map_polarization, HasDerivAt.const_sub, hasDerivWithinAt_add_const_iff, LinearOrder.strictConcaveOn_of_lt, NonUnitalNonAssocSemiring.nat_isScalarTower, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, SameRay.nonneg_smul_left, Convex.intrinsicClosure, MeasureTheory.integral_convexOn_of_integrand_ae, mellin_eq_fourier, Real.sSup_smul_of_nonpos, SchwartzMap.instLineDerivLeftSMulReal, NonUnitalStarSubalgebra.instSMulMemClass, CStarRing.norm_unitary_smul, Module.mem_annihilator, AnalyticOnNhd.smul, HasDerivAtFilter.sum, Ideal.Cotangent.lift_comp_toCotangent, PolyEquivTensor.toFunBilinear_apply_eq_sum, binomialSeries_eq_ordinaryHypergeometricSeries, Polynomial.lcoeff_comp_mapAlgHom_eq, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, StarAddMonoid.toStarModuleNNRat, StarAlgEquiv.ofLeftInverse'_apply, Ideal.tensorCotangentEquiv_tmul, SchwartzMap.integral_sesq_fourier_fourier, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, OreLocalization.oreDiv_add_char, Asymptotics.IsBigOTVS.congr', Submodule.isScalarTower, PowerSeries.IsRestricted.smul, Nat.floorDiv_eq_div, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Filter.IsBoundedUnder.smul_tendsto_zero, MeasureTheory.charFun_eq_fourierIntegral', Submodule.smul_def, DiffContOnCl.circleAverage_poissonKernel_smul', Real.hasFDerivAt_fourierChar_neg_bilinear_left, HasDerivWithinAt.Iio_of_Iic, RootPairing.Polarization_apply, PolynomialModule.comp_single, smul_finsum_mem, hasStrictDerivAt_intCast, Balanced.smul_mem_iff, segment_subset_closedBall_right, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, NonUnitalAlgHom.mk_coe, isSMulRegular_iff_mem_nonZeroSMulDivisors, MeasureTheory.convolution_eq_right', TrivSqZeroExt.snd_pow, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, smul_eq_zero_iff_eq, MeasureTheory.eLpNormEssSup_const_smul, gauge_def', Submodule.set_smul_le_iff, AffineMap.coe_smul, Asymptotics.isBigO_const_smul_right, MeasureTheory.hausdorffMeasure_segment, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, CategoryTheory.Linear.instMonoHSMulHomOfInvertible, IsSMulRegular.skewMonoidAlgebra, curveIntegral_smul, Quaternion.snd_imJ_dualNumberEquiv_symm, IntervalIntegrable.smul_continuousOn, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1, Orientation.inner_rotation_pi_div_two_right_smul, MultilinearMap.map_update_smul, Orientation.oangle_add_left_smul_rotation_pi_div_two, CFC.monotoneOn_one_sub_one_add_inv, RootPairing.coroot_eq_polarizationEquiv_apply_root, Subring.center.smulCommClass_right, derivWithin_smul, Real.fderiv_fourierIntegral, hasStrictFDerivAt_list_prod_finRange', MeasureTheory.integral_smul_nnreal_measure, ContinuousMultilinearMap.map_smul_univ, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, MvPolynomial.rTensor_apply_tmul_apply, InnerProductSpace.rankOne_one_left_eq_innerSL, LinearIndependent.pair_add_smul_right_iff, Seminorm.le_finset_sup_apply, Asymptotics.IsThetaTVS.trans_isBigOTVS, FormalMultilinearSeries.smul_apply, Complex.circleTransformDeriv_eq, LinearMap.IsSymmetric.restrictScalars, Seminorm.norm_sub_map_le_sub, bddBelow_smul_iff_of_neg, StrongDual.norm_extendRCLike, IsBaseChange.comp_iff, PowerSeries.heval_C, QuadraticAlgebra.coe_mul_eq_smul, HasFiniteFPowerSeriesAt.neg, Submodule.mem_ideal_smul_span_iff_exists_sum, nnnorm_cfcₙ_nnreal_le_iff, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, Balanced.smul_congr, MvPolynomial.rTensorAlgEquiv_apply, Algebra.Generators.H1Cotangent.δAux_mul, Pi.image_update_openSegment, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, ContinuousLinearMap.map_add_add, Set.smul_set_neg, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, SeminormFamily.basisSets_smul_right, MeasureTheory.Measure.integral_comp_mul_right, Convex.convex_isRCLikeNormedField, intervalIntegral.inv_smul_integral_comp_div_add, Antivary.smul_add_smul_le_smul_add_smul, MeromorphicOn.divisor_fun_smul, TrivSqZeroExt.lift_inlAlgHom_inrHom, Bornology.IsVonNBounded.of_sub_left, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, HasDerivWithinAt.div_const, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, StarAlgEquiv.ofStarAlgHom_symm_apply, Real.hasDerivAt_sigmoid, MeasureTheory.IntegrableOn.continuousOn_smul, taylorWithinEval_hasDerivAt_Ioo, AlternatingMap.map_vecCons_smul, ContDiffMapSupportedIn.seminorm_monoLM_eq, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, fderivWithin_fun_smul, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Module.End.smul_def, Finset.weightedVSubOfPoint_apply, HasDerivWithinAt.congr_mono, complexOfReal_hasDerivWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, MvPolynomial.scalarRTensor_apply_monomial_tmul, Real.fourierIntegralInv_eq', AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, LinearIndependent.pair_add_smul_left_iff, StrictConvex.is_linear_image, Matrix.single_vecMul, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, RingTheory.Sequence.isWeaklyRegular_cons_iff', SkewMonoidAlgebra.coeff_single_one_mul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, MeasureTheory.VectorMeasure.coe_smul, Finset.sum_smul, Quaternion.star_smul, hasDerivAt_integral_of_dominated_loc_of_lip, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, finsuppTensorFinsupp_apply, Convex.smul_preimage, AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff, curveIntegrable_segment, Submodule.toConvexCone_inf, ContDiffOn.smul_const, MvPolynomial.universalFactorizationMap_comp_map, Module.Basis.equivFun_symm_apply, MDifferentiableAt.cle_arrowCongr, Absorbs.eventually_nhds_zero, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul', PolynomialModule.smul_def, Seminorm.bot_eq_zero, Submodule.set_smul_span, ContinuousLinearMap.smul_apply, CFC.monotone_nnrpow, Complex.integral_boundary_rect_eq_zero_of_differentiableOn, ContinuousLinearMap.continuousSMul, Ideal.relNorm_smul, hasFTaylorSeriesUpToOn_top_iff_right, Seminorm.smul_comp, CochainComplex.HomComplex.Cocycle.coe_smul, ConvexCone.mem_positive, LinearIsometry.map_smul, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, MeasureTheory.Lp.const_smul_mem_Lp, RootPairing.reflectionPerm_eq_iff_smul_root, IsBaseChange.finsuppPow, strictConvex_Iic, AddSubgroupClass.coe_zmod_smul, absorbs_zero_iff, ConvexOn.smul, Module.End.HasUnifEigenvector.pow_apply, AffineSubspace.setOf_sSameSide_eq_image2, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, intervalIntegral.integral_hasDerivWithinAt_right, TrivSqZeroExt.snd_pow_eq_sum, Bornology.isVonNBounded_add_of_nonempty, norm_add_eq_iff_real, Monotone.quasiconcaveOn, Complex.integral_comp_pi_polarCoord_symm, FormalMultilinearSeries.radius_pi_eq_iInf, ProperCone.convex, contDiffAt_norm_smul_iff, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, SchwartzMap.pairing_apply_apply, MeasureTheory.integral_domSMul, InnerProductSpace.isIdempotentElem_rankOne_self, norm_iteratedFDerivWithin_smul_le, Submodule.tensorEquivSpan_apply_tmul, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, IsLprojection.Lnorm, AddCommGroup.intIsScalarTower, Complex.real_smul, Polynomial.smul_mem_rootSet, MeasureTheory.weightedSMul_apply, NonUnitalSubalgebra.instIsScalarTower', LineDifferentiableWithinAt.smul, egauge_prod_mk, Differentiable.clm_comp, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport, Commute.cfcₙ_nnreal, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, Matrix.mul_mul_left, IsScalarTower.to_smulCommClass', ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, HasStrictDerivAt.pow, IsExposed.isExtreme, ContinuousLinearMap.isUniformEmbedding_restrictScalars, RingTheory.Sequence.isWeaklyRegular_cons_iff, ConvexCone.canLift, hasDerivWithinAt_taylorWithinEval, map_ratCast_smul, FormalMultilinearSeries.changeOriginSeriesTerm_apply, AffineSubspace.smul_mem_smul_iff₀, Asymptotics.isLittleOTVS_one, SkewMonoidAlgebra.support_single_mul, Seminorm.finset_sup_apply, HasDerivAt.hasDerivWithinAt, ContinuousLinearMap.hasDerivAtFilter, span_fourier_closure_eq_top, Real.fourierIntegral_eq, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, HasDerivWithinAt.fun_div, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, CategoryTheory.ShortComplex.Homotopy.smul_h₁, StarConvex.affine_preimage, HasFPowerSeriesOnBall.add, LinearMap.BilinForm.smul_left_of_tower, HasDerivWithinAt.complexToReal_fderiv', circleIntegral_def_Icc, NumberField.RingOfIntegers.instSMulDistribClass, convexJoin_singletons, MeasureTheory.integral_unique, setIntegral_withDensity_eq_setIntegral_smul₀, Complex.hasSum_taylorSeries_of_entire, ContinuousMap.toLp_denseRange, IsCovariantDerivativeOn.difference_apply, ProbabilityTheory.hasSum_integral_poissonMeasure, Submodule.pow_pOrder_smul, Bornology.isVonNBounded_add_self, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, intervalIntegral.intervalIntegral_eq_integral_uIoc, Seminorm.ball_smul_closedBall, ContinuousLinearMap.integral_apply, CochainComplex.HomComplex.Cochain.leftShift_smul, FixedPoints.mem_addSubgroup, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, segment_inter_subset_endpoint_of_linearIndependent_sub, AddMonoidAlgebra.isScalarTower_self, Polynomial.nnqsmul_eq_C_mul, HasDerivAt.fun_finset_prod, LocalizedModule.restrictScalars_map_eq, circleIntegrable_iff, Summable.const_smul, PolynomialModule.map_smul, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, convex_iff_sum_mem, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, ConcaveOn.mul_convexOn', NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded, ContMDiffCovariantDerivativeOn.affine_combination, WithSeminorms.mem_nhds_iff, Convex.vadd, LinearMap.IsSymmetric.diagonalization_apply_self_apply, TensorProduct.sum_tmul_basis_right_injective, LinearMap.extendScalarsOfIsLocalization_apply, Memℓp.const_smul, StrictConvex.diff_interior_subset_extremePoints, Real.fourier_continuousLinearMap_apply, DirectSum.of_smul, Unitization.real_cfcₙ_eq_cfc_inr, real_inner_smul_self_left, neg_smul, fderivWithin_fun_pow', intervalIntegral.fderiv_integral_of_tendsto_ae, ZMod.invDFT_apply, SMulPosReflectLE_iff_smulPosReflectLT, Convex.combo_interior_closure_mem_interior, NormedSpace.isBounded_iff_subset_smul_ball, HasFDerivWithinAt.clm_apply, Balanced.sub, hasFPowerSeriesOnBall_pi_iff, SmoothPartitionOfUnity.contMDiffAt_finsum, imaginaryPart_I_smul, Continuous.convolution_integrand_fst, ContinuousAlternatingMap.vecCons_smul, MDifferentiableOn.smul_const_section, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, Module.Ray.neg_units_smul, MvPolynomial.leibniz_iff_X, DilationEquiv.smulTorsor_symm_apply, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, Convex.convex_remove_iff_notMem_convexHull_remove, Representation.freeLift_single_single, ConvexOn.lt_left_of_right_lt', HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, diam_smul₀, Seminorm.uniformContinuous_of_forall, TensorAlgebra.toTrivSqZeroExt_ι, abs_smul, Polynomial.homogenize_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul, Algebra.to_smulCommClass, LieModule.traceForm_eq_sum_finrank_nsmul', DomMulAct.smul_linearMap_apply, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, Polynomial.sum_smul_index', AddSubgroup.smul_mem_pointwise_smul_iff, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, segment_translate_preimage, convexHull_eq_iInter, SeminormFamily.filter_eq_iInf, toMul_uzpow, aemeasurable_smul_const, DifferentiableWithinAt.fun_const_smul, SchwartzMap.integral_bilin_fourierInv_eq, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, HasFTaylorSeriesUpTo.hasFDerivAt, TensorProduct.AlgebraTensorModule.rid_tmul, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Ideal.smul_closure, MeasureTheory.Measure.toSphere_apply_aux, Bornology.IsVonNBounded.of_neg, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, PolynomialModule.comp_smul, Unitization.splitMul_apply, tendsto_integral_peak_smul_of_integrable_of_tendsto, ContMDiffOn.clm_postcomp, inner_eq_norm_mul_iff, Seminorm.restrictScalars_closedBall, smulPosMono_iff_smulPosStrictMono, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, Matrix.Semiring.smulCommClass, tendsto_smul_comp_nat_floor_of_tendsto_mul, LinearMap.adjoint_eq_toCLM_adjoint, Asymptotics.IsLittleOTVS.tendsto_div, DirectSum.instIsCentralScalar, Seminorm.bddAbove_range_iff, AntivaryOn.sub_smul_sub_nonpos, Module.Basis.basis_singleton_iff, convex_iff_pairwise_pos, descPochhammer_succ_comp_X_sub_one, NormedSpace.image_isVonNBounded_iff, VectorField.mpullbackWithin_smul, ContinuousMap.range_toLp, eqOn_dslope_sub_smul, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div, HahnSeries.embDomain_smul, convex_Iic, Seminorm.closedBall_iSup, Differentiable.fun_smul, Subbimodule.smul_mem', TemperedDistribution.fourierMultiplierCLM_smul, hasDerivAt_bernoulliFun, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, derivWithin_fderivWithin, WithLp.isBoundedSMulSeminormedAddCommGroupToProd, SkewMonoidAlgebra.smul_of, Submodule.smul_mem_span_smul, intervalIntegral.integral_deriv_smul_comp', IsSelfAdjoint.smul_mem_skewAdjoint, DualNumber.range_lift, StarConvex.add_smul_mem, QuotSMulTop.equivTensorQuot_naturality, MeasureTheory.condExpIndL1Fin_smul, StrictConvexOn.neg, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, MultilinearMap.mkContinuousMultilinear_apply, AddSubgroup.mem_inv_pointwise_smul_iff, PosSMulReflectLE_iff_posSMulReflectLT, CliffordAlgebraDualNumber.equiv_symm_eps, Monovary.sum_smul_comp_perm_le_sum_smul, InnerProductGeometry.angle_smul_right_of_pos, tsum_const_smul', StrongDual.norm_extendRCLike_bound, TemperedDistribution.lineDerivOp_fourier_eq, Units.smul_coe, Matrix.mul_smul, WeakFEPair.symm_Λ₀_eq, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, SpecialLinearGroup.mem_center_iff_spec, Seminorm.smul_inf, Ideal.mem_pointwise_smul_iff_inv_smul_mem, Submodule.Quotient.instIsBoundedSMul, intervalIntegral.integral_comp_sub_div, Subsemiring.mem_smul_pointwise_iff_exists, HasDerivAt.comp_ofReal, tangentConeAt_nonempty_of_properSpace, AdicCompletion.instIsScalarTower_1, convexJoin_singleton_left, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, intervalIntegral.integral_comp_mul_left, AnalyticAt.fun_const_smul, Submodule.ideal_span_singleton_smul, Continuous.integral_hasStrictDerivAt, AffineBasis.coe_smul, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, ZeroAtInftyContinuousMap.instIsScalarTower, stdSimplex_fin_two, deriv_const_smul, fderiv_clm_comp, StrictConcaveOn.sub_convexOn, Submodule.top_eq_ofList_cons_smul_iff, BoxIntegral.unitPartition.mem_smul_span_iff, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, TensorProduct.smul_tmul, intervalIntegral.integral_comp_mul_sub, mdifferentiableWithinAt_smul_const_section, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, RingAut.smul_def, AlternatingMap.smulRight_apply, Ideal.exists_smul_eq_of_isGaloisGroup, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, IsConformalMap.is_complex_or_conj_linear, Bornology.isVonNBounded_pi_iff, fderiv_continuousAlternatingMap_apply_const, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', Fintype.expect_dite_eq, Module.Basis.isScalarTower_of_nonempty, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, Prod.image_mk_openSegment_left, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, TrivSqZeroExt.inv_inl, HasDerivAt.clm_apply, SemilinearMapClass.toMulActionSemiHomClass, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_symm_apply_mk_tmul, ContDiffMapSupportedIn.seminorm_fderivLM_le, LinearMap.IsRefl.ker_flip_eq_bot, RKHS.coe_smul, Bundle.RiemannianMetric.isVonNBounded, vadd_right_mem_affineSpan_pair, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContDiffMapSupportedIn.seminorm_fderivLM_top, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Convex.affine_image, NormedSpace.toIsBoundedSMul, UniformConvergenceCLM.smul_apply, Fintype.mem_span_image_iff_exists_fun, HasFPowerSeriesAt.neg, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux, Seminorm.continuous_of_forall', AlgEquiv.apply_smulCommClass', curveIntegralFun_smul, addInvariantVectorField_smul, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt, RootPairing.span_orbit_eq_top, VertexOperator.of_coeff_apply_coeff, neg_strictConvexOn_iff, Module.Basis.smul_eq_zero, ContinuousLinearMap.coe_smul', DomMulAct.smul_mulDistribActionHom_apply, BoundedContinuousFunction.instSMulCommClass_1, smul_lt_smul_of_neg_left, MeasureTheory.Measure.domSMul_apply, groupHomology.single_isCycle₂_iff_inv, egauge_ball_le_of_one_lt_norm, Ideal.subset_pointwise_smul_iff, CategoryTheory.Quotient.Linear.smul_eq, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, ContinuousAffineMap.smul_apply, MvPolynomial.algHom_ext'_iff, Polynomial.natDegree_smul, MonovaryOn.sum_smul_comp_perm_le_sum_smul, hasDerivWithinAt_iff_isLittleO, TensorPower.gMul_eq_coe_linearMap, GeneralSchauderBasis.proj_apply, hasStrictFDerivAt_iff_isLittleOTVS, CStarMatrix.mapₗ_reindexₐ, ContinuousAlternatingMap.smul_apply, derivWithin_fun_const_smul_field, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, StarAlgEquiv.ofStarAlgHom_apply, Submodule.mem_smul_span_singleton, Finsupp.sum_smul_index_linearMap', MeasureTheory.IntegrableOn.smul_continuousOn, ContinuousAlternatingMap.piLIE_apply_apply, AffineSubspace.wOppSide_smul_vsub_vadd_left, ContinuousLinearMap.applySMulCommClass', PreInnerProductSpace.Core.smul_left, inv_intCast_smul_eq, extremePoints_prod, Subsemiring.smul_mem_pointwise_smul_iff, combo_mem_ball_of_ne, lintegral_fderiv_lineMap_eq_edist, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, balancedCoreAux_maximal, hasDerivWithinAt_zero, HasStrictDerivAt.pow', TestFunction.monoCLM_eq_zero, CategoryTheory.Abelian.Ext.smul_hom, coe_convexAddSubmonoid, TopologicalGroup.IsSES.integral_inducedMeasure, hasDerivAt_star_conj_iff, AbsolutelyContinuousOnInterval.const_smul, ContDiffAt.hasStrictDerivAt, Seminorm.neg_ball, TrivSqZeroExt.inv_one, RatFunc.mk_smul, FormalMultilinearSeries.hasSum_of_finite, CStarMatrix.mul_smul, LieAlgebra.of_smul, Matrix.vecMul_vecMulVec, StrictConcaveOn.translate_right, hasDerivAtFilter_ofNat, SkewMonoidAlgebra.support_mul_single, Asymptotics.IsBigO.smul, AdicCompletion.val_smul_eq_evalₐ_smul, instStarModuleNNRealOfReal, VectorField.mlieBracket_smul_left, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, Seminorm.continuous', FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, Complex.hasSum_taylorSeries_on_ball, Submodule.mem_span_image_iff_exists_fun, IsScalarTower.right, QuadraticMap.map_smul_of_tower, Asymptotics.IsBigOTVS.add, MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff, HasFPowerSeriesOnBall.restrictScalars, smul_nonneg_iff_neg_imp_nonpos, StrictConcaveOn.inf, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, ContinuousLinearMap.isometry_mul_flip, Quaternion.snd_re_dualNumberEquiv_symm, ZSpan.smul, HasStrictFDerivAt.mul', Module.AEval.of_symm_smul, Mathlib.Tactic.Module.NF.eval_neg, Module.Ray.units_smul_of_neg, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, AlgebraicGeometry.StructureSheaf.const_add, LocalizedModule.mk_add_mk, conformal_const_smul, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, HasStrictFDerivAt.comp_hasStrictDerivAt, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, ClosedSubmodule.inf_orthogonal, LinearMap.coe_toContinuousLinearMap', ContDiffWithinAt.fun_smul, balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, ConvexCone.coe_zero, CharacterModule.smul_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Module.Free.instFaithfulSMulOfNontrivial, contDiffOn_iff_continuousOn_differentiableOn, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, convexJoin_segments, ClosedSubmodule.instSMulMemClass, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, CStarModule.innerSL_apply, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt, MeromorphicOn.fun_smul, monomial_has_deriv_aux, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, LieRinehartAlgebra.LieRinehartRing.leibniz_smul_right, LinearIsometryEquiv.conjStarAlgEquiv_apply, MultilinearMap.smul_apply, MeasureTheory.smul_convolution, Bundle.ContinuousLinearMap.vectorBundle, Real.vector_fourierIntegral_eq_integral_exp_smul, VectorField.mlieBracketWithin_const_smul_right, HasDerivWithinAt.sub, PadicInt.mahlerTerm_apply, AlternatingMap.map_update_smul, WithLp.smul_snd, MeasureTheory.ConvolutionExistsAt.integrable, CompactlySupportedContinuousMap.nnrealPart_smul_neg, Complex.taylorSeries_eq_of_entire, egauge_add_add_le, HVertexOperator.coeff_isPWOsupport, exists_pos_right_iff_sameRay, Real.fourier_real_eq_integral_exp_smul, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, Monotone.quasilinearOn, Asymptotics.IsBigOWith.const_smul_self, Asymptotics.isLittleOTVS_prodMk_left, ExteriorAlgebra.toTrivSqZeroExt_comp_map, AntivaryOn.sum_comp_perm_smul_eq_sum_smul_iff, inner_smul_left_eq_star_smul, ProbabilityTheory.covarianceOperator_apply, BoundedContinuousFunction.toContinuousMapLinearMap_apply, nndist_smul₀, InnerProductGeometry.angle_smul_left_of_neg, Module.exists_smul_eq_zero_and_mk_eq, Asymptotics.IsBigOTVS.comp_tendsto, MeasureTheory.integral_tilted, Submodule.span_smul_eq_of_isUnit, WithSeminorms.continuousSMul, IsSl2Triple.lie_lie_smul_f, LinearMap.ortho_smul_left, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, ContinuousMultilinearMap.mkPiRing_apply, Ideal.LiesOver.smul, hasDerivAt_of_hasDerivAt_of_ne, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, MeasureTheory.average_mem_openSegment_compl_self, TestFunction.continuous_iff_continuous_comp, HasFiniteFPowerSeriesOnBall.sum, MeasureTheory.L1.integral_smul, Distribution.IsVanishingOn.smulLeftCLM, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, inv_natCast_smul_eq, DifferentiableOn.smul_const, Polynomial.C_mul', Quaternion.imJ_fst_dualNumberEquiv, InnerProductSpace.inner_left_rankOne_apply, cfcₙHom_nnreal_eq_restrict, TestFunction.toBoundedContinuousFunctionCLM_apply, Conformal.const_smul, MeasureTheory.Lp.instFourierInvSMul, CochainComplex.HomComplex.Cocycle.coe_units_smul, Bornology.isVonNBounded_neg, AlternatingMap.smul_apply, hasStrictDerivAt_abs_pos, ContinuousLinearMap.smul_compLp, DomMulAct.smul_addMonoidHom_apply, difference_quotients_converge_uniformly, TrivSqZeroExt.snd_list_prod, hasDerivWithinAt_abs_pos, HasDerivWithinAt.sub_const, ContinuousLinearMap.norm_extendTo𝕜, Module.Basis.toMatrix_smul, LocalizedModule.lift'_smul, HasSum.hasSum_at_zero, Seminorm.continuousAt_zero_of_forall', HasFPowerSeriesAt.add, lineDifferentiableAt_smul_iff, TrivSqZeroExt.fstHom_comp_map, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, Matrix.conjTranspose_natCast_smul, LinearMap.sum_repr_mul_repr_mulₛₗ, cfcₙ_map_pi, ContinuousLinearMap.hasBasis_nhds_zero, Bornology.IsVonNBounded.of_add_right, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, AddSubmonoid.smul_mem_smul, Module.End.apply_smulCommClass', HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, CochainComplex.HomComplex.Cochain.units_smul_comp, AddCircle.integral_haarAddCircle, WithCStarModule.inner_def, InnerProductSpace.HarmonicAt.const_smul, Seminorm.ball_mem_nhds, eventually_nhds_norm_smul_sub_lt, CentroidHom.smul_def, CircleIntegrable.const_smul, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, Module.IsTorsionFree.isSMulRegular, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, ContMDiffAt.clm_postcomp, Matrix.smul_one_eq_diagonal, scalarSMulCLE_symm_apply, Real.fourier_deriv, RightPreLieAlgebra.toIsScalarTower, ContMDiffWithinAt.clm_postcomp, iteratedDeriv_scomp_three, fderiv_fun_pow', hasDerivWithinAt_pi, StarAddMonoid.toStarModuleRat, Real.integrable_prod_sub, Orientation.oangle_smul_left_of_neg, NormedSpace.isVonNBounded_ball, locallyConvexSpace_iff, MDifferentiable.smul, strictConvex_Icc, antivary_iff_smul_rearrangement, norm_smul_inv_norm, Submodule.pointwise_smul_def, ContinuousLinearMap.eq_adjoint_iff, ConcaveOn.smul_convexOn', IsLocalizedModule.mk'_eq_zero', tangentConeAt_univ, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, convexHull_union_neg_eq_absConvexHull, SubMulAction.neg_mem, ContinuousLinearMap.toSpanSingleton_apply, ConcaveOn.add_const, smul_vsub_rev_vadd_mem_affineSpan_pair, KaehlerDifferential.isScalarTower', Submodule.mem_torsion_iff, derivWithin.scomp, DifferentiableOn.circleIntegral_sub_inv_smul, Derivation.linearEquiv_coe_to_linearMap_comp, Submodule.isTorsion'_powers_iff, Submodule.sum_smul_mem, Prod.segment_subset, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, smul_nonpos_iff, HasFPowerSeriesAt.comp, HasFDerivAt.continuousMultilinear_apply_const, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousLinearMap.IsPositive.smul_of_nonneg, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, InnerProductSpace.rankOne_apply, Convex.combo_eq_smul_sub_add, ConcaveOn.smul_convexOn, FormalMultilinearSeries.sum_of_finite, RingTheory.Sequence.isRegular_cons_iff, Ideal.finsuppTotal_apply_eq_of_fintype, ConcaveOn.comp_linearMap, HahnSeries.instSMulCommClass, ContinuousLinearEquiv.map_smul, extremePoints_pi, Submodule.reflection_singleton_apply, SkewMonoidAlgebra.mapDomain_mul, IntermediateField.isScalarTower, smul_unitClosedBall_of_nonneg, HasFTaylorSeriesUpToOn.zero_eq', KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, Asymptotics.IsLittleOTVS.trans_isThetaTVS, Fintype.expect_ite_eq, MulSemiringActionHom.map_smulₛₗ, MultilinearMap.map_insertNth_smul, QuotSMulTop.equivTensorQuot_naturality_mk, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, IsSMulRegular.of_right_eq_zero_of_smul, Subring.mem_pointwise_smul_iff_inv_smul_mem, isIntegralCurveAt_comp_mul_ne_zero, smulMemClass, HasStrictDerivAt.clm_comp, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, PiLp.isBoundedSMulSeminormedAddCommGroupToPi, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, inv_intCast_smul_comm, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, ContDiffMapSupportedIn.monoLM_apply, HasDerivWithinAt.Iic_of_Iio, ContinuousMultilinearMap.norm_smulRightL_le, Multiset.sum_smul_sum, balancedCore_nonempty_iff, StrictConvex.affine_image, WeakFEPair.h_feq, derivWithin_clm_comp, LinearMap.ker_restrictScalars, differentiableAt_smul_iff, Antitone.convex_le, ContinuousLinearMap.precompL_apply, Seminorm.closedBall_smul_ball, egauge_univ, Algebra.normalizedTrace_algebraMap, Subalgebra.coe_pointwise_smul, IsSelfAdjoint.adjoint_eq, Antitone.quasiconvexOn, Submodule.smul_mem', Submodule.mem_ideal_smul_span_iff_exists_sum', MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', mem_tangentConeAt_of_segment_subset, Asymptotics.IsLittleOTVS.prodMk, TrivSqZeroExt.fst_exp, DirectSum.mk_smul, curveIntegralFun_segment, HasDerivWithinAt.clm_apply, SchwartzMap.integral_fourierInv_smul_eq, Submodule.smul_iSup', DifferentiableAt.hasDerivAt, MonovaryOn.sum_comp_perm_smul_le_sum_smul, OrderDual.instIsStrictOrderedModule, RootPairing.coroot_eq_smul_coroot_iff, RKHS.kernel_apply, HasDerivAt.finCons, Seminorm.bound_of_continuous_normedSpace, Besicovitch.SatelliteConfig.exists_normalized_aux2, HasDerivAtFilter.add, groupHomology.isBoundary₁_of_mem_boundaries₁, exists_nonneg_left_iff_sameRay, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, LinearMap.BilinForm.isOrtho_smul_left, FormalMultilinearSeries.radius_le_smul, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, DistribMulAction.toAddMonoidHom_apply, Absorbs.of_neg_neg, MDifferentiable.clm_postcomp, IsArtinian.exists_pow_succ_smul_dvd, TrivSqZeroExt.map_inr, AntivaryOn.smul_add_smul_le_smul_add_smul, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, MeasureTheory.VectorMeasure.smul_apply, CStarMatrix.toCLM_injective, biUnion_associatedPrimes_eq_compl_regular, Asymptotics.IsLittleOTVS.insert, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, Complex.integral_circleTransform, ContinuousLinearMap.isPositive_self_comp_adjoint, iteratedDeriv_scomp_eq_sum_orderedFinpartition, convexOn_univ_dist, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, MeasureTheory.Measure.IsAddHaarMeasure.domSMul, hasDerivAt_iff_isLittleO, LinearMap.rTensor_comp_flip_mk, Algebra.TensorProduct.sMulCommClass_right, Absorbs.eventually_nhdsNE_zero, Unitization.sqrt_inr, UniqueDiffWithinAt.smul, TopModuleCat.continuousSMul, LocallyConvexSpace.convex_basis_zero, NormedSpace.isBounded_iff_subset_smul_closedBall, KaehlerDifferential.isLocalizedModule_of_isLocalizedModule, BoundedContinuousFunction.instSMulCommClass_2, hasFPowerSeriesAt_const, Multiset.smul_sum, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, UniformOnFun.continuousSMul_induced_of_image_bounded, Subalgebra.inclusion.isScalarTower_left, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, Finsupp.linearCombination_smul, ConcaveOn.smul'', HasFDerivWithinAt.fun_const_smul, neg_one_smul, HasStrictFDerivAt.const_smul, Fintype.bilinearCombination_apply_single, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, Subring.mem_pointwise_smul_iff_inv_smul_mem₀, FormalMultilinearSeries.radius_compNeg, Fintype.expect_ite_zero, NormedAddGroupHom.smul_apply, LinearMap.coe_smul, IsBoundedBilinearMap.smul_left, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, quasispectrum.mem_iff_of_isUnit, SchwartzMap.integral_bilin_fourierIntegral_eq, TopologicalGroup.IsSES.pushforward_def, SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM, Real.fourierIntegral_continuousMultilinearMap_apply, ProbabilityTheory.HasGaussianLaw.smul, StrictConcaveOn.lt_map_sum, MonotoneOn.convex_ge, QuotSMulTop.map_comp_mkQ, HasStrictDerivAt.fun_sum, LinearIsometryEquiv.adjoint_eq_symm, smul_mem_closure_star_mul, extDeriv_fun_smul, VectorField.mpullback_const_smul_apply, Ideal.finsuppTotal_apply, IsLocalizedModule.exist_integer_multiples, ContinuousAlternatingMap.toAlternatingMap_curryLeft, TensorProduct.flip_mk_surjective, LinearMap.smul_apply, StrictConvex.neg, Bornology.IsVonNBounded.image_multilinear', Finset.expect_ite_zero, Quaternion.imI_fst_dualNumberEquiv, HasDerivAt.congr_of_eventuallyEq, Complex.im_nnqsmul, mem_tangentConeAt_of_pow_smul, analyticOrderAt_smul_eq_top_of_left, mem_openSegment_sub_add, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, WithSeminorms.tendsto_nhds', ContinuousLinearMap.opNorm_mul, MvPowerSeries.smul_eq_C_mul, skewAdjoint.val_smul, Seminorm.pullback_apply, collinear_iff_of_mem, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, sameRay_iff_inv_norm_smul_eq_of_ne, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, norm_sum_lt_of_strictConvexSpace, Seminorm.bddAbove_of_absorbent, smul_rayOfNeZero, UniformConvexOn.strictConvexOn, TemperedDistribution.smulLeftCLM_neg, Module.Dual.im_extendRCLike_apply, InnerProductSpace.Core.inner_smul_ofReal_right, Orientation.oangle_sign_sub_smul_left, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', MeasureTheory.SimpleFunc.integral_eq_sum_filter, egauge_zero_zero, Differentiable.fun_const_smul, Matrix.conjTranspose_inv_intCast_smul, TestFunction.lineDerivOpCLM_eq_lineDerivCLM, MDifferentiable.cle_arrowCongr, Asymptotics.IsLittleOTVS.neg_right, gauge_le_eq, segment_subset_convexHull, MeasureTheory.Measure.quasiMeasurePreserving_smul, HasSum.smul_eq, Polynomial.monic_of_isUnit_leadingCoeff_inv_smul, HasFTaylorSeriesUpTo.fderiv_eq, HasDerivAt.fun_pow', Unitization.nnnorm_def, LieModule.mem_weightSpace, instSMulCommClassMatrixFinOfNatNatProd, PowerSeries.le_order_smul, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Algebra.Extension.Cotangent.smul_eq_zero_of_mem, TestFunction.fderivCLM_ofSupportedIn, convexHull_toCone_eq_sInf, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson, ConcaveOn.inf, Finset.zero_mem_smul_finset_iff, LinearMap.smulRight_apply, HasFDerivAt.fun_smul, Module.AEval'.X_smul_of, AdjoinRoot.smul_mk, Function.HasTemperateGrowth.toTemperedDistribution_apply, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, IsIntegralCurveOn.comp_mul, Orthonormal.inner_left_fintype, lie_smul, HasLineDerivAt.tendsto_slope_zero_right, Filter.TendstoCofinite.mapDomain_smul, Balanced.convexHull, Complex.hasDerivAt_GammaIntegral, AntitoneOn.convex_le, fderiv_continuousAlternatingMapCompContinuousLinearMap, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, IncidenceAlgebra.instIsScalarTower, Absorbent.gauge_set_nonempty, Submodule.pointwise_smul_toAddSubgroup, AddMonoid.nat_smulCommClass', RatFunc.Luroth.algEquiv_apply, Convex.cthickening, NonarchimedeanRing.left_mul_subset, PiTensorProduct.mapL_smul, SchwartzMap.integral_sesq_fourier_eq, DFinsupp.instSMulPosMono, DualNumber.lift_apply_eps, Real.fderiv_fourier, CategoryTheory.ShortComplex.Homotopy.smul_h₂, ContinuousLinearMap.adjointAux_norm, MeasureTheory.L1.setToL1_smul_left, Representation.smul_ofModule_asModule, CStarMatrix.norm_def', KaehlerDifferential.instIsScalarTowerTensorProduct, algebra_compatible_smul, AntitoneOn.convex_gt, MeasureTheory.Integrable.smul_bdd, MDifferentiable.clm_bundle_apply₂, Fintype.expect_dite_eq', MeasureTheory.convolution_smul, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, neg_smul_neg, hasDerivAtFilter_natCast, LinearMap.flip_injective_iff₁, Finsupp.linearCombination_one_tmul, CategoryTheory.Linear.units_smul_comp, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, ConvexCone.coe_map, HahnSeries.SummableFamily.hsum_smul_module, ContinuousAlternatingMap.instContinuousSMul, DualNumber.inv_eps, IsLocalizedModule.map_linearMap_of_isLocalization, HasFDerivAt.restrictScalars, balancedHull_subset_convexHull_union_neg, StrictConvex.extremePoints_eq_diff_interior, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, SameRay.exists_eq_smul_add, CategoryTheory.Functor.Linear.map_smul, stereoInvFunAux_apply, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, StrongFEPair.functional_equation, MulSemiringAction.toRingEquiv_apply, MonotoneOn.convex_le, norm_curveIntegral_segment_le, Ideal.smul_sup, MonoidAlgebra.smulCommClass_self, Representation.ofDistribMulAction_apply_apply, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, Submodule.coe_torsion', LocalizedModule.mk_eq, IsLinearMap.isLinearMap_smul', MonoidAlgebra.instIsPushout, TensorProduct.AlgebraTensorModule.restrictScalars_curry, HasFDerivAtFilter.isThetaTVS_sub, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH, MonotoneOn.quasiconvexOn, HahnSeries.single_zero_mul_eq_smul, Finset.mem_convexHull', StarConvex.affine_image, iteratedDeriv_smul_const, circleIntegral.integral_sub_inv_smul_sub_smul, Action.smul_hom, HasStrictFDerivAt.list_prod', CliffordAlgebra.foldr'Aux_foldr'Aux, SchwartzMap.fourier_lineDerivOp_eq, DifferentiableAt.smul, HasFDerivWithinAt.isThetaTVS_sub, Algebra.TensorProduct.basis_repr_tmul, LieAdmissibleAlgebra.toSMulCommClass, LinearMap.isBigOTVS_rev_comp, LinearMap.toContinuousBilinearMap_apply, segment_single_subset_stdSimplex, Algebra.Extension.instIsScalarTowerH1CotangentOfCotangent, TemperedDistribution.instLineDerivLeftSMulReal, Submodule.span_singleton_eq_top_iff, CStarMatrix.inner_toCLM_conjTranspose_left, RootPairing.reflection_apply_root', hasStrictDerivAt_exp_smul_const, Submodule.FG.restrictScalars, PolynomialModule.monomial_smul_single, Subsemiring.smul_mem_pointwise_smul, Derivation.leibniz_div, EuclideanGeometry.inversion_vsub_center, Filter.EventuallyEq.ftaylorSeries, isBoundedBilinearMap_comp, StarConvex.smul_mem, lp.instIsCentralScalarPreLp, set_smul_sphere_zero, MeasureTheory.Integrable.essSup_smul, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, ContMDiff.smul, hasStrictDerivAt_add_const_iff, hasLineDerivWithinAt_smul_iff, Asymptotics.IsBigO.const_smul_left, Asymptotics.IsTheta.smul, TemperedDistribution.fourierInv_lineDerivOp_eq, MDifferentiable.const_smul, TrivSqZeroExt.lift_comp_inrHom, MeasureTheory.condExpL2_indicator_ae_eq_smul, Convex.openSegment_self_interior_subset_interior, SkewPolynomial.φ_iterate_apply, Asymptotics.IsBigOTVS.neg_right, ModuleCat.smulShortComplex_X₃_isAddCommGroup, conformalAt_const_smul, Submodule.span_smul_le, Ideal.pointwise_smul_subset_iff, IsMIntegralCurveOn.hasDerivWithinAt, IsLocalizedModule.mk'_add_mk', Polynomial.X_pow_smul_rTensor_monomial, FormalMultilinearSeries.rightInv_removeZero, IsUnit.smul_sub_iff_sub_inv_smul, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ClosedSubmodule.orthogonal_closure'', Submodule.smul_bot', instIsPushoutFractionRingPolynomial_1, HasDerivWithinAt.comp, hasStrictDerivAt_exp_smul_const', KaehlerDifferential.mapBaseChange_tmul, Module.DirectLimit.quotMk_of, openSegment_translate_image, egauge_univ_pi, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq, AffineSubspace.smul_vsub_vadd_mem, MeromorphicAt.fun_smul, Real.fourier_iteratedFDeriv, CFC.negPart_smul_of_nonpos, HasDerivAt.add, SchwartzMap.smulLeftCLM_real_smul, strictConvex_uIcc, MeasureTheory.Measure.integral_comp_inv_mul_left, HasMFDerivAt.smul, TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm, HasStrictDerivAt.div, NormMulClass.toNormSMulClass_op, RootPairing.pairing_one_four_iff', ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, MeasureTheory.measure_smul_average, MDifferentiableOn.smul, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, TrivSqZeroExt.fst_invOf, Ideal.instCovariantClassHSMulLe, Orientation.oangle_sign_sub_smul_right, hasDerivAtFilter_zero, Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone, segment_subset_convexJoin, StrictConvex.is_linear_preimage, Algebra.Generators.H1Cotangent.δAux_C, Complex.integral_comp_polarCoord_symm, NormedAddGroupHom.isCentralScalar, Seminorm.map_eq_zero_of_norm_zero, smul_closedBall', spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, HasFDerivAt.fun_const_smul, ConvexCone.coe_comap, LinearOrder.strictConvexOn_of_lt, Convex.combo_interior_closure_subset_interior, LocalizedModule.mk_cancel, PresheafOfModules.Sheafify.map_smul_eq, convex_iff_openSegment_subset, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Orientation.oangle_smul_left_self_of_nonneg, Monotone.convex_ge, UnitAddTorus.mFourierCoeff_toLp, NonUnitalSubalgebra.unitization_injective, Submodule.coe_toConvexCone, Submodule.smul_mem_pointwise_smul, ContinuousLinearMap.uniformContinuous_restrictScalars, Submodule.instSMulCommClass, TensorProduct.finsuppLeft_smul', MvPolynomial.sumAlgEquiv_comp_rename_inr, LieSubmodule.instSMulMemClass, SubmodulesBasis.smul, ContinuousLinearMap.mulLeftRight_apply, mem_openSegment_translate, PowerSeries.coe_smul, isModuleTopologyOfFiniteDimensional, MvPolynomial.aevalTower_toAlgHom, LinearMap.extendTo𝕜'_apply, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, MonotoneOn.convex_gt, fromTangentSpace_mfderiv_smul_apply, Differentiable.const_smul, Seminorm.ball_eq_emptyset, ArchimedeanClass.mk_le_mk_smul, taylor_tendsto, dslope_sub_smul, rescale_to_shell_semi_normed_zpow, HasFDerivAt.curveIntegral_segment_source, Algebra.TensorProduct.basisAux_map_smul, balancedCore_mem_nhds_zero, convexJoin_segment_singleton, SameRay.exists_eq_smul, DirectSum.instSMulCommClass, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, CentroidHom.instSMulCommClass_2, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, deriv_fun_smul, ConvexCone.salient_strictlyPositive, iteratedFDeriv_comp_const_smul, LocalizedModule.mem_ker_mkLinearMap_iff, Algebra.IsInvariant.exists_smul_of_under_eq, HasStrictDerivAt.mul, PresheafOfModules.Derivation.d_mul, Matrix.smul_vecMul, Bundle.Trivialization.eq_sum_localFrame_coeff_smul, LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, MeasureTheory.convolution_lsmul, QuadraticMap.map_smul, MDifferentiableAt.clm_postcomp, fderiv_continuousAlternatingMap_apply, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, abs_nnqsmul, SeminormFamily.finset_sup_comp, Module.Dual.norm_extendRCLike_apply_sq, Submodule.mem_span_finset, Bornology.isVonNBounded_iff_absorbing_le, Module.AEval.instIsScalarTowerOrigPolynomial, CategoryTheory.Pretriangulated.Triangle.smul_hom₂, ContDiffMapSupportedIn.monoLM_eq_of_scalars, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim, Module.AEval.C_smul, Algebra.Extension.CotangentSpace.map_tmul, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, element_smul_restrictScalars, strongConcaveOn_zero, integral_withDensity_eq_integral_smul, Representation.ofMulAction_self_smul_eq_mul, intervalIntegral.integral_comp_add_div, Matrix.instSMulCommClassForall_1, convex_singleton, HasDerivAt.pow, deriv_fderiv, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, RegularNormedAlgebra.isometry_mul', fwdDiff_const_smul, convexJoin_singleton_segment, cauchyPowerSeries_apply, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, mem_smul_of_egauge_lt, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, DifferentiableAt.const_smul, RootPairing.mem_range_root_of_mem_range_reflection_of_mem_range_root, BoxIntegral.HasIntegral.smul, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, Ideal.range_mul, integral_smul_const, CStarModule.inner_smul_right_real, Module.exists_nontrivial_relation_of_finrank_lt_card, MDifferentiableWithinAt.clm_bundle_apply₂, TrivSqZeroExt.algHom_ext'_iff, fun_meromorphicOrderAt_smul, SameRay.inv_norm_smul_eq, TestFunction.limitCLM_apply, Module.IsTorsionBySet.mk_smul, hasDerivWithinAt_abs, Algebra.TensorProduct.linearMap_comp_rid, hasFPowerSeriesOnBall_const, CentroidHom.toEnd_smul, Summable.tsum_const_smul, HasFDerivAt.clm_apply, openSegment_eq_image', HasStrictDerivAt.const_mul, ContDiffMapSupportedIn.seminorm_le_iff, ConcaveOn.convex_strict_hypograph, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, NonUnitalStarSubalgebra.unitization_range, smul_nonpos_iff_pos_imp_nonpos, MeasureTheory.Measure.integral_comp_smul_of_nonneg, Polynomial.sum_smul_index, VectorFourier.hasFDerivAt_fourierIntegral, DiffContOnCl.circleIntegral_sub_inv_smul, Submodule.smul_sup', HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, TensorProduct.Algebra.smul_def, LinearMap.flip_surjective_iff₁, LaurentPolynomial.smeval_C_mul, Seminorm.ball_norm_mul_subset, IsLocalizedModule.exist_integer_multiples_of_finset, WeakDual.instContinuousConstSMul, List.sum_smul, ClosedSubmodule.inner_real_eq_re_inner, hasFDerivAt_ringInverse, ContinuousMultilinearMap.opNorm_smul_le, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, Matrix.toLinearMap₂'_apply, HasFDerivAt.continuousAlternatingMap_apply, MeasureTheory.convolution_precompR_apply, PolynomialModule.single_smul, gc_floorDiv_mul, SchwartzMap.compSubConstCLM_apply, IsNilpotent.exp_smul_eq_sum, MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc, VectorFourier.fourierIntegral_iteratedFDeriv, TopologicalAddGroup.IsSES.pushforward_apply_apply, rank_lt_rank_dual', QuotSMulTop.map_surjective, InformationTheory.hasDerivAt_klFun, IsLocalizedModule.mk'_eq_mk'_iff, InnerProductSpace.nnnorm_rankOne, iteratedDeriv_fun_const_smul, FreeLieAlgebra.liftAux_map_smul, Seminorm.closedBall_zero_eq_preimage_closedBall, MonotoneOn.quasilinearOn, Polynomial.smul_eq_C_mul, fderiv_smul, ArithmeticFunction.one_smul', OrthonormalBasis.orthogonalProjection_apply_eq_sum, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, Filter.BoundedAtFilter.smul, NonUnitalSubalgebra.unitization_range, LieModule.LinearWeights.map_smul, SemimoduleCat.Algebra.instIsScalarTowerCarrier, instIsOrderedModule, iteratedFDerivWithin_const_smul_apply, ModuleCat.CoextendScalars.smul_apply, HasDerivAt.fun_pow, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, starConvex_compl_Ici, LocalizedModule.equivTensorProduct_symm_apply_tmul, ContinuousLinearMap.norm_toSpanSingleton, FormalMultilinearSeries.continuousOn_of_finite, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, TensorProduct.finsuppScalarRight_apply_tmul, Submodule.topologicalClosure_map, Submodule.toConvexCone_top, Representation.single_smul, OrderDual.instSMulPosStrictMono, FormalMultilinearSeries.ofScalars_series_of_subsingleton, Ideal.under_smul, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, affinity_unitClosedBall, ContinuousLinearMap.flip_smul, Module.FinitePresentation.linearEquivMap_symm_apply, ContDiffMapSupportedIn.coe_smul, HasDerivAtFilter.mono, PadicInt.mahlerSeries_apply, HasFDerivAt.isBigOTVS_sub, HasDerivWithinAt.fun_pow', LieModuleHom.coe_smul, AffineSubspace.coe_smul, Module.Dual.extendRCLike_apply, MeasureTheory.integral_singleton', HasCompactSupport.hasDerivAt_convolution_right, Finsupp.coe_pointwise_smul, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, OreLocalization.oreDiv_add_char', HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, Finset.affineCombination_eq_linear_combination, HasDerivWithinAt.const_add, SameRay.pos_smul_left, Coalgebra.TensorProduct.lid_tmul, Module.Basis.constrL_apply, Module.AEval'.of_symm_X_smul, QuadraticMap.associated_apply, HasFDerivWithinAt.const_smul, ModuleFilterBasis.smul_right, MeasureTheory.ConvolutionExistsAt.integrable_swap, NormedSpace.expSeries_sum_eq, norm_inner_eq_norm_iff, MeasureTheory.FinMeasAdditive.smul, IsLocalizedModule.finsetIntegerMultiple_image, RootPairing.weylGroup_apply_root, Real.circleAverage_eq_circleIntegral, HasFiniteFPowerSeriesOnBall.eq_partialSum, image_openSegment, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, hasDerivAt_tsum_of_isPreconnected, subset_balancedCore, Submodule.mul_mem_smul_iff, FormalMultilinearSeries.ofScalars_add, ContinuousAlternatingMap.coe_smul, ContMDiffCovariantDerivativeOn.finite_affine_combination, convexOn_dist, LinearIsometryEquiv.smul_apply, convexOn_iff_forall_pos, nnnorm_cfcₙ_nnreal_lt, inner_eq_norm_mul_iff_div, convex_Ico, Submodule.topologicalClosure_eq_self, Submodule.smul_subset_smul, SameRay.nonneg_smul_right, LinearMap.hasStrictDerivAt, real_linearMap_map_smul_complex, AffineMap.hasDerivAt_lineMap, fderivWithin_continuousAlternatingMap_apply_const_apply, MeasureTheory.setToFun_smul_left', ratCast_smul_eq, MeasureTheory.integral_smul, Seminorm.convexOn, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left', Subring.coe_pointwise_smul, mellinInv_eq_fourierIntegralInv, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, ProbabilityTheory.strong_law_ae, HasDerivWithinAt.fun_finset_prod, Convex.semilinear_image, Derivation.comp_aeval_eq, Algebra.Extension.Cotangent.val_smul''', HasDerivWithinAt.norm_sq, CStarModule.inner_smul_right_complex, HasGradientAtFilter.hasDerivAtFilter', ContDiffOn.const_smul, instIsPushoutPolynomial_1, Polynomial.cauchyBound_smul, Seminorm.balanced_closedBall_zero, zmod_smul_mem, dualTensorHom_apply, LinearEquiv.mem_fixedSubmodule_transvection_iff, SmoothPartitionOfUnity.contDiffAt_finsum, IsInvariantSubring.smul_mem, ContMDiffAt.smul, Mathlib.Tactic.Module.NF.add_eq_eval₃, TrivSqZeroExt.map_comp_inlAlgHom, intervalIntegral.integral_hasDerivWithinAt_left, GeneralSchauderBasis.expansion, ofNat_smul_eq_nsmul, HasFPowerSeriesOnBall.fderiv_eq, Finsupp.weight_single, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, Seminorm.coe_restrictScalars, strictConvex_closedBall, NormedSpace.toNormSMulClass, Finset.sum_smul_const_vsub_eq_vsub_affineCombination, Quaternion.fst_imK_dualNumberEquiv_symm, midpoint_eq_smul_add, IsCovariantDerivativeOn.smul_const, Submodule.smul_le_self_of_tower, RootPairing.Equiv.root_indexEquiv_eq_smul, Asymptotics.IsLittleOTVS.zero, isBigO_rpow_top_log_smul, HasDerivAtFilter.fun_add, AffineMap.left_vsub_lineMap, SchwartzMap.smulLeftCLM_sum, midpoint_sub_right, Submodule.smul_mem_span_smul_of_mem, AffineMap.hasDerivWithinAt_lineMap, Asymptotics.IsLittleOTVS.congr_left, ContinuousLinearMap.fderiv_of_bilinear, TestFunction.coe_smul, has_fderiv_at_filter_real_equiv, MeasureTheory.setIntegral_condExpInd, Seminorm.gaugeSeminorm_ball, MeasureTheory.Measure.addHaarScalarFactor_smul_congr, ContinuousLinearMap.nnnorm_toSpanSingleton, FixedPoints.mem_addSubmonoid, ContinuousAlternatingMap.alternatizeUncurryFin_smul, PresheafOfModules.map_smul, fderiv_mul_const', tendsto_integral_exp_smul_cocompact, Matrix.linftyOpIsBoundedSMul, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Complex.hasDerivAt_Gammaℝ_one, Ring.uniformContinuousConstSMul, ContDiffMapSupportedIn.monoCLM_eq_of_scalars, curveIntegral_segment, Module.Ray.linearEquiv_smul_eq_map, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, DualNumber.fst_eq_zero_iff_eps_dvd, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Asymptotics.isBigOTVS_iff_smallSets, Derivation.leibniz_inv, Real.fourierIntegral_continuousLinearMap_apply, smul_left_inj, LinearMap.isAlt_iff_eq_neg_flip, Submodule.adjoint_subtypeL, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, Mathlib.Tactic.LinearCombination.smul_lt_const, ConvexOn.sub, Polynomial.aevalTower_toAlgHom, HasDerivAtFilter.sub, midpoint_mem_openSegment, gauge_norm_smul, MatrixEquivTensor.toFunBilinear_apply, InnerProductSpace.Core.cauchy_schwarz_aux, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, ContinuousLinearMap.opNorm_mul_apply, ContinuousLinearMap.norm_smulRightL, SMulCommClass.toDistribMulActionHom_toFun, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, TrivSqZeroExt.inl_mul_inr, DFinsupp.toFinsupp_smul, Asymptotics.IsBigOWith.const_smul_left, TrivSqZeroExt.fst_list_prod, AddConstMap.coe_smul, convexOn_univ_norm, ext_iff, HasFDerivWithinAt.fun_smul, AffineMap.lineMap_vsub_right, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, Submodule.exists_isTorsionBy, intervalIntegral.integral_deriv_comp_smul_deriv', strictAnti_smul_left, MeasureTheory.convolution_def, QuaternionAlgebra.star_smul', ContinuousMultilinearMap.curryLeft_norm, Seminorm.ball_zero_eq_preimage_ball, lp.norm_const_smul, finsuppTensorFinsuppLid_symm_single_smul, Module.reflection_mul_reflection_pow_apply, CategoryTheory.Abelian.Ext.mk₀_smul, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MeasureTheory.Submartingale.smul_nonneg, MDifferentiableWithinAt.cle_arrowCongr, Balanced.add, ConvexOn.openSegment_subset_strict_epigraph, TensorProduct.tmul_smul, CStarModule.inner_smul_left_complex, openSegment_subset_ball_of_ne, HasFPowerSeriesWithinOnBall.prod, units_smul_eq_self_iff, NormedSpace.normalize_smul, MDifferentiableWithinAt.clm_precomp, smul_add_smul_lt_smul_add_smul, HasDerivAt.fun_add, SchwartzMap.fourierMultiplierCLM_sum, MeasureTheory.integrable_withDensity_iff_integrable_smul', HasDerivAt.neg, ContMDiffVectorBundle.continuousLinearMap, DFinsupp.mapRange_smul, IsMIntegralCurveOn.comp_mul, DenseRange.topologicalClosure_map_submodule, Prod.image_mk_segment_left, Matrix.isBoundedSMul, HasDerivAt.star, MvPolynomial.scalarRTensor_apply_tmul, Matrix.conjTranspose_inv_natCast_smul, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, RootPairing.mem_range_coroot_of_mem_range_coreflection_of_mem_range_coroot, ConvexBody.coe_smul, Polynomial.smeval_smul, Convex.combo_self_interior_subset_interior, infEDist_smul₀, Bornology.IsVonNBounded.neg, ContinuousLinearMap.continuous_restrictScalars, UniqueDiffWithinAt.dense_tangentConeAt, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, InnerProductGeometry.angle_eq_zero_iff, RootPairing.EmbeddedG2.twoShortAddLongRoot_eq, smul_add_smul_le_smul_add_smul, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, Asymptotics.IsBigOTVS.fun_add, AnalyticAt.smul, hasLineDerivAt_smul_iff, VectorField.lieBracket_const_smul_left, SameRay.sameRay_nonneg_smul_left, LinearIndependent.pair_smul_iff, neg_convexOn_iff, ENNReal.smul_top, Submodule.mem_smul_iff_inv_mul_mem, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, ContinuousAlternatingMap.map_piecewise_smul, mellinInv_eq_fourierInv, units_smul_eq_neg_iff, HasFPowerSeriesOnBall.uniform_geometric_approx, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_monotoneOn, Module.End.algebraMap_isUnit_inv_apply_eq_iff', ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, IsNilpotent.exp_smul, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, Convex.strictConvex, IsSl2Triple.mem_toLieSubalgebra_iff, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, HasDerivAtFilter.const_smul, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, NonUnitalAlgHom.coe_distribMulActionHom_mk, Submodule.mem_torsionBySet_iff, Asymptotics.isBigOTVS_fun_neg_left, Ideal.stabilizerEquiv_symm_apply_smul, norm_smul_of_nonneg, sub_smul, VectorFourier.fourierIntegral_const_smul, HasFPowerSeriesWithinAt.fderivWithin_eq, Convex.span_tangentConeAt, inCoordinates_apply_eq₂, Asymptotics.isBigOTVS_fun_neg_right, CompactlySupportedContinuousMap.instSMulCommClass, KaehlerDifferential.tensorKaehlerEquivBase_tmul, AddSubmonoid.smul_le, ContDiffAt.contDiffAt_norm_smul, Real.fourier_real_eq, CentroidHom.smul_apply, MeasureTheory.setToFun_smul, SkewMonoidAlgebra.coeff_mul_right, FormalMultilinearSeries.id_comp', Seminorm.rescale_to_shell_zpow, FormalMultilinearSeries.ofScalars_sub, Asymptotics.IsEquivalent.smul, MeasureTheory.distribHaarChar_apply, MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_poles, prodXSubSMul.smul, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, Convex.openSegment_interior_self_subset_interior, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, Matrix.toEuclideanCLM_toLp, PiTensorProduct.liftAux.smul, Seminorm.smul_closedBall_zero, HasDerivAt.comp, AddMonoid.End.smul_apply, Seminorm.balanced_ball_zero, hasSum_fourier_series_L2, DualNumber.lift_inlAlgHom_eps, DifferentiableWithinAt.hasDerivWithinAt, isSMulRegular_submodule_iff_right_eq_zero_of_smul, Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNil, mem_openSegment_of_ne_left_right, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, Ioo_smul_sphere_zero, HasFPowerSeriesOnBall.sum, Real.tendsto_integral_gaussian_smul', HasFDerivAt.comp_hasDerivAt, Mathlib.Tactic.Module.NF.eq_cons_const, Real.hasFDerivAt_fourier, LinearOrder.convexOn_of_lt, HasDerivWithinAt.mul, absorbs_iff_eventually_nhdsNE_zero, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, Antitone.convex_lt, CategoryTheory.ShortComplex.Homotopy.smul_h₀, AddMonoidAlgebra.smulCommClass_symm_self, QuadraticMap.polar_smul, fderiv_inverse, smul_sphere', SchwartzMap.smulLeftCLM_fun_neg, ClosedSubmodule.mulI_sup, two_smul, Ideal.IsPrime.smul_iff, PiLp.instNormSMulClass, MeasureTheory.setIntegral_countable, ContMDiffOn.clm_precomp, CategoryTheory.ShortComplex.Homotopy.smul_h₃, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, contDiffOn_nat_iff_continuousOn_differentiableOn, Module.Basis.isScalarTower_finsupp, CategoryTheory.ShortComplex.cyclesMap_smul, TensorProduct.finsuppLeft_symm_apply_single, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Submodule.smul_coe_torsionBy, Fintype.not_linearIndependent_iffₛ, iteratedFDeriv_const_smul_apply', InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, map_nnrat_smul, stereoInvFun_apply, monovaryOn_iff_forall_smul_nonneg, TrivSqZeroExt.mul_left_eq_one, StrictConvexOn.translate_left, analyticAt_smul, Seminorm.restrictScalars_ball, Filter.EventuallyEq.hasDerivAt_iff, ConvexBody.coe_mk, LieAlgebra.Basis.baseSupp_apply_smul_f, InnerProductSpace.rankOne_eq_zero, egauge_le_one, Real.fourierIntegral_convergent_iff', fderivWithin_continuousMultilinear_apply_const_apply, NonUnitalNonAssocRing.int_isScalarTower, LieModuleHom.smul_apply, Submodule.mem_annihilator, hasDerivAt_deriv_iff, Unitization.splitMul_injective_of_clm_mul_injective, RCLike.mul_wInner_left, Seminorm.continuous, Function.Antiperiodic.const_inv_smul₀, StrictConvexOn.translate_right, CliffordAlgebra.ι_mul_ι_mul_ι, ContinuousAlternatingMap.norm_curryLeft, Module.End.HasEigenvector.apply_eq_smul, MeasureTheory.integral_indicatorConstLp, CFC.nnrpow_map_pi, inner_map_polarization', HasStrictDerivAt.clog_real, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal, hasDerivAt_of_hasDerivAt_of_ne', intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, LieDerivation.ofGradingSum_of, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, QuadraticMap.polar_smul_left_of_tower, ContinuousLinearMapWOT.smul_apply, MeasureTheory.Measure.integral_comp_smul, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, Asymptotics.isBigOTVS_iff_isBigO, Asymptotics.IsLittleO.smul, setIntegral_withDensity_eq_setIntegral_smul₀', LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, Bornology.isVonNBounded_sub_of_nonempty, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, subset_tangentConeAt_prod_right, TrivSqZeroExt.snd_exp, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, MeasureTheory.condExpIndSMul_smul, fderivWithin_inv', KaehlerDifferential.isScalarTower_of_tower, TannakaDuality.FiniteGroup.sumSMulInv_apply, Submodule.isTorsion'_iff_torsion'_eq_top, hasDerivAt_add_const_iff, not_disjoint_segment_convexHull_triple, AlgEquiv.smul_def, MeasureTheory.Measure.hausdorffMeasure_smul₀, real_inner_div_norm_mul_norm_eq_one_iff, Monotone.ae_hasDerivAt, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, star_natCast_smul, ContinuousLinearMap.fderivWithin_of_bilinear, Module.Basis.smul_det, HasFPowerSeriesOnBall.compContinuousLinearMap, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonpos, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', lineMap_mem_openSegment, iteratedDeriv_const_smul, Fintype.sum_single_smul, gaugeSeminorm_ball_one, LinearMap.BilinForm.smul_right_of_tower, ContinuousMultilinearMap.cons_smul, DiffContOnCl.deriv_eq_smul_circleIntegral, ContinuousLinearMap.applyFaithfulSMul, DifferentiableOn.deriv_eq_smul_circleIntegral, ContDiffMapSupportedIn.uniformSpace_eq_iInf, DomMulAct.coe_smul_addMonoidHom, Submodule.mem_span_singleton, iteratedFDerivWithin_smul_const_apply, Algebra.Generators.H1Cotangent.δAux_monomial, PiTensorProduct.liftIsometry_tprodL, VectorField.mpullback_smul_apply, DualNumber.isNilpotent_iff_eps_dvd, TrivSqZeroExt.map_comp_inrHom, RootPairing.reflectionPerm_coroot, Disjoint.exists_open_convexes, UniformConvergenceCLM.continuousSMul, curveIntegral_segment_const, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, hasDerivWithinAt_one, ConvexOn.smul_concaveOn', le_egauge_smul_left, sub_smul_slope_vadd, LieRinehartAlgebra.toIsScalarTower, Algebra.Extension.instIsScalarTowerCotangent, Bundle.Trivialization.eventually_eq_localFrame_sum_coeff_smul, DualNumber.isMaximal_span_singleton_eps, HahnSeries.SummableFamily.smul_hsum, Seminorm.finset_sup_apply_lt, Convex.second_derivative_within_at_symmetric, AffineSubspace.setOf_wOppSide_eq_image2, BoxIntegral.BoxAdditiveMap.volume_apply, spinGroup.conjAct_smul_range_ι, ConvexCone.isGenerating_bot, ProbabilityTheory.HasGaussianLaw.fun_smul, ModuleCat.Derivation.d_mul, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, MeasureTheory.Integrable.toL1_smul, InnerProductSpace.rankOne_eq_rankOne_iff_comm, realPart_add_I_smul_imaginaryPart, ContinuousLinearMap.uniformContinuousConstSMul, Ideal.Quotient.smul_top, HasLineDerivAt.tendsto_slope_zero, Asymptotics.IsLittleOTVS.fst, SemilinearMapClass.map_smul_inv, HasDerivWithinAt.inner, subset_tangentConeAt_prod_left, LocalizedModule.mk_cancel_common_left, strictConvex_Ioo, ConvexBody.convex, ContinuousLinearMap.holder_smul_left, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, sameRay_smul_left_iff, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, Submodule.FG.restrictScalars_iff, Seminorm.comp_smul, IsGreatest.nnnorm_cfcₙ_nnreal, LieRinehartRing.lie_smul_eq_mul', absorbent_nhds_zero, ContMDiffAt.const_smul_section, Submodule.pointwise_smul_toAddSubmonoid, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Real.fourierIntegral_iteratedDeriv, MultilinearMap.dfinsuppFamily_smul, intervalIntegral.smul_integral_comp_mul_sub, Derivation.leibniz', Derivation.leibniz_zpow, iteratedDerivWithin_smul_const, Mathlib.Tactic.Module.NF.sub_eq_eval₃, MeasureTheory.hasFDerivAt_convolution_right_with_param, InnerProductSpace.exists_of_rankOne_eq_rankOne, fderiv_pow', MeasureTheory.Lp.coeFn_smul, SkewMonoidAlgebra.sum_smul_index', ContMDiffSection.coe_smul, Asymptotics.IsLittleO.isLittleOTVS, hasDerivAt_ofNat, SchwartzMap.postcompCLM_apply, Asymptotics.IsLittleOTVS.neg_left, Ideal.tensorCotangentHom_tmul, iteratedFDerivWithin_eq_equiv_comp, Matrix.smul_kroneckerTMul, DifferentiableAt.isBigOTVS_sub, nhds_basis_balanced, Module.Quotient.mk_smul_mk, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ContDiffWithinAt.const_smul, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, differentialIdeal_le_iff, IsLocalizedModule.exist_integer_multiples_of_finite, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, RightPreLieAlgebra.toSMulCommClass, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, LinearMap.lsmul_flip_apply, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, IsModuleTopology.instProd, LinearIndependent.smul_left_injective, isLocalizedModule_iff, HahnEmbedding.Partial.exists_sub_mem_ball, Representation.asModuleEquiv_symm_map_smul, Asymptotics.IsLittleOTVS.pi, Submodule.mem_span_iff_exists_finset_subset, LinearEquiv.transvection.apply, DualNumber.lift_smul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, SameRay.exists_pos_right, MeasureTheory.SimpleFunc.integral_eq_sum, Coalgebra.sum_counit_smul, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, iteratedDerivWithin_const_smul_field, Quaternion.imK_fst_dualNumberEquiv, MvPolynomial.rTensor_apply_X_tmul, Bundle.Pretrivialization.continuousLinearMap.isLinear, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonneg, HahnSeries.of_symm_smul_of_eq_mul, CFC.posPart_smul, TotallyBounded.isVonNBounded, UpperHalfPlane.hasStrictDerivAt_smul, smul_min_of_nonpos, NormedSpace.normalize_smul_of_pos, Seminorm.comp_zero, ContinuousLinearMap.adjoint_inner_left, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, lift_rank_lt_rank_dual', Subring.mem_inv_pointwise_smul_iff, PointwiseConvergenceCLM.isInducing_inducingFn, KaehlerDifferential.tensorKaehlerEquiv_tmul, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, DomMulAct.coe_smul_linearMap, IsStrictOrderedRing.toIsStrictOrderedModule, Module.AEval'.X_pow_smul_of, Bornology.IsVonNBounded.image_multilinear, StarConvex.sub, groupHomology.isCycle₂_of_mem_cycles₂, LieRinehartAlgebra.Hom.map_smul_apply', Algebra.Generators.H1Cotangent.δAux_toAlgHom, ContDiffMapSupportedIn.seminorm_monoLM_le, Finsupp.linearCombination_single_index, intervalIntegral.integral_comp_smul_deriv'', Monovary.smul_add_smul_le_smul_add_smul, CochainComplex.HomComplex.Cochain.shift_smul, ContinuousLinearMap.isBoundedBilinearMap, WeakFEPair.Λ₀_eq, LinearMap.restrictScalars_self, ContinuousMultilinearMap.hasBasis_nhds_zero, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, LinearMap.extendTo𝕜_apply, RingTheory.Sequence.isWeaklyRegular_singleton_iff, HasDerivAt.sub, intervalIntegral.integral_comp_smul_deriv, SkewMonoidAlgebra.support_mul_single_eq_image, Module.piEquiv_apply_apply, LinearMap.BilinForm.smul_left, egauge_pi, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, Finsupp.lift_apply, ConvexOn.convex_epigraph, HasLineDerivWithinAt.smul, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, RatFunc.Luroth.algEquiv_algebraMap, Submodule.dualCoannihilator_map_linearEquiv_flip, mdifferentiable_smul_const_section, HasStrictDerivAt.sum, Polynomial.adjSylvester_comp_sylveserMap, Finset.expect_eq_single_of_mem, FormalMultilinearSeries.apply_eq_pow_smul_coeff, fderivWithin_continuousMultilinear_apply_const, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, MeasureTheory.setIntegral_condExpIndSMul, Finset.weightedVSub_smul, totallyBounded_absConvexHull, Prod.smul_mk_zero, Asymptotics.isBigOTVS_congr, ContinuousLinearMap.toSpanSingleton_smul, MulSemiringAction.charpoly_eq_prod_smul, MeasureTheory.integrable_withDensity_iff_integrable_smul₀, AdicCompletion.AdicCauchySequence.smul_apply, inv_norm_smul_mem_unitClosedBall, Seminorm.neg_mem_ball_zero, star_ratCast_smul, Submodule.mapsTo_smul_closure, MulSemiringAction.smul_coeff_charpoly, LinearMap.isScalarTower_of_injective, Ideal.torsionOf_eq_span_pow_pOrder, ContinuousLinearEquiv.symm_smul_apply, Asymptotics.isBigOTVS_neg_right, TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply, VectorField.lieBracketWithin_smul_left, VectorField.mlieBracketWithin_const_smul_left, convex_halfSpace_ge, AffineMap.right_vsub_lineMap, Quaternion.re_fst_dualNumberEquiv, ContinuousAlternatingMap.ofSubsingletonLIE_apply, IsDivSequence.smul, ConvexOn.translate_left, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, MulSemiringActionHom.map_smul, TemperedDistribution.fourierMultiplierCLM_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, convex_list_sum, Seminorm.bound_of_continuous, ContDiff.euclidean_dist, cfcₙ_real_eq_complex, HasStrictDerivAt.smul, inner_eq_sum_norm_sq_div_four, AntivaryOn.sum_smul_le_sum_comp_perm_smul, intervalIntegral.integral_comp_add_mul, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, constFormalMultilinearSeries_apply_zero, ConvexBody.ext_iff, hasDerivAt_tsum, DifferentiableAt.fderiv_restrictScalars, starConvex_iff_forall_ne_pos, AnalyticAt.fun_smul, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, Matrix.Module.smul_def, Representation.IntertwiningMap.smul_apply, MeasureTheory.setIntegral_rnDeriv_smul, LinearIsometryEquiv.conjStarAlgEquiv_trans, FormalMultilinearSeries.radius_smul_eq, RootPairing.smul_coroot_eq_of_root_add_root_eq, traceForm_dualSubmodule_adjoin, Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, ContinuousLinearMap.bilinearComp_zero_right, SkewMonoidAlgebra.single_mul_single, DivisibleHull.instIsStrictOrderedModuleNNRat, IsContMDiffRiemannianBundle.exists_contMDiff, ConcaveOn.comp_affineMap, Unitization.isStarProjection_inr_iff, ModuleCat.smulShortComplex_g, StarConvex.zero_smul, Function.support_smul, DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul, BaireSpace.instBarrelledSpace, hasDerivAtFilter_add_const_iff, TrivSqZeroExt.inl_smul, MultilinearMap.map_update_smul_left, hasDerivAt_jacobiTheta₂_fst, HomologicalComplex.units_smul_f_apply, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, HasDerivWithinAt.scomp_of_eq, MDifferentiableAt.const_smul, SkewMonoidAlgebra.support_single_mul_eq_image, MvPowerSeries.constantCoeff_smul, CFC.nnrpow_def, VertexOperator.ncoeff_apply, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, IsSl2Triple.lie_h_e_smul, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, TrivSqZeroExt.inr_mul_inr, convex_openSegment, Convex.taylor_approx_two_segment, DiffContOnCl.const_smul, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, LinearMap.flip_bijective_iff₁, subset_balancedHull, ConvexCone.pointed_positive, VectorFourier.fourierIntegral_convergent_iff, LinearMap.flip_bijective_iff₂, WithConv.matrixToLin'StarAlgEquiv_apply, IsLocalizedModule.subsingleton_iff, ContinuousLinearMap.adjointAux_apply, RCLike.real_smul_eq_coe_smul, IsTopologicalSemiring.toIsModuleTopology, cfcₙ_comp_re, integral_comp_polarCoord_symm, Set.zero_mem_smul_set_iff, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, BoundedContinuousFunction.instIsScalarTower_1, IsCompactOperator.hasEigenvalue_or_mem_resolventSet, fderivWithin_fun_mul', CategoryTheory.Functor.map_smul, sup_eq_half_smul_add_add_abs_sub', Module.Basis.coe_smul, ProperCone.innerDual_singleton, VonNeumannAlgebra.coe_mk, Algebra.TensorProduct.isScalarTower_right, Asymptotics.IsLittleO.smul_isBigO, MonotoneOn.convex_lt, HasFPowerSeriesWithinOnBall.sub, TemperedDistribution.fourierMultiplierCLM_const, MvPolynomial.tensorEquivSum_one_tmul_C, HasLineDerivAt.tendsto_slope_zero_left, StrictConvexOn.add, Submodule.coe_pointwise_smul, Balanced.subset_smul, ConcaveOn.mul', ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, derivWithin_const_smul_field, StrictConvexOn.map_sum_eq_iff, MvPolynomial.rTensor_apply_tmul, Antitone.convex_ge, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, hasFDerivAt_integral_of_dominated_loc_of_lip', CliffordAlgebra.invOf_ι_mul_ι_mul_ι, ConvexCone.coe_strictlyPositive, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, Asymptotics.isLittleO_const_smul_left, DifferentiableOn.fun_const_smul, RKHS.kerFun_dense, VectorField.mpullback_const_smul, InnerProductSpace.rankOne_def, HasDerivAt.smul_const, ConvexOn.add_strictConvexOn, contDiff_const_smul, smul_vsub_vadd_mem_affineSpan_pair, HasDerivAtFilter.sub_const, smul_nonneg_of_nonpos_of_nonpos, ContinuousLinearMap.coe_flipₗᵢ', MDifferentiableAt.clm_bundle_apply₂, WeakFEPair.h_feq', star_nnrat_smul, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, uniqueDiffWithinAt_iff, SchwartzMap.convolution_apply, Polynomial.smul_mem_rootSet_iff, Submodule.IsPrincipal.mem_iff_eq_smul_generator, PointedCone.pointed_toConvexCone, fderivWithin_fderivWithin_eq_of_mem_nhds, Submodule.IsLattice.smul, ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, Set.zero_mem_smul_iff, contDiff_iff_continuous_differentiable, Asymptotics.IsLittleOTVS.exists_eventuallyLE_mul_ennreal, Finsupp.instFaithfulSMulOfNonempty, hasDerivAt_const, dslope_sub_smul_of_ne, Finset.centerMass_smul_left, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Submodule.coe_tensorSpanEquivSpan_apply_tmul, Module.End.aeval_apply_of_hasEigenvector, CategoryTheory.Abelian.Ext.smul_comp, fderiv_mul', Filter.EventuallyEq.ftaylorSeriesWithin, UniformSpace.Completion.norm_toComplL, Seminorm.uniformContinuous_of_continuousAt_zero, IsRegular.smul_right_injective, fderivWithin_const_smul_of_field, Bornology.IsVonNBounded.tendsto_smallSets_nhds, Matrix.toLin_self, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, ContinuousMap.toLp_def, ContDiffAt.const_smul, OrderDual.instSMulPosReflectLE, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, instSMulDistribClassAlgEquiv, Complex.hasDerivAt_Gammaℂ_one, MulSemiringAction.smul_charpoly, VectorField.lieBracket_fmul_left, Module.Basis.SmithNormalForm.snf, Asymptotics.IsBigOTVS.snd, iteratedDerivWithin_fun_const_smul_field, sup_eq_half_smul_add_add_abs_sub, RootPairing.pairing_neg_one_neg_four_iff, SchwartzMap.integral_bilin_fourier_eq, HasFDerivWithinAt.lim, KaehlerDifferential.ker_map, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, smul_neg, ConcaveOn.quasiconcaveOn, DifferentiableOn.clm_comp, ContDiffMapSupportedIn.monoCLM_apply, ftaylorSeriesWithin_zero, LinearMap.CompatibleSMul.finsupp_dom, ContinuousMultilinearMap.prodL_apply, Seminorm.add_comp, Finset.smul_neg, segment_eq_image, HasStrictDerivAt.mul_const, Matrix.conjTranspose_inv_ofNat_smul, InnerProductSpace.HarmonicContOnCl.const_smul, set_smul_mem_nhds_zero_iff, affinity_unitBall, convex_eball, instPosSMulStrictMono, hasFTaylorSeriesUpToOn_succ_iff_right, StrictConcaveOn.convex_gt, ContinuousOn.clm_bundle_apply₂, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, StrictConvex.add_left, Seminorm.bddAbove_iff, Convex.is_linear_preimage, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, LinearEquiv.map_smulₛₗ, IsGaloisGroup.faithful, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, MulActionHom.coe_sub, ModuleFilterBasis.smul_left', SchwartzMap.compCLMOfAntilipschitz_apply, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, HasDerivWithinAt.fun_neg, LinearIsometryEquiv.conjStarAlgEquiv_refl, HasDerivAt.tendsto_slope_zero_left, InnerProductSpace.laplacian_smul, MeasureTheory.setToFun_smul_left, HasDerivAt.complexToReal_fderiv', IsBaseChange.lift_comp, LinearMap.separatingRight_iff_flip_ker_eq_bot, AddMonoid.End.smul_def, MvPolynomial.mkDerivationₗ_monomial, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, starConvex_iff_openSegment_subset, mem_segment_iff_sameRay, derivWithin_fun_const_smul, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', ContinuousAlternatingMap.map_update_smul, eventually_singleton_add_smul_subset, MeasureTheory.L1.setToL1_smul_left', Matrix.fin_two_smul_prod, TensorProduct.finsuppScalarRight_smul, Module.Ray.units_smul_of_pos, Antivary.sum_smul_lt_sum_comp_perm_smul_iff, mem_extremePoints_iff_forall_segment, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, Asymptotics.IsBigOTVS.fun_symm, Submodule.mem_singleton_set_smul, Orientation.map_eq_det_inv_smul, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, Seminorm.continuousAt_zero', ContinuousLinearMap.coe_restrict_scalarsL', fderivWithin_fderivWithin_eq_of_eventuallyEq, StandardSubspace.IsCyclic, IsSMulRegular.submodule, Real.fourierIntegral_real_eq_integral_exp_smul, ConvexCone.mem_map, CochainComplex.HomComplex.Cochain.leftUnshift_smul, InnerProductSpace.laplacianWithin_smul, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2, StrongDual.polarSubmodule_eq_polar, HasDerivWithinAt.Ici_of_Ioi, Algebra.IsInvariant.orbit_eq_primesOver, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, StrictConvex.affinity, algebraMap_smul, finsuppTensorFinsupp_single, Real.deriv_fourierIntegral, PiTensorProduct.liftEquiv_symm_apply, PiToModule.fromMatrix_apply_single_one, Algebra.Extension.CotangentSpace.map_sub_map, TestFunction.coe_ofSupportedInLM, HasStrictDerivAt.cexp, QuadraticMap.associated_toQuadraticMap, RingHom.applyFaithfulSMul, Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, extDerivWithin_fun_smul, inner_smul_real_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Asymptotics.isLittleOTVS_fun_neg_right, ftaylorSeries_fun_zero, SchauderBasis.proj_apply, TensorProduct.CompatibleSMul.smul_tmul, IsLocalizedModule.mem_ker_iff, ConvexCone.strictlyPositive_le_positive, ContDiffWithinAt.smul, HasDerivAt.add_const, cfcₙ_comp_im, Asymptotics.IsLittleOTVS.triangle, Seminorm.closedBall_finset_sup, AddSubmonoid.smul_mem_pointwise_smul, Antivary.sum_smul_le_sum_smul_comp_perm, MeasureTheory.SignedMeasure.re_toComplexMeasure, TemperedDistribution.smulLeftCLM_sub, fromTangentSpace_mfderiv_smul', HasDerivAt.of_isLittleO, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, ZMod.algebraOfModule.proof, Seminorm.uniformSpace_eq_of_hasBasis, Nat.ceilRoot_def, eq_pos_convex_span_of_mem_convexHull, SchwartzMap.postcompCLM_postcompCLM, OreLocalization.oreDiv_add_oreDiv, TensorProduct.lid_tmul, PolynomialModule.isScalarTower', IsBoundedLinearMap.smul, DualNumber.exists_mul_left_or_mul_right, iteratedDerivWithin_scomp_eq_sum_orderedFinpartition, SModEq.smul', intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, fourierCoeff.const_smul, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, BddBelow.smul_of_nonpos, monovary_iff_forall_smul_nonneg, Submodule.smul_le_smul, closure_openSegment, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', HasDerivAt.sub_const, biUnion_associatedPrimes_eq_zero_divisors, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, IsLocalizedModule.map_linearCombination, hasSum_cauchyPowerSeries_integral, Convex.combo_interior_self_subset_interior, ContinuousLinearMap.aestronglyMeasurable_comp₂, MeasureTheory.Lp.instFourierSMul, SchwartzMap.smulLeftCLM_const, MeasureTheory.integral_fintype, uniformContinuousConstSMul_of_continuousConstSMul, smul_top_inf_eq_smul_of_isSMulRegular_on_quot, LinearEquiv.piRing_symm_apply, MDifferentiableAt.smul_section, ConvexCone.disjoint_hull_left_of_convex, Set.OrdConnected.convex, Asymptotics.IsBigOTVS.congr_left, Mathlib.Tactic.LinearCombination.smul_le_const, strictConvexSpace_iff, intervalIntegral.smul_integral_comp_sub_mul, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, Asymptotics.IsLittleOTVS.smul_left, Ideal.inertiaEquiv_apply_smul, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, hasDerivAt_of_tendstoUniformlyOn, Asymptotics.isLittleO_const_smul_right, smul_right_injective, Asymptotics.IsBigOTVS.proj, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, StarConvex.linear_image, Orientation.inner_rotation_pi_div_two_left_smul, sameRay_smul_left_iff_of_ne, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, smul_sphere, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, strictConvex_Iio, MeasureTheory.Measure.toSignedMeasure_smul, star_inv_intCast_smul, HVertexOperator.compHahnSeries_smul, HasStrictDerivAt.scomp_of_eq, DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap, HasStrictDerivAt.fun_finset_prod, ConvexCone.toPointedCone_top, fourierIntegral_eq_half_sub_half_period_translate, LinearMap.range_toContinuousLinearMap, Bornology.IsVonNBounded.of_sub_right, linearDepOn_iff, Ideal.exact_mulQuot_quotOfMul, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, fderiv_const_smul_of_invertible, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, Matrix.inner_toEuclideanCLM, Ideal.Cotangent.smul_eq_zero_of_mem, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, Subring.mem_smul_pointwise_iff_exists, hasFDerivWithinAt_pow', IsGaloisGroup.mulEquivAlgEquiv_apply_apply, hasStrictDerivAt_finCons', Submodule.mem_colon_iff_le, LinearMap.transvection.apply, AffineSubspace.smul_mem_smul_iff_of_isUnit, hasDerivWithinAt_taylorWithinEval_at_Icc, ContinuousLinearMap.isBoundedLinearMap_comp_right, AdjoinRoot.smul_of, Matrix.toLinearMapₛₗ₂_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Matrix.mul_mul_right, HasFPowerSeriesWithinAt.pi, MultilinearMap.freeDFinsuppEquiv_single, Module.Basis.isUnitSMul_apply, NormedSpace.isVonNBounded_iff', VonNeumannAlgebra.mem_carrier, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, TestFunction.lineDerivCLM_add, hasStrictDerivAt_finCons, PiTensorProduct.liftEquiv_apply, intervalIntegral.integral_deriv_comp_smul_deriv, Asymptotics.IsLittleOTVS.trans_isBigOTVS, WeakDual.isBounded_iff_isVonNBounded, StarAlgEquiv.ofBijective_apply, Matrix.convex_colStochastic, HasDerivWithinAt.congr_of_eventuallyEq_of_mem, Matrix.vecMul_eq_sum, has_antideriv_at_fourier_neg, hasFTaylorSeriesUpTo_top_iff', MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, Set.neg_smul, groupHomology.isBoundary₂_of_mem_boundaries₂, fderivWithin_iteratedFDerivWithin, fromTangentSpace_mfderiv_smul_apply', Convex.isLittleO_alternate_sum_square, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, HahnModule.instIsScalarTowerHahnSeries_1, rescale_to_shell, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, Polynomial.smul_X, mem_openSegment_add_sub, ConvexOn.map_sum_le, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, Submodule.mem_span_set, GradedMonoid.smulCommClass_right, Subspace.flip_quotDualCoannihilatorToDual_bijective, PiTensorProduct.liftAux_tprodCoeff, Polynomial.smul_sum, closure_convexHull_extremePoints, ContinuousLinearMap.deriv_of_bilinear, balanced_neg, Orientation.areaForm'_apply, HasStrictDerivAt.comp_of_eq, segment_inter_eq_endpoint_of_linearIndependent_of_ne, openSegment_eq_image, Continuous.cfcₙ_nnreal, ContinuousLinearMap.nnnorm_holder_apply_apply_le, LinearMap.toSpanSingleton_smul, TrivSqZeroExt.mul_inv_cancel, Polynomial.coe_smul, AffineMap.isCentralScalar, Asymptotics.isTheta_const_smul_left, intervalIntegral.integral_smul_measure, upperBounds_smul_of_neg, signedDist_smul_of_pos, Distribution.mapCLM_apply, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange, HasDerivAtFilter.star, isSMulRegular_of_isSMulRegular_on_submodule_on_quotient, WeakDual.CharacterSpace.toAlgHom_apply, TensorProduct.finsuppScalarRight_apply_tmul_apply, Derivation.coe_comp, DFinsupp.instPosSMulStrictMono, ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule, infEdist_smul₀, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, Unitization.inrRangeEquiv_apply_coe_snd, Bornology.isVonNBounded_iff_smul_tendsto_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, Monotone.convex_lt, Ideal.Quotient.stabilizerHom_apply, Module.Basis.repr_symm_single, Module.reflection_reflection_iterate, TrivSqZeroExt.inv_mul_cancel, Polynomial.smul_eq_map, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, Convex.smul, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, lp.instSMulCommClassSubtypePreLpMemAddSubgroup, Subsemiring.smul_mem_pointwise_smul_iff₀, HasDerivAtFilter.scomp, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, AffineMap.lineMap_apply_module', LinearMap.flip_apply, MultilinearMap.freeDFinsuppEquiv_def, TensorProduct.finsuppLeft_apply, Submodule.orthogonal_orthogonal_eq_closure, Pi.single_smul, LieRinehartRing.leibniz_smul_right', AnalyticOn.const_smul, StrictConvex.linear_preimage, isSMulRegular_iff_torsionBy_eq_bot, AffineSubspace.convex, Submodule.smul_starProjection_singleton, finsuppTensorFinsuppRid_symm_single_smul, ContinuousLinearMap.map_smulₛₗ, SMulCommClass.complexToReal, contMDiff_smul, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonpos, smul_add_one_sub_smul, PointedCone.convex, UniformFun.continuousSMul_induced_of_range_bounded, ConvexOn.neg, intervalIntegral.integral_hasStrictFDerivAt, with_gaugeSeminormFamily, CStarAlgebra.linear_combination_nonneg, fderivWithin_mul_const', Submodule.mem_span_finset', ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, NonUnitalStarSubalgebra.unitization_injective, intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right, HasDerivWithinAt.fun_smul, IsBilinearMap.toContinuousBilinearMap_apply, smul_left_injective, SkewMonoidAlgebra.domCongr_refl, right_mem_openSegment_iff, inv_natCast_smul_comm, NonUnitalSubalgebra.smul_mem', ZMod.invDFT_def', TestFunction.lineDerivOp_eq_lineDerivCLM, ConvexCone.blunt_strictlyPositive, Module.toCentroidHom_apply_toFun, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, NonUnitalStarSubalgebra.unitization_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, aestronglyMeasurable_smul_const_iff, absConvexHull_add_subset, MvPowerSeries.le_weightedOrder_smul, HasStrictDerivAt.fun_div, PartitionOfUnity.finsum_smul_mem_convex, CliffordAlgebra.foldr'_algebraMap, differentiableAt_complex_iff_differentiableAt_real, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, IsRegular.isSMulRegular, Convex.exists_forall_hasDerivWithinAt, intervalIntegral.inv_smul_integral_comp_sub_div, ConvexCone.IsGenerating.top_le_span, hasDerivWithinAt_taylor_coeff_within, UniformConvexOn.convexOn, Seminorm.iSup_apply, HasFPowerSeriesAt.hasStrictDerivAt, SchwartzMap.fourierMultiplierCLM_apply, AnalyticOn.smul, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable, DFinsupp.sigmaCurry_smul, ClosedSubmodule.mem_symplComp_iff, ContinuousAt.cfcₙ_nnreal, WithSeminorms.tendsto_nhds, hasFDerivAt_list_prod_finRange', ContDiff.smulRight, not_linearIndependent_iffₒₛ, ContinuousMultilinearMap.flipLinear_apply_apply, Asymptotics.IsBigOTVS.trans_isLittleOTVS, ConvexOn.translate_right, Representation.instIsScalarTowerMonoidAlgebraAsModule, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, Module.FinitePresentation.linearEquivMap_apply, ContinuousMap.coe_smul', CochainComplex.HomComplex.δ_smul, LinearMap.hasDerivWithinAt, WithSeminorms.isOpen_iff_mem_balls, CStarMatrix.toCLM_apply_single, hasSum_two_pi_I_cauchyPowerSeries_integral, Real.fourier_fderiv, convexHull_pair, Set.Subsingleton.strictConvex, rescale_to_shell_semi_normed, MvPolynomial.rTensorAlgHom_toLinearMap, FormalMultilinearSeries.comp_id, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousMap.nnnorm_smul_const, smul_eq_zero_iff_left, ContinuousMap.adjoin_id_eq_span_one_union, CategoryTheory.Linear.comp_units_smul, MeasureTheory.condExp_smul, AlgebraicGeometry.StructureSheaf.smul_const, TrivSqZeroExt.invOf_eq_inv, Seminorm.const_isBounded, hasFTaylorSeriesUpTo_succ_nat_iff_right, IsCovariantDerivativeOn.leibniz, Seminorm.preimage_metric_closedBall, tangentConeAt_of_mem_nhds, SchwartzMap.compSubConstCLM_zero, ContDiffMapSupportedIn.seminorm_top_le_iff, neg_concaveOn_iff, convexOn_of_convex_epigraph, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, NonUnitalSubalgebra.instSMulCommClass, Algebra.Extension.CotangentSpace.map_cotangentComplex, LocalizedModule.mk_cancel_common_right, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, RCLike.wInner_smul_right, Complex.restrictScalars_one_smulRight, QuotSMulTop.equivQuotTensor_naturality, IsModuleTopology.isoₛₗ, ClosedSubmodule.iInf_orthogonal, Polynomial.smul_eval_smul, Asymptotics.isLittleOTVS_iff_smallSets, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, smul_add_smul_lt_smul_add_smul', MeasureTheory.smul_extend, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity', HahnEmbedding.Partial.eval_smul, HasDerivAt.clm_comp, MeasureTheory.Measure.Regular.domSMul, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, iteratedDerivWithin_scomp_three, ProperCone.dual_singleton, ContinuousLinearMap.uncurryBilinear_apply, LinearPMap.coe_smul, Algebra.TensorProduct.basisAux_tmul, StrongDual.extendRCLikeₗ_apply, HasFDerivWithinAt.smul_const, AntivaryOn.card_smul_sum_le_sum_smul_sum, Seminorm.sSup_empty, KaehlerDifferential.derivationQuotKerTotal_apply, AdicCompletion.transitionMap_comp_reduceModIdeal, MeasureTheory.integral_posConvolution, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, Algebra.Extension.tensorCotangentSpace_tmul, MeasureTheory.LocallyIntegrableOn.smul_continuousOn, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, IsOpen.smul_sphere, EuclideanGeometry.Sphere.secondInter_smul, Subring.smul_closure, monovary_iff_smul_rearrangement, Module.AEval.X_pow_smul_of, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, strongConcaveOn_iff_convex, iteratedFDeriv_eq_equiv_comp, Real.smul_iInf_of_nonpos, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, MeasureTheory.condExpIndL1_smul, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, Matrix.conjTranspose_ratCast_smul, Differentiable.continuousMultilinearMapCompContinuousLinearMap, Unitization.norm_eq_sup, MonovaryOn.sum_smul_sum_le_card_smul_sum, LinearEquiv.toSpanNonzeroSingleton_apply, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Submodule.mem_span_insert', Matrix.ofLp_toEuclideanCLM, Ideal.coe_restrictScalars, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Fourier.fourierIntegral_const_smul, TrivSqZeroExt.inl_mul, HasDerivWithinAt.comp_hasDerivAt_of_eq, QuadraticMap.smul_apply, hasDerivAtFilter_iff_isLittleO, Absorbent.eventually_nhdsNE_zero, HasDerivAt.fun_const_smul, HasDerivAt.fun_sub, CStarMatrix.toCLM_apply_eq_sum, Set.Subsingleton.convex, Submodule.span_algebraMap_image_of_tower, HasStrictFDerivAt.restrictScalars, LinearMap.exact_smul_id_smul_top_mkQ, MeasureTheory.Measure.ae_smul_measure_iff, TwoSidedIdeal.instSMulMemClass, StarAlgEquiv.coe_ofBijective, balancedHull_add_subset, Projectivization.mk_eq_mk_iff, StarConvex.preimage_smul, MeasureTheory.Measure.instSMulCommClassDomMulActNNReal, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ConvexOn.quasiconvexOn, strictConvex_Ici, hasDerivAt_exp_smul_const, AddMonoidAlgebra.instIsPushout, HasDerivAtFilter.add_const, Meromorphic.fun_smul, HasSum.smul, Asymptotics.isBigOTVS_neg_left, MeasureTheory.Measure.NullMeasurableSet.const_smul, Balanced.closure, MeasureTheory.eLpNormEssSup_smul_measure, affineIndependent_smul, ContDiffMapSupportedIn.locallyConvexSpace, hasFDerivWithinAt_comp_smul_smul_iff, fourierCoeff_toLp, IsLocalizedModule.mk'_cancel', ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Algebra.Generators.H1Cotangent.δAux_ofComp, Algebra.Extension.CotangentSpace.map_tmul_eq_tmul_map, ContinuousMultilinearMap.smul_prod_smul, CategoryTheory.Functor.mapExactFunctor_smul, smul_unitBall_of_pos, smul_lt_smul_iff_of_neg_left, HasStrictDerivAt.congr_deriv, ProbabilityTheory.hasDerivAt_complexMGF, AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff, map_real_smul, RootPairing.reflectionPerm_root, DifferentiableWithinAt.isBigOTVS_sub, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, LinearOrder.concaveOn_of_lt, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', LinearIsometryEquiv.toSpanUnitSingleton_apply, Asymptotics.IsBigOWith.smul, gc_mul_ceilDiv, Asymptotics.IsLittleOTVS.congr', IsScalarTower.rat, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', Convex.translate, LinearEquiv.apply_smulCommClass, StrictConvexOn.map_sum_lt, map_inv_natCast_smul, iteratedDeriv_comp_const_smul, norm_inner_eq_norm_tfae, Real.circleAverage_def, Submodule.map₂_span_singleton_eq_map_flip, LinearPMap.mkSpanSingleton'_apply, CategoryTheory.ShortComplex.smul_τ₃, LinearMap.pi_apply_eq_sum_univ, DilationEquiv.smulTorsor_apply, FormalMultilinearSeries.changeOrigin_eval_of_finite, Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite, Module.sum_smul_eq_zero_of_isTrivialRelation, intervalIntegral.integral_smul, ZMod.dft_apply, Seminorm.map_eq_zero_of_norm_eq_zero, Algebra.TensorProduct.distribBaseChange_comp_includeLeftSubRight, sigmaFinsuppEquivDFinsupp_smul, Rep.ofDistribMulAction_ρ_apply_apply, Quaternion.fst_imJ_dualNumberEquiv_symm, exists_nonneg_right_iff_sameRay, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, iteratedFDerivWithin_two_apply', HasDerivAt.const_smul, UniqueDiffWithinAt.smul_iff, Convex.add_smul_mem, Balanced.interior, cfcₙ_tsub, deriv.scomp, balancedCoreAux_balanced, HasStrictDerivAt.add, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, MeasureTheory.DominatedFinMeasAdditive.smul, StarConvex.add_left, concaveOn_univ_piecewise_Ici_of_antitoneOn_Ici_monotoneOn_Iic, hasDerivAt_taylorWithinEval_succ, CFC.monotoneOn_one_sub_one_add_inv_real, Convex.closure, Bornology.IsBounded.smul₀, MemHolder.smul, HVertexOperator.of_coeff_coeff, Module.Basis.mem_submodule_iff', skewAdjoint.negISMul_apply_coe, Submodule.smithNormalFormBotBasis_def, insert_endpoints_openSegment, PMF.integral_eq_tsum, not_linearIndependent_iffₛ, DiffContOnCl.circleAverage_smul_div, groupHomology.isCycle₁_of_mem_cycles₁, QuadraticAlgebra.C_mul_eq_smul, IsLocalFrameOn.eventually_eq_sum_coeff_smul, AddMonoidAlgebra.instIsPushout', lp.infty_smulCommClass, Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, intervalIntegral.integral_comp_div, Submodule.instCovariantClassHSMulLe, TensorProduct.lid'_apply_tmul, HasSum.exists_hasSum_smul_of_apply_eq_zero, Finsupp.smul_single', KaehlerDifferential.instSMulCommClassTensorProduct_1, Algebra.Extension.Cotangent.val_smul', Finsupp.weight_single_index, DiscreteConvolution.ConvolutionExistsAt.smul_convolution, HVertexOperator.coeff_inj_iff, HasFPowerSeriesAt.fderiv_eq, CategoryTheory.endomorphism_simple_eq_smul_id, Orientation.oangle_sign_smul_left, Finset.sum_Ico_by_parts, HasDerivAtFilter.scomp_of_eq, ContinuousWithinAt.cfcₙ_nnreal, ContinuousLinearMap.coe_restrictScalarsIsometry, MeasureTheory.Integrable.bdd_smul, Finsupp.linearCombination_apply, rank_eq_one_iff, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, MonoidAlgebra.smul_of, Submodule.mem_set_smul_of_mem_mem, MatrixModCat.mem_toModuleCatObj, HasDerivAt.scomp_hasDerivWithinAt_of_eq, Nat.factorization_ceilRoot, GradedAlgHom.restrictScalars_coe_linearMap, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, ConvexBody.isBounded, VectorField.mlieBracketWithin_smul_left, Convex.combo_self, Unitization.inrRangeEquiv_apply_coe_fst, CStarMatrix.reindexₐ_apply, WeakBilin.instContinuousSMul, ContinuousLinearMap.isometry_iff_adjoint_comp_self, continuousMultilinearCurryFin0_apply, smul_le_smul_iff_of_neg_left, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, AddGroup.int_smulCommClass', IsUnit.smul_eq_zero, LocalizedModule.smul'_mk, PiTensorProduct.dualSeminorms_bounded, FormalMultilinearSeries.radius_neg, Module.Flat.isSMulRegular_of_isRegular, HasFDerivWithinAt.mul_const', InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, extDeriv_smul, homeomorphUnitSphereProd_symm_apply_coe, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, Algebra.Extension.Cotangent.map_comp, HasDerivAt.comp_const_sub, taylorWithinEval_succ, convex_Ioo, Submodule.mulRightMap_eq_mulMap_comp, HasDerivAt.norm_sq, StarConvex.smul, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, HasDerivWithinAt.add, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, StrictConvexSpace.strictConvex_closedBall, Real.fourier_eq, Algebra.trace_comp_trace_of_basis, AffineMap.lineMap_vadd_apply, Mathlib.Tactic.LinearCombination.smul_lt_const_weak, differentialIdeal_le_fractionalIdeal_iff, Submodule.span_set_smul, HasStrictFDerivAt.continuousMultilinear_apply_const, Asymptotics.IsLittleOTVS.sup, AddMonoid.End.isCentralScalar, ContDiffMapSupportedIn.monoLM_eq_zero, SMulPosReflectLT.toSMulPosReflectLE, sameRay_neg_smul_left_iff_of_ne, Set.OrdConnected.convex_of_chain, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, MultilinearMap.freeFinsuppEquiv_def, ConvexOn.convex_lt, Prod.openSegment_subset, WeakBilin.instIsScalarTower, Orientation.oangle_sign_smul_add_smul_smul_add_smul, DoubleCentralizer.algebraMap_snd, Finset.expect_dite_eq', Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, Convex.add, Polynomial.aeval_smul, MeasureTheory.Measure.integral_comp_mul_left, lp.instStarModuleSubtypePreLpMemAddSubgroup, AnalyticAt.analyticOrderNatAt_eq_iff, groupHomology.isBoundary₀_of_mem_coinvariantsKer, MeasureTheory.integrable_smul_const, SchauderBasis.RankOneDecomposition.basisCoeff_spec, hasFiniteFPowerSeriesOnBall_const, Module.End.smulLeft_apply, HahnModule.SMulCommClass, ZMod.invDFT_apply', iteratedFDerivWithin_succ_apply_left, HasFDerivAtFilter.fun_const_smul, Submodule.starProjection_unit_singleton, Matrix.dualNumberEquiv_symm_apply, Finset.weightedVSub_const_smul, SchwartzMap.fourier_evalCLM_eq, ContinuousWithinAt.integral_sub_linear_isLittleO_ae, convex_convexHull, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, DualNumber.exp_eps, Submodule.mul_smul_mul_eq_smul_mul_smul, Asymptotics.IsBigOTVS.prodMk, Polynomial.iterate_derivative_X_pow_eq_smul, KaehlerDifferential.tensorKaehlerEquiv_left_inv, DifferentiableAt.fun_const_smul, AdicCompletion.pow_smul_top_eq_ker_eval, hasDerivWithinAt_natCast, IsTopologicalSemiring.toOppositeIsModuleTopology, CliffordAlgebra.foldl_algebraMap, Orientation.oangle_sign_smul_sub_left, RatFunc.div_smul, fderiv_pow_ring', LinearMap.toSpanSingleton_apply, MeasureTheory.memL1_smul_of_L1_withDensity, ContinuousLinearMap.bilinearComp_apply, analyticAt_iff_analytic_fun_smul, imaginaryPart_eq_neg_I_smul_skewAdjointPart, AddSubmonoid.mem_inv_pointwise_smul_iff₀, midpoint_vsub_left, MeasureTheory.Measure.toSphere_apply', DiscreteConvolution.ConvolutionExistsAt.convolution_smul, TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, RatFunc.minpolyX_aeval_X, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOn, LieAlgebra.smulCommClass, range_cfcₙ_nnreal_eq_image_cfcₙ_real, Matrix.Module.instIsScalarTowerForall, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, Polynomial.smeval_C_mul, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, Matrix.smul_eq_mul_diagonal, Subsemiring.center.smulCommClass_right, DiffContOnCl.smul_const, RootPairing.InvariantForm.apply_weylGroup_smul, Convex.linear_image, ContMDiffWithinAt.clm_bundle_apply₂, MeasureTheory.condExpIndL1_smul', Submodule.singleton_smul, LinearMap.conjugate_apply, Filter.Tendsto.cfcₙ_nnreal, TopologicalGroup.IsSES.integrate_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, HasDerivAt.fun_div, Submodule.toConvexCone_le_toConvexCone, tsum_const_smul'', vadd_segment, Matrix.Module.scalar_smul, mem_parallelepiped_iff, Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy, contDiff_smul_const, MeasureTheory.integral_biUnion_eq_sum_powerset, HasFTaylorSeriesUpToOn.fderivWithin, Prod.image_mk_openSegment_right, CStarMatrix.toCLM_apply, KaehlerDifferential.kerTotal_map, AddSubmonoid.smul_closure, LieModule.lie_smul, DoubleCentralizer.algebraMap_toProd, continuousMultilinearCurryFin0_symm_apply_apply, HasDerivWithinAt.fun_const_smul, ConcaveOn.le_map_sum, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ContinuousLinearMap.ker_self_comp_adjoint, Quaternion.fst_imI_dualNumberEquiv_symm, differentiableAt_norm_smul, exists_nontrivial_relation_sum_zero_of_not_affine_ind, FormalMultilinearSeries.id_comp, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, invOf_two_smul_add_invOf_two_smul, Real.circleAverage_eq_integral_add, isSMulRegular_algebraMap_iff, HasFPowerSeriesAt.restrictScalars, hasDerivAt_integral_of_dominated_loc_of_deriv_le, intervalIntegral.inv_smul_integral_comp_div_sub, ConcaveOn.convex_hypograph, rank_dual_eq_card_dual_of_aleph0_le_rank', ContinuousLinearMap.instStarModuleId, ContDiff.smul_const, RCLike.wInner_smul_left, Matrix.toLinearMapₛₗ₂'_apply, edist_smul₀, Absorbs.sub, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right, Seminorm.convex_ball, VectorField.mlieBracketWithin_smul_right, Convex.combo_closure_interior_subset_interior, CategoryTheory.ShiftedHom.comp_smul, PolynomialModule.eval_lsingle, MultilinearMap.map_nonempty, DoubleCentralizer.instIsCentralScalar, Subsemiring.mem_inv_pointwise_smul_iff₀, groupHomology.single_isCycle₁_iff, HasDerivWithinAt.const_mul, ContinuousLinearMapWOT.instContinuousSMul, HasFDerivAt.continuousAlternatingMap_apply_const, CochainComplex.HomComplex.Cochain.smul_comp, Submodule.span_eq_closure, AddSubgroup.mem_smul_pointwise_iff_exists, Finset.smul_finset_neg, PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, PartitionOfUnity.sum_finsupport_smul_eq_finsum, LieAdmissibleAlgebra.toIsScalarTower, norm_fderiv_iteratedFDeriv, IsCompact.extremePoints_nonempty, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1, TestFunction.lineDerivCLM_eq_fderivCLM, TopologicalAddGroup.IsSES.integrate_mono, HasDerivWithinAt.div, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, Bornology.IsVonNBounded.sub, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, Path.range_segment, instIsStrictOrderedModuleOfIsCancelAdd, segment_subset_Icc, convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic, TemperedDistribution.fourier_lineDerivOp_eq, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, groupHomology.inhomogeneousChains.d_single, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', Matrix.l2_opNNNorm_def, ContinuousLinearEquiv.strictConvex_image, ContinuousMultilinearMap.instIsBoundedSMul, hasDerivAtFilter_sub_const_iff, SmoothPartitionOfUnity.finsum_smul_mem_convex, spectrum.hasDerivAt_resolvent, Module.Basis.sum_toMatrix_smul_self, AdicCompletion.val_apply_mem_smul_top_iff, ContinuousLinearMap.adjointAux_adjointAux, MvPolynomial.mkDerivation_monomial, smul_nonpos_iff_neg_imp_nonneg, Finsupp.linearCombination_single, HasStrictDerivAt.const_add, realPart_I_smul, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, Submodule.exists_smul_notMem_of_rank_lt, Convex.add_smul, Ideal.coe_smul_primesOver_mk, linearIndependent_smul, Seminorm.exists_apply_eq_finset_sup, PolynomialModule.smul_apply, ContMDiffAt.clm_precomp, NonUnitalAlgHom.coe_mulHom_mk, gauge_def, MultilinearMap.coe_smul, Complex.hasDerivAt_logTaylor, TestFunction.lineDerivCLM_apply, Multiset.sum_smul, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem, Mathlib.Tactic.Module.NF.zero_sub_eq_eval, deriv_smul, nnnorm_cfcₙ_nnreal_lt_iff, Prod.image_mk_segment_right, VectorField.mpullbackWithin_smul_apply, PositiveLinearMap.gnsStarAlgHom_apply, Absorbs.add, NNReal.coe_nnqsmul, Real.fourier_iteratedDeriv, MonoidAlgebra.smul_single', MeasureTheory.Integrable.smul_of_top_left, MeasureTheory.integral_comp_rpow_Ioi, Asymptotics.IsBigOTVS.symm, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, Polynomial.wronskianBilin_apply, convex_closedEBall, hasDerivAt_iff_tendsto_slope_zero, StrictConvex.affine_preimage, ConvexOn.convex_re_epigraph, IsExposed.convex, LinearMap.norm_extendTo𝕜'_apply_sq, Asymptotics.isLittleOTVS_iff_isLittleO, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, AffineSubspace.wSameSide_smul_vsub_vadd_left, TrivSqZeroExt.inv_inv, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, HasFTaylorSeriesUpToOn.hasFDerivAt, WeakFEPair.hf_zero, convex_ball, prodXSubSMul.coeff, real_inner_smul_right, groupHomology.isBoundary₂_iff, scalarSMulCLE_apply, ContinuousLinearMap.flip_add, QuadraticMap.polar_smul_left, exists_pos_left_iff_sameRay, hasFiniteFPowerSeriesAt_const, MeasureTheory.Integrable.toL1_smul', Seminorm.uniformContinuous, infDist_smul₀, Submodule.smul_mem_iff_of_isUnit, ContinuousAlternatingMap.hasBasis_nhds_zero, Orientation.oangle_sub_right_smul_rotation_pi_div_two, MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport, Bornology.isBounded_iff_isVonNBounded, Antivary.sum_smul_lt_sum_smul_comp_perm_iff, Convex.min_le_combo, monovaryOn_iff_smul_rearrangement, VectorFourier.fourierSMulRight_apply, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, ConcaveOn.translate_right, Derivation.leibniz, ContinuousLinearMap.isSelfAdjoint_iff', HasFDerivWithinAt.restrictScalars, LinearIsometry.map_smulₛₗ, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, OrthonormalBasis.equiv_apply_euclideanSpace, RootPairing.PolarizationIn_apply, Polynomial.sylvesterDeriv_updateRow, Convex.interior, StrongConcaveOn.strictConcaveOn, CochainComplex.HomComplex.Cochain.rightShift_smul, RatFunc.instIsScalarTowerPolynomial, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, LinearMap.liftQ₂_mk, Matrix.mulVec_smul, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Seminorm.coe_sSup_eq', ContinuousMultilinearMap.uncurryRight_apply, HasDerivAt.comp_const_add, ContinuousLinearMap.isVonNBounded_iff, SchwartzMap.fourierMultiplierCLM_ofReal, InnerProductSpace.Core.inner_smul_ofReal_left, Real.isScalarTower, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, differentiableWithinAt_iff_restrictScalars, IsModuleTopology.iso, NormedSpace.normalize_smul_of_neg, TrivSqZeroExt.exp_def, derivWithin_comp_mul_left, Seminorm.coe_bot, hasDerivAt_circleMap, vectorSpan_segment, ProperCone.smul_mem, derivWithin_fun_smul, ContinuousLinearMap.bilinearComp_zero, MeasureTheory.integral_fun_norm_addHaar, HasFDerivAt.fun_pow', LocalizedModule.subsingleton_iff, Convex.mem_toCone, MeasureTheory.setIntegral_ge_of_const_le, HasDerivWithinAt.scomp_hasDerivAt_of_eq, imaginaryPart_apply_coe, ContinuousLinearMap.isVonNBounded_image2_apply, segment_same, MulSemiringActionHom.map_one', iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, pinGroup.conjAct_smul_range_ι, LinearMap.lsmul_apply, HasMFDerivWithinAt.mul', intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, segment_subset_closedBall_left, UnitAddTorus.hasSum_mFourier_series_L2, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, Submodule.smul_closure_subset, HasFTaylorSeriesUpToOn.shift_of_succ, CentroidHom.instSMulCommClass_1, ConvexCone.mem_add, SemimoduleCat.Algebra.instSMulCommClassCarrier, QuotSMulTop.map_exact, Representation.asModuleEquiv_symm_map_rho, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, HasDerivWithinAt.neg, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, ContinuousLinearMap.norm_extendTo𝕜'_bound, sum_mem_ball_of_strictConvexSpace, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, Polynomial.degree_sum_eq_of_linearIndepOn, le_egauge_smul_right, ContinuousMultilinearMap.integral_apply, NonUnitalSubalgebra.unitization_apply, SeminormFamily.basisSets_smul, iteratedDerivWithin_const_smul, DualNumber.lift_apply_apply, HasStrictDerivAt.smul_const, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LocalizedModule.smul_def, Submodule.span_eq_iUnion_nat, HasStrictDerivAt.sub, groupHomology.single_isCycle₂_iff, SameRay.sameRay_nonneg_smul_right, MeasureTheory.SimpleFunc.setToSimpleFunc_smul, HasFiniteFPowerSeriesOnBall.neg, ModuleTopology.eq_coinduced_of_surjectiveₛₗ, CentroidHom.instIsScalarTower_1, Basis.multilinearMap_apply_apply, HasDerivWithinAt.Ioo_of_Ioi, Finset.weightedVSubOfPoint_smul, MeasureTheory.average_union_mem_segment, lineDifferentiableWithinAt_smul_iff, Fintype.expect_ite_mem, LinearMap.convexOn, DifferentiableWithinAt.smul_const, SMulCommClass.rat', MultilinearMap.dfinsuppFamilyₗ_apply, cfcₙ_real_eq_nnreal, Submodule.le_span_singleton_iff, hasDerivAt_fourier, HahnSeries.SummableFamily.coeff_smul, Asymptotics.IsBigOTVS.congr_right, ContinuousLinearEquiv.smulLeft_apply_apply, DiffContOnCl.circleAverage_poissonKernel_smul, QuadraticMap.half_moduleEnd_apply_eq_half_smul, smul_lie, Seminorm.neg_closedBall, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, AffineMap.lineMap_apply, Finsupp.linearCombination_unique, DistribMulAction.toLinearEquiv_apply, TrivSqZeroExt.inr_mul_inl, smul_eq_zero_iff_right, AntivaryOn.sum_smul_comp_perm_eq_sum_smul_iff, StrongDual.extendRCLikeₗᵢ_symm_apply, Asymptotics.IsThetaTVS.isBigOTVS, MultilinearMap.map_update_smul', Real.fourier_bilin_convolution_eq, BoxIntegral.BoxAdditiveMap.toSMul_apply, RatFunc.irreducible_minpolyX, IsLocalizedModule.mk'_cancel_right, AntitoneOn.quasiconcaveOn, segment_eq_image', CStarMatrix.mul_entry_mul_eq_inner_toCLM, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Module.supportDim_quotSMulTop_succ_eq_supportDim, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, ConvexOn.smul_concaveOn, homeomorphSphereProd_symm_apply_coe, Subring.smul_mem_pointwise_smul_iff₀, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Submodule.convex, ExteriorAlgebra.toTrivSqZeroExt_ι, FormalMultilinearSeries.le_comp_radius_of_summable, ContinuousLinearMap.le_opNorm₂, ContinuousLinearMap.lpPairing_eq_integral, TrivSqZeroExt.snd_invOf, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, slope_fun_def, Seminorm.continuous_iff, HasFDerivAt.smul_const, MeasureTheory.integrable_tilted_iff, Submodule.mem_smul_pointwise_iff_exists, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀, ContinuousLinearMap.norm_uncurryMid, Submodule.torsionBy.mk_ideal_smul, TopologicalGroup.IsSES.pushforward_apply_apply, isIntegralCurveOn_comp_mul_ne_zero, Submodule.mem_span_iff_of_fintype, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, ContinuousLinearMap.uncurryLeft_norm, DualNumber.ringHom_ext_iff, star_inv_natCast_smul, TestFunction.instLineDerivLeftSMulRealTopENat, mellin_eq_fourierIntegral, mem_vectorSpan_pair_rev, PiTensorProduct.smul_tprodCoeff_aux, hasStrictDerivAt_abs_neg, HasFDerivAt.comp_hasDerivWithinAt, ContinuousLinearMap.holder_smul_right, WithSeminorms.continuous_seminorm, HasFPowerSeriesOnBall.tendstoUniformlyOn', extremePoints_closedBall_subset_sphere, HasFPowerSeriesWithinOnBall.const_smul, HVertexOperator.coeff_inj, PolynomialModule.smul_single_apply, TensorProduct.rid_tmul, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, Asymptotics.IsLittleOTVS.comp_tendsto, TrivSqZeroExt.inl_mul_inl, Subalgebra.smul_mem_pointwise_smul, Mathlib.Tactic.Module.NF.neg_eq_eval, Representation.TensorProduct.rid_apply, SchwartzMap.fourierMultiplierCLM_const, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, fderivWithin_const_smul_of_invertible, Real.fourierIntegral_eq', Real.circleAverage_fun_smul, RootPairing.coroot_root_two, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, TestFunction.monoCLM_eq_of_scalars, Ideal.inertiaEquiv_symm_apply_smul, UniformConvergenceCLM.isVonNBounded_image2_apply, CategoryTheory.ShortComplex.cyclesMap'_smul, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', intervalIntegral.integral_comp_smul_deriv', EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Complex.hasSum_taylorSeries_on_emetric_ball, LinearEquiv.smulOfNeZero_apply, HasStrictDerivAt.of_notMem_tsupport, fderiv_continuousMultilinear_apply_const_apply, MeasureTheory.integrable_withDensity_iff_integrable_smul, Asymptotics.IsLittleOTVS.congr, MeasureTheory.Integrable.convolution_integrand, LieModule.exists_forall_lie_eq_smul, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Projectivization.exists_smul_eq_mk_rep, Module.reflection_mul_reflection_pow_apply_self, DivisibleHull.qsmul_def, hasFPowerSeriesOn_cauchy_integral, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, MvPolynomial.coeff_rTensorAlgHom_tmul, antitone_smul_left, LinearEquiv.fixedReduce_eq_smul_iff, concaveOn_of_convex_hypograph, StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, EuclideanGeometry.inversion_def, Matrix.trace_single_mul, NormedSpace.vonNBornology_eq, KaehlerDifferential.isBaseChange, Function.Periodic.const_smul₀, ConvexBody.smul_le_of_le, ConvexOn.lt_right_of_left_lt', SchwartzMap.integral_bilinear_laplacian_right_eq_left, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, KaehlerDifferential.instSMulCommClassTensorProduct, iteratedDeriv_fun_const_smul_field, DomMulAct.mk_smul_mulDistribActionHom_apply, HasFDerivAt.lim, RatFunc.Luroth.algEquiv_X, Seminorm.comp_apply, hasDerivWithinAt_const, openSegment_eq_image_lineMap, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', intervalIntegral.integral_comp_sub_mul, multiple_mem_span_of_mem_localization_span, OrthonormalBasis.sum_repr_symm, homeomorphUnitSphereProd_apply_fst_coe, CFC.posPart_smul_of_nonneg, MultilinearMap.cons_smul, Pi.single_smul₀, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, DifferentiableWithinAt.restrictScalars_fderivWithin, isCompact_closedAbsConvexHull_of_totallyBounded, HasStrictFDerivAt.continuousAlternatingMap_apply, Orthonormal.inner_left_sum, NonUnitalSubalgebra.instSMulMemClass, Orientation.inner_smul_rotation_pi_div_two_right, MatrixEquivTensor.invFun_smul, UniformConcaveOn.concaveOn, DiscreteConvolution.AddConvolutionExistsAt.convolution_vadd, StrongDual.extendRCLikeₗ_symm_apply, HasDerivAtFilter.congr_of_eventuallyEq, HasStrictDerivAt.complexToReal_fderiv', Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric, constFormalMultilinearSeries_apply_of_nonzero, RootPairing.CoPolarization_apply, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', Matrix.linftyOpNormSMulClass, finsuppTensorFinsuppRid_single_tmul_single, Real.circleAverage_smul, LieModule.shiftedGenWeightSpace.coe_lie_shiftedGenWeightSpace_apply, star_qsmul, Subalgebra.inclusion.isScalarTower_right, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, WithLp.normSMulClassSeminormedAddCommGroupToProd, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, VectorField.lieBracket_const_smul_right, Module.preReflection_apply, Asymptotics.isBigOTVS_pi, SkewMonoidAlgebra.sum_smul_index, DFinsupp.instPosSMulReflectLE, Derivation.smul_apply, PiLp.smul_apply, TrivSqZeroExt.hasSum_expSeries_of_smul_comm, DifferentiableWithinAt.clm_comp, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, MDifferentiableOn.cle_arrowCongr, PiLp.normSMulClassSeminormedAddCommGroupToPi, Polynomial.degree_smul_of_isRightRegular_leadingCoeff, MeasureTheory.uniformIntegrable_average, LinearIsometryEquiv.strictConvex_image, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', CochainComplex.HomComplex.Cochain.shift_units_smul, Algebra.Extension.contangentEquiv_tmul, Unitization.norm_def, convex_uIcc, ContMDiff.clm_bundle_apply₂, RatFunc.natDegree_minpolyX, ModuleTopology.eq_coinduced_of_surjective, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, Ideal.quotOfMul_surjective, Real.iteratedDeriv_fourier, map_natCast_smul, SchwartzMap.eLpNorm_le_seminorm, MDifferentiableAt.smul, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, HasStrictDerivAt.const_smul, StrictConvex.add, HasDerivAt.fun_sum, hasFDerivAtFilter_iff_isLittleOTVS, MeasureTheory.setIntegral_rnDeriv_smul', FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, TensorProduct.finsuppScalarLeft_apply_tmul_apply, TrivSqZeroExt.snd_pow_of_smul_comm, second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonneg, ContinuousMultilinearMap.curryRight_apply, CategoryTheory.Abelian.Ext.comp_smul, Ideal.pointwise_smul_eq_comap, Distribution.dsupport_smulLeftCLM_subset, ArithmeticFunction.mul_smul', DFinsupp.instPosSMulMono, Balanced.absorbs_self, CategoryTheory.Linear.comp_smul, star_nnqsmul, HasFPowerSeriesOnBall.uniform_geometric_approx', image_segment, intervalIntegral.smul_integral_comp_mul_left, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul, AddMonoidHom.coe_smul, ZeroAtInftyContinuousMap.instSMulCommClass, Function.support_const_smul_of_ne_zero, ContinuousLinearMap.extendTo𝕜_apply, Submodule.starConvex, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, PowerSeries.coeff_smul, Module.AEval.of_symm_X_smul, MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct, HasFDerivAt.comp_hasDerivWithinAt_of_eq, Convex.gauge_le, convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Ici, Derivation.leibniz_of_mul_eq_one, matrixEquivTensor_apply_symm, uniformConcaveOn_zero, AffineSubspace.mem_affineSpan_insert_iff, ConvexCone.pointed_zero, LieModule.traceForm_eq_sum_finrank_nsmul, LieAlgebra.Basis.baseSupp_apply_smul_e, Seminorm.closedBall_eq_emptyset, Convex.strictConvex', egauge_le_of_smul_mem, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, LinearMap.det_restrictScalars, hasStrictFDerivAt_pow', convex_Icc, IsBoundedSMul.of_enorm_smul_le, ContinuousLinearMap.applySMulCommClass, strictConvex_Ioc, LinearMap.flip_injective_iff₂, RestrictScalars.ringEquiv_map_smul, AddSubmonoid.smul_mem_pointwise_smul_iff₀, ContinuousLinearMap.norm_extendTo𝕜', InnerProductGeometry.angle_smul_smul, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, RestrictScalars.lsmul_apply_apply, IsIntegralClosure.range_le_span_dualBasis, Matrix.toLin_apply, IsStarProjection.inr, Asymptotics.IsLittleOTVS.fun_symm, HasDerivAtFilter.const_add, smul_sub, HasDerivWithinAt.of_notMem_tsupport, StrictConvex.preimage_smul, not_linearIndependent_iff_finsupp, MDifferentiableAt.clm_precomp, ModelWithCorners.convex_range, ContDiffMapSupportedIn.postcompCLM_apply, SchwartzMap.compSubConstCLM_comp, HasDerivWithinAt.mono_of_mem_nhdsWithin, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, ContinuousAlternatingMap.curryLeft_zero, RootPairing.reflection_dualMap_eq_coreflection, Matrix.Module.smul_apply, DualNumber.coe_lift_symm_apply, ContDiffBump.integral_normed_smul, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, MultilinearMap.freeFinsuppEquiv_apply, Orientation.oangle_sign_smul_right, Module.Basis.constr_apply_fintype, fwdDiff_smul, Asymptotics.IsTheta.isThetaTVS, LieSubmodule.Quotient.isCentralScalar, AddMonoidAlgebra.liftMagma_apply_apply, ContinuousAlternatingMap.cons_smul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, inhomogeneousCochains.d_hom_apply, ZMod.dft_dft, SmoothBumpFunction.contMDiff_smul, Quaternion.imJ_snd_dualNumberEquiv, HasDerivWithinAt.Ioi_of_Ioo, HasDerivWithinAt.fun_mul, DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap, AbsConvex.closure, Filter.Tendsto.zero_smul_isBoundedUnder_le, fderiv_fun_mul', TrivSqZeroExt.liftEquivOfComm_apply, Finset.centerMass_segment', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFDerivAt.const_smul, AdicCompletion.pow_smul_top_le_ker_eval, NormedSpace.expSeries_sum_eq_rat, Submodule.top_le_span_range_iff_forall_exists_fun, HasFPowerSeriesWithinAt.prod, HasDerivWithinAt.pow', LinearPMap.map_smul, ContMDiffMap.coe_smul, Set.neg_smul_set, LinearMap.concaveOn, MulSemiringActionHom.map_mul', Derivation.instIsCentralScalar, IsLocalizedModule.exists_integer_multiple, ContinuousLinearMap.adjoint_comp_self_injective_iff, Convex.is_linear_image, FormalMultilinearSeries.leftInv_coeff_one, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul', Module.Basis.smul_eq_map, MultilinearMap.smulRight_apply, Submodule.singleton_set_smul, PosSMulReflectLT.toPosSMulReflectLE, SkewMonoidAlgebra.support_mul_single_subset, sameRay_iff_inv_norm_smul_eq, mdifferentiableOn_continuousLinearMapCoordChange, instIsPushoutPolynomial, hasDerivAtFilter_intCast, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, MonoidAlgebra.instIsPushout', Asymptotics.IsThetaTVS.symm, Polynomial.aeval_apply_smul_mem_of_le_comap', BoxIntegral.integral_smul, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH, AddMonoidAlgebra.liftNC_smul, Submodule.exists_smith_normal_form_of_rank_eq, MeasureTheory.L1.setToL1_smul, hasFPowerSeriesAt_pi_iff, IsEllDivSequence.smul, MeasureTheory.eLpNorm'_const_smul, IsBaseChange.iff_lift_unique, QuadraticMap.canLift', ProbabilityTheory.integral_tilted_mul_eq_mgf, MeasureTheory.integral_simpleFunc_larger_space, Antitone.convex_gt, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, finrank_eq_one_iff', ContDiffBump.apply, TrivSqZeroExt.isUnit_inv_iff, CStarMatrix.smul_mul, Seminorm.ball_zero_absorbs_ball_zero, Module.Basis.smulTower'_apply, Submodule.pointed_toConvexCone, Orientation.oangle_sign_add_smul_left, Submodule.span_range_update_sub_smul, Submodule.topologicalClosure_mem_invtSubmodule, HasFDerivAt.lim_real, OrderDual.instSMulPosMono, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, exists_open_convex_of_notMem, lp.coeFn_smul, smul_upperBounds_subset_lowerBounds_smul, InnerProductSpace.isStarProjection_rankOne_self, MulSemiringAction.charpoly_eq, StrictConvex.smul, ProperCone.relative_hyperplane_separation, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, affineSegment_eq_segment, DomMulAct.mk_smul_linearMap_apply, ContinuousAffineMap.coe_smul, Quaternion.snd_imK_dualNumberEquiv_symm, strictConvex_Ico, HasFPowerSeriesAt.hasFDerivAt, StrictConvex.linearIsometry_preimage, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, ConcaveOn.openSegment_subset_strict_hypograph, smul_add, ConvexCone.coe_positive, Bornology.IsVonNBounded.extend_scalars, ContinuousMultilinearMap.smul_apply, analyticAt_iff_analytic_smul, Asymptotics.IsBigOTVS.congr, LinearEquiv.smul_apply, instInvertibleReprₛ, Submodule.range_powSMulQuotInclusion, StrongDual.extendRCLikeₗᵢ_apply, UniformConcaveOn.strictConcaveOn, Subalgebra.inclusion.faithfulSMul, HasDerivAt.ofReal_comp, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, ContinuousOn.cfcₙ_nnreal', DFinsupp.sigmaUncurry_smul, DivisibleHull.qsmul_of_nonneg, LinearMap.mkContinuous₂_norm_le, CochainComplex.HomComplex.Cochain.units_smul_v, IsBilinearMap.smul_left, MvPowerSeries.le_order_smul, SkewMonoidAlgebra.coeff_mul_single, HomologicalComplex.smul_f_apply, IsLocalizedModule.smul_inj, FormalMultilinearSeries.zero_radius, smul_unitBall, IsLocalization.linearMap_compatibleSMul, IsCompactOperator.smul_unit_iff, intervalIntegral.integral_const_of_cdf, Algebra.Extension.H1Cotangent.val_smul, DifferentiableWithinAt.const_smul, PolynomialModule.instIsScalarTower, NonUnitalAlgHom.toFun_eq_coe, WithSeminorms.congr_equiv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Matrix.detp_smul_adjp, intervalIntegral.integral_const', TrivSqZeroExt.inv_neg, MeasureTheory.condExp_smul_of_aestronglyMeasurable_left, VertexOperator.ext_iff, StrictConcaveOn.map_sum_eq_iff', Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral, hasStrictDerivAt_const, Set.smul_mem_center, SkewMonoidAlgebra.support_mul, DistribMulAction.toAddEquiv_apply, PosSMulMono.toSMulPosMono, Derivation.coe_smul, intervalIntegral.integral_smul_deriv_eq_deriv_smul, ContinuousLinearMap.self_comp_adjoint_injective_iff, Module.algebraMap_end_apply, hasStrictFDerivAt_list_prod_attach', Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsLocalizedModule.iso_symm_apply_aux, HasStrictDerivAt.scomp, Orientation.oangle_sub_left_smul_rotation_pi_div_two, HasFPowerSeriesWithinAt.restrictScalars, tangentConeAt_real_subset_isRCLikeNormedField, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, integral_withDensity_eq_integral_toReal_smul, ZLattice.covolume.tendsto_card_div_pow', MvPolynomial.ker_eval₂Hom_universalFactorizationMap, WithCStarModule.instContinuousSMul, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, MeasureTheory.Lp.instIsCentralScalar, fderiv_continuousAlternatingMap_apply_apply, Matrix.scalar_comm_iff, SchwartzMap.hasDerivAt, HasDerivWithinAt.fun_sub, Module.End.mem_eigenspace_iff, lp.single_smul, Seminorm.inf_apply, TrivSqZeroExt.sndHom_comp_map, PiTensorProduct.mapLMultilinear_apply_apply, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, RatFunc.minpolyX_eq_zero_iff, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, Units.neg_smul, HasFDerivWithinAt.clm_comp, AddMonoid.End.smulCommClass, ContinuousLinearMap.evalL_apply, AddMonoidAlgebra.smul_single', LinearPMap.supSpanSingleton_apply_smul_self, CategoryTheory.Functor.map_units_smul, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, ContinuousLinearEquiv.map_smulₛₗ, Submodule.mem_span_range_iff_exists_fun, Unitization.nnreal_cfcₙ_eq_cfc_inr, exteriorPower.presentation_relation, NonUnitalSeminormedRing.isBoundedSMul, StarConvex.add_smul_sub_mem, hasDerivAtFilter_iff_tendsto, AddMonoid.End.applyFaithfulSMul, Matrix.single_mul_eq_updateRow_zero, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, convex_hyperplane, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, CStarModule.inner_smul_left_real, HasStrictDerivAt.comp, HVertexOperator.ext_iff, Finset.weightedVSubOfPoint_apply_const, PosSMulMono.toPosSMulStrictMono, InnerProductSpace.HarmonicOnNhd.const_smul, hasStrictFDerivAt_ringInverse, KaehlerDifferential.map_compDer, OrderDual.instSMulPosReflectLT, MeasureTheory.setIntegral_indicatorConstLp, InnerProductSpace.HarmonicContOnCl.fun_const_smul, LinearMap.liftBaseChange_tmul, ContinuousLinearMap.mul_apply', starConvex_singleton, AffineSubspace.wOppSide_smul_vsub_vadd_right, fromTangentSpace_mfderiv_smul, TrivSqZeroExt.map_comp_map, CStarMatrix.reindexₐ_symm, ContDiff.smul, ConcaveOn.add, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, signedDist_smul, LieModule.Cohomology.smul_apply_apply, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_pos, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, smulAddHom_apply, MeasureTheory.convolution_lsmul_swap, Orientation.oangle_add_right_smul_rotation_pi_div_two, TestFunction.mkCLM_apply, FixedPoints.smul_polynomial, PolyEquivTensor.toFunBilinear_apply_apply, Ideal.IsPrime.smul, LinearEquiv.apply_smulCommClass', HasDerivAtFilter.comp_of_eq, Module.End.instSMulCommClass', Orientation.inner_smul_rotation_pi_div_two_left, lp.instIsCentralScalarSubtypePreLpMemAddSubgroup, hasDerivAtFilter_finCons', Asymptotics.IsBigOTVS.eventually_smallSets, MeasureTheory.Supermartingale.smul_nonpos, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Matrix.ofNat_mulVec, PolyEquivTensor.toFunLinear_tmul_apply, TensorProduct.smul_tmul', ContinuousMap.toLp_injective, StrictConcaveOn.map_sum_eq_iff, TestFunction.fderivCLM_eq_of_scalars, midpoint_vsub_right, setIntegral_withDensity_eq_setIntegral_smul, IsLocalizedModule.mk'_smul_mk', ConcaveOn.translate_left, Function.Antiperiodic.const_smul₀, Module.End.instIsScalarTower, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, StrictConvexOn.convex_lt, hasDerivWithinAt_finCons', AffineMap.coe_lineMap, mellin_comp_rpow, ProbabilityTheory.integral_poissonMeasure, TrivSqZeroExt.instL1IsBoundedSMul, VectorField.mpullbackWithin_const_smul_apply, Finsupp.toDFinsupp_smul, IsAddUnit.smul_left, MeasureTheory.Submartingale.sum_smul_sub', Asymptotics.Filter.Tendsto.isBigOTVS_one, StarConvex.preimage_add_left, antivaryOn_iff_smul_rearrangement, MulActionHom.coe_neg, TestFunction.lineDerivCLM_eq_of_scalars, convex_RCLike_iff_convex_real, PointedCone.mem_span_set, Representation.norm_ofDistribMulAction_eq, Module.End.HasUnifEigenvector.apply_eq_smul, MultilinearMap.freeFinsuppEquiv_single, IsFractionRing.stabilizerHom_apply_apply_mk, intervalIntegral.smul_integral_comp_mul_add, dotProduct_smul, IsIntegralCurveAt.comp_mul_ne_zero, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Module.AEval.X_smul_of, Convex.combo_closure_interior_mem_interior, InnerProductSpace.rankOne_comp, CochainComplex.HomComplex.Cochain.rightShift_units_smul, Module.End.apply_smulCommClass, Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Finset.sum_range_by_parts, Asymptotics.IsTheta.const_smul_left, CliffordAlgebra.invOf_ι, DifferentiableWithinAt.fun_smul, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, Rep.leftRegularHom_hom_single, HasDerivWithinAt.scomp, lp.instIsScalarTowerPreLp, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, TrivSqZeroExt.snd_pow_of_smul_comm', Asymptotics.IsLittleOTVS.snd, hasFPowerSeriesWithinAt_pi_iff, CircleIntegrable.const_fun_smul, IsLocalizedModule.exists_of_eq, MeasureTheory.eLpNorm_const_smul, hasDerivWithinAt_comp_mul_left_smul_iff, Ideal.restrictScalars_mul, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, hasDerivAt_iff_isLittleO_nhds_zero, inner_smul_right, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, QuadraticMap.toFun_smul, SchwartzMap.tsupport_smulLeftCLM_subset, DFinsupp.instSMulPosReflectLT, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, HasFDerivWithinAt.continuousMultilinear_apply_const, Bornology.IsVonNBounded.vadd, LinearMap.equivariantProjection_apply, cfcₙHom_real_eq_restrict, MvPolynomial.rTensor_symm_apply_single, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, LinearMap.polar_AbsConvex, vadd_openSegment, MeasureTheory.ComplexMeasure.im_apply, LinearMap.IsPerfPair.bijective_right, PiTensorProduct.liftIsometry_comp_mapL, iteratedFDeriv_smul_const_apply, FractionalIdeal.den_mul_self_eq_num, HasStrictDerivAt.fun_const_smul, MeasureTheory.Measure.addHaar_smul_of_nonneg, add_smul, HasDerivWithinAt.congr_deriv, CochainComplex.HomComplex.Cochain.rightUnshift_smul, Seminorm.continuous_iSup, RootPairing.pairingIn_one_four_iff, MeasureTheory.Lp.instIsBoundedSMul, RootPairing.Equiv.instSMulCommClassAut, InnerProductSpace.isSymmetric_rankOne_self, AddSubgroup.smul_mem_pointwise_smul, Orientation.oangle_smul_right_of_neg, ContinuousLinearMap.toSpanSingleton_comp_toSpanSingleton, Seminorm.ball_smul_ball, IsSMulRegular.of_flat_of_isBaseChange, ContinuousMap.coe_toLp, Real.fourierIntegral_convergent_iff, SkewMonoidAlgebra.smul_sum, skewAdjointPart_apply_coe, continuousMultilinearCurryLeftEquiv_apply, SkewMonoidAlgebra.coeff_mul_single_one, IsIntegralCurveAt.hasDerivAt, convex_stdSimplex, linearIndependent_add_smul_iff, MonoidAlgebra.GroupSMul.linearMap_apply, ContinuousMapZero.instSMulCommClass', MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff, Seminorm.coe_sSup_eq, Ideal.smul_mem_pointwise_smul, ConvexBody.nonempty, MeasureTheory.integral_rnDeriv_smul, Asymptotics.IsBigOTVS.rfl, fourierCoeff_eq_intervalIntegral, Seminorm.bddBelow_range_add, NonUnitalSubalgebra.instSMulCommClass', CStarAlgebra.conjugate_le_norm_smul', Asymptotics.IsLittleOTVS.bot, IsSemisimpleModule.exists_end_algEquiv, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, RootPairing.weylGroup.ofIdx_smul, ContinuousLinearMap.isBigOTVS_comp, ContDiffAt.smul_const, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, Module.supportDim_le_supportDim_quotSMulTop_succ, AnalyticAt.exists_eq_sum_add_pow_mul, QuotSMulTop.equivQuotTensor_naturality_mk, inner_sum_smul_sum_smul_of_sum_eq_zero, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, WithLp.smul_fst, iteratedDerivWithin_comp_const_smul, StrictConvexSpace.extremePoints_closedBall_eq_sphere, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Rat.instIsScalarTowerRight, Complex.taylorSeries_eq_on_eball, MeasureTheory.Measure.map_addHaar_smul, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, ContinuousLinearMap.intervalIntegral_apply, Function.noZeroSMulDivisors, span_fourierLp_closure_eq_top, smul_finsum', selfAdjointPartL_apply_coe, HasFDerivWithinAt.comp_hasDerivWithinAt, PMF.integral_eq_sum, MeasureTheory.average_add_measure, hasDerivAt_intCast, Seminorm.absorbent_ball_zero, IsRegular.smul_eq_zero_iff_right, PiTensorProduct.liftIsometry_symm_apply, Derivation.tensorProductTo_mul, IsCompactOperator.smul_iff₀, fderivWithin_continuousAlternatingMap_apply_apply, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, RootPairing.pairingIn_neg_one_neg_four_iff, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonpos, Polynomial.smeval_at_zero, RestrictScalars.addEquiv_symm_map_smul_smul, IsBilinearMap.smul_right, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, PowerSeries.constantCoeff_smul, FormalMultilinearSeries.leftInv_comp, LieModule.smul_lie, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Submodule.span_range_update_add_smul, ValuationSubring.ofPrime_scalar_tower, IsLocalization.smul_mem_iff, Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, HasFPowerSeriesAt.const_smul, iteratedFDeriv_succ_eq_comp_right, Complex.re_qsmul, ContinuousMultilinearMap.changeOriginSeries_support, WeakFEPair.functional_equation₀, DiscreteConvolution.AddConvolutionExistsAt.vadd_convolution, CFC.nnrpow_le_nnrpow, Finsupp.linearCombination_comp_addSingleEquiv, convex_multiset_sum, Real.tendsto_integral_cexp_sq_smul, Asymptotics.isBigOTVS_fun_comm, TrivSqZeroExt.algebraMap_eq_inl, ContDiffMapSupportedIn.seminorm_apply, AddMonoidHom.smul_apply, AffineSubspace.sSameSide_smul_vsub_vadd_right, Matrix.toLinAlgEquiv_apply, WithSeminorms.tendsto_nhds_atTop, Submodule.mem_smul_top_iff, aemeasurable_withDensity_iff, derivWithin_const_smul, HasFDerivAt.isThetaTVS_sub, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, DifferentiableAt.clm_comp, SubmodulesRingBasis.leftMul, Fintype.not_linearIndependent_iff, DistribMulActionHom.map_zero', Monovary.sum_smul_comp_perm_lt_sum_smul_iff, MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff, QuadraticMap.weightedSumSquares_apply, CochainComplex.HomComplex.Cochain.smul_v, ODE.hasDerivWithinAt_picard_Icc, Module.support_quotSMulTop, signedDist_smul_of_neg, MeasureTheory.lpNorm_const_smul, VectorField.lieBracket_smul_left, DualNumber.range_inlAlgHom_sup_adjoin_eps, Submodule.smul_one_eq_span, ContinuousLinearMap.rotation_apply, Real.iteratedFDeriv_fourier, Seminorm.smul_closedBall_subset, Submodule.span_singleton_smul_eq, circleAverage_sub_sub_inv_smul_of_differentiable_on, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, TopologicalAddGroup.IsSES.pushforward_def, DoubleCentralizer.algebraMap_fst, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, Submodule.mem_span_image_finset_iff_exists_fun, deriv_clm_comp, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, Submodule.mem_annihilator_span, Bornology.IsVonNBounded.of_topologicalSpace_le, DifferentiableAt.fun_smul, circleIntegral.integral_smul_const, ContDiffMapSupportedIn.structureMapCLM_top_apply, inner_smul_real_left, Submodule.span_smul, Balanced.zero_insert_interior, DistribMulActionHom.map_add', Submodule.map_pointwise_smul, Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card, IsLocalization.map_eq_toLinearMap_mapₐ, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, IsClosed.balancedCore, toSpanSingleton_derivWithin, Asymptotics.IsBigOTVS.triangle, fderiv_norm_smul, IsOrderedModule.of_smul_nonneg, isMIntegralCurveAt_comp_mul_ne_zero, ContinuousLinearMap.isEmbedding_restrictScalars, lowerBounds_smul_of_neg, spectrum.hasFDerivAt_resolvent, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, HasFDerivAt.hasFDerivAt_norm_smul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, HasFiniteFPowerSeriesOnBall.eq_partialSum', VectorField.mlieBracket_const_smul_left, exists_lt_of_gauge_lt, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, CategoryTheory.ShortComplex.homologyMap'_smul, StarModule.complexToReal, AffineSubspace.smul_mem_smul_iff, IsScalarTower.to_smulCommClass, HasDerivAt.comp_hasDerivWithinAt, Complex.wedgeIntegral_add_wedgeIntegral_eq, IsMIntegralCurve.comp_mul, IsBoundedBilinearMap.toContinuousLinearMap_apply, Module.annihilator_eq_bot, isSMulRegular_of_ker_lsmul_eq_bot, Bornology.isVonNBounded_sub, ModuleFilterBasis.smul', MatrixModCat.isScalarTower_toModuleCat, HasFDerivWithinAt.curveIntegral_segment_source, ModuleCat.restrictScalars.smul_def, LinearIndependent.sum_smul_of_nondegenerate, Subsemiring.coe_pointwise_smul, HasFPowerSeriesOnBall.pi, Submodule.toSubMulAction_strictMono, HasFPowerSeriesWithinOnBall.fderivWithin_eq, jacobson_density, nhds_basis_closed_balanced, Finsupp.instIsScalarTowerForall, ContinuousMultilinearMap.piₗᵢ_symm_apply, ray_pos_smul, Matrix.instIsScalarTowerForall, convex_parallelepiped, HasDerivAt.scomp, ContDiffMapSupportedIn.structureMapLM_top_apply, ContinuousLinearMap.ker_adjoint_comp_self, AnalyticAt.analyticOrderAt_ne_top, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, CochainComplex.HomComplex.Cochain.comp_units_smul, ContinuousLinearMap.smulRight_comp_smulRight, balancedCoreAux_subset, iteratedDerivWithin_fun_const_smul, Submodule.mem_span_pair, Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable, Matrix.toLinearMap₂_apply, Filter.Tendsto.isVonNBounded_range, HasDerivAt.const_mul, Real.hasFDerivAt_fourierIntegral, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, HasDerivWithinAt.congr, SchwartzMap.integralCLM_apply, IsCovariantDerivativeOn.add_one_form, Submodule.set_smul_eq_iSup, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, PolynormableSpace.withSeminorms', toAddMonoidHom_apply, ConvexBody.isClosed, hasDerivAt_one, HasDerivAtFilter.fun_neg, SameRay.exists_nonneg_left, MultilinearMap.freeDFinsuppEquiv_apply, CliffordAlgebra.forall_mul_self_eq_iff, LinearMap.IsSymmetric.apply_eigenvectorBasis, IsOpen.strictConvex_iff, RootPairing.coroot_root_eq_pairing, Matrix.Module.single_smul, hasFDerivAt_iff_isLittleOTVS, Polynomial.map_smul, Representation.smul_tprod_one_asModule, CFC.nnrpow_eq_nnrpow_pi, IsBoundedSMul.of_nnnorm_smul_le, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, AnalyticAt.const_smul, smul_nonneg_iff, KaehlerDifferential.kerTotal_mkQ_single_smul, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, MvPolynomial.rTensor_apply_monomial_tmul, ContinuousAt.clm_bundle_apply₂, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, HahnSeries.SummableFamily.binomialFamily_apply, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, ZMod.map_smul, Algebra.Generators.repr_CotangentSpaceMap, ContinuousMultilinearMap.isVonNBounded_image2_apply, DividedPowerAlgebra.dp_sum_smul, hasLineDerivAt_iff_tendsto_slope_zero, MultilinearMap.piFamily_smul, Ideal.mem_iInf_smul_pow_eq_bot_iff, HasFDerivAt.list_prod', MeasureTheory.SignedMeasure.singularPart_smul_nnreal, Function.Even.smul_odd, ProbabilityTheory.strong_law_Lp, separatingDual_iff_injective, fderivWithin_const_smul_field, Pi.openSegment_subset, fderiv_continuousMultilinearMapCompContinuousLinearMap, deriv_fun_const_smul, MeasureTheory.integral_const, LinearEquiv.isSMulRegular_congr', Module.Basis.smulTower_apply, Function.Antiperiodic.const_smul, LinearMap.map_smul₂, IsLocalizedModule.isScalarTower_module, AffineMap.homothety_apply, HasDerivWithinAt.smul_const, CStarAlgebra.star_left_conjugate_le_norm_smul, LinearMap.intrinsicStarModule, DifferentiableOn.smul, contDiff_nat_iff_continuous_differentiable, hasFDerivAt_pow', ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, sameRay_smul_right_iff_of_ne, absorbent_ball, MeasureTheory.Lp.simpleFunc.coe_smul, Seminorm.zero_or_exists_apply_eq_finset_sup, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, Module.End.span_orbit_mem_invtSubmodule, StarConvex.affinity, hasDerivAt_abs, LinearMap.IsContPerfPair.bijective_right, HasFiniteFPowerSeriesOnBall.add, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, iteratedDeriv_comp_const_sub, Submodule.coe_smul, ContinuousLinearMap.opNorm_lsmul_le, LinearMapClass.map_smul, Seminorm.ball_comp, FixedBy.intermediateField_mem_iff, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.mkContinuousMultilinear_norm_le, WithLp.instProdNormSMulClass, le_floorDiv_iff_mul_le, RootPairing.polarizationEquiv_symm_apply_coroot, ContDiffMapSupportedIn.monoCLM_eq_zero, StrictConvex.sum_mem_interior, DualNumber.commute_eps_left, KaehlerDifferential.isLocalizedModule, MulSemiringAction.toAlgEquiv_apply, hasDerivAt_natCast, IsMprojection.Mnorm, smul_vsub_rev_mem_vectorSpan_pair, HasDerivAtFilter.fun_sub, TrivSqZeroExt.kerIdeal_sq, RingHom.smul_def, ContinuousMap.coeFn_toLp, Seminorm.rescale_to_shell, AffineSubspace.direction_affineSpan_pair_le_iff_exists_smul, HasDerivWithinAt.union, gaugeRescale_def, Matrix.smul_mul, Nat.factorization_floorRoot, ConvexBody.isCompact, Real.hasDerivAt_Gamma_one, Convex.toCone_isLeast, segment_translate_image, ArithmeticFunction.smul_map, Real.fourier_bilin_convolution_eq_integral, Derivation.map_aeval, closedBall_normSeminorm, Complex.coe_smul, SchauderBasis.RankOneDecomposition.exists_coeff, ContinuousWithinAt.clm_bundle_apply₂, range_cfcₙ_nnreal_subset, Matrix.smul_eq_mulVec, ContinuousLinearMap.coe_restrictScalarsL, ModuleFilterBasis.smul_left, MemHolder.nnHolderNorm_smul, Matrix.detp_smul_add_adjp, Convex.combo_interior_self_mem_interior, HasDerivWithinAt.add_const, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, MeasureTheory.Integrable.integral_smul, lp.mem_lp_const_smul, Matrix.star_dotProduct_gram_mulVec, Bornology.IsVonNBounded.of_add_left, OpenPartialHomeomorph.univUnitBall_apply, LocalizedModule.instIsScalarTower, ContinuousLinearMap.norm_compL_le, Seminorm.continuousAt_zero_of_forall, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, Nat.floorRoot_def, EulerSine.antideriv_cos_comp_const_mul, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, Module.isTorsionBySet_quotient_iff, fderivWithin_clm_comp, integralClosure.coe_smul, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, sameRay_neg_smul_right_iff_of_ne, meromorphicOrderAt_smul_of_ne_zero, HasDerivWithinAt.congr_set, Submodule.mem_smul_span, Matrix.normSMulClass, Bornology.isVonNBounded_add, DualNumber.algHom_ext_iff, HasFPowerSeriesAt.sub, MvPolynomial.support_smul_eq, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, MeasureTheory.Lp.instSMulCommClass, BoxIntegral.integralSum_smul, taylor_integral_remainder_aux, OrderDual.instIsOrderedModule, Finset.centerMass_segment, Finsupp.sum_option_index_smul, OrthogonalFamily.range_linearIsometry, isIntegralCurve_comp_mul_ne_zero, TensorProduct.finsuppScalarLeft_apply_tmul, Real.tendsto_integral_exp_smul_cocompact, mellin_convergent_iff_norm, RestrictScalars.isScalarTower, MeasureTheory.setIntegral_tilted', fderiv_continuousMultilinear_apply_const, HasDerivWithinAt.smul, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq, Mathlib.Tactic.LinearCombination.smul_const_lt, ContinuousOn.integral_sub_linear_isLittleO_ae, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, MvPolynomial.tensorEquivSum_X_tmul_X, MeasureTheory.L1.SimpleFunc.integral_smul, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one, iteratedDerivWithin_smul, NonUnitalStarSubalgebra.instSMulCommClass', ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, ContinuousLinearMap.opNNNorm_mul_flip_apply, HasDerivWithinAt.fun_pow, PiTensorProduct.smul_tprodCoeff', HasDerivWithinAt.finset_prod, smul_le_smul_of_nonpos_left, IsNilpotent.exp_eq_sum, Nonneg.instNonUnitalContinuousFunctionalCalculus, ConvexOn.sub_strictConcaveOn, HasFPowerSeriesOnBall.hasFDerivAt, egauge_eq_zero_iff, HasDerivWithinAt.mono, Orientation.oangle_smul_smul_self_of_nonneg, AddSubmonoid.smul_subset_smul, Algebra.Extension.Cotangent.val_smul, MeromorphicNFAt.smul_analytic, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, zero_mem_absConvexHull, Submodule.powSMulQuotInclusion_mk, ContinuousMultilinearMap.curryMid_apply, AntitoneOn.quasilinearOn, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, inv_smul_lt_iff_of_neg, HasFDerivWithinAt.comp_hasDerivAt, SchwartzMap.compCLM_apply, AddSubgroup.smul_mem_pointwise_smul_iff₀, convex_Ici, Finset.weightedVSub_eq_linear_combination, TemperedDistribution.fourierMultiplierCLM_apply_apply, Module.Basis.map_orientation_eq_det_inv_smul, ClosedSubmodule.sInf_orthogonal, AlternatingMap.coeFn_smul, intervalIntegral.fderivWithin_integral_of_tendsto_ae, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, concaveOn_iff_pairwise_pos, HasDerivAt.mul, ContinuousMap.toLp_comp_toContinuousMap, Function.HasTemperateGrowth.smul, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Bornology.IsVonNBounded.add, HasStrictFDerivAt.isBigOTVS_sub, rescale_to_shell_zpow, ConvexCone.mem_zero, ContMDiff.clm_postcomp, Asymptotics.IsLittleOTVS.tendsto_inv_smul, PolynomialModule.eval_apply, LieAlgebra.isScalarTower, balanced_closedBall_zero, integrableOn_peak_smul_of_integrableOn_of_tendsto, TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent, Finset.neg_smul_finset, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, ModelWithCorners.convex_range', MeasureTheory.Lp.smul_comm, Submodule.smul_mem_iff, Module.End.baseChangeHom_apply_apply, isBoundedBilinearMap_smul, fderivWithin_continuousAlternatingMap_apply_const, ConcaveOn.map_add_sum_le, NonUnitalAlgHom.map_mul', EulerSine.antideriv_sin_comp_const_mul, LinearMap.map_smul, Module.End.instSMulCommClass, mapsTo_tangentConeAt_pi, Finset.sum_smul_sum_eq_sum_perm, strictConvex_singleton, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, ContinuousLinearMap.norm_restrictScalars, Asymptotics.IsLittleOTVS.isBigOTVS, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, coe_normSeminorm, MvPolynomial.tensorEquivSum_C_tmul_one, Submodule.restrictScalars.isScalarTower, Module.reflection_mul_reflection_zpow_apply_self, ConvexCone.coe_add, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, parallelepiped_eq_sum_segment, MDifferentiableWithinAt.clm_postcomp, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, WeakDual.instContinuousSMul, convex_Iio, Matrix.toLinAlgEquiv_self, RootPairing.coreflection_apply, convex_halfSpace_gt, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, HasDerivWithinAt.const_sub, Matrix.isAddUnit_detp_smul_mul_adjp, Algebra.Extension.tensorCotangentInvFun_smul_mk, ContDiffBump.convolution_eq_right, ContinuousMultilinearMap.map_update_smul, TemperedDistribution.instFourierInvSMul, sameRay_neg_smul_right_iff, MeasureTheory.AEEqFun.Integrable.smul, ExistsContDiffBumpBase.w_def, HasDerivWithinAt.const_smul, MeasureTheory.Measure.setIntegral_comp_smul, ContDiffOn.smul, mem_vectorSpan_pair, WeakFEPair.hf_modif_FE, HasDerivWithinAt.hasDerivAt, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, ContinuousLinearMap.opNorm_mul_apply_le, deriv_smul_const, intervalIntegral.integral_hasFDerivWithinAt, HasFPowerSeriesAt.tendsto_partialSum, Complex.ofReal_qsmul, TopologicalGroup.IsSES.pushforward_mono, ContinuousLinearMap.smul_def, ContinuousLinearMap.orthogonal_range, Antitone.quasilinearOn, HasFiniteFPowerSeriesAt.add, Matrix.conjTranspose_intCast_smul, HasFPowerSeriesAt.hasDerivAt, TensorProduct.AlgebraTensorModule.lift_apply, RatFunc.natDegree_num_le_natDegree_minpolyX, hasDerivWithinAt_congr_set', Finsupp.mem_span_range_iff_exists_finsupp, Module.Finite.toModuleEnd_moduleEnd_surjective, ContinuousLinearMap.isThetaTVS_comp, DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul, StrictConcaveOn.neg, fourierIntegral_half_period_translate, ediam_smul₀, CategoryTheory.ShiftedHom.map_smul, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, AddCommMonoid.nat_isScalarTower, ContinuousLinearMap.opNorm_smul_le, tendsto_smul_congr_of_tendsto_left_cobounded_of_isBoundedUnder, StrictConvexSpace.sphere_subset_extremePoints_closedBall, TestFunction.fderivCLM_apply_of_gt, MeasureTheory.withDensitySMulLI_apply, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivWithinAt_const_add_iff, convexHull_toCone_isLeast, ConvexCone.IsGenerating.span_eq_top, MeasureTheory.Measure.addHaar_nnreal_smul, ContinuousLinearMap.spectralRadius_eq_nnnorm, Complex.taylorSeries_eq_on_emetric_ball, finsuppTensorFinsuppLid_apply_apply, EuclideanGeometry.hasFDerivAt_inversion, MeasureTheory.convolutionExistsAt_iff_integrable_swap, dist_div_norm_sq_smul, mem_segment_iff_wbtw, torusIntegral_smul, PolyEquivTensor.toFunBilinear_apply_eq_smul, WithConv.symm_matrixToLin'StarAlgEquiv_apply, AddGroup.int_smulCommClass, ConcaveOn.neg, VectorField.mpullback_smul, hasDerivAt_ofReal_cpow_const, Monovary.sum_comp_perm_smul_eq_sum_smul_iff, Monovary.sum_comp_perm_smul_le_sum_smul, Submodule.factorPow_comp_powSMulQuotInclusion, CliffordAlgebraDualNumber.equiv_ι, Derivation.leibniz_pow, convex_iff_div, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType, hasDerivAt_norm_rpow, ContinuousLinearMap.spectrum_eq, HasStrictFDerivAt.fun_const_smul, IsLocalizedModule.smul_injective, TrivSqZeroExt.snd_map, Subring.center.smulCommClass_left, Ideal.mem_torsionOf_iff, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem, smul_algebra_smul_comm, fderivWithin_const_smul, concaveOn_univ_piecewise_Iic_of_monotoneOn_Iic_antitoneOn_Ici, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, Submodule.mem_span_triple, Matrix.instSMulCommClassForall, HasStrictDerivAt.fun_sub, HasDerivWithinAt.star, Submodule.mem_torsionBy_iff, Matrix.kroneckerTMul_smul, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, Ideal.smul_bot, TensorProduct.smul_tmul_smul, Module.Invertible.instFaithfulSMul, Seminorm.smul_closedBall_preimage, HasFDerivWithinAt.unique_on, MeromorphicOn.extract_zeros_poles, CategoryTheory.Free.lift_map_single, ProbabilityTheory.IsGaussianProcess.smul, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, ContinuousLinearMap.norm_bilinearRestrictScalars, ContinuousLinearMap.nhds_zero_eq, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HasDerivAt.sum, ProbabilityTheory.covarianceBilin_map, zero_mem_tangentConeAt, SchwartzMap.instFourierSMul, CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, HasFPowerSeriesOnBall.prod, MonoidAlgebra.smulCommClass_symm_self, Unitization.nnnorm_eq_sup, Orientation.two_zsmul_oangle_smul_right_self, Finsupp.sum_smul_index_semilinearMap', MvPowerSeries.instIsScalarTower, SchwartzMap.fourierTransformCLM_apply, HasFDerivAt.curveIntegral_segment_source', LinearEquiv.isSMulRegular_congr, HasFPowerSeriesWithinOnBall.neg, selfAdjointPart_apply_coe, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, Seminorm.bound_of_shell_sup, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Finset.expect_univ, WeakSpace.instContinuousSMul, intervalIntegral.integral_deriv_smul_deriv_comp, AlgEquiv.moduleEndSelfOp_symm_apply, TensorProduct.directSumRight'_restrict, ConcaveOn.mul, skewAdjointPartL_apply_coe, Finset.weightedVSub_apply, ContinuousLinearMap.bilinearComp_zero_left, HasStrictDerivAt.finCons, ContinuousLinearMap.nnnorm_smulRight_apply, mem_tangentConeAt_of_openSegment_subset, RootPairing.pairing_neg_one_neg_four_iff', hasFPowerSeriesWithinOnBall_pi_iff, HasDerivAt.fun_smul, hasDerivAt_zero, Convex.add_smul_sub_mem_interior', SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, IsLocalizedModule.mk'_smul, CStarModule.inner_mul_inner_swap_le, HasFDerivWithinAt.isLittleOTVS, ConvexOn.sup, Multiset.pow_smul_esymm, mellin_const_smul, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, ContMDiffOn.const_smul_section, LinearIndependent.units_smul, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, Seminorm.gauge_ball, FreeLieAlgebra.Rel.smulOfTower, NormedSpace.exp_smul, Fintype.sum_smul_sum, MeasureTheory.integral_fun_fst, SmoothPartitionOfUnity.contMDiff_finsum_smul, hasDerivWithinAt_inter', MeasureTheory.pdf.integrable_pdf_smul_iff, Seminorm.coe_comp, LinearMap.map_smulₛₗ, DirectSum.GAlgebra.smul_def, HasDerivWithinAt.scomp_hasDerivAt, MDifferentiableOn.clm_precomp, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, VectorField.lieBracketWithin_smul_right, AddSubmonoid.mem_inv_pointwise_smul_iff, DualNumber.commute_eps_right, ConvexOn.mul_concaveOn, StrictConvexOn.sup, fderiv_fun_const_smul, hasDerivAt_exp_smul_const_of_mem_ball', extremePoints_convexHull_subset, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, LinearEquiv.isScalarTower, instIsPushoutFractionRingPolynomial, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, StarConvex.is_linear_preimage, gauge_lt_eq', deriv_comp_mul_left, Submodule.mem_span_image_finset_iff_exists_fun', hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, Module.End.mem_genEigenspace_one, intervalIntegral.integral_hasDerivAt_right, hasFTaylorSeriesUpToOn_succ_iff_left, HasDerivWithinAt.mul_const, mem_segment_iff_div, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Absorbs.neg_neg, MonotoneOn.quasiconcaveOn, HasCompactSupport.hasDerivAt_convolution_left, SkewMonoidAlgebra.isScalarTower_self, toLinearMap_apply, HasDerivWithinAt.cexp, Balanced.starConvex, MvPolynomial.aevalTower_comp_toAlgHom, DualNumber.instIsLocalRing, VectorFourier.integral_bilin_fourierIntegral_eq_flip, smul_inv_le_iff_of_neg, Ideal.pointwise_smul_le_pointwise_smul_iff, deriv_clm_apply, Module.End.apply_faithfulSMul, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, CFC.monotone_sqrt, HasFPowerSeriesWithinOnBall.add, exposedPoints_subset_extremePoints, Module.isTorsionBy_quotient_iff, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK, Finset.centerMass_pair, contDiff_smul, exists_maximal_linearIndepOn, AffineMap.hasStrictDerivAt, Finset.smul_sum, ConvexBody.iInter_smul_eq_self, InnerProductSpace.toLinearMap_rankOne, openSegment_translate_preimage, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, HasDerivWithinAt.Ioi_of_Ici, Module.reflection_mul_reflection_zpow_apply, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, VectorField.mpullback_mfderivWithin_apply_smul, VectorField.mpullbackWithin_const_smul, MeromorphicOn.smul, Seminorm.finset_sup_smul, Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real, Complex.taylorSeries_eq_on_ball, TemperedDistribution.instLineDerivSMulComplex, StrictConcaveOn.translate_left, CStarAlgebra.conjugate_le_norm_smul, HasStrictFDerivAt.clm_apply, ContMDiffAt.clm_bundle_apply₂, Nat.cast_smul_eq_nsmul, ContDiffMapSupportedIn.fderivLM_apply, finsuppTensorFinsupp_symm_single, smul_lowerBounds_subset_upperBounds_smul, Seminorm.isBounded_sup, norm_midpoint_lt_iff, LinearMap.prodMap_smul, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LinearMap.trace_tensorProduct, continuousMultilinearCurryRightEquiv_symm_apply', AntitoneOn.convex_ge, MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', NormedSpace.expSeries_sum_eq_div, Summable.tsum_smul_const, Homotopy.smul_hom, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, Convex.add_smul_mem_interior', LinearEquiv.mem_stabilizer_fixedSubmodule, HahnSeries.C_mul_eq_smul, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, measurable_smul_const, AffineSubspace.wSameSide_smul_vsub_vadd_right, WeakFEPair.functional_equation, MeasureTheory.Submartingale.sum_smul_sub, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, LinearEquiv.map_smul, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, convex_Ioc, MvPolynomial.pderiv_inr_universalFactorizationMap_X, Submodule.smul_torsionBy, intervalIntegral.integral_comp_smul_deriv''', TrivSqZeroExt.fst_map, HasDerivWithinAt.fun_add, LinearMap.BilinForm.smul_right, LinearMap.isStarProjection_toContinuousLinearMap_iff, CategoryTheory.Limits.IsColimit.ι_smul, Matrix.Semiring.isScalarTower, MeromorphicOn.divisor_smul, Matrix.natCast_mulVec, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, IsLinearMap.isLinearMap_smul, LocalizedModule.mk'_smul_mk, Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, HasFDerivAtFilter.isLittleOTVS, Representation.ofModule_asAlgebraHom_apply_apply, Submodule.smul_le, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, iteratedDerivWithin_eq_equiv_comp, Matrix.convex_rowStochastic, MvPowerSeries.coeff_smul, HasDerivAt.const_add, slope_sub_smul, iteratedFDerivWithin_two_apply, Matrix.conjTranspose_ofNat_smul, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, extDerivWithin_smul, AddAction.automorphize_smul_left, Derivation.compAEval_eq, ContDiffMapSupportedIn.seminorm_postcompLM_le, Ideal.Quotient.smulCommClass', CategoryTheory.MonoidalLinear.smul_whiskerRight, Derivation.tensorProductTo_tmul, IsExtreme.convex_diff, MeasureTheory.integral_countable, DoubleCentralizer.coe_fst, HasStrictFDerivAt.fun_smul, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul, Polynomial.aeval_endomorphism, MvPolynomial.instIsPushout_1, smul_inv_lt_iff_of_neg, CompactlySupportedContinuousMap.toReal_smul, Derivation.map_smul, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, norm_cfcₙ_one_sub_one_add_inv_lt_one, Seminorm.closedBall_bot, LocallyConvexSpace.convex_open_basis_zero, Submodule.adjoint_orthogonalProjection, CategoryTheory.MonoidalLinear.whiskerLeft_smul, Filter.HasBasis.isBigOTVS_iff, Real.sInf_smul_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, HasFDerivAt.pow', IsCompactOperator.smul, continuousOn_cfcₙ_nnreal, Function.Odd.smul_even, HasStrictFDerivAt.pow', ContDiffWithinAt.smul_const, surjOn_extremePoints_image, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, Convex.smul_mem_of_zero_mem, Real.fourierIntegral_continuousLinearMap_apply', CurveIntegrable.smul, BoxIntegral.Integrable.smul, RootPairing.rootFormIn_self_smul_coroot, LinearEquiv.smul_def, Finset.centroid_pair, TopModuleCat.hom_smul, isMIntegralCurveOn_comp_mul_ne_zero, ContinuousLinearMap.hasFDerivAt_of_bilinear, starConvex_iff_forall_pos, Submodule.tensorToSpan_apply_tmul, lp.infty_isScalarTower, FormalMultilinearSeries.min_radius_le_radius_add, hasStrictDerivAt_one, FormalMultilinearSeries.ofScalars_comp_neg_id, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, RootPairing.corootForm_self_smul_root, HasDerivWithinAt.of_isLittleO, KaehlerDifferential.mvPolynomialBasis_repr_D, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_apply_tmul, StrongDual.extendRCLike_apply, ContinuousLinearMap.closed_range_of_antilipschitz, tendsto_integral_comp_smul_smul_of_integrable, Matrix.frobeniusNormSMulClass, MonoidAlgebra.liftNC_smul, HasDerivAt.div_const, strictConvex_iff_div, HasDerivAt.scomp_of_eq, VonNeumannAlgebra.coe_toStarSubalgebra, LieAlgebra.SemiDirectSum.smul_eq_mk, BddAbove.smul_of_nonpos, lie_eq_smul, SeminormFamily.basisSets_singleton_mem, Ideal.ofList_cons_smul, Module.AEval.of_aeval_smul, Finset.centerMass_eq_of_sum_1, Pi.single_smul', Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, ContDiffMapSupportedIn.continuous_iff_comp_order_le, Mathlib.Tactic.Module.NF.sub_eq_eval₂, TensorialAt.mkHom₂_apply, ConvexCone.disjoint_hull_right_of_convex, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, TopologicalAddGroup.IsSES.integral_inducedMeasure, IsScalarTower.complexToReal, HasFPowerSeriesAt.pi, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, StrictConcaveOn.add_concaveOn, smul_ball, Subalgebra.instIsScalarTowerSubtypeMem, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', map_intCast_smul, AddAut.mulLeft_apply_apply, IntervalIntegrable.continuousOn_smul, Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, SameRay.exists_pos, VectorFourier.fourierPowSMulRight_apply, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, finsuppTensorFinsuppRid_apply_apply, Module.Basis.repr_sum_self, SameRay.smul, inner_eq_norm_mul_iff_real, HasDerivAt.cexp, ContinuousAlternatingMap.prodLIE_apply, Finsupp.linearCombination_option, MeasureTheory.Submartingale.smul_nonpos, SkewMonoidAlgebra.support_single_mul_subset, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, image_extremePoints, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, Summable.smul_const, MeasureTheory.Lp.simpleFunc.toLp_smul, LieAlgebra.IsKilling.chainLength_smul, IsEllSequence.smul, segment_eq_image_lineMap, sub_smul_slope, dist_smul₀, convexCombination_eq_sum, concaveOn_iff_forall_pos, ftaylorSeries_zero, PadicInt.mahlerEquiv_apply, Module.Basis.toMatrix_smul_left, Submodule.span_singleton_eq_range, CentroidHom.instIsCentralScalar, SchwartzMap.convolution_flip, Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul, HasDerivWithinAt.isLittleO, Matrix.diagonal_const_mulVec, ContinuousLinearMap.opNorm_flip, LieRinehartAlgebra.Hom.map_smul_apply, Module.Basis.parallelepiped_map, Seminorm.bound_of_shell_smul, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, Filter.Tendsto.integral_sub_linear_isLittleO_ae, FormalMultilinearSeries.radius_compContinuousLinearMap_le, MeasureTheory.distribHaarChar_eq_div, hasDerivWithinAt_derivWithin_iff, IsCompactOperator.smul_isUnit_iff, hasDerivAt_sub_const_iff, midpoint_mem_segment, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, LinearMap.smulRightₗ_apply_apply, HasDerivAt.div, Complex.isometryOfOrthonormal_apply, IsConformalMap.smul, Matrix.vecMulVec_mul_vecMulVec, AddSubgroup.coe_pointwise_smul, intervalIntegral.smul_integral_comp_mul_right, HasDerivWithinAt.pow, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity, Matrix.dualNumberEquiv_apply, intervalIntegral.integral_comp_div_add, ConvexCone.isGenerating_top, ConvexBody.zero_mem_of_symmetric, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, CategoryTheory.Pretriangulated.Triangle.smul_hom₃, Complex.hasDerivAt_Gamma_one, TemperedDistribution.fourierMultiplierCLM_sum, LinearMap.restrictScalars_extendScalarsOfIsLocalization, intervalIntegral.integral_smul_const, FormalMultilinearSeries.derivSeries_eq_zero, InnerProductSpace.laplacianWithin_smul_nhds, AntitoneOn.quasiconvexOn, QuotientGroup.automorphize_smul_left, TestFunction.lineDerivCLM_smul, Unitization.instStarModule, Algebra.Generators.H1Cotangent.δ_eq_δAux, ContDiffWithinAt.smulRight, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, HasDerivWithinAt.congr_of_eventuallyEq, HasDerivAtFilter.isEquivalent_sub, AddSubmonoid.coe_pointwise_smul, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ContinuousLinearMap.star_eq_adjoint, SchwartzMap.integral_fourier_smul_eq, Real.dimH_segment, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, FormalMultilinearSeries.comp_rightInv, IsSMulRegular.skewMonoidAlgebra_iff, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable, IsBaseChange.equiv_tmul, Polynomial.fwdDiff_iter_degree_eq_factorial, ContinuousMultilinearMap.curryLeft_apply, Finset.centerMass_smul, Monotone.quasiconvexOn, Submodule.mem_toConvexCone, AffineSpace.asymptoticNhds_eq_smul, smul_max_of_nonpos, HasStrictDerivAt.fun_neg, ContDiffAt.fun_smul, HasFPowerSeriesWithinAt.neg, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, RootPairing.pairing_smul_coroot_eq, Function.Antiperiodic.smul, Bornology.IsVonNBounded.closure, HasFDerivAt.hasFDerivAt_norm_smul_neg, QuotSMulTop.map_comp, finsuppTensorFinsuppLid_single_tmul_single, Asymptotics.isThetaTVS_comm, Ideal.pointwise_central_scalar, fderivWithin_list_prod', AlternatingMap.mkContinuousLinear_norm_le, FreeLieAlgebra.instIsCentralScalar, ProperCone.hyperplane_separation_of_notMem, ConvexOn.mul', MeasureTheory.charFun_map_smul_comp, fderiv_clm_apply, DualNumber.eps_pow_two, ContinuousAlternatingMap.curryLeftLI_apply, smul_pos_iff_of_neg_left, ContMDiffWithinAt.const_smul_section, ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasis, ContinuousLinearEquiv.smul_apply, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, HasFDerivWithinAt.fun_mul', ContinuousLinearMap.norm_compSL_le, TestFunction.monoCLM_apply, ContinuousAlternatingMap.instIsCentralScalar, fderivWithin_smul_const, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, Balanced.neg, ContDiffMapSupportedIn.withSeminorms, Polynomial.rootSet.coe_smul, ConvexCone.mem_strictlyPositive, AnalyticOn.fun_const_smul, MeasureTheory.withDensityᵥ_smul, wbtw_or_wbtw_smul_vadd_of_nonneg, ContDiffAt.exists_eventually_eq_hasDerivAt, MvPolynomial.instIsPushout, ContinuousLinearEquiv.continuousSMul, DivisibleHull.qsmul_of_nonpos, TopologicalAddGroup.IsSES.pushforward_mono, Bornology.isVonNBounded_vadd, star_mul_self_sub_self_mul_star, MeasureTheory.integrable_comp_smul_iff, MeasureTheory.distribHaarChar_mul, derivWithin_fun_const_smul', convex_halfSpace_le, Convex.openSegment_closure_interior_subset_interior, mem_openSegment_of_gauge_lt_one, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ, cfcₙ_nnreal_eq_real, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, Matrix.trace_smul, ConvexOn.convex_strict_epigraph, HasFDerivWithinAt.isBigOTVS_sub, DirectSum.support_smul, convexHull_isClosed, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, iteratedDeriv_const_smul_field, Seminorm.absorbent_closedBall, SemilinearEquivClass.map_smulₛₗ, IsMIntegralCurveAt.comp_mul_ne_zero, CategoryTheory.NatTrans.app_smul, inf_eq_half_smul_add_sub_abs_sub, InnerProductSpace.isIdempotentElem_rankOne_self_iff, HasDerivAt.tendsto_slope_zero, fderivWithin_continuousLinearEquiv_comp, ContinuousMultilinearMap.toUniformOnFun_toFun, Quaternion.re_snd_dualNumberEquiv, Ideal.pointwise_smul_toAddSubgroup, sub_mem_posTangentConeAt_of_openSegment_subset, MulSemiringAction.toAlgHom_apply, IsLocalization.instCompatibleSMulLocalizationOfIsScalarTower, Submodule.span_singleton_mul, div_le_egauge_ball, TrivSqZeroExt.algebraMap_eq_inlHom, hasDerivAtFilter_pi, stereographic_apply, Asymptotics.IsThetaTVS.trans, Orientation.rotation_apply, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, ContinuousSMul.of_basis_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, SameRay.norm_smul_eq, Representation.leftRegular_norm_apply, segment_subset_uIcc, Matrix.cons_vecMulVec, TensorProduct.liftAux.smul, inner_map_polarization, not_linearIndepOn_finset_iff, UniformConvergenceCLM.instContinuousConstSMul, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, AddMonoid.End.isScalarTower, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Matrix.cons_vecMul, Real.iteratedFDeriv_fourierIntegral, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonneg, SMulPosMono.toSMulPosStrictMono, Mathlib.Tactic.Module.NF.eval_smul, StieltjesFunction.measure_smul, MeasureTheory.Lp.coe_LpSubmodule, Submodule.exists_of_finrank_lt, Bornology.isVonNBounded_insert, Algebra.Generators.CotangentSpace.map_toComp_injective, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, HahnSeries.instIsScalarTower, StieltjesFunction.ae_hasDerivAt, InnerProductSpaceable.innerProp, Continuous.clm_bundle_apply₂, MeasureTheory.withDensityᵥ_rnDeriv_smul, FormalMultilinearSeries.ofScalars_series_eq_zero, CochainComplex.HomComplex.Cochain.leftShift_units_smul, differentiableWithinAt_smul_iff, Antivary.sum_smul_comp_perm_eq_sum_smul_iff, Asymptotics.IsLittleOTVS.mono, fderivWithin_pow_ring', ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, LocalizedModule.mk_smul_mk, TensorProduct.finsuppLeft_apply_tmul, ConvexCone.mem_hull_of_convex, LinearEquiv.coord_apply_smul, FormalMultilinearSeries.changeOrigin_eval, VertexOperator.ncoeff_of_coeff, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, LinearMap.toSeminorm_ball_zero, Polynomial.smul_mem_rootSet_iff_of_isUnit, AffineMap.homothety_def, convex_doublyStochastic, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ExteriorAlgebra.liftAlternating_algebraMap, StrictConvex.add_smul_sub_mem, inner_smul_left_eq_smul, Finset.expect_dite_eq, StrongConvexOn.strictConvexOn, DifferentiableOn.const_smul, Convex.sum_mem, CategoryTheory.Free.lift_map, midpoint_sub_left, Submodule.mem_span_set', ContinuousLinearMap.reApplyInnerSelf_smul, ConcaveOn.smul', NonUnitalCStarAlgebra.toIsScalarTower, MeasureTheory.integral_indicator_const, Asymptotics.IsThetaTVS.trans_isLittleOTVS, ConcaveOn.smul, VertexOperator.ncoeff_eq_zero_of_lt_order, IsSelfAdjoint.adjoint_conj, Asymptotics.IsBigOTVS.trans_isThetaTVS, Bornology.IsVonNBounded.image, not_linearIndependent_iff, Matrix.vecMulVec_cons, closedAbsConvexHull_eq_closure_absConvexHull, MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff, RootPairing.pairing_smul_root_eq, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasDerivAt.inner, HasFPowerSeriesAt.prod, TensorProduct.lidOfCompatibleSMul_tmul, midpoint_vsub, LinearMap.toSeminorm_apply, LinearIndependent.units_smul_iff, linearDepOn_iffₛ, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, convex_sum, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonneg, CFC.sqrt_le_sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ZMod.invDFT_def, skewAdjoint.smul_mem, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, lineDeriv_smul, ContinuousMap.smul_apply', MeasureTheory.integrable_rnDeriv_smul_iff, AlternatingMap.mkContinuousAlternating_norm_le_max, LinearMap.map_smul', OrthonormalBasis.sum_rankOne_eq_id, ProbabilityTheory.strong_law_ae_simpleFunc_comp, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, hasDerivAt_finCons', HasStrictDerivAt.hasDerivAt, segment.lift, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Asymptotics.IsLittleOTVS.trans, absorbs_iff_eventually_nhds_zero, Finsupp.support_smul_eq, RootPairing.Equiv.reflection_smul, StrictConvex.add_smul_mem, Matrix.cons_vecMul_cons, TensorProduct.equivFinsuppOfBasisRight_symm, TensorProduct.AlgebraTensorModule.ker_mapOfCompatibleSMul, GradedMonoid.isScalarTower_right, HasFPowerSeriesWithinAt.add, Antivary.card_smul_sum_le_sum_smul_sum, ContDiffMapSupportedIn.fderivCLM_apply_of_le, inf_eq_half_smul_add_sub_abs_sub', ContinuousLinearMap.adjoint_inner_right, Real.tendsto_integral_gaussian_smul, map_nnratCast_smul, HVertexOperator.compHahnSeries_coeff, LinearMap.liftBaseChange_comp, HahnSeries.map_smul, IsSMulRegular.subsingleton_linearMap_iff, LieDerivation.smul_apply, HasFDerivWithinAt.fun_pow', StarAlgEquiv.ofInjective'_apply, Module.Basis.orientation_unitsSMul, ConvexOn.comp_affineMap, IntervalIntegrable.integral_smul, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, groupHomology.isBoundary₀_iff, StrictConvex.convex, HasStrictFDerivAt.continuousAlternatingMap_apply_const, VectorFourier.fourierIntegral_comp_add_right, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, ContDiffMapSupportedIn.postcompLM_apply, DFinsupp.instSMulPosReflectLE, Submodule.mem_colon_singleton, UnitAddTorus.span_mFourier_closure_eq_top, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, Convex.combo_le_max, MeasureTheory.withDensityᵥ_smul', AlgEquiv.apply_faithfulSMul, differentiableAt_iff_restrictScalars, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, smul_mem_asymptoticCone_iff, Mathlib.Tactic.Module.NF.add_eq_eval, MonoidAlgebra.isScalarTower_self, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, DirectSum.smul_apply, intervalIntegral.integral_deriv_smul_comp''', Filter.Tendsto.cesaro_smul, Algebra.Extension.Hom.sub_tmul, StrictConvex.preimage_add_right, LinearEquiv.reduce_mk, deriv_fun_const_smul_field, Convex.combo_self_interior_mem_interior, Matrix.ofNat_kronecker, SubMulAction.val_neg, NNRat.instIsScalarTowerRight, tendsto_integral_exp_inner_smul_cocompact, QuadraticMap.polar_smul_right_of_tower, CategoryTheory.Linear.instEpiHSMulHomOfInvertible, StrictConvex.linear_image, Finset.centroid_pair_fin, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, MeasureTheory.Measure.addHaarScalarFactor_domSMul, inner_smul_right_eq_smul, NonUnitalAlgHom.coe_mk, ProperCone.pointed_toConvexCone, ConvexCone.Pointed.of_nonempty_of_isClosed, StarConvex.is_linear_image, QuadraticMap.apply_linearCombination, RingAut.apply_faithfulSMul, IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul, MulAction.automorphize_smul_left, DualNumber.exp_smul_eps, AddSubmonoid.smul_mem_pointwise_smul_iff, SchwartzMap.integral_smul_laplacian_right_eq_left, StrictConvexOn.convexOn, ContinuousMultilinearMap.smulRight_apply, StrictConcaveOn.add_const, tsum_smul_tsum, Set.OrdConnected.strictConvex, TrivSqZeroExt.map_inl, FormalMultilinearSeries.radius_prod_eq_min, imaginaryPart_smul, CliffordAlgebra.foldr_algebraMap, Quaternion.snd_imI_dualNumberEquiv_symm, OrthonormalBasis.coe_equiv_euclideanSpace, StrongDual.im_extendRCLike_apply, VectorFourier.fourierIntegral_probChar, CompactlySupportedContinuousMap.nnrealPart_smul_pos, ModuleCat.restrictScalars.smul_def', SkewMonoidAlgebra.coeff_mul_left, Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass, Mathlib.Tactic.Module.NF.eq_const_cons, openSegment_same, QuaternionAlgebra.star_smul, Seminorm.preimage_metric_ball, NonUnitalCommCStarAlgebra.toSMulCommClass, LocallyConvexSpace.convex_basis, Submodule.smul_mem_span_smul', HasFDerivAt.mul_const', Set.smul_neg, MvPolynomial.derivation_C_mul, essSup_smul_measure, RatFunc.C_minpolyX, mem_segment_add_sub, IsCyclic.mulAutMulEquiv_symm_apply_apply, Module.toAddMonoidEnd_apply_apply, Orientation.two_zsmul_oangle_smul_left_self, ContinuousLinearMap.le_of_opNorm₂_le_of_le, AddSubgroup.mem_inv_pointwise_smul_iff₀, Fourier.fourierIntegral_def, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, NonUnitalStarSubalgebra.instIsScalarTower, Complex.IsExactOn.with_val_at, LinearMap.rid_comp_lTensor, ContinuousMultilinearMap.currySum_apply, exists_convex_convex_compl_subset, Submodule.mem_colon, NormSMulClass.toIsBoundedSMul, Ideal.Quotient.smulCommClass, Matrix.Module.diagonal_const_smul, MeasureTheory.ComplexMeasure.re_apply, FormalMultilinearSeries.ofScalars_comp_neg, MvPolynomial.tensorEquivSum_one_tmul_X, SeminormedSpace.Core.norm_smul, Seminorm.comp_mono, HasDerivAt.pow', Unitization.norm_splitMul_snd_sq, SameRay.sameRay_pos_smul_right, HasStrictFDerivAt.fun_pow', CentroidHom.coe_smul, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, le_egauge_ball_one, ConcaveOn.left_lt_of_lt_right', Coalgebra.lTensor_counit_comp_comul, TestFunction.instLineDerivSMulTopENat, rank_eq_zero_iff, Finsupp.smul_sum, NonUnitalSubalgebra.instIsScalarTowerSubtypeMem, TemperedDistribution.lineDerivOp_fourierInv_eq, QuotientAddGroup.automorphize_smul_left, fourierCoeffOn_eq_integral, MeasureTheory.SimpleFunc.integral_const, Submodule.smul_span, CompactConvergenceCLM.continuousSMul, mfderiv_smul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, hasStrictDerivAt_zero, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousLinearMap.isBigOTVS_fun_comp, Orientation.oangle_sign_smul_add_smul_right, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, Coalgebra.TensorProduct.rid_tmul, Pi.image_update_segment, HasDerivAtFilter.finCons, Finset.sum_smul_vsub_const_eq_weightedVSub, MeasureTheory.integral_deriv_smul_comp_Ioi, le_egauge_of_forall_ne_zero, IsBoundedSMul.of_norm_smul_le, Finset.sum_smul_vsub_const_eq_affineCombination_vsub, realPart_apply_coe, convex_of_nonneg_surjective_algebraMap, FormalMultilinearSeries.coeff_iterate_fslope, QuotSMulTop.map_apply_mk, HasFPowerSeriesAt.eq_zero, AbsolutelyContinuousOnInterval.fun_smul, Matrix.cramer_smul, Matrix.represents_iff', ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, deriv_const_smul', ContDiffMapSupportedIn.fderivCLM_apply, DualNumber.lift_apply_inl, intervalIntegral.integral_comp_mul_right, hasStrictDerivAt_exp_smul_const_of_mem_ball', tangentConeAt_subset_zero, ContinuousLinearMap.extendTo𝕜'_apply, LocalizedModule.smul_eq_iff_of_mem, TestFunction.fderivCLM_apply, Matrix.conjTranspose_rat_smul, MeasureTheory.integral_concaveOn_of_integrand_ae, ContinuousLinearMap.isAdjointPair_inner, LinearMap.coe_smulRight, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, EuclideanGeometry.dist_smul_vadd_eq_dist, PolynomialModule.monomial_smul_apply, posSMulMono_iff_posSMulStrictMono, MeasureTheory.integral_singleton, intervalIntegral.integral_comp_div_sub, SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply, isSelfAdjoint_smul_of_mem_skewAdjoint, Submodule.setSemiring_smul_def, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, complexOfReal_hasDerivAt, ConvexBody.hausdorffDist_coe, LieSubmodule.exists_smul_add_of_span_sup_eq_top, MeasureTheory.integral_comp_smul_deriv_Ioi, not_linearIndepOn_finset_iffₛ, Convex.starConvex_iff, openSegment_subset_Ioo, Convex.add_smul_sub_mem, IsLocalRing.ResidueField.residue_smul, HVertexOperator.coeff_comp, DifferentiableAt.smul_const, StrictConvexOn.add_const, convexHull_smul, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, Finset.sum_Ioc_by_parts, Complex.re_nnqsmul, Real.fourier_continuousMultilinearMap_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h, Unitization.splitMul_injective, LaurentPolynomial.smul_eq_C_mul, WeakFEPair.f_modif_aux1, MDifferentiableAt.smul_const_section, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, collinear_iff_exists_forall_eq_smul_vadd, MeasureTheory.Lp.smul_assoc, ContDiffMapSupportedIn.continuous_iff_comp, Asymptotics.IsTheta.const_smul_right, ContinuousLinearMap.smulRight_comp, Algebra.normalizedTrace_trans, DualNumber.lift_op_smul, ContMDiffOn.smul_section_of_tsupport, Seminorm.uniformContinuous', HasStrictDerivAt.div_const, HasStrictDerivAt.fun_mul, autEquivRootsOfUnity_apply_rootOfSplit, ContMDiffWithinAt.smul_section, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, TrivSqZeroExt.mul_right_eq_one, UniformConvergenceCLM.instUniformContinuousConstSMul, fderivWithin_continuousAlternatingMap_apply, ContinuousMultilinearMap.instIsCentralScalar, IsBaseChange.comp, smul_mem_asymptoticCone, absConvexHull_eq_convexHull_balancedHull, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, ProbabilityTheory.hasDerivAt_mgf, HasFPowerSeriesAt.eq_zero_of_eventually, SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply, NormedSpace.norm_smul_normalize, Set.OrdConnected.starConvex, Derivation.apply_aeval_eq', smul_add_smul_le_smul_add_smul', HVertexOperator.coeff_apply_apply, div_le_egauge_closedBall, StrictConcaveOn.add, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, hasStrictFDerivAt_inv', MeasureTheory.Integrable.smul_prod, LinearMap.mem_span_iff_bound, Representation.asModuleEquiv_map_smul, homeomorphSphereProd_apply_fst_coe, ContinuousOn.cfcₙ_nnreal, WithSeminorms.partial_sups, Convex.lift, ConcaveOn.sub, SameRay.exists_pos_left, HasDerivAt.scomp_hasDerivWithinAt, MeasureTheory.Lp.toTemperedDistribution_apply, Finset.smul_expect, SchwartzMap.smulLeftCLM_sub, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, HasStrictDerivAt.add_const, wbtw_or_wbtw_smul_vadd_of_nonpos, Subring.smul_mem_pointwise_smul, Module.Basis.smul_apply, ConvexCone.salient_positive, Bornology.IsVonNBounded.smul_tendsto_zero, intervalIntegral.integral_hasStrictDerivAt_right, strongConvexOn_zero, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, fromModuleCatToModuleCatLinearEquiv_apply, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, Asymptotics.isBigO_const_smul_left, ConvexBody.hausdorffEDist_coe, Fintype.linearCombination_apply_single, LinearEquiv.symm_smul_apply, HVertexOperator.of_coeff_apply, MDifferentiableOn.smul_section, MeasureTheory.SimpleFunc.integral_eq, integral_withDensity_eq_integral_toReal_smul₀, SchwartzMap.fourier_convolution_apply, Seminorm.smul_ball_zero, Complex.hasStrictFDerivAt_log_real, ceilDiv_le_iff_le_mul, Fintype.linearCombination_apply, mem_openSegment_iff_div, MvPolynomial.totalDegree_smul_le, Real.iteratedDeriv_fourierIntegral, Asymptotics.isBigOTVS_map, Projectivization.generalLinearGroup_smul_def, iteratedFDeriv_two_apply, starConvex_compl_Iic, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, PointedCone.mem_toConvexCone, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, MeasureTheory.setIntegral_finset, real_inner_smul_left, ContDiffAt.smul, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, TemperedDistribution.smulLeftCLM_sum, intervalIntegral.integral_hasStrictDerivAt_left, StrictConvex.sub, MeasureTheory.SimpleFunc.integral_smul, Asymptotics.IsBigOTVS.neg_left, ModuleCat.Algebra.instSMulCommClassCarrier, antivaryOn_iff_forall_smul_nonpos, Module.End.apply_isScalarTower, gauge_smul, ConvexCone.isGenerating_bot_iff, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, MDifferentiable.clm_precomp, InnerProductSpace.laplacian_smul_nhds, Polynomial.scaleRoots_zero, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, ConvexBody.hausdorffEdist_coe, ContDiffMapSupportedIn.fderivLM_apply_of_le, sameRay_smul_right_iff, Pi.segment_subset, MultilinearMap.mkPiRing_apply, IsLocalizedModule.eq_iff_exists, fderiv_norm_smul_pos, Fintype.expect_ite_eq', CFC.sqrt_map_pi, Convex.strictConvex_of_isOpen, FormalMultilinearSeries.le_radius_pi, Polynomial.smul_eval, AffineSpace.asymptoticNhds_eq_smul_vadd, continuousMultilinearCurryLeftEquiv_symm_apply, MultilinearMap.map_smul_univ, WithLp.unitization_mul, UnitAddTorus.mFourierCoeff_eq_integral, FixedPoints.smul, hasDerivAt_exp_smul_const', CategoryTheory.ShortComplex.smul_τ₁, TrivSqZeroExt.exp_def_of_smul_comm, DoubleCentralizer.instStarModule, HasStrictDerivAt.finset_prod, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, ContinuousMultilinearMap.smulRightL_apply, NNReal.instIsStrictOrderedModule, StrictConcaveOn.concaveOn, Representation.smul_one_tprod_asModule, CStarAlgebra.star_right_conjugate_le_norm_smul, smul_nonneg_iff_pos_imp_nonneg, Convex.second_derivative_within_at_symmetric_of_mem_interior, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, NNReal.instContinuousMapZero.UniqueHom, iteratedDerivWithin_scomp_two, exists_pos_left_iff_sameRay_and_ne_zero, CochainComplex.HomComplex.Cochain.comp_smul, sameRay_neg_smul_left_iff, LieSubalgebra.instIsScalarTowerSubtypeMem, lp.norm_const_smul_le, TestFunction.instContinuousSMulReal, MeasureTheory.integral_comp_mul_left_Ioi, Asymptotics.IsLittleOTVS.congr_right, ContinuousMap.norm_smul_const, iteratedFDeriv_succ_eq_comp_left, ContinuousMapZero.toNNReal_neg_smul, Submodule.smul_mem_smul, antivary_iff_forall_smul_nonpos, ContinuousLinearMap.smul_compLpL, MeasureTheory.Measure.addHaarScalarFactor_smul_congr', VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, Submodule.instSMulCommClass_1, MeasureTheory.SimpleFunc.map_integral, infinite_range_add_smul_iff, Polynomial.qsmul_eq_C_mul, ContDiffMapSupportedIn.fderivLM_apply_of_gt, IsLocalizedModule.smul_mem_finsetIntegerMultiple_span, HasDerivAt.hasDerivAtFilter, Convex.sub, cfcₙ_const_mul, AffineMap.homothety_add, SkewPolynomial.instSMulCommClass, CategoryTheory.ShortComplex.smul_τ₂, AddMonoid.End.coe_smul, HasDerivAt.comp_hasDerivWithinAt_of_eq, ContinuousLinearMap.opNorm_mulLeftRight_le, ConvexOn.mul, Polynomial.natDegree_sum_eq_of_linearIndepOn, gauge_smul_left, Finset.sum_smul_vsub_eq_affineCombination_vsub, MeasureTheory.measure_smul_setAverage, ClosedSubmodule.orthogonal_closure, Nat.ceilDiv_eq_add_pred_div, DualNumber.lift_comp_inlHom, ModuleFilterBasis.smul, AntivaryOn.sum_smul_le_sum_smul_comp_perm, AlgHom.linearMapMk_toAddHom, MeasureTheory.Integrable.comp_smul, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, ContDiffMapSupportedIn.structureMapCLM_zero_injective, Seminorm.ball_finset_sup_eq_iInter, LinearMap.lflip_symm, HasFDerivWithinAt.curveIntegral_segment_source', ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, Module.Basis.opNNNorm_le, Polynomial.evalEval_smul, Derivation.leibniz_div_const, TrivSqZeroExt.inl_mul_eq_smul, ContMDiffWithinAt.clm_precomp, Polynomial.mirror_smul, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Convex.exists_mem_add_smul_eq, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, HasDerivAtFilter.comp, DualNumber.algHom_ext'_iff, MeasureTheory.Integrable.fourier_smul, LinearMap.coe_toContinuousLinearMap_symm, IsCompactOperator.smul_iff, hasStrictFDerivAt_list_prod', finsum_smul', right_sub_midpoint, balancedHull.balanced, Submodule.torsionBySet.mk_smul, continuousMultilinearCurryFin1_symm_apply, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, HasStrictDerivAt.fun_add, Convex.toCone_eq_sInf, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, FixedPoints.smulCommClass', balancedCore_zero_mem, intervalIntegral.integral_comp_mul_add, HasSum.smul_const, Set.smul_mem_centralizer, FormalMultilinearSeries.radius_pi_le, DualNumber.ideal_trichotomy, NonUnitalStarAlgHom.coe_mk, HasDerivAt.comp_of_eq, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, VectorFourier.integral_fourierIntegral_smul_eq_flip, AffineSubspace.sOppSide_smul_vsub_vadd_left, Complex.integral_boundary_rect_of_differentiableOn_real, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, smul_vsub_mem_vectorSpan_pair, Orientation.inner_smul_rotation_pi_div_two_smul_left, Submodule.mem_annihilator_span_singleton, Module.reflection_apply, CategoryTheory.Functor.linear_iff, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, ConvexCone.coe_hull_of_convex, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, HasStrictFDerivAt.smul_const, SchwartzMap.coe_apply, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, IsInvariantSubfield.smul_mem, sub_smul_dslope, ConvexOn.smul', PointedCone.dual_eq_comap_dual_eval, UniformOnFun.continuousSMul_submodule_of_image_bounded, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, LinearMap.trace_comp_comm, MeasureTheory.condExp_bot', WeakSpace.instIsScalarTower, Subbimodule.smul_mem, SchwartzMap.smulLeftCLM_ofReal, StarConvex.sub', Orientation.oangle_smul_right_of_pos, norm_iteratedFDeriv_smul_le, KaehlerDifferential.instIsScalarTowerTensorProduct_1, Function.Periodic.const_smul, realPart_smul, exists_eq_smul_of_parallel, ContDiffAt.differentiableAt_iteratedFDeriv, TrivSqZeroExt.inv_zero, SMulCommClass.nnrat, abs_real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivAt.hasFDerivAt_norm_smul_pos, MeasureTheory.Integrable.smul_const, Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, Monotone.convex_le, ContinuousMultilinearMap.nnnorm_smulRight, HasDerivAt.finset_prod, Ring.uniformContinuousConstSMul_op, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, zero_mem_tangentConeAt_iff, ContDiffOn.smulRight, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, Convex.subset_toCone, LinearIsometryEquiv.map_smul, DualNumber.eps_mul_eps, MeasureTheory.lpMeasToLpTrim_smul, RootPairing.pairing_one_four_iff, MvPolynomial.rTensor_apply, disjoint_interior_extremePoints, MDifferentiableOn.smul_section_of_tsupport, MeasureTheory.integral_finset, TwoSidedIdeal.coe_smul, ConcaveOn.mul_convexOn, ContinuousLinearMap.norm_adjoint_comp_self, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, Pi.evalStarAlgHom_apply, Orientation.inner_smul_rotation_pi_div_two_smul_right, hasDerivWithinAt_intCast, MeasureTheory.integral_bilinear_hasDerivAt_eq_sub, Convex.add_smul_sub_mem_interior, Asymptotics.IsBigO.const_smul_self, ContinuousAt.integral_sub_linear_isLittleO_ae, CircleIntegrable.out, PolynomialModule.monomial_smul_lsingle, ContMDiff.clm_precomp, birkhoffAverage_apply_sub_birkhoffAverage, IsLinearTopology.tendsto_smul_zero, locallyConvexSpace_iff_zero, TensorProduct.Algebra.moduleAux_apply, ContinuousLinearMap.continuousConstSMul_apply, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousLinearMap.isCentralScalar, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, ConcaveOn.lt_right_of_left_lt', Real.hasDerivAt_fourierIntegral, fderivWithin_fun_const_smul, Antivary.sum_smul_le_sum_comp_perm_smul, SameRay.sameRay_pos_smul_left, Antitone.quasiconcaveOn, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearEquiv.strictConvex_preimage, DividedPowerAlgebra.dp_smul, CategoryTheory.ShortComplex.rightHomologyMap'_smul, LinearMap.BilinMap.polarBilin_toQuadraticMap, Mathlib.Tactic.LinearCombination.smul_const_le, ContinuousLinearMap.hasDerivWithinAt, Submodule.Convex.semilinear_range, Antivary.sub_smul_sub_nonpos, Mathlib.Tactic.Module.NF.sub_eq_eval, LinearPMap.smul_apply, HasDerivWithinAt.comp_of_eq, FormalMultilinearSeries.derivSeries_apply_diag, CFC.negPart_smul, Seminorm.coe_iSup_eq, StrictConvex.preimage_add_left, SameRay.exists_nonneg_right, lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup, ClosedSubmodule.symplComp_sup, DistribMulActionSemiHomClass.toMulActionSemiHomClass, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, groupCohomology.isCocycle₂_of_mem_cocycles₂, LinearMap.map_smul_inv, Asymptotics.IsLittleOTVS.add, convex_vadd, ContinuousLinearMap.opNorm_lsmul, IsLocalizedModule.map_integerMultiple, Seminorm.zero_comp, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, Submodule.mem_set_smul, FormalMultilinearSeries.norm_changeOriginSeriesTerm, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Seminorm.continuous_of_continuousAt_zero, left_mem_openSegment_iff, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, LeftPreLieAlgebra.toIsScalarTower, Polynomial.eval₂_smul, finsum_smul, TrivSqZeroExt.instIsScalarTower, Subsemiring.smul_closure, VectorField.lieBracketWithin_const_smul_right, ContinuousMapZero.instIsScalarTower', HasGradientAt.hasDerivAt, Matrix.intCast_mulVec, ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, StrictConvexOn.add_convexOn, Algebra.FormallyUnramified.comp_sec, HasFTaylorSeriesUpTo.zero_eq', AffineSubspace.setOf_sOppSide_eq_image2, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, ConvexBody.coe_add, ContinuousAlternatingMap.map_smul_univ, map_rat_smul, Finsupp.linearCombination_comapDomain, fourierCoeffOn.const_smul, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, Function.Odd.smul_odd, ModuleCat.smulShortComplex_X₃_isModule, inv_smul_le_iff_of_neg, MeasureTheory.convolution_eq_swap, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Real.fourierInv_eq, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, mulInvariantVectorField_smul, hasDerivAt_const_add_iff, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonpos, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', Convex.translate_preimage_left, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, Projectivization.mk_eq_mk_iff', InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, MeasureTheory.Measure.euclideanHausdorffMeasure_smul₀, WithSeminorms.continuous_iff_continuous_comp, WeakDual.seminormFamily_apply, MeasureTheory.condExpIndSMul_ae_eq_smul, HasFTaylorSeriesUpTo.fderiv, concaveOn_iff_convex_hypograph, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, Seminorm.ball_finset_sup, DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul, ConvexOn.add, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, mem_tangentConeAt_of_add_smul_mem, neg_strictConcaveOn_iff, StarAlgEquiv.ofLeftInverse'_symm_apply, IsRegular.smul_right_inj, IsModuleTopology.instPi, Submodule.span_smul_span, ContinuousLinearMap.norm_holderL_le, SmoothPartitionOfUnity.contMDiff_smul, Polynomial.isScalarTower_right, gaugeSeminorm_lt_one_of_isOpen, Asymptotics.IsLittleOTVS.fun_add, PolynormableSpace.withSeminorms, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, interval_average_eq, hasFDerivWithinAt_iff_isLittleOTVS, TensorProduct.AlgebraTensorModule.range_lTensor_idealMap, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, segment_subset_closure_openSegment, gaugeSeminormFamily_ball, Mathlib.Tactic.Module.NF.add_eq_eval₂, ConvexOn.add_const, HahnModule.instIsTorsionFree, mdifferentiable_smul_section, isSMulRegular_iff_ker_lsmul_eq_bot, SubMulAction.neg_mem_iff, HasFDerivWithinAt.mul', PresheafOfModules.germ_ringCat_smul, rank_le_one_iff, QuadraticMap.polarSym2_map_smul, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, SchwartzMap.instFourierInvSMul, Seminorm.comp_smul_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, TemperedDistribution.derivCLM_apply_apply, gauge_lt_eq, groupCohomology.isCoboundary₂_of_mem_coboundaries₂, AffineBasis.linear_combination_coord_eq_self, TorusIntegrable.function_integrable, RootPairing.smul_coroot_eq_of_root_eq_smul, AffineSubspace.setOf_wSameSide_eq_image2, Submodule.coe_toSubMulAction, MeasureTheory.Supermartingale.smul_nonneg, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, hasDerivWithinAt_Ici_of_tendsto_deriv, spectrum.hasDerivAt_resolvent_const_left, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson, LinearMap.hasDerivAt, Submodule.smulMemClass, CategoryTheory.ShortComplex.rightHomologyMap_smul, MDifferentiableWithinAt.smul, Module.Basis.sum_equivFun, IsCovariantDerivativeOn.affine_combination, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, egauge_smul_right, MeasureTheory.weightedSMul_smul_measure, VectorField.lieBracket_smul_right, midpoint_vsub_midpoint_same_left, TensorProduct.piScalarRightHom_tmul, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, HasFDerivAtFilter.restrictScalars, Balanced.smul_eq, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, convex_halfSpace_lt, intervalIntegral.integral_hasFDerivAt, LinearMap.flip_surjective_iff₂, Subalgebra.pointwise_smul_toSubmodule, HasFiniteFPowerSeriesOnBall.fderiv_eq, ConvexOn.pow, Bialgebra.mul_compr₂_comul, smul_closedBall, PointedCone.to_isOrderedModule, ContMDiffOn.smul, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, IsLocalFrameOn.coeff_sum_eq, IsBaseChange.linearMapRight, Complex.hasDerivAt_log_sub_logTaylor, PointedCone.mem_hull_set, TestFunction.lineDerivCLM_apply_of_gt, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real, WithSeminorms.isVonNBounded_iff_seminorm_bounded, DualNumber.snd_mul, ContinuousLinearMap.smulRight_apply, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, intervalIntegral.fderiv_integral, right_vsub_midpoint, MeasureTheory.IntegrableOn.continuousOn_smul_of_subset, intervalIntegral.integral_unitInterval_deriv_eq_sub, RootPairing.reflection_apply, ContinuousLinearMap.analyticAt_bilinear, integral_withDensity_eq_integral_smul₀, Complex.ofReal_nnqsmul, IsModuleFiltration.toGradedSMul, HasFDerivWithinAt.comp_hasDerivAt_of_eq, HasFPowerSeriesAt.hasStrictFDerivAt, Polynomial.aevalTower_comp_toAlgHom, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, HasDerivWithinAt.comp_hasDerivAt, AnalyticOnNhd.fun_const_smul, QuadraticMap.coeFn_smul, MeasureTheory.integral_prod_smul, Set.add_smul_subset, QuotSMulTop.map_id, convex_closed_sInter, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AddMonoidHom.smulLeft_apply, Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Submodule.map_dualCoannihilator_linearEquiv_flip, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, Module.Basis.constr_apply, fderivWithin_mul', AffineSubspace.sSameSide_smul_vsub_vadd_left, Derivation.leibniz_invOf, hasStrictDerivAt_exp_smul_const_of_mem_ball, Module.Baer.ExtensionOfMaxAdjoin.eqn, smul_neg_iff_of_neg_left, ContMDiff.const_smul_section, HasDerivWithinAt.fun_sum, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, Ideal.map_pointwise_smul, lp.instSMulCommClassPreLp, Ideal.smul_mem_pointwise_smul_iff, Real.hasDerivAt_Gamma_nat, Orientation.oangle_smul_right_self_of_nonneg, Convex.affinity, TopologicalGroup.IsSES.integrate_mono, LinearPMap.supSpanSingleton_apply_mk, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, NormedAddGroupHom.coe_smul, TensorProduct.toLinearMap_symm_rid, hasDerivAt_pi, strictConvex_uIoc, MeasureTheory.ContinuousMap.inner_toLp, convexOn_const, HasDerivAt.of_notMem_tsupport, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, RestrictScalars.isCentralScalar, MeasureTheory.integrable_fun_norm_addHaar, integral_bilinear_fderiv_right_eq_neg_left_of_integrable, CategoryTheory.Linear.toCatCenter_apply_app, skewAdjoint.I_smul_neg_I, Derivation.linearEquiv_coe_comp, hasFDerivAt_inv', ModuleCat.sMulCommClass_mk, PowerSeries.smul_eq_C_mul, Matrix.vecMul_cons, SeminormFamily.basisSets_mem, LinearMap.flip_flip, MvPolynomial.tensorEquivSum_X_tmul_one, Polynomial.smul_X_eq_monomial, Submodule.powSMulQuotInclusion_injective, HasDerivAt.fun_mul, Finset.zero_mem_smul_iff, HasStrictDerivAt.const_sub, hasDerivWithinAt_finCons, TensorProduct.AlgebraTensorModule.coe_rTensor, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, PresheafOfModules.germ_smul, CFC.abs_smul, exists_continuousLinearEquiv_fderiv_symm_eq, HasDerivAt.smul, FormalMultilinearSeries.rightInv_coeff, Seminorm.absorbent_ball, Meromorphic.smul, Convex.mem_toCone', TensorialAt.mkHom₂_apply_eq_extend, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Module.Basis.dvd_coord_smul, tangentConeAt_eq_univ, Orientation.oangle_sign_smul_add_smul_left, Matrix.Module.smul_def', tendsto_integral_comp_smul_smul_of_integrable', IsLinearMap.map_smul, LinearMap.map_smulₛₗ₂, SModEq.smul, Convex.affine_preimage, not_linearIndepOn_finset_iffₒₛ, isClosedMap_smul_left, Asymptotics.IsBigOTVS.mono, Asymptotics.IsLittleOTVS.proj, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, LinearMap.dualCoannihilator_range_eq_ker_flip, ContDiffOn.differentiableOn_iteratedFDerivWithin, MeasureTheory.average_union_mem_openSegment, PosSMulStrictMono.toSMulPosStrictMono, ConcaveOn.add_strictConcaveOn, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, ZMod.instIsScalarTower, Real.fourierInv_eq', RestrictScalars.addEquiv_symm_map_algebraMap_smul, Asymptotics.IsBigOTVS.trans, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div', ConvexBody.coe_nsmul, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, ConvexCone.mem_toPointedCone, ModuleCat.isScalarTower_of_algebra_moduleCat, mem_segment_translate, TensorProduct.lift_mk_compr₂, Convex.convexJoin, RootPairing.CoPolarizationIn_apply, HasStrictDerivAt.neg, MellinConvergent.cpow_smul, MatrixEquivTensor.toFunAlgHom_apply, ContDiffOn.fun_smul, Real.fourierIntegral_deriv, Seminorm.closedBall_comp, ContinuousLinearMap.holderL_apply_apply, FormalMultilinearSeries.comp_rightInv_aux2, CFC.negPart_smul_of_nonneg, Matrix.mulVec_cons, TrivSqZeroExt.mul_inv_rev, Algebra.Extension.CotangentSpace.map_comp, Module.Basis.units_smul_span_eq_top, MeasureTheory.integral_fun_snd, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, fwdDiff_smul_const, ZLattice.covolume.tendsto_card_div_pow'', Asymptotics.isLittleOTVS_insert, IsScalarTower.restrictScalars, AdicCompletion.ofPowSMul_val_apply, isClosedEmbedding_smul_left, ModuleCat.Algebra.instIsScalarTowerCarrier, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, real_inner_smul_self_right, Submodule.smul_mem_iff'', hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, dist_smul_add_one_sub_smul_le, ConvexOn.comp_linearMap, MeromorphicAt.smul, SeminormFamily.basisSets_iff, VectorFourier.hasFDerivAt_fourierChar_smul, Ideal.coe_smul_primesOver, MeasureTheory.LocallyIntegrableOn.continuousOn_smul, Finset.neg_smul, ConvexCone.IsReproducing.sub_eq_univ, LinearMap.IsAdjointPair.smul, Matrix.vecMul_smul, NonUnitalStarAlgHom.map_star', Real.fourierIntegral_real_eq, ContMDiffWithinAt.cle_arrowCongr, Matrix.scalar_commute_iff, fderiv_const_smul_of_field, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, groupHomology.single_isCycle₁_of_mem_fixedPoints, HasLineDerivAt.smul, OrthonormalBasis.sum_repr', Finset.expect_ite_eq, continuousMultilinearCurryRightEquiv_apply, Seminorm.convex_closedBall, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, HasDerivAt.comp_add_const, Bornology.isVonNBounded_of_smul_tendsto_zero, Module.Presentation.tautologicalRelations_relation, Module.End.HasEigenvector.pow_apply, ContDiffMapSupportedIn.structureMapLM_zero_apply, nnnorm_cfcₙ_nnreal_le, FixedPoints.mem_intermediateField_iff, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, MeasureTheory.average_union, Ideal.exists_map_eq_of_isGalois, OpenPartialHomeomorph.univUnitBall_symm_apply, Module.p_pow_smul_lift, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countable, convex_zero, Subring.smul_mem_pointwise_smul_iff, concaveOn_const, AnalyticOnNhd.const_smul, DifferentiableOn.hasDerivAt, Seminorm.continuous_of_forall, Bornology.sUnion_isVonNBounded_eq_univ, StarConvex.add_right, LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmodule, finrank_eq_one_iff_of_nonzero', SchwartzMap.integral_smul_deriv_right_eq_neg_left, QuadraticMap.polar_smul_right, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcₙ_nnreal, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left', Matrix.smul_eq_diagonal_mul, smul_inv'', intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Orientation.two_zsmul_oangle_smul_smul_self, ContMDiffAt.smul_section, fderiv_list_prod', SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, Module.Basis.unitsSMul_apply, intervalIntegral.integral_deriv_smul_comp'', SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, UnitAddTorus.span_mFourierLp_closure_eq_top, fderivWithin_comp_smul, Orientation.rotation_symm_apply, nnratCast_smul_eq, strictConvex_Ioi, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Orthonormal.inner_right_fintype, MultilinearMap.snoc_smul, NonUnitalStarSubalgebra.instSMulCommClass, LinearEquiv.smul_refl, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, HasFPowerSeriesAt.compContinuousLinearMap, MvPolynomial.scalarRTensor_apply_tmul_apply, Asymptotics.IsBigOTVS.refl, LieSubalgebra.instSMulMemClass, convex_closedConvexHull, WeakFEPair.f_modif_aux2, cfcₙ_comp_const_mul, Asymptotics.isTheta_const_smul_right, continuousOn_cfcₙ_nnreal_setProd, Prod.smul_zero_mk, fderivWithin_clm_apply, IsLocalizedModule.mk'_cancel, Algebra.trace_comp_trace, exists_continuousLinearEquiv_fderivWithin_symm_eq, MulActionHom.coe_add, ProbabilityTheory.HasIndepIncrements.smul, eHolderNorm_smul, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', mellin_cpow_smul, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, QuotSMulTop.mem_annihilator, Module.Basis.sum_repr, fderiv_continuousAlternatingMap_apply_const_apply, Differentiable.smul_const, WithLp.instProdIsBoundedSMul, RootPairing.coreflection_apply_coroot, ZMod.dft_const_smul, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, Ideal.Quotient.isScalarTower_right, LieDerivation.ofGrading_apply_apply, Submodule.toSubMulAction_one, absorbs_neg_neg, ContinuousLinearMap.isBigOTVS_id, PointedCone.instCanLiftConvexConeToConvexConePointed, MeasureTheory.condExpIndL1Fin_smul', RatFunc.natDegree_denom_le_natDegree_minpolyX, ContinuousLinearMap.norm_holder_apply_apply_le, ClosedSubmodule.symplComp_inf, intervalIntegral.integral_deriv_smul_comp, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, UniformConvergenceCLM.isVonNBounded_iff, DualNumber.instIsPrincipalIdealRing, Algebra.Generators.CotangentSpace.map_ofComp_surjective, Absorbent.vadd_absorbs, absorbent_ball_zero, Asymptotics.IsBigOTVS.fst, SMulCommClass.nnrat', DFinsupp.smul_sum, Matrix.mul_adjp_add_detp, RootPairing.Equiv.instSMulCommClassMulOppositeAut, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, MvPolynomial.tensorEquivSum_C_tmul_C, List.smul_sum, constFormalMultilinearSeries_apply_succ, StrictConvex.vadd, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, StrictConvexOn.sub, FormalMultilinearSeries.continuousOn, ZMod.smul_mem, Mathlib.Tactic.Module.NF.smul_eq_eval, HasStrictFDerivAt.clm_comp, ZMod.dft_smul_const, ProbabilityTheory.Kernel.integral_withDensity, Orientation.oangle_sign_smul_sub_right, AlgebraicGeometry.structureSheafInType.smul_apply, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, LieAlgebra.of_symm_smul, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, Submodule.basis_of_pid_aux, Submodule.span_singleton_eq_span_singleton, MonotoneOn.nnnorm_cfcₙ, Projectivization.smul_mk, Representation.IntertwiningMap.coe_smul, Function.Odd.const_smul, VectorFourier.fourierIntegral_fderiv, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, Convex.finsum_mem, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, KaehlerDifferential.map_liftBaseChange_smul, WeakFEPair.Λ_residue_zero, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', LieSubalgebra.instIsCentralScalarSubtypeMem, Seminorm.continuous_iff_continuous_comp, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, gaugeRescale_smul, constFormalMultilinearSeries_zero, StarConvex.add, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, Asymptotics.IsBigOTVS.of_egauge_le_mul, Asymptotics.IsLittleOTVS.symm, Real.fourierIntegralInv_eq, Convex.thickening, HasStrictFDerivAt.continuousMultilinearMap_apply, Submodule.instSMulCommClassSubtypeMemTorsion', cfcₙ_const_mul_id, Asymptotics.IsBigO.isBigOTVS, Int.cast_smul_eq_zsmul, IsScalarTower.nnrat, CliffordAlgebra.contractLeftAux_apply_apply, isSMulRegular_iff_right_eq_zero_of_smul, taylor_within_apply, Asymptotics.isLittleOTVS_neg_left, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top, LinearIsometryEquiv.toContinuousLinearEquiv_smul, Function.Antiperiodic.const_inv_smul, ContinuousLinearMap.opNNNorm_mul_apply, le_comap_range_rTensor, LaurentPolynomial.instIsScalarTowerPolynomial, ContinuousMultilinearMap.curryFinFinset_apply, LieRinehartAlgebra.LieRinehartRing.lie_smul_eq_mul, ContDiffAt.smulRight, Unitization.inrRangeEquiv_symm_apply, HasSum.const_smul, Affine.Simplex.ninePointCircle_center, Convex.add_smul_mem_interior, TestFunction.injective_toBoundedContinuousFunctionCLM, Submodule.le_traceDual_iff_map_le_one, VertexOperator.coeff_eq_ncoeff, derivWithin_smul_const, FormalMultilinearSeries.changeOriginSeriesTerm_bound, HasDerivWithinAt.sum, MeasureTheory.integral_smul_measure, Fintype.not_linearIndependent_iffₒₛ, KaehlerDifferential.kerTotal_map', convex_Ioi, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, Antivary.sum_mul_lt_sum_mul_comp_perm_iff, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, Asymptotics.IsLittleOTVS.of_tendsto_div, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, smul_pos_of_neg_of_neg, ContinuousLinearMap.norm_precompL_le, HasFTaylorSeriesUpToOn.restrictScalars, Differentiable.smul, isConformalMap_iff_is_complex_or_conj_linear, ZMod.dft_def, starConvex_iff_div, ProbabilityTheory.integral_poissonMeasure', HasDerivAtFilter.neg, IsArithFrobAt.conj, ContinuousLinearMap.apply_apply, ConcaveOn.sub_strictConvexOn, AbsolutelyContinuousOnInterval.smul, egauge_zero_right, Module.Presentation.tautological_relation, Asymptotics.isThetaTVS_iff_isTheta, Finsupp.mapDomain_smul, Algebra.Extension.CotangentSpace.map_comp_apply, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, Real.fourierIntegral_continuousMultilinearMap_apply', AddMonoid.nat_smulCommClass, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, GroupWithZero.toNoZeroSMulDivisors, HVertexOperator.comp_apply, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, PiTensorProduct.mapLMultilinear_opNorm, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, hasDerivWithinAt_inter, fderivWithin_restrictScalars_comp, isSMulRegular_of_range_eq_ker, Seminorm.uniformContinuous_of_forall', PiLp.instIsBoundedSMul, hasFPowerSeriesAt_iff', StarConvex.neg, Matrix.diagonal_comp_single, CategoryTheory.ShiftedHom.smul_comp, StrictConvex.smul_mem_of_zero_mem, Real.fourier_eq', CompactlySupportedContinuousMap.instIsScalarTower, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, hasDerivAt_exp_smul_const_of_mem_ball, Module.IsTorsionBy.mk_smul, Polynomial.eval_smul', LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, RingTheory.Sequence.isRegular_cons_iff', Real.fourierIntegral_iteratedFDeriv, hasMellin_const_smul, Algebra.Extension.CotangentSpace.map_comp_cotangentComplex, star_rat_smul, deriv_const_smul_field, NonUnitalCStarAlgebra.toSMulCommClass, mem_convexJoin, HasFDerivAt.mul', DirectSum.instIsScalarTower, WeakFEPair.Λ_residue_k, convex_iff_forall_pos, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, WithSeminorms.hasBasis_ball, ContDiff.fun_smul, Convex.openSegment_interior_closure_subset_interior, Monovary.sum_smul_sum_le_card_smul_sum, smul_add, exteriorPower.presentation.relations_relation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, Orientation.rotationAux_apply, Fourier.fourierIntegral_comp_add_right, derivWithin_clm_apply, Finset.sum_smul_sum, smul_finsum, Quaternion.fst_re_dualNumberEquiv_symm, TrivSqZeroExt.mem_kerIdeal_iff_inr, SchwartzMap.fourierMultiplierCLM_smul, MeasureTheory.MemLp.toLp_const_smul, QuadraticMap.basisRepr_apply, Set.Finite.isVonNBounded, slope_def_module, fwdDiff_iter_const_smul, openSegment_subset_union, smul_right_inj, IsBaseChange.endHom_comp, HasStrictDerivAt.congr_of_eventuallyEq, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_div, IsSMulRegular.of_isLocalizedModule, Quaternion.imI_snd_dualNumberEquiv, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, MeasureTheory.IntegrableOn.smul_continuousOn_of_subset, Algebra.forall_mem_adjoin_smul_eq_self_iff, AddMonoidAlgebra.smulCommClass_self, HasCompactSupport.convolution_integrand_bound_right, bddAbove_smul_iff_of_neg, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, MonovaryOn.smul_add_smul_le_smul_add_smul, integral_comp_pi_polarCoord_symm, CategoryTheory.ShiftedHom.mk₀_smul, Matrix.smul_mulVec, SkewPolynomial.smul_monomial, Submodule.mem_span_insert, DirectSum.decompose_smul, Asymptotics.isBigOTVS_comm, Submodule.toConvexCone_bot, Seminorm.finset_sup_le_sum, HasDerivAt.comp_semilinear, IsLocalizedModule.isInteger_smul, convexJoin_singleton_right, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, IsSMulRegular.of_ne_zero, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, HasDerivAt.clog_real, HasDerivAt.comp_sub_const, ModuleFilterBasis.smul_right', MeasureTheory.charFun_map_smul, convexHull_eq_self, convex_closedBall, intervalIntegral.integral_deriv_smul_deriv_comp', Algebra.Extension.Cotangent.ker_mk, ContMDiffAt.cle_arrowCongr, VertexOperator.coeff_eq_zero_of_lt_order, groupHomology.isBoundary₁_iff, IsLocalizedModule.mk'_cancel_left, Matrix.op_smul_eq_vecMul, convexOn_iff_convex_epigraph, HasFDerivAt.clm_comp, ContinuousLinearMap.adjoint_innerSL_apply, IsGaloisGroup.commutes, SameRay.pos_smul_right, StrictConvexOn.map_sum_eq_iff', sameRay_iff_norm_smul_eq, LSeries.hasDerivAt_term, TrivSqZeroExt.mul_inl_eq_op_smul, gaugeSeminorm_toFun, Ideal.pointwise_smul_toAddSubmonoid, Finset.expect_ite_eq', polyEquivTensor_symm_apply_tmul_eq_smul, IsBoundedBilinearMap.smul_right, Asymptotics.isLittleOTVS_pi, Module.finrank_eq_zero_iff, Bundle.Pretrivialization.continuousLinearMapCoordChange_apply, DifferentiableWithinAt.smul, IsOrderedRing.toIsOrderedModule, ContDiffMapSupportedIn.structureMapLM_apply, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, LieDerivation.instSMulBase, derivWithin_const_smul', Convex.mem_smul_of_zero_mem, isBoundedLinearMap_prod_multilinear, Module.reflection_mul_reflection_mul_reflection_pow_apply_self, LinearEquiv.reduce_mkQ, Orthonormal.inner_sum, Module.End.algebraMap_isUnit_inv_apply_eq_iff, ContDiff.const_smul, HasCompactSupport.convolution_integrand_bound_right_of_subset, hasStrictDerivAt_of_hasDerivAt_of_continuousAt, Finsupp.weight_apply, HasStrictDerivAt_ofNat, Function.Periodic.const_inv_smul₀, Real.fourier_smul_convolution_eq, Module.reflection_mul_reflection_mul_reflection_zpow_apply_self, PointedCone.smul_mem, lipschitzGroup.conjAct_smul_range_ι, balancedCore_eq_iInter, ConcaveOn.convex_gt, AntitoneOn.convex_lt, HasFiniteFPowerSeriesAt.comp, Submodule.exists_smith_normal_form_of_le, Subring.mem_inv_pointwise_smul_iff₀, second_derivative_symmetric_of_eventually_of_real, hasDerivWithinAt_iff_tendsto, lp.instIsScalarTowerSubtypePreLpMemAddSubgroup, Convex.convexIndependent_extremePoints, balancedHull_convexHull_subseteq_absConvexHull, ContDiffAt.hasStrictDerivAt', StrictConvex.mem_smul_of_zero_mem, MeasureTheory.integral_countable', finrank_le_one_iff, TemperedDistribution.laplacianCLM_apply, isBigO_rpow_zero_log_smul, Seminorm.finset_sup_apply_le, ConvexBody.coe_smul', IsLocalization.mem_span_iff, Monovary.sub_smul_sub_nonneg, PresheafOfModules.Sheafify.SMulCandidate.h, HasDerivAt.star_conj, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, Wbtw.mem_segment, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, Bornology.IsVonNBounded.insert, groupCohomology.isCoboundary₁_of_mem_coboundaries₁, Subsemiring.mem_inv_pointwise_smul_iff, segment_inter_eq_endpoint_of_linearIndependent_sub, IsLocalizedModule.mk'_eq_iff, NonUnitalStarSubalgebra.instIsScalarTower', Seminorm.continuousAt_zero, ftaylorSeriesWithin_fun_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, Submodule.torsionBy.mk_smul, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, Submodule.mem_torsion'_iff, HasFDerivAt.smul, Real.deriv_fourier, CStarAlgebra.exists_sum_four_nonneg, RootPairing.EmbeddedG2.threeShortAddLongRoot_eq, CategoryTheory.Linear.smul_comp, Mathlib.Tactic.LinearCombination.smul_const_lt_weak, cfcₙ_complex_eq_real, Submodule.toSubMulAction_injective, CategoryTheory.Pretriangulated.Triangle.smul_hom₁, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, LinearIndependent.pair_add_smul_add_smul_iff, KaehlerDifferential.instIsScalarTowerTensorProduct_2, DoubleCentralizer.coe_snd, MemHolder.smul_iff, ContinuousLinearMap.opNorm_le_bound₂, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, MeasureTheory.integral_convolution, Seminorm.closedBall_finset_sup_eq_iInter, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, PosSMulMono.of_smul_nonneg, CategoryTheory.ShortComplex.leftHomologyMap_smul, IsLocalRing.spanFinrank_eq_finrank_quotient, Seminorm.comp_add_le, DivisibleHull.nnqsmul_mk, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, Polynomial.mkDerivation_apply, Ideal.mem_inv_pointwise_smul_iff, RightDerivMeasurableAux.le_of_mem_A, Representation.TensorProduct.lid_apply, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, TrivSqZeroExt.snd_expSeries_of_smul_comm, ContinuousMultilinearMap.norm_curryMid, Submodule.smul_mem, zero_mem_tangentCone, ContinuousAffineMap.instIsCentralScalar, CategoryTheory.ShortComplex.opcyclesMap'_smul, TopologicalAddGroup.IsSES.integrate_apply, aestronglyMeasurable_withDensity_iff, Affine.Simplex.points_vsub_eulerPoint, hasDerivAt_of_tendstoUniformlyOnFilter, Ideal.pointwise_smul_def, Submodule.starProjection_tendsto_closure_iSup, MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff, LieSubalgebra.smul_mem, InnerProductGeometry.angle_smul_left_of_pos, SMulCommClass.rat, domain_mvt, TrivSqZeroExt.inv_inr, MeasureTheory.Lp.toTemperedDistribution_smul_eq, SchwartzMap.laplacian_eq_fourierMultiplierCLM, Asymptotics.IsBigOTVS.pi, egauge_le_of_smul_mem_of_ne, HasFDerivAt.isLittleOTVS, HVertexOperator.coeff_of_coeff, IsAddUnit.smul_right, MeasureTheory.Lp_toLp_restrict_smul, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, const_smul_mfderiv, Filter.EventuallyEq.hasDerivAtFilter_iff, Seminorm.smul_le_smul, HasMFDerivAt.const_smul, HasDerivAtFilter.fun_sum, IsCovariantDerivativeOn.finite_affine_combination, NonUnitalCommCStarAlgebra.toIsScalarTower, MeasureTheory.condExp_bot_ae_eq, map_inv_intCast_smul, FormalMultilinearSeries.hasFPowerSeriesOnBall, KaehlerDifferential.mulActionBaseChange_smul_tmul, ModuleFilterBasis.continuousSMul, ContinuousLinearMap.coe_mulₗᵢ, deriv_fun_const_smul', LinearMap.BilinForm.apply_smul_sub_smul_sub_eq, TensorProduct.instIsCentralScalar, balancedCoreAux_empty, Function.Periodic.const_inv_smul, MDifferentiableOn.clm_bundle_apply₂, Seminorm.sSup_apply, Module.isTorsionBy_quotient_element_smul, Seminorm.ball_bot, SkewMonoidAlgebra.coeff_single_mul, egauge_pi', Asymptotics.IsBigO.smul_isLittleO, left_sub_midpoint, HasFDerivWithinAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.innerSL_apply_comp, Module.Finite.of_isComplemented_codomain, Balanced.smul_mono, CategoryTheory.ShortComplex.leftHomologyMap'_smul, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, mem_convexAddSubmonoid, midpoint_vsub_midpoint_same_right, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Algebra.lsmul_coe, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Affine.Simplex.centroid_vsub_eq, Orientation.oangle_smul_left_of_pos, openSegment.lift, HilbertBasis.hasSum_repr_symm, ContinuousLinearMap.map_smul, CStarMatrix.norm_def, ContinuousAlternatingMap.smulRight_apply, AlternatingMap.instIsCentralScalar, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_deriv₂, IsMIntegralCurveAt.eventually_hasDerivAt, openSegment_subset_iff_segment_subset, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, RestrictScalars.smul_def, ContMDiffOn.clm_bundle_apply₂, inner_smul_left, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', TrivSqZeroExt.eq_smul_exp_of_invertible, Submodule.restrictScalars_self, DomMulAct.mk_smul_addMonoidHom_apply, TensorProduct.finsuppLeft'_apply, balanced_iff_neg_mem, DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, Seminorm.continuous_of_le, mem_segment_sub_add, AddSubmonoid.mem_smul_pointwise_iff_exists, ContinuousLinearMap.adjoint_adjoint, StrictConvexOn.sub_concaveOn, HasCompactSupport.hasFDerivAt_convolution_left, TrivSqZeroExt.map_id, Submodule.flip_quotDualCoannihilatorToDual_injective, Algebra.Extension.H1Cotangent.map_comp, LinearMap.lflip_apply, HolderWith.smul_iff, SkewMonoidAlgebra.liftNC_smul, MeasureTheory.Integrable.smul_of_top_right, Bundle.ContinuousRiemannianMetric.isVonNBounded, MonovaryOn.sub_smul_sub_nonneg, IsBaseChange.linearMapLeftRightHom_comp, HasDerivWithinAt.finCons, HasStrictDerivAt.clm_apply, IsLocalizedModule.fromLocalizedModule'_smul, TemperedDistribution.smulLeftCLM_apply_apply, HasDerivAt.congr_deriv, HasDerivAt.tendsto_slope_zero_right, Submodule.toSubMulAction_mono, WithSeminorms.hasBasis_zero_ball, Finset.sum_smul_vsub_eq_weightedVSub_sub, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, DFinsupp.instSMulPosStrictMono, ContinuousLinearMap.hasDerivAt_of_bilinear, Circle.norm_smul, ConvexOn.map_add_sum_le, instIsPushoutFractionRingMvPolynomial_1, locallyConvexSpace_iff_exists_convex_subset_zero, second_derivative_symmetric_of_eventually, uniformConvexOn_zero, Convex.mem_extremePoints_iff_convex_diff, HasFDerivAt.comp_hasDerivAt_of_eq, VectorField.lieBracketWithin_const_smul_left, mellin_comp_mul_left, DifferentiableOn.fun_smul, convexOn_iff_pairwise_pos, Convex.combo_affine_apply, convex_segment, vadd_left_mem_affineSpan_pair, Finsupp.linearCombination_onFinset, MeasureTheory.SignedMeasure.im_toComplexMeasure, HasDerivAtFilter.const_sub, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, left_vsub_midpoint, Module.Basis.groupSMul_apply, LinearMap.IsRefl.ker_flip, AnalyticAt.hasStrictDerivAt, BoxIntegral.unitPartition.tag_mem_smul_span, Asymptotics.IsThetaTVS.refl, Asymptotics.IsLittleO.const_smul_left, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, AffineMap.coe_homothety, ContMDiff.smul_section, Continuous.cfcₙ_nnreal', Filter.EventuallyEq.hasDerivWithinAt_iff, Seminorm.neg_mem_closedBall_zero, NonUnitalStarAlgHom.mk_coe, intervalIntegral.inv_smul_integral_comp_add_div, AlgebraicGeometry.Scheme.Modules.map_smul, SeminormFamily.basisSets_smul_left, InnerProductSpace.norm_rankOne, MeasureTheory.Measure.ae_smul_measure_eq, Ideal.stabilizerEquiv_apply_smul, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, Complex.hasDerivAt_Gamma_nat, Pi.noZeroSMulDivisors, RestrictScalars.addEquiv_map_smul, hasFDerivAt_integral_of_dominated_loc_of_lip, smul_eq_zero, tendsto_smul_comp_nat_floor_of_tendsto_nsmul, ArchimedeanClass.mk_smul, Submodule.pointwiseCentralScalar, Antivary.sum_comp_perm_smul_eq_sum_smul_iff, Submodule.smul_coe, PiTensorProduct.mapLMultilinear_toFun_apply, IsLocalizedModule.eq_zero_iff, VectorField.mlieBracket_smul_right, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, CStarMatrix.inner_toCLM_conjTranspose_right, FixedBy.subfield_mem_iff, HasDerivAtFilter.fun_const_smul, instSMulMemClassHomogeneousSubmodule, LinearIsometryEquiv.map_smulₛₗ, MeasureTheory.integral_sum_dirac, real_inner_I_smul_self, AnalyticWithinAt.smul, Seminorm.closedBall_smul_closedBall, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, balancedCore_subset_balancedCoreAux, Orthonormal.inner_right_sum, mellin_comp_mul_right, IsLocalizedModule.surj, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, PointedCone.dual_singleton, RingFilterBasis.SubmodulesBasis.smul, convexOn_norm, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, bernsteinApproximation.apply, LinearMap.sum_repr_mul_repr_mul, fderiv_eq_smul_deriv, StrictConvex.add_right, CStarMatrix.toCLM_apply_single_apply, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Submodule.instIsScalarTower, LinearMap.ker_toContinuousLinearMap, groupCohomology.isCocycle₁_of_mem_cocycles₁, PointedCone.salient_iff_inter_neg_eq_singleton, MeasureTheory.integral_sum_dirac_eq_tsum, Submodule.span_smul_of_span_eq_top, Polynomial.C_smul_derivation_apply, exists_pos_right_iff_sameRay_and_ne_zero, closedConvexHull_isClosed, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, ContinuousSMul.induced, PointedCone.toConvexCone_injective, HasDerivAt.mul_const, HasStrictDerivAt.fun_smul, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀, Matrix.smul_mat_empty, Monotone.convex_gt, ContinuousLinearMap.algebraMap_apply, LinearEquiv.apply_faithfulSMul, Representation.leftRegularMapEquiv_symm_apply_toFun, Seminorm.uniformity_eq_of_hasBasis, AlgEquiv.apply_smulCommClass, MeasureTheory.average_eq, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, MDifferentiableWithinAt.smul_section, ContMDiffOn.smul_section, StarConvex.linear_preimage, TensorProduct.liftAux.smulₛₗ, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, WithSeminorms.finset_sups, LinearEquiv.conjAlgEquiv_ext_iff, MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOn, Submodule.restrictScalars_map, hasDerivWithinAt_sub_const_iff, Convex.linear_preimage, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, TensorProduct.restrictScalar_directSumRight, intervalIntegral.smul_integral_comp_add_mul, Complex.restrictScalars_toSpanSingleton', AffineSubspace.sOppSide_smul_vsub_vadd_right, HasFDerivWithinAt.list_prod', HasFDerivAt.continuousMultilinearMap_apply, Complex.hasSum_taylorSeries_on_eball, ofMul_uzpow, exists_smul_eq_of_finrank_eq_one, Quaternion.imK_snd_dualNumberEquiv, Module.Flat.isSMulRegular_of_nonZeroDivisors, fderiv_inv', MeasureTheory.Measure.integral_comp_inv_mul_right, TensorProduct.finsuppLeft_apply_tmul_apply, ContinuousLinearMapWOT.ext_inner_iff, Besicovitch.SatelliteConfig.exists_normalized_aux3, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, NormedSpace.exp_eq_expSeries_sum, TwoSidedIdeal.coe_mop_smul, Convex.asymptoticCone, Monovary.sum_smul_comp_perm_eq_sum_smul_iff, instIsPushoutFractionRingMvPolynomial, PolynomialModule.eval_single, VectorField.mlieBracket_const_smul_right, norm_inner_div_norm_mul_norm_eq_one_iff, Valuation.HasExtension.instIsScalarTowerInteger, Submodule.disjoint_span_singleton'', HasStrictDerivAt.star, ProbabilityTheory.integral_tilted_mul_eq_cgf, FormalMultilinearSeries.comp_assoc, egauge_smul_left, MeasureTheory.Measure.addHaar_smul, HasFPowerSeriesWithinAt.comp, IsLocalizedModule.mk'_sub_mk', ContinuousSMul.of_nhds_zero, MeasureTheory.hasSum_integral_sum_dirac, MeasureTheory.L1.SimpleFunc.setToL1S_smul, MvPolynomial.pderiv_inl_universalFactorizationMap_X, autEquivRootsOfUnity_smul, fderivWithin_pow', Algebra.Extension.Cotangent.val_smul'', balanced_zero, continuousMultilinearCurryFin1_apply, locallyConvexSpace_iff_exists_convex_subset, RootPairing.reflection_apply_root, LineDifferentiableAt.smul, StarConvex.mem_smul, IsLocalizedModule.injective_iff_isRegular, star_intCast_smul, RootPairing.reflectionPerm_eq_iff_smul_coroot, LinearMap.dualAnnihilator_ker_eq_range_flip, TensorialAt.smul, HilbertBasis.finite_spans_dense, Derivation.apply_aeval_eq, Module.notMem_support_iff', smul_dotProduct, AffineSubspace.smul_span, MeasureTheory.setIntegral_const, HasStrictDerivAt.fun_pow, norm_combo_lt_of_ne, Matrix.GeneralLinearGroup.fin_two_smul_prod, Ideal.mulQuot_injective, Subsemiring.center.smulCommClass_left, LinearIsometry.adjoint_comp_self, Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun, ConvexCone.mem_comap, MvPolynomial.rTensorAlgHom_apply_eq bridge: BoxIntegral.hasIntegralIndicatorConst

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero toSMulZeroClass	—	—	—
ext_iff 📖	mathematical	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero toSMulZeroClass	—	ext
smul_add 📖	mathematical	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero toSMulZeroClass AddZero.toAdd	—	—
toAddMonoidHom_apply 📖	mathematical	—	DFunLike.coe AddMonoidHom AddZeroClass.toAddZero AddMonoidHom.instFunLike toAddMonoidHom SMulZeroClass.toSMul AddZero.toZero toSMulZeroClass	—	—

Function.Injective

Definitions

Name	Category	Theorems
distribMulAction 📖	CompOp	—
distribSMul 📖	CompOp	—
mulActionWithZero 📖	CompOp	—
smulWithZero 📖	CompOp	—
smulZeroClass 📖	CompOp	—

Function.Surjective

Definitions

Name	Category	Theorems
distribMulAction 📖	CompOp	—
distribSMul 📖	CompOp	—
distribSMulLeft 📖	CompOp	—
mulActionWithZero 📖	CompOp	—
smulWithZero 📖	CompOp	—
smulZeroClassLeft 📖	CompOp	—

MonoidWithZero

Definitions

Name	Category	Theorems
toMulActionWithZero 📖	CompOp	17 math math: nonZeroDivisorsLeft_eq_nonZeroSMulDivisors, OreLocalization.nontrivial, LaurentSeries.derivative_iterate_coeff, OreLocalization.subsingleton_iff, Polynomial.smeval_at_natCast, Ring.smeval_ascPochhammer_nat_cast, OreLocalization.nontrivial_of_nonZeroDivisorsRight, OreLocalization.mul_inv_cancel, ModuleCat.extendScalarsComp_hom_app_one_tmul, OreLocalization.zero_oreDiv', Polynomial.leval_coe_eq_smeval, Polynomial.eval_eq_smeval, OreLocalization.inv_zero, OreLocalization.nontrivial_of_nonZeroDivisorsLeft, OreLocalization.nontrivial_iff, OreLocalization.nontrivial_of_nonZeroDivisors, OreLocalization.inv_def
toOppositeMulActionWithZero 📖	CompOp	—

MulActionWithZero

Definitions

Name	Category	Theorems
compHom 📖	CompOp	—
toMulAction 📖	CompOp	16 math math: nonZeroDivisorsLeft_eq_nonZeroSMulDivisors, smulMonoidWithZeroHom_apply, OreLocalization.nontrivial, zero_smul, OreLocalization.subsingleton_iff, smul_zero, OreLocalization.nontrivial_of_nonZeroDivisorsRight, OreLocalization.mul_inv_cancel, ModuleCat.extendScalarsComp_hom_app_one_tmul, IsSMulRegular.mem_nonZeroSMulDivisors, OreLocalization.zero_oreDiv', OreLocalization.inv_zero, OreLocalization.nontrivial_of_nonZeroDivisorsLeft, OreLocalization.nontrivial_iff, OreLocalization.nontrivial_of_nonZeroDivisors, OreLocalization.inv_def
toSMulWithZero 📖	CompOp	73 math math: MeasureTheory.eLpNormEssSup_const_smul_le, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, MeasureTheory.MemLp.smul, Set.natCard_smul_set₀, IsClosed.smul₀, gauge_smul_of_nonneg, ZeroAtInftyContinuousMap.instIsScalarTower, Pi.single_apply_smul, lowerBounds_smul_of_pos, left_mem_segment, Finsupp.single_smul, LaurentPolynomial.smeval_T_pow, Real.sInf_smul_of_nonneg, HahnSeries.SummableFamily.hsum_smul_module, Real.sSup_smul_of_nonneg, closure_smul₀, TensorProduct.equivFinsuppOfBasisRight_apply_tmul, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul, LaurentPolynomial.smeval_C_mul, IsNilpotent.smul, HahnSeries.SummableFamily.smul_hsum, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', Polynomial.smeval_C, MeasureTheory.MemLp.const_smul, ConvexCone.strictlyPositive_le_positive, Set.univ_smul_nhds_zero, gauge_smul_left_of_nonneg, inr_comp_cfcₙHom_eq_cfcₙAux, Filter.top_smul_nhds_zero, LaurentPolynomial.leval_apply, IsSMulRegular.zero, HahnSeries.SummableFamily.coeff_smul, Cardinal.mk_smul_set₀, MeasureTheory.eLpNorm_const_smul_le, ZeroAtInftyContinuousMap.instSMulCommClass, MeasureTheory.Lp.coeFn_lpSMul, MeasurableSet.const_smul₀, smul_floorDiv, floorDiv_one, smul_ceilDiv, MeasureTheory.Integrable.smul_essSup, ceilDiv_one, MeasureTheory.Lp.smul_def, smul_inv₀, boole_smul, ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity, NormedDivisionRing.toNormSMulClass, Polynomial.smeval_monomial, right_mem_segment, IsSMulRegular.not_zero, LaurentPolynomial.smeval_one, VectorField.mpullback_mfderivWithin_apply_smul, HahnModule.one_smul', MeasureTheory.integrable_smul_iff, MeasureTheory.eLpNorm'_const_smul_le, Real.smul_iSup_of_nonneg, IsSMulRegular.not_zero_iff, bddBelow_smul_iff_of_pos, bddAbove_smul_iff_of_pos, IsUnit.integrable_smul_iff, IsSMulRegular.zero_iff_subsingleton, gauge_smul_left, isClosedMap_smul₀, MeasureTheory.hasFiniteIntegral_smul_iff, MeasureTheory.integrable_fun_smul_iff, LaurentPolynomial.smeval_add, HahnSeries.SummableFamily.powerSeriesFamily_smul, upperBounds_smul_of_pos, MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, Real.smul_iInf_of_nonneg, ite_zero_smul, PosSMulStrictMono.toPosSMulReflectLT, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
nontrivial 📖	mathematical	—	Nontrivial	—	subsingleton_or_nontrivial not_subsingleton subsingleton
smul_zero 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MonoidWithZero.toMonoid MulAction.toSemigroupAction toMulAction	—	—
subsingleton 📖	—	—	—	—	one_smul zero_smul
zero_smul 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MonoidWithZero.toMonoid MulAction.toSemigroupAction toMulAction MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass	—	—

MulZeroClass

Definitions

Name	Category	Theorems
toOppositeSMulWithZero 📖	CompOp	20 math math: Matrix.op_smul_one_eq_diagonal, Matrix.op_smul_eq_mul_diagonal, Matrix.mul_single_eq_updateCol_zero, Matrix.vecMul_ofNat, Finset.inv_smul_finset_distrib₀, Set.inv_smul_set_distrib₀, IsLeftCancelMulZero.toFaithfulSMul_opposite, Matrix.kronecker_ofNat, Matrix.mulVec_eq_sum, Finset.inv_op_smul_finset_distrib₀, NonUnitalSeminormedRing.isBoundedSMulOpposite, Matrix.vecMul_diagonal_const, Matrix.vecMul_natCast, Matrix.trace_mul_single, Matrix.vecMulVec_mulVec, TwoSidedIdeal.instSMulMemClassMulOpposite, Matrix.mulVec_single, Matrix.vecMul_intCast, Matrix.kronecker_diagonal, Set.inv_op_smul_set_distrib₀
toSMulWithZero 📖	CompOp	37 math math: Subring.center.smulCommClass_right, Complex.UnitDisc.instIsScalarTower_circle, Complex.UnitDisc.instSMulCommClass_closedBall_left, LinearOrderedField.smul_Iio, Finsupp.sum_smul_index, Complex.UnitDisc.instSMulCommClass_circle_left, LinearOrderedField.smul_Ico, HahnSeries.SummableFamily.embDomain_succ_smul_powers, Set.smul_indicator_one_apply, ProperCone.innerDual_singleton, isScalarTower_closedBall_ball_ball, ThreeGPFree.smul_set₀, Finset.inv_smul_finset_distrib₀, LinearOrderedField.smul_Ioo, Set.inv_smul_set_distrib₀, Complex.UnitDisc.instSMulCommClass_closedBall_right, Complex.UnitDisc.instIsScalarTower_closedBall, Finset.inv_op_smul_finset_distrib₀, Complex.UnitDisc.instSMulCommClass_circle_right, Rat.instIsScalarTowerRight, Matrix.diagonal_kronecker, instSMulCommClass_sphere_ball_ball, Matrix.isDiag_smul_one, Subring.center.smulCommClass_left, LinearOrderedField.smul_Ici, LinearOrderedField.smul_Ioi, HahnSeries.SummableFamily.hsum_smul, LinearOrderedField.smul_Ioc, isScalarTower_sphere_ball_ball, NNRat.instIsScalarTowerRight, LinearOrderedField.smul_Iic, DualNumber.inr_eq_smul_eps, LinearOrderedField.smul_Icc, Finsupp.smul_single_one, threeGPFree_smul_set₀, HahnSeries.SummableFamily.mul_eq_smul, Set.inv_op_smul_set_distrib₀

Pi

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
single_apply_smul 📖	mathematical	—	SMulZeroClass.toSMul SMulWithZero.toSMulZeroClass MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass MulActionWithZero.toSMulWithZero single MulOne.toOne MulOneClass.toMulOne MulZeroOneClass.toMulOneClass	—	single_apply ite_smul one_smul zero_smul

SMulWithZero

Definitions

Name	Category	Theorems
compHom 📖	CompOp	—
toSMulZeroClass 📖	CompOp	204 math math: Set.Nonempty.zero_smul, LaurentPolynomial.smeval_eq_sum, MeasureTheory.eLpNormEssSup_const_smul_le, HahnModule.support_smul_subset_vadd_support', MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, Subring.center.smulCommClass_right, Complex.UnitDisc.instIsScalarTower_circle, MeasureTheory.MemLp.smul, smul_nonpos_of_nonpos_of_nonneg, ZeroAtInftyContinuousMap.instIsCentralScalar, Finset.Nonempty.zero_smul, Set.natCard_smul_set₀, HahnModule.coeff_single_smul_vadd, Set.zero_smul_subset, IsClosed.smul₀, ZeroAtInftyContinuousMap.coe_smul, gauge_smul_of_nonneg, PosSMulStrictMono.toPosSMulMono, smul_neg_of_neg_of_pos, Complex.UnitDisc.instSMulCommClass_closedBall_left, ZeroAtInftyContinuousMap.smul_apply, Function.support_smul_subset_left, Pi.instPosSMulStrictMono, Pi.single_apply_smul, lowerBounds_smul_of_pos, PosSMulReflectLT.of_pos, Filter.NeBot.zero_smul_nonneg, HahnModule.add_smul, left_mem_segment, Finsupp.single_smul, Unitization.isIdempotentElem_inr_iff, LinearOrderedField.smul_Iio, smul_eq_smul_iff_eq_and_eq_of_pos', IsStrictOrderedModule.toIsOrderedModule, CompactlySupportedContinuousMap.instStarModule, Real.sInf_smul_of_nonneg, smul_pos', smul_eq_smul_iff_eq_and_eq_of_pos, Matrix.op_smul_one_eq_diagonal, Real.sSup_smul_of_nonneg, Finsupp.sum_smul_index, smul_pos_iff_of_pos_right, closure_smul₀, TensorProduct.equivFinsuppOfBasisRight_apply_tmul, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul, HahnSeries.SummableFamily.smul_apply, smul_nonneg', Complex.UnitDisc.instSMulCommClass_circle_left, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, Filter.zero_smul_filter_nonpos, smul_eq_zero_of_left, LinearOrderedField.smul_Ico, Filter.NeBot.smul_zero_nonneg, PosSMulMono.of_pos, IsNilpotent.smul, SMulPosStrictMono.toSMulPosMono, LaurentPolynomial.smeval_C, HahnSeries.SummableFamily.smul_support_subset_prod, Set.smul_indicator_one_apply, Unitization.inr_mul, HahnSeries.SummableFamily.smul_toFun, HahnSeries.SummableFamily.smul_support_finite, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', Filter.zero_smul_filter, Polynomial.smeval_C, MeasureTheory.MemLp.const_smul, HasCompactSupport.smul_right, LocallyFinite.smul_left, Matrix.op_smul_eq_mul_diagonal, Finsupp.instSMulPosReflectLT, SMulPosMono.of_pos, Balanced.smul_mem_mono, HahnModule.coeff_smul_order_add_order, isScalarTower_closedBall_ball_ball, Set.univ_smul_nhds_zero, Matrix.mul_single_eq_updateCol_zero, starConvex_zero_iff, Set.subsingleton_zero_smul_set, ThreeGPFree.smul_set₀, gauge_smul_left_of_nonneg, inr_comp_cfcₙHom_eq_cfcₙAux, Finsupp.instPosSMulStrictMono, Matrix.vecMul_ofNat, Finset.inv_smul_finset_distrib₀, HahnSeries.SummableFamily.hasFiniteSupport_smul, Filter.top_smul_nhds_zero, Set.indicator_smul_const, LinearOrderedField.smul_Ioo, Set.zero_smul_set, Set.inv_smul_set_distrib₀, IsSMulRegular.zero, Pi.instSMulPosReflectLT, Pi.instSMulPosStrictMono, Complex.UnitDisc.instSMulCommClass_closedBall_right, PartitionOfUnity.continuous_finsum_smul, CompactlySupportedContinuousMap.instIsCentralScalar, Complex.UnitDisc.instIsScalarTower_closedBall, Cardinal.mk_smul_set₀, Set.indicator_smul_const_apply, Set.indicator_smul_apply_left, MeasureTheory.eLpNorm_const_smul_le, HahnModule.coeff_single_zero_smul, IsLeftCancelMulZero.toFaithfulSMul_opposite, zero_smul, MeasureTheory.Lp.coeFn_lpSMul, Matrix.kronecker_ofNat, Matrix.mulVec_eq_sum, MeasurableSet.const_smul₀, Finset.inv_op_smul_finset_distrib₀, NonUnitalSeminormedRing.isBoundedSMulOpposite, Unitization.IsIdempotentElem.inr, Prod.instSMulPosStrictMono, Matrix.vecMul_diagonal_const, Complex.UnitDisc.instSMulCommClass_circle_right, smul_floorDiv, hammingNorm_smul_le_hammingNorm, Rat.instIsScalarTowerRight, HahnSeries.SummableFamily.smulFamily_toFun, Matrix.diagonal_kronecker, floorDiv_one, smul_ceilDiv, MeasureTheory.Integrable.smul_essSup, HahnModule.orderTop_vAdd_le_orderTop_smul, ceilDiv_one, MeasureTheory.Lp.smul_def, LaurentPolynomial.smeval_single, Matrix.vecMul_natCast, Unitization.instIsStarNormal, Nonneg.instIsOrderedModule, SMulPosReflectLE.toSMulPosReflectLT, instSMulCommClass_sphere_ball_ball, smul_inv₀, Matrix.isDiag_smul_one, Finsupp.instSMulPosStrictMono, boole_smul, ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity, NormedDivisionRing.toNormSMulClass, HahnModule.zero_smul', Subring.center.smulCommClass_left, Matrix.trace_mul_single, Polynomial.smeval_monomial, right_mem_segment, HahnSeries.SummableFamily.sum_vAddAntidiagonal_eq, Finset.zero_smul_finset, LinearOrderedField.smul_Ici, IsSMulRegular.not_zero, VectorField.mpullback_mfderivWithin_apply_smul, HahnModule.one_smul', MeasureTheory.integrable_smul_iff, Finsupp.smul_eq, LinearOrderedField.smul_Ioi, hammingNorm_smul, MeasureTheory.eLpNorm'_const_smul_le, LinearOrderedField.smul_Ioc, Finsupp.smul_apply_addAction, Real.smul_iSup_of_nonneg, HahnModule.support_smul_subset_vadd_support, isScalarTower_sphere_ball_ball, zero_smul, NNRat.instIsScalarTowerRight, Matrix.vecMulVec_mulVec, LaurentPolynomial.smeval_C_mul_T_n, HahnSeries.SummableFamily.hsum_smulFamily, HahnModule.instIsScalarTowerHahnSeries, IsSMulRegular.not_zero_iff, bddBelow_smul_iff_of_pos, Set.indicator_smul_left, bddAbove_smul_iff_of_pos, HahnModule.coeff_smul_left, TwoSidedIdeal.instSMulMemClassMulOpposite, IsUnit.integrable_smul_iff, IsSMulRegular.zero_iff_subsingleton, LinearOrderedField.smul_Iic, gauge_smul_left, SMulPosReflectLT.of_pos, Matrix.mulVec_single, Prod.instSMulPosReflectLT, DualNumber.inr_eq_smul_eps, isClosedMap_smul₀, LinearOrderedField.smul_Icc, PosSMulReflectLE.toPosSMulReflectLT, Finsupp.smul_single_one, Finset.zero_smul_finset_subset, Finset.zero_smul_subset, Matrix.vecMul_intCast, MeasureTheory.hasFiniteIntegral_smul_iff, MeasureTheory.integrable_fun_smul_iff, PartitionOfUnity.continuous_smul, threeGPFree_smul_set₀, Set.zero_smul_set_subset, Matrix.kronecker_diagonal, tsupport_smul_subset_left, upperBounds_smul_of_pos, MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, Prod.instPosSMulStrictMono, Real.smul_iInf_of_nonneg, Balanced.smul_mono, ite_zero_smul, PosSMulStrictMono.toPosSMulReflectLT, Set.inv_op_smul_set_distrib₀, Unitization.isStarNormal_inr, HahnModule.single_zero_smul_eq_smul, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, Nonneg.instIsStrictOrderedModule

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zero_smul 📖	mathematical	—	SMulZeroClass.toSMul toSMulZeroClass	—	—

SMulZeroClass

Definitions

Name	Category	Theorems
compFun 📖	CompOp	—
toSMul 📖	CompOp	6963 math, 1 bridge math: AnalyticWithinAt.const_smul, MultilinearMap.map_piecewise_smul, Finsupp.instSMulPosReflectLE, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, range_cfcₙ_nnreal, Matrix.l2_opNorm_toEuclideanCLM, AffineIndependent.smul, LinearMap.det_toContinuousLinearMap, HasDerivAt.fun_neg, LieSubmodule.coe_smul, SubMulAction.zero_mem, units_inv_smul, TestFunction.lineDerivCLM_apply_of_le, absorbent_iff_eventually_nhdsNE_zero, LeftPreLieAlgebra.toSMulCommClass, MeasureTheory.Measure.integral_comp_inv_smul, SkewMonoidAlgebra.mapDomain_smul, CategoryTheory.ShortComplex.opcyclesMap_smul, StarConvex.preimage_add_right, iteratedDeriv_scomp_two, HasDerivAt.isLittleO, LinearMap.IsSymmetric.clm_adjoint_eq, Finset.expect_ite_mem, ContinuousLinearMap.rayleigh_smul, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, ContinuousMap.toLp_inj, Real.hasDerivAt_fourier, InnerProductSpace.Core.inner_smul_right, AffineSpace.asymptoticNhds_smul, Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe, ContinuousMultilinearMap.map_piecewise_smul, LinearIsometryEquiv.strictConvex_preimage, TemperedDistribution.lineDerivOpCLM_eq, Set.Nonempty.zero_smul, IsIntegralCurve.comp_mul, vsub_midpoint, LinearMap.restrictScalars_toMatrix, LaurentPolynomial.smeval_eq_sum, Orientation.oangle_sign_smul_add_right, DiffContOnCl.smul, MeasureTheory.Lp.toTemperedDistributionCLM_apply, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Complex.im_qsmul, HasStrictDerivAt.fun_pow', ConvexCone.convex, Convex.translate_preimage_right, MeasureTheory.setIntegral_tilted, IsGaloisGroup.smul_mem_of_normal, RootPairing.rootForm_self_smul_coroot, CochainComplex.HomComplex.δ_units_smul, FormalMultilinearSeries.comp_rightInv_aux1, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, norm_smul_le, Seminorm.isBounded_const, PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective, LinearMap.mkContinuous₂_norm_le', AffineMap.lineMap_apply_module, HasDerivWithinAt.clog_real, MeasureTheory.eLpNormEssSup_const_smul_le, ContinuousMultilinearMap.norm_mkPiRing, taylor_integral_remainder, CFC.posPart_smul_of_nonpos, Finsupp.linearCombination_apply_of_mem_supported, ContinuousLinearMap.derivWithin_of_bilinear, HahnModule.support_smul_subset_vadd_support', Submodule.mem_colon_span_singleton, ConvexOn.smul'', EuclideanGeometry.dist_smul_vadd_sq, StrictConcaveOn.sub, Bundle.ContMDiffRiemannianMetric.isVonNBounded, HasDerivWithinAt.clm_comp, PointedCone.toConvexCone_closure_pointed, NonUnitalAlgHom.map_smul, real_inner_div_norm_mul_norm_eq_neg_one_iff, HasDerivWithinAt.congr_of_mem, Convex.neg, ConvexOn.mul_concaveOn', hasDerivWithinAt_Iio_iff_Iic, LinearMap.BilinForm.isOrtho_smul_right, HasStrictFDerivAt.fun_mul', Derivation.apply_eval_eq, LinearMap.mkContinuous₂_apply, LieDerivation.coe_smul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, Bundle.ContMDiffRiemannianMetric.contMDiff, HahnModule.smul_add, InnerProductSpace.isPositive_rankOne_self, AffineMap.lineMap_vsub_left, MonoidAlgebra.liftMagma_apply_apply, MeasureTheory.condExpL1_smul, Seminorm.absorbent_closedBall_zero, LinearMap.ortho_smul_right, ModuleCat.FilteredColimits.colimit_smul_mk_eq, ordinaryHypergeometric_sum_eq, AlgEquiv.moduleEndSelfOp_apply_apply, MeasureTheory.Lp.instIsScalarTower, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, IsSMulRegular.finsupp, CategoryTheory.ShortComplex.homologyMap_smul, Module.Basis.mem_submodule_iff, HasFDerivWithinAt.continuousMultilinearMap_apply, Polynomial.smeval_monomial_mul, RootPairing.pairing_smul_root_eq_of_not_linearIndependent, MDifferentiableOn.clm_postcomp, OrthonormalBasis.orthogonalProjection_eq_sum, hasDerivWithinAt_ofNat, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', Seminorm.bound_of_shell, Matrix.frobeniusIsBoundedSMul, HasCompactSupport.convolution_integrand_bound_left, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, MeasureTheory.Martingale.smul, LinearMap.IsSymmetric.inner_map_polarization, HasDerivAt.const_sub, hasDerivWithinAt_add_const_iff, LinearOrder.strictConcaveOn_of_lt, NonUnitalNonAssocSemiring.nat_isScalarTower, IncidenceAlgebra.constSMul_apply, Finsupp.instPosSMulReflectLE, LinearMap.coe_toSeminorm, FormalMultilinearSeries.comp_partialSum, SameRay.nonneg_smul_left, Convex.intrinsicClosure, MeasureTheory.integral_convexOn_of_integrand_ae, mellin_eq_fourier, Real.sSup_smul_of_nonpos, SchwartzMap.instLineDerivLeftSMulReal, NonUnitalStarSubalgebra.instSMulMemClass, smul_nonneg, CStarRing.norm_unitary_smul, Module.mem_annihilator, AnalyticOnNhd.smul, HasDerivAtFilter.sum, Ideal.Cotangent.lift_comp_toCotangent, binomialSeries_eq_ordinaryHypergeometricSeries, Polynomial.lcoeff_comp_mapAlgHom_eq, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, StarAddMonoid.toStarModuleNNRat, StarAlgEquiv.ofLeftInverse'_apply, Ideal.tensorCotangentEquiv_tmul, SchwartzMap.integral_sesq_fourier_fourier, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, OreLocalization.oreDiv_add_char, Asymptotics.IsBigOTVS.congr', Submodule.isScalarTower, PowerSeries.IsRestricted.smul, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Filter.IsBoundedUnder.smul_tendsto_zero, MeasureTheory.charFun_eq_fourierIntegral', Submodule.smul_def, DiffContOnCl.circleAverage_poissonKernel_smul', Real.hasFDerivAt_fourierChar_neg_bilinear_left, HasDerivWithinAt.Iio_of_Iic, RootPairing.Polarization_apply, PolynomialModule.comp_single, smul_finsum_mem, hasStrictDerivAt_intCast, Balanced.smul_mem_iff, segment_subset_closedBall_right, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, IncidenceAlgebra.coe_constSMul, NonUnitalAlgHom.mk_coe, isSMulRegular_iff_mem_nonZeroSMulDivisors, MeasureTheory.convolution_eq_right', TrivSqZeroExt.snd_pow, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, smul_eq_zero_iff_eq, MeasureTheory.eLpNormEssSup_const_smul, gauge_def', Submodule.set_smul_le_iff, AffineMap.coe_smul, Asymptotics.isBigO_const_smul_right, MeasureTheory.hausdorffMeasure_segment, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, CategoryTheory.Linear.instMonoHSMulHomOfInvertible, IsSMulRegular.skewMonoidAlgebra, curveIntegral_smul, Quaternion.snd_imJ_dualNumberEquiv_symm, IntervalIntegrable.smul_continuousOn, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1, Orientation.inner_rotation_pi_div_two_right_smul, MultilinearMap.map_update_smul, Orientation.oangle_add_left_smul_rotation_pi_div_two, CFC.monotoneOn_one_sub_one_add_inv, RootPairing.coroot_eq_polarizationEquiv_apply_root, Subring.center.smulCommClass_right, derivWithin_smul, Real.fderiv_fourierIntegral, hasStrictFDerivAt_list_prod_finRange', MeasureTheory.integral_smul_nnreal_measure, ContinuousMultilinearMap.map_smul_univ, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, InnerProductSpace.rankOne_one_left_eq_innerSL, LinearIndependent.pair_add_smul_right_iff, Seminorm.le_finset_sup_apply, Asymptotics.IsThetaTVS.trans_isBigOTVS, FormalMultilinearSeries.smul_apply, Complex.circleTransformDeriv_eq, LinearMap.IsSymmetric.restrictScalars, Seminorm.norm_sub_map_le_sub, bddBelow_smul_iff_of_neg, StrongDual.norm_extendRCLike, IsBaseChange.comp_iff, QuadraticAlgebra.coe_mul_eq_smul, HasFiniteFPowerSeriesAt.neg, Submodule.mem_ideal_smul_span_iff_exists_sum, nnnorm_cfcₙ_nnreal_le_iff, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, Balanced.smul_congr, Algebra.Generators.H1Cotangent.δAux_mul, Pi.image_update_openSegment, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, ContinuousLinearMap.map_add_add, Set.smul_set_neg, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, Complex.UnitDisc.instIsScalarTower_circle, SeminormFamily.basisSets_smul_right, MeasureTheory.Measure.integral_comp_mul_right, SkewMonoidAlgebra.ofFinsupp_smul, Convex.convex_isRCLikeNormedField, intervalIntegral.inv_smul_integral_comp_div_add, Antivary.smul_add_smul_le_smul_add_smul, smul_ite_zero, MeromorphicOn.divisor_fun_smul, TrivSqZeroExt.lift_inlAlgHom_inrHom, Bornology.IsVonNBounded.of_sub_left, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, HasDerivWithinAt.div_const, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, StarAlgEquiv.ofStarAlgHom_symm_apply, Real.hasDerivAt_sigmoid, MeasureTheory.IntegrableOn.continuousOn_smul, taylorWithinEval_hasDerivAt_Ioo, AlternatingMap.map_vecCons_smul, ContDiffMapSupportedIn.seminorm_monoLM_eq, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, fderivWithin_fun_smul, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Module.End.smul_def, Finset.weightedVSubOfPoint_apply, HasDerivWithinAt.congr_mono, complexOfReal_hasDerivWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, MvPolynomial.scalarRTensor_apply_monomial_tmul, Real.fourierIntegralInv_eq', AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, LinearIndependent.pair_add_smul_left_iff, Finsupp.filter_smul, StrictConvex.is_linear_image, Matrix.single_vecMul, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, RingTheory.Sequence.isWeaklyRegular_cons_iff', SkewMonoidAlgebra.coeff_single_one_mul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, MeasureTheory.VectorMeasure.coe_smul, Finset.sum_smul, Quaternion.star_smul, hasDerivAt_integral_of_dominated_loc_of_lip, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, Convex.smul_preimage, MeasureTheory.FinStronglyMeasurable.const_smul, AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff, curveIntegrable_segment, Submodule.toConvexCone_inf, ContDiffOn.smul_const, Module.Basis.equivFun_symm_apply, MDifferentiableAt.cle_arrowCongr, Absorbs.eventually_nhds_zero, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul', PolynomialModule.smul_def, Seminorm.bot_eq_zero, Submodule.set_smul_span, ContinuousLinearMap.smul_apply, CFC.monotone_nnrpow, Complex.integral_boundary_rect_eq_zero_of_differentiableOn, ContinuousLinearMap.continuousSMul, Ideal.relNorm_smul, hasFTaylorSeriesUpToOn_top_iff_right, Seminorm.smul_comp, CochainComplex.HomComplex.Cocycle.coe_smul, ConvexCone.mem_positive, LinearIsometry.map_smul, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, MeasureTheory.Lp.const_smul_mem_Lp, RootPairing.reflectionPerm_eq_iff_smul_root, strictConvex_Iic, AddSubgroupClass.coe_zmod_smul, absorbs_zero_iff, MeasureTheory.MemLp.smul, ConvexOn.smul, smul_nonpos_of_nonpos_of_nonneg, Module.End.HasUnifEigenvector.pow_apply, AffineSubspace.setOf_sSameSide_eq_image2, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, intervalIntegral.integral_hasDerivWithinAt_right, TrivSqZeroExt.snd_pow_eq_sum, Bornology.isVonNBounded_add_of_nonempty, norm_add_eq_iff_real, Monotone.quasiconcaveOn, Complex.integral_comp_pi_polarCoord_symm, FormalMultilinearSeries.radius_pi_eq_iInf, ZeroAtInftyContinuousMap.instIsCentralScalar, ProperCone.convex, contDiffAt_norm_smul_iff, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, Polynomial.degree_smul_of_smul_regular, SchwartzMap.pairing_apply_apply, MeasureTheory.integral_domSMul, InnerProductSpace.isIdempotentElem_rankOne_self, norm_iteratedFDerivWithin_smul_le, Submodule.tensorEquivSpan_apply_tmul, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, IsLprojection.Lnorm, AddCommGroup.intIsScalarTower, Complex.real_smul, Polynomial.smul_mem_rootSet, MeasureTheory.weightedSMul_apply, NonUnitalSubalgebra.instIsScalarTower', LineDifferentiableWithinAt.smul, Finset.Nonempty.zero_smul, egauge_prod_mk, SkewMonoidAlgebra.toFinsupp_smul, Differentiable.clm_comp, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport, Commute.cfcₙ_nnreal, Mathlib.Tactic.ComputeDegree.degree_smul_le_of_le, ceilDiv_le_iff_le_smul, ZeroHom.instSMulCommClass, dist_smul_le, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, Matrix.mul_mul_left, IsScalarTower.to_smulCommClass', ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, HasStrictDerivAt.pow, IsExposed.isExtreme, ContinuousLinearMap.isUniformEmbedding_restrictScalars, RingTheory.Sequence.isWeaklyRegular_cons_iff, ConvexCone.canLift, hasDerivWithinAt_taylorWithinEval, map_ratCast_smul, FormalMultilinearSeries.changeOriginSeriesTerm_apply, AffineSubspace.smul_mem_smul_iff₀, Asymptotics.isLittleOTVS_one, SkewMonoidAlgebra.support_single_mul, Seminorm.finset_sup_apply, HasDerivAt.hasDerivWithinAt, ContinuousLinearMap.hasDerivAtFilter, span_fourier_closure_eq_top, Real.fourierIntegral_eq, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, Set.natCard_smul_set₀, HahnModule.coeff_single_smul_vadd, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, HasDerivWithinAt.fun_div, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, FloorDiv.floorDiv_gc, CategoryTheory.ShortComplex.Homotopy.smul_h₁, StarConvex.affine_preimage, HasFPowerSeriesOnBall.add, LinearMap.BilinForm.smul_left_of_tower, HasDerivWithinAt.complexToReal_fderiv', DFinsupp.equivProdDFinsupp_smul, circleIntegral_def_Icc, NumberField.RingOfIntegers.instSMulDistribClass, convexJoin_singletons, MeasureTheory.integral_unique, setIntegral_withDensity_eq_setIntegral_smul₀, Complex.hasSum_taylorSeries_of_entire, ContinuousMap.toLp_denseRange, IsCovariantDerivativeOn.difference_apply, ProbabilityTheory.hasSum_integral_poissonMeasure, Submodule.pow_pOrder_smul, Bornology.isVonNBounded_add_self, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, intervalIntegral.intervalIntegral_eq_integral_uIoc, Seminorm.ball_smul_closedBall, ContinuousLinearMap.integral_apply, CochainComplex.HomComplex.Cochain.leftShift_smul, FixedPoints.mem_addSubgroup, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, segment_inter_subset_endpoint_of_linearIndependent_sub, AddMonoidAlgebra.isScalarTower_self, Polynomial.nnqsmul_eq_C_mul, SkewMonoidAlgebra.coeff_single_mul_of_not_exists_mul, HasDerivAt.fun_finset_prod, LocalizedModule.restrictScalars_map_eq, circleIntegrable_iff, Summable.const_smul, PolynomialModule.map_smul, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, convex_iff_sum_mem, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, ConcaveOn.mul_convexOn', NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded, ContMDiffCovariantDerivativeOn.affine_combination, WithSeminorms.mem_nhds_iff, Convex.vadd, LinearMap.IsSymmetric.diagonalization_apply_self_apply, TensorProduct.sum_tmul_basis_right_injective, LinearMap.extendScalarsOfIsLocalization_apply, Memℓp.const_smul, Set.zero_smul_subset, StrictConvex.diff_interior_subset_extremePoints, Real.fourier_continuousLinearMap_apply, DirectSum.of_smul, Unitization.real_cfcₙ_eq_cfc_inr, real_inner_smul_self_left, neg_smul, fderivWithin_fun_pow', intervalIntegral.fderiv_integral_of_tendsto_ae, ZMod.invDFT_apply, SMulPosReflectLE_iff_smulPosReflectLT, IsClosed.smul₀, Convex.combo_interior_closure_mem_interior, NormedSpace.isBounded_iff_subset_smul_ball, HasFDerivWithinAt.clm_apply, Balanced.sub, hasFPowerSeriesOnBall_pi_iff, SmoothPartitionOfUnity.contMDiffAt_finsum, imaginaryPart_I_smul, Continuous.convolution_integrand_fst, ContinuousAlternatingMap.vecCons_smul, MDifferentiableOn.smul_const_section, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, Module.Ray.neg_units_smul, MvPolynomial.leibniz_iff_X, DilationEquiv.smulTorsor_symm_apply, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, Convex.convex_remove_iff_notMem_convexHull_remove, Representation.freeLift_single_single, ConvexOn.lt_left_of_right_lt', HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, diam_smul₀, Seminorm.uniformContinuous_of_forall, TensorAlgebra.toTrivSqZeroExt_ι, abs_smul, Polynomial.homogenize_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul, Algebra.to_smulCommClass, LieModule.traceForm_eq_sum_finrank_nsmul', DomMulAct.smul_linearMap_apply, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, Polynomial.sum_smul_index', AddSubgroup.smul_mem_pointwise_smul_iff, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, segment_translate_preimage, convexHull_eq_iInter, SeminormFamily.filter_eq_iInf, toMul_uzpow, aemeasurable_smul_const, ZeroAtInftyContinuousMap.coe_smul, DifferentiableWithinAt.fun_const_smul, SchwartzMap.integral_bilin_fourierInv_eq, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, HasFTaylorSeriesUpTo.hasFDerivAt, TensorProduct.AlgebraTensorModule.rid_tmul, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Set.indicator_smul, Ideal.smul_closure, MeasureTheory.Measure.toSphere_apply_aux, Bornology.IsVonNBounded.of_neg, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, PolynomialModule.comp_smul, Unitization.splitMul_apply, tendsto_integral_peak_smul_of_integrable_of_tendsto, ContMDiffOn.clm_postcomp, inner_eq_norm_mul_iff, Seminorm.restrictScalars_closedBall, smulPosMono_iff_smulPosStrictMono, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, Matrix.Semiring.smulCommClass, smul_pos_iff_of_pos_left, tendsto_smul_comp_nat_floor_of_tendsto_mul, LinearMap.adjoint_eq_toCLM_adjoint, Asymptotics.IsLittleOTVS.tendsto_div, DirectSum.instIsCentralScalar, Seminorm.bddAbove_range_iff, AntivaryOn.sub_smul_sub_nonpos, Module.Basis.basis_singleton_iff, convex_iff_pairwise_pos, descPochhammer_succ_comp_X_sub_one, NormedSpace.image_isVonNBounded_iff, VectorField.mpullbackWithin_smul, ContinuousMap.range_toLp, eqOn_dslope_sub_smul, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div, convex_Iic, Seminorm.closedBall_iSup, gauge_smul_of_nonneg, Differentiable.fun_smul, Subbimodule.smul_mem', TemperedDistribution.fourierMultiplierCLM_smul, hasDerivAt_bernoulliFun, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, derivWithin_fderivWithin, WithLp.isBoundedSMulSeminormedAddCommGroupToProd, SkewMonoidAlgebra.smul_of, Submodule.smul_mem_span_smul, intervalIntegral.integral_deriv_smul_comp', IsSelfAdjoint.smul_mem_skewAdjoint, PosSMulStrictMono.toPosSMulMono, DualNumber.range_lift, StarConvex.add_smul_mem, QuotSMulTop.equivTensorQuot_naturality, MeasureTheory.condExpIndL1Fin_smul, StrictConvexOn.neg, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, MultilinearMap.mkContinuousMultilinear_apply, AddSubgroup.mem_inv_pointwise_smul_iff, PosSMulReflectLE_iff_posSMulReflectLT, CliffordAlgebraDualNumber.equiv_symm_eps, Monovary.sum_smul_comp_perm_le_sum_smul, InnerProductGeometry.angle_smul_right_of_pos, tsum_const_smul', StrongDual.norm_extendRCLike_bound, TemperedDistribution.lineDerivOp_fourier_eq, Units.smul_coe, Matrix.mul_smul, WeakFEPair.symm_Λ₀_eq, smul_neg_of_neg_of_pos, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, SpecialLinearGroup.mem_center_iff_spec, Seminorm.smul_inf, Ideal.mem_pointwise_smul_iff_inv_smul_mem, Submodule.Quotient.instIsBoundedSMul, intervalIntegral.integral_comp_sub_div, Finsupp.sum_smul_index', Complex.UnitDisc.instSMulCommClass_closedBall_left, Subsemiring.mem_smul_pointwise_iff_exists, HasDerivAt.comp_ofReal, tangentConeAt_nonempty_of_properSpace, AdicCompletion.instIsScalarTower_1, convexJoin_singleton_left, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, intervalIntegral.integral_comp_mul_left, AnalyticAt.fun_const_smul, Submodule.ideal_span_singleton_smul, Continuous.integral_hasStrictDerivAt, AffineBasis.coe_smul, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, ZeroAtInftyContinuousMap.instIsScalarTower, stdSimplex_fin_two, ZeroAtInftyContinuousMap.smul_apply, deriv_const_smul, fderiv_clm_comp, StrictConcaveOn.sub_convexOn, Submodule.top_eq_ofList_cons_smul_iff, BoxIntegral.unitPartition.mem_smul_span_iff, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, TensorProduct.smul_tmul, intervalIntegral.integral_comp_mul_sub, cfc_comp_smul, mdifferentiableWithinAt_smul_const_section, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, RingAut.smul_def, AlternatingMap.smulRight_apply, Ideal.exists_smul_eq_of_isGaloisGroup, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, IsConformalMap.is_complex_or_conj_linear, Bornology.isVonNBounded_pi_iff, fderiv_continuousAlternatingMap_apply_const, Function.support_smul_subset_left, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', Fintype.expect_dite_eq, Module.Basis.isScalarTower_of_nonempty, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, Prod.image_mk_openSegment_left, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, TrivSqZeroExt.inv_inl, HasDerivAt.clm_apply, SemilinearMapClass.toMulActionSemiHomClass, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_symm_apply_mk_tmul, ContDiffMapSupportedIn.seminorm_fderivLM_le, Polynomial.derivative_smul, LinearMap.IsRefl.ker_flip_eq_bot, RKHS.coe_smul, Bundle.RiemannianMetric.isVonNBounded, vadd_right_mem_affineSpan_pair, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContDiffMapSupportedIn.seminorm_fderivLM_top, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Convex.affine_image, NormedSpace.toIsBoundedSMul, UniformConvergenceCLM.smul_apply, Fintype.mem_span_image_iff_exists_fun, HasFPowerSeriesAt.neg, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux, Seminorm.continuous_of_forall', AlgEquiv.apply_smulCommClass', curveIntegralFun_smul, addInvariantVectorField_smul, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt, RootPairing.span_orbit_eq_top, VertexOperator.of_coeff_apply_coeff, neg_strictConvexOn_iff, Module.Basis.smul_eq_zero, ContinuousLinearMap.coe_smul', DomMulAct.smul_mulDistribActionHom_apply, BoundedContinuousFunction.instSMulCommClass_1, smul_lt_smul_of_neg_left, MeasureTheory.Measure.domSMul_apply, groupHomology.single_isCycle₂_iff_inv, egauge_ball_le_of_one_lt_norm, Ideal.subset_pointwise_smul_iff, CategoryTheory.Quotient.Linear.smul_eq, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, ContinuousAffineMap.smul_apply, Polynomial.natDegree_smul, MonovaryOn.sum_smul_comp_perm_le_sum_smul, hasDerivWithinAt_iff_isLittleO, TensorPower.gMul_eq_coe_linearMap, GeneralSchauderBasis.proj_apply, hasStrictFDerivAt_iff_isLittleOTVS, CStarMatrix.mapₗ_reindexₐ, ContinuousAlternatingMap.smul_apply, Pi.instPosSMulStrictMono, derivWithin_fun_const_smul_field, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, StarAlgEquiv.ofStarAlgHom_apply, Submodule.mem_smul_span_singleton, Finsupp.sum_smul_index_linearMap', MeasureTheory.IntegrableOn.smul_continuousOn, ContinuousAlternatingMap.piLIE_apply_apply, AffineSubspace.wOppSide_smul_vsub_vadd_left, ContinuousLinearMap.applySMulCommClass', PreInnerProductSpace.Core.smul_left, inv_intCast_smul_eq, extremePoints_prod, Subsemiring.smul_mem_pointwise_smul_iff, combo_mem_ball_of_ne, lintegral_fderiv_lineMap_eq_edist, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, balancedCoreAux_maximal, hasDerivWithinAt_zero, HasStrictDerivAt.pow', TestFunction.monoCLM_eq_zero, CategoryTheory.Abelian.Ext.smul_hom, coe_convexAddSubmonoid, TopologicalGroup.IsSES.integral_inducedMeasure, Pi.single_apply_smul, hasDerivAt_star_conj_iff, AbsolutelyContinuousOnInterval.const_smul, ContDiffAt.hasStrictDerivAt, Seminorm.neg_ball, TrivSqZeroExt.inv_one, Normal.minpoly_eq_iff_mem_orbit, RatFunc.mk_smul, FormalMultilinearSeries.hasSum_of_finite, Finsupp.smulCommClass, CStarMatrix.mul_smul, LieAlgebra.of_smul, Matrix.vecMul_vecMulVec, StrictConcaveOn.translate_right, hasDerivAtFilter_ofNat, SkewMonoidAlgebra.support_mul_single, Asymptotics.IsBigO.smul, AdicCompletion.val_smul_eq_evalₐ_smul, instStarModuleNNRealOfReal, VectorField.mlieBracket_smul_left, MvPolynomial.smul_monomial, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, Seminorm.continuous', FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, Complex.hasSum_taylorSeries_on_ball, Submodule.mem_span_image_iff_exists_fun, IsScalarTower.right, QuadraticMap.map_smul_of_tower, Asymptotics.IsBigOTVS.add, MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff, HasFPowerSeriesOnBall.restrictScalars, smul_nonneg_iff_neg_imp_nonpos, lowerBounds_smul_of_pos, StrictConcaveOn.inf, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, ContinuousLinearMap.isometry_mul_flip, Quaternion.snd_re_dualNumberEquiv_symm, ZSpan.smul, HasStrictFDerivAt.mul', Module.AEval.of_symm_smul, Unitization.inl_mul_inr, Mathlib.Tactic.Module.NF.eval_neg, Module.Ray.units_smul_of_neg, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, AlgebraicGeometry.StructureSheaf.const_add, LocalizedModule.mk_add_mk, conformal_const_smul, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, HasStrictFDerivAt.comp_hasStrictDerivAt, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, ClosedSubmodule.inf_orthogonal, LinearMap.coe_toContinuousLinearMap', ContDiffWithinAt.fun_smul, balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, ConvexCone.coe_zero, CharacterModule.smul_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Module.Free.instFaithfulSMulOfNontrivial, contDiffOn_iff_continuousOn_differentiableOn, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, convexJoin_segments, ClosedSubmodule.instSMulMemClass, PosSMulReflectLT.of_pos, sum_cauchyPowerSeries_eq_integral, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, CStarModule.innerSL_apply, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt, MeromorphicOn.fun_smul, monomial_has_deriv_aux, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, LieRinehartAlgebra.LieRinehartRing.leibniz_smul_right, LinearIsometryEquiv.conjStarAlgEquiv_apply, MultilinearMap.smul_apply, MeasureTheory.smul_convolution, Bundle.ContinuousLinearMap.vectorBundle, Real.vector_fourierIntegral_eq_integral_exp_smul, VectorField.mlieBracketWithin_const_smul_right, HasDerivWithinAt.sub, PadicInt.mahlerTerm_apply, AlternatingMap.map_update_smul, WithLp.smul_snd, MeasureTheory.ConvolutionExistsAt.integrable, Complex.taylorSeries_eq_of_entire, egauge_add_add_le, HVertexOperator.coeff_isPWOsupport, exists_pos_right_iff_sameRay, Real.fourier_real_eq_integral_exp_smul, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, Monotone.quasilinearOn, Asymptotics.IsBigOWith.const_smul_self, Asymptotics.isLittleOTVS_prodMk_left, ExteriorAlgebra.toTrivSqZeroExt_comp_map, AntivaryOn.sum_comp_perm_smul_eq_sum_smul_iff, inner_smul_left_eq_star_smul, ProbabilityTheory.covarianceOperator_apply, BoundedContinuousFunction.toContinuousMapLinearMap_apply, nndist_smul₀, InnerProductGeometry.angle_smul_left_of_neg, Module.exists_smul_eq_zero_and_mk_eq, Asymptotics.IsBigOTVS.comp_tendsto, MeasureTheory.integral_tilted, Submodule.span_smul_eq_of_isUnit, WithSeminorms.continuousSMul, IsSl2Triple.lie_lie_smul_f, LinearMap.ortho_smul_left, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, ContinuousMultilinearMap.mkPiRing_apply, Ideal.LiesOver.smul, hasDerivAt_of_hasDerivAt_of_ne, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, MeasureTheory.average_mem_openSegment_compl_self, TestFunction.continuous_iff_continuous_comp, HasFiniteFPowerSeriesOnBall.sum, MeasureTheory.L1.integral_smul, Distribution.IsVanishingOn.smulLeftCLM, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, inv_natCast_smul_eq, DifferentiableOn.smul_const, Polynomial.C_mul', Quaternion.imJ_fst_dualNumberEquiv, InnerProductSpace.inner_left_rankOne_apply, cfcₙHom_nnreal_eq_restrict, Filter.NeBot.zero_smul_nonneg, TestFunction.toBoundedContinuousFunctionCLM_apply, Conformal.const_smul, MeasureTheory.Lp.instFourierInvSMul, CochainComplex.HomComplex.Cocycle.coe_units_smul, HahnModule.add_smul, Bornology.isVonNBounded_neg, Set.indicator_const_smul, AlternatingMap.smul_apply, hasStrictDerivAt_abs_pos, MonoidAlgebra.coeff_smul, ContinuousLinearMap.smul_compLp, DomMulAct.smul_addMonoidHom_apply, difference_quotients_converge_uniformly, TrivSqZeroExt.snd_list_prod, hasDerivWithinAt_abs_pos, HasDerivWithinAt.sub_const, ContinuousLinearMap.norm_extendTo𝕜, Module.Basis.toMatrix_smul, LocalizedModule.lift'_smul, HasSum.hasSum_at_zero, Seminorm.continuousAt_zero_of_forall', HasFPowerSeriesAt.add, left_mem_segment, lineDifferentiableAt_smul_iff, TrivSqZeroExt.fstHom_comp_map, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, Matrix.conjTranspose_natCast_smul, LinearMap.sum_repr_mul_repr_mulₛₗ, cfcₙ_map_pi, ContinuousLinearMap.hasBasis_nhds_zero, Finsupp.single_smul, Bornology.IsVonNBounded.of_add_right, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, AddSubmonoid.smul_mem_smul, Module.End.apply_smulCommClass', HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, CochainComplex.HomComplex.Cochain.units_smul_comp, AddCircle.integral_haarAddCircle, WithCStarModule.inner_def, InnerProductSpace.HarmonicAt.const_smul, Seminorm.ball_mem_nhds, eventually_nhds_norm_smul_sub_lt, CentroidHom.smul_def, CircleIntegrable.const_smul, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, Module.IsTorsionFree.isSMulRegular, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, ContMDiffAt.clm_postcomp, Matrix.smul_one_eq_diagonal, scalarSMulCLE_symm_apply, Real.fourier_deriv, RightPreLieAlgebra.toIsScalarTower, ContMDiffWithinAt.clm_postcomp, iteratedDeriv_scomp_three, fderiv_fun_pow', hasDerivWithinAt_pi, StarAddMonoid.toStarModuleRat, Real.integrable_prod_sub, Orientation.oangle_smul_left_of_neg, NormedSpace.isVonNBounded_ball, locallyConvexSpace_iff, MDifferentiable.smul, strictConvex_Icc, antivary_iff_smul_rearrangement, norm_smul_inv_norm, Submodule.pointwise_smul_def, ContinuousLinearMap.eq_adjoint_iff, ConcaveOn.smul_convexOn', IsLocalizedModule.mk'_eq_zero', Finsupp.comapDomain_smul_of_injective, tangentConeAt_univ, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, Unitization.isIdempotentElem_inr_iff, convexHull_union_neg_eq_absConvexHull, SubMulAction.neg_mem, ContinuousLinearMap.toSpanSingleton_apply, ConcaveOn.add_const, smul_vsub_rev_vadd_mem_affineSpan_pair, KaehlerDifferential.isScalarTower', Submodule.mem_torsion_iff, derivWithin.scomp, DifferentiableOn.circleIntegral_sub_inv_smul, Derivation.linearEquiv_coe_to_linearMap_comp, Submodule.isTorsion'_powers_iff, Submodule.sum_smul_mem, Prod.segment_subset, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, smul_nonpos_iff, HasFPowerSeriesAt.comp, HasFDerivAt.continuousMultilinear_apply_const, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousLinearMap.IsPositive.smul_of_nonneg, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, InnerProductSpace.rankOne_apply, Convex.combo_eq_smul_sub_add, ConcaveOn.smul_convexOn, FormalMultilinearSeries.sum_of_finite, RingTheory.Sequence.isRegular_cons_iff, Ideal.finsuppTotal_apply_eq_of_fintype, ConcaveOn.comp_linearMap, ContinuousLinearEquiv.map_smul, extremePoints_pi, Submodule.reflection_singleton_apply, SkewMonoidAlgebra.mapDomain_mul, LinearOrderedField.smul_Iio, IntermediateField.isScalarTower, smul_unitClosedBall_of_nonneg, HasFTaylorSeriesUpToOn.zero_eq', KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, Asymptotics.IsLittleOTVS.trans_isThetaTVS, Fintype.expect_ite_eq, MulSemiringActionHom.map_smulₛₗ, MultilinearMap.map_insertNth_smul, QuotSMulTop.equivTensorQuot_naturality_mk, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, IsSMulRegular.of_right_eq_zero_of_smul, Subring.mem_pointwise_smul_iff_inv_smul_mem, isIntegralCurveAt_comp_mul_ne_zero, smulMemClass, HasStrictDerivAt.clm_comp, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, PiLp.isBoundedSMulSeminormedAddCommGroupToPi, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, inv_intCast_smul_comm, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, smul_eq_smul_iff_eq_and_eq_of_pos', MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, ValuationSubring.mem_inv_pointwise_smul_iff, ContDiffMapSupportedIn.monoLM_apply, HasDerivWithinAt.Iic_of_Iio, ContinuousMultilinearMap.norm_smulRightL_le, Multiset.sum_smul_sum, balancedCore_nonempty_iff, StrictConvex.affine_image, WeakFEPair.h_feq, derivWithin_clm_comp, LinearMap.ker_restrictScalars, differentiableAt_smul_iff, Antitone.convex_le, ContinuousLinearMap.precompL_apply, Seminorm.closedBall_smul_ball, egauge_univ, Algebra.normalizedTrace_algebraMap, Subalgebra.coe_pointwise_smul, IsSelfAdjoint.adjoint_eq, Antitone.quasiconvexOn, Submodule.smul_mem', Submodule.mem_ideal_smul_span_iff_exists_sum', MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', mem_tangentConeAt_of_segment_subset, Asymptotics.IsLittleOTVS.prodMk, TrivSqZeroExt.fst_exp, DirectSum.mk_smul, curveIntegralFun_segment, HasDerivWithinAt.clm_apply, SchwartzMap.integral_fourierInv_smul_eq, Submodule.smul_iSup', DifferentiableAt.hasDerivAt, MonovaryOn.sum_comp_perm_smul_le_sum_smul, OrderDual.instIsStrictOrderedModule, RootPairing.coroot_eq_smul_coroot_iff, RKHS.kernel_apply, HasDerivAt.finCons, Seminorm.bound_of_continuous_normedSpace, Besicovitch.SatelliteConfig.exists_normalized_aux2, HasDerivAtFilter.add, groupHomology.isBoundary₁_of_mem_boundaries₁, exists_nonneg_left_iff_sameRay, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, DFinsupp.smul_apply, LinearMap.BilinForm.isOrtho_smul_left, FormalMultilinearSeries.radius_le_smul, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, DistribMulAction.toAddMonoidHom_apply, Absorbs.of_neg_neg, MDifferentiable.clm_postcomp, IsArtinian.exists_pow_succ_smul_dvd, TrivSqZeroExt.map_inr, ZeroHom.smul_comp, AntivaryOn.smul_add_smul_le_smul_add_smul, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, MeasureTheory.VectorMeasure.smul_apply, CStarMatrix.toCLM_injective, biUnion_associatedPrimes_eq_compl_regular, Asymptotics.IsLittleOTVS.insert, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, Complex.integral_circleTransform, ContinuousLinearMap.isPositive_self_comp_adjoint, MonoidAlgebra.smulCommClass, iteratedDeriv_scomp_eq_sum_orderedFinpartition, convexOn_univ_dist, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, MeasureTheory.Measure.IsAddHaarMeasure.domSMul, hasDerivAt_iff_isLittleO, LinearMap.rTensor_comp_flip_mk, IsStrictOrderedModule.toIsOrderedModule, Algebra.TensorProduct.sMulCommClass_right, Absorbs.eventually_nhdsNE_zero, Unitization.sqrt_inr, UniqueDiffWithinAt.smul, TopModuleCat.continuousSMul, LocallyConvexSpace.convex_basis_zero, NormedSpace.isBounded_iff_subset_smul_closedBall, KaehlerDifferential.isLocalizedModule_of_isLocalizedModule, BoundedContinuousFunction.instSMulCommClass_2, hasFPowerSeriesAt_const, Multiset.smul_sum, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, UniformOnFun.continuousSMul_induced_of_image_bounded, Subalgebra.inclusion.isScalarTower_left, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, Finsupp.linearCombination_smul, ConcaveOn.smul'', HasFDerivWithinAt.fun_const_smul, neg_one_smul, HasStrictFDerivAt.const_smul, Fintype.bilinearCombination_apply_single, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, Subring.mem_pointwise_smul_iff_inv_smul_mem₀, FormalMultilinearSeries.radius_compNeg, Fintype.expect_ite_zero, NormedAddGroupHom.smul_apply, LinearMap.coe_smul, IsBoundedBilinearMap.smul_left, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, quasispectrum.mem_iff_of_isUnit, SchwartzMap.integral_bilin_fourierIntegral_eq, TopologicalGroup.IsSES.pushforward_def, SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM, Real.fourierIntegral_continuousMultilinearMap_apply, ProbabilityTheory.HasGaussianLaw.smul, StrictConcaveOn.lt_map_sum, MonotoneOn.convex_ge, QuotSMulTop.map_comp_mkQ, HasStrictDerivAt.fun_sum, LinearIsometryEquiv.adjoint_eq_symm, smul_mem_closure_star_mul, extDeriv_fun_smul, VectorField.mpullback_const_smul_apply, Quaternion.im_smul, Ideal.finsuppTotal_apply, IsLocalizedModule.exist_integer_multiples, ContinuousAlternatingMap.toAlternatingMap_curryLeft, TensorProduct.flip_mk_surjective, LinearMap.smul_apply, StrictConvex.neg, Bornology.IsVonNBounded.image_multilinear', Finset.expect_ite_zero, Quaternion.imI_fst_dualNumberEquiv, HasDerivAt.congr_of_eventuallyEq, Complex.im_nnqsmul, mem_tangentConeAt_of_pow_smul, analyticOrderAt_smul_eq_top_of_left, mem_openSegment_sub_add, VectorFourier.fourierPowSMulRight_eq_comp, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, WithSeminorms.tendsto_nhds', ContinuousLinearMap.opNorm_mul, MvPowerSeries.smul_eq_C_mul, skewAdjoint.val_smul, Seminorm.pullback_apply, collinear_iff_of_mem, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, sameRay_iff_inv_norm_smul_eq_of_ne, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, norm_sum_lt_of_strictConvexSpace, Seminorm.bddAbove_of_absorbent, smul_rayOfNeZero, UniformConvexOn.strictConvexOn, Real.sInf_smul_of_nonneg, TemperedDistribution.smulLeftCLM_neg, Module.Dual.im_extendRCLike_apply, InnerProductSpace.Core.inner_smul_ofReal_right, Orientation.oangle_sign_sub_smul_left, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', MeasureTheory.SimpleFunc.integral_eq_sum_filter, egauge_zero_zero, smul_pos', Differentiable.fun_const_smul, Matrix.conjTranspose_inv_intCast_smul, TestFunction.lineDerivOpCLM_eq_lineDerivCLM, MDifferentiable.cle_arrowCongr, Asymptotics.IsLittleOTVS.neg_right, gauge_le_eq, segment_subset_convexHull, MeasureTheory.Measure.quasiMeasurePreserving_smul, HasSum.smul_eq, Polynomial.monic_of_isUnit_leadingCoeff_inv_smul, HasFTaylorSeriesUpTo.fderiv_eq, HasDerivAt.fun_pow', Unitization.nnnorm_def, LieModule.mem_weightSpace, instSMulCommClassMatrixFinOfNatNatProd, PowerSeries.le_order_smul, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, smul_eq_smul_iff_eq_and_eq_of_pos, Algebra.Extension.Cotangent.smul_eq_zero_of_mem, TestFunction.fderivCLM_ofSupportedIn, convexHull_toCone_eq_sInf, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson, ConcaveOn.inf, ediam_smul_le, Finset.zero_mem_smul_finset_iff, LinearMap.smulRight_apply, HasFDerivAt.fun_smul, Module.AEval'.X_smul_of, AdjoinRoot.smul_mk, Function.HasTemperateGrowth.toTemperedDistribution_apply, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, IsIntegralCurveOn.comp_mul, Orthonormal.inner_left_fintype, lie_smul, HasLineDerivAt.tendsto_slope_zero_right, Filter.TendstoCofinite.mapDomain_smul, Balanced.convexHull, Complex.hasDerivAt_GammaIntegral, AntitoneOn.convex_le, fderiv_continuousAlternatingMapCompContinuousLinearMap, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, Matrix.op_smul_one_eq_diagonal, IncidenceAlgebra.instIsScalarTower, Absorbent.gauge_set_nonempty, Submodule.pointwise_smul_toAddSubgroup, AddMonoid.nat_smulCommClass', Convex.cthickening, NonarchimedeanRing.left_mul_subset, PiTensorProduct.mapL_smul, SchwartzMap.integral_sesq_fourier_eq, DFinsupp.instSMulPosMono, DualNumber.lift_apply_eps, Real.fderiv_fourier, CategoryTheory.ShortComplex.Homotopy.smul_h₂, ContinuousLinearMap.adjointAux_norm, MeasureTheory.L1.setToL1_smul_left, Representation.smul_ofModule_asModule, CStarMatrix.norm_def', KaehlerDifferential.instIsScalarTowerTensorProduct, algebra_compatible_smul, AntitoneOn.convex_gt, MeasureTheory.Integrable.smul_bdd, MDifferentiable.clm_bundle_apply₂, Fintype.expect_dite_eq', MeasureTheory.convolution_smul, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, neg_smul_neg, hasDerivAtFilter_natCast, LinearMap.flip_injective_iff₁, Finsupp.linearCombination_one_tmul, CategoryTheory.Linear.units_smul_comp, meromorphicOrderAt_ne_top_iff, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, ConvexCone.coe_map, HahnSeries.SummableFamily.hsum_smul_module, ContinuousAlternatingMap.instContinuousSMul, DualNumber.inv_eps, IsLocalizedModule.map_linearMap_of_isLocalization, HasFDerivAt.restrictScalars, balancedHull_subset_convexHull_union_neg, StrictConvex.extremePoints_eq_diff_interior, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, SameRay.exists_eq_smul_add, CategoryTheory.Functor.Linear.map_smul, stereoInvFunAux_apply, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, StrongFEPair.functional_equation, MulSemiringAction.toRingEquiv_apply, MonotoneOn.convex_le, norm_curveIntegral_segment_le, Ideal.smul_sup, MonoidAlgebra.smulCommClass_self, Unitization.inl_mul, Representation.ofDistribMulAction_apply_apply, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, Submodule.coe_torsion', LocalizedModule.mk_eq, IsLinearMap.isLinearMap_smul', TensorProduct.AlgebraTensorModule.restrictScalars_curry, HasFDerivAtFilter.isThetaTVS_sub, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH, MonotoneOn.quasiconvexOn, Finset.mem_convexHull', StarConvex.affine_image, iteratedDeriv_smul_const, circleIntegral.integral_sub_inv_smul_sub_smul, Action.smul_hom, HasStrictFDerivAt.list_prod', Polynomial.natDegree_smul_of_smul_regular, CliffordAlgebra.foldr'Aux_foldr'Aux, SchwartzMap.fourier_lineDerivOp_eq, DifferentiableAt.smul, HasFDerivWithinAt.isThetaTVS_sub, Algebra.TensorProduct.basis_repr_tmul, LieAdmissibleAlgebra.toSMulCommClass, LinearMap.isBigOTVS_rev_comp, DFinsupp.smulCommClass, Real.sSup_smul_of_nonneg, LinearMap.toContinuousBilinearMap_apply, segment_single_subset_stdSimplex, Algebra.Extension.instIsScalarTowerH1CotangentOfCotangent, TemperedDistribution.instLineDerivLeftSMulReal, Submodule.span_singleton_eq_top_iff, CStarMatrix.inner_toCLM_conjTranspose_left, RootPairing.reflection_apply_root', hasStrictDerivAt_exp_smul_const, Submodule.FG.restrictScalars, PolynomialModule.monomial_smul_single, Subsemiring.smul_mem_pointwise_smul, Derivation.leibniz_div, EuclideanGeometry.inversion_vsub_center, Filter.EventuallyEq.ftaylorSeries, isBoundedBilinearMap_comp, StarConvex.smul_mem, lp.instIsCentralScalarPreLp, set_smul_sphere_zero, MeasureTheory.Integrable.essSup_smul, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, ContMDiff.smul, hasStrictDerivAt_add_const_iff, hasLineDerivWithinAt_smul_iff, Asymptotics.IsBigO.const_smul_left, Asymptotics.IsTheta.smul, TemperedDistribution.fourierInv_lineDerivOp_eq, MDifferentiable.const_smul, TrivSqZeroExt.lift_comp_inrHom, MeasureTheory.condExpL2_indicator_ae_eq_smul, Convex.openSegment_self_interior_subset_interior, SkewPolynomial.φ_iterate_apply, Asymptotics.IsBigOTVS.neg_right, ModuleCat.smulShortComplex_X₃_isAddCommGroup, conformalAt_const_smul, Submodule.span_smul_le, Ideal.pointwise_smul_subset_iff, IsMIntegralCurveOn.hasDerivWithinAt, IsLocalizedModule.mk'_add_mk', Polynomial.X_pow_smul_rTensor_monomial, Finsupp.sum_smul_index, FormalMultilinearSeries.rightInv_removeZero, IsUnit.smul_sub_iff_sub_inv_smul, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ClosedSubmodule.orthogonal_closure'', Submodule.smul_bot', HasDerivWithinAt.comp, hasStrictDerivAt_exp_smul_const', KaehlerDifferential.mapBaseChange_tmul, Module.DirectLimit.quotMk_of, openSegment_translate_image, egauge_univ_pi, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq, AffineSubspace.smul_vsub_vadd_mem, MeromorphicAt.fun_smul, Real.fourier_iteratedFDeriv, smul_pos_iff_of_pos_right, Polynomial.smul_monomial, CFC.negPart_smul_of_nonpos, HasDerivAt.add, SchwartzMap.smulLeftCLM_real_smul, strictConvex_uIcc, MeasureTheory.Measure.integral_comp_inv_mul_left, HasMFDerivAt.smul, TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm, HasStrictDerivAt.div, NormMulClass.toNormSMulClass_op, RootPairing.pairing_one_four_iff', ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, MeasureTheory.measure_smul_average, MDifferentiableOn.smul, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, TrivSqZeroExt.fst_invOf, Ideal.instCovariantClassHSMulLe, Orientation.oangle_sign_sub_smul_right, hasDerivAtFilter_zero, Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone, segment_subset_convexJoin, StrictConvex.is_linear_preimage, Algebra.Generators.H1Cotangent.δAux_C, Complex.integral_comp_polarCoord_symm, NormedAddGroupHom.isCentralScalar, Seminorm.map_eq_zero_of_norm_zero, smul_closedBall', spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, closure_smul₀, HasFDerivAt.fun_const_smul, ConvexCone.coe_comap, LinearOrder.strictConvexOn_of_lt, Convex.combo_interior_closure_subset_interior, LocalizedModule.mk_cancel, PresheafOfModules.Sheafify.map_smul_eq, convex_iff_openSegment_subset, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Orientation.oangle_smul_left_self_of_nonneg, Monotone.convex_ge, UnitAddTorus.mFourierCoeff_toLp, NonUnitalSubalgebra.unitization_injective, Submodule.coe_toConvexCone, Submodule.smul_mem_pointwise_smul, ContinuousLinearMap.uniformContinuous_restrictScalars, Submodule.instSMulCommClass, TensorProduct.finsuppLeft_smul', LieSubmodule.instSMulMemClass, SubmodulesBasis.smul, ContinuousLinearMap.mulLeftRight_apply, mem_openSegment_translate, PowerSeries.coe_smul, isModuleTopologyOfFiniteDimensional, LinearMap.extendTo𝕜'_apply, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, MonotoneOn.convex_gt, fromTangentSpace_mfderiv_smul_apply, Differentiable.const_smul, Seminorm.ball_eq_emptyset, ArchimedeanClass.mk_le_mk_smul, taylor_tendsto, dslope_sub_smul, MeasureTheory.IntegrableAtFilter.smul, rescale_to_shell_semi_normed_zpow, HasFDerivAt.curveIntegral_segment_source, Algebra.TensorProduct.basisAux_map_smul, balancedCore_mem_nhds_zero, convexJoin_segment_singleton, SameRay.exists_eq_smul, DirectSum.instSMulCommClass, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, CentroidHom.instSMulCommClass_2, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, deriv_fun_smul, AddMonoidAlgebra.smulCommClass, ConvexCone.salient_strictlyPositive, iteratedFDeriv_comp_const_smul, LocalizedModule.mem_ker_mkLinearMap_iff, Algebra.IsInvariant.exists_smul_of_under_eq, HasStrictDerivAt.mul, PresheafOfModules.Derivation.d_mul, TensorProduct.equivFinsuppOfBasisRight_apply_tmul, Matrix.smul_vecMul, Bundle.Trivialization.eq_sum_localFrame_coeff_smul, LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, MeasureTheory.convolution_lsmul, QuadraticMap.map_smul, MDifferentiableAt.clm_postcomp, fderiv_continuousAlternatingMap_apply, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, abs_nnqsmul, SeminormFamily.finset_sup_comp, Module.Dual.norm_extendRCLike_apply_sq, Submodule.mem_span_finset, Bornology.isVonNBounded_iff_absorbing_le, Module.AEval.instIsScalarTowerOrigPolynomial, CategoryTheory.Pretriangulated.Triangle.smul_hom₂, ContDiffMapSupportedIn.monoLM_eq_of_scalars, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim, Module.AEval.C_smul, Algebra.Extension.CotangentSpace.map_tmul, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, element_smul_restrictScalars, strongConcaveOn_zero, integral_withDensity_eq_integral_smul, Representation.ofMulAction_self_smul_eq_mul, intervalIntegral.integral_comp_add_div, Matrix.instSMulCommClassForall_1, convex_singleton, HasDerivAt.pow, deriv_fderiv, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, RegularNormedAlgebra.isometry_mul', fwdDiff_const_smul, convexJoin_singleton_segment, cauchyPowerSeries_apply, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, mem_smul_of_egauge_lt, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, DifferentiableAt.const_smul, RootPairing.mem_range_root_of_mem_range_reflection_of_mem_range_root, BoxIntegral.HasIntegral.smul, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, Ideal.range_mul, integral_smul_const, CStarModule.inner_smul_right_real, Module.exists_nontrivial_relation_of_finrank_lt_card, MDifferentiableWithinAt.clm_bundle_apply₂, TrivSqZeroExt.algHom_ext'_iff, fun_meromorphicOrderAt_smul, SameRay.inv_norm_smul_eq, TestFunction.limitCLM_apply, Module.IsTorsionBySet.mk_smul, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul, hasDerivWithinAt_abs, Algebra.TensorProduct.linearMap_comp_rid, hasFPowerSeriesOnBall_const, CentroidHom.toEnd_smul, Summable.tsum_const_smul, HasFDerivAt.clm_apply, openSegment_eq_image', HasStrictDerivAt.const_mul, ContDiffMapSupportedIn.seminorm_le_iff, HahnSeries.SummableFamily.smul_apply, ConcaveOn.convex_strict_hypograph, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, NonUnitalStarSubalgebra.unitization_range, smul_nonneg', Complex.UnitDisc.instSMulCommClass_circle_left, smul_nonpos_iff_pos_imp_nonpos, MeasureTheory.Measure.integral_comp_smul_of_nonneg, Polynomial.sum_smul_index, VectorFourier.hasFDerivAt_fourierIntegral, DiffContOnCl.circleIntegral_sub_inv_smul, Submodule.smul_sup', HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, TensorProduct.Algebra.smul_def, LinearMap.flip_surjective_iff₁, LaurentPolynomial.smeval_C_mul, Seminorm.ball_norm_mul_subset, IsLocalizedModule.exist_integer_multiples_of_finset, WeakDual.instContinuousConstSMul, List.sum_smul, ClosedSubmodule.inner_real_eq_re_inner, ZeroHom.instIsCentralScalar, hasFDerivAt_ringInverse, ContinuousMultilinearMap.opNorm_smul_le, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, Matrix.toLinearMap₂'_apply, HasFDerivAt.continuousAlternatingMap_apply, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, MeasureTheory.convolution_precompR_apply, PolynomialModule.single_smul, SchwartzMap.compSubConstCLM_apply, IsNilpotent.exp_smul_eq_sum, MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc, VectorFourier.fourierIntegral_iteratedFDeriv, TopologicalAddGroup.IsSES.pushforward_apply_apply, rank_lt_rank_dual', QuotSMulTop.map_surjective, InformationTheory.hasDerivAt_klFun, IsLocalizedModule.mk'_eq_mk'_iff, InnerProductSpace.nnnorm_rankOne, iteratedDeriv_fun_const_smul, FreeLieAlgebra.liftAux_map_smul, Seminorm.closedBall_zero_eq_preimage_closedBall, MonotoneOn.quasilinearOn, Polynomial.smul_eq_C_mul, fderiv_smul, Filter.zero_smul_filter_nonpos, ArithmeticFunction.one_smul', OrthonormalBasis.orthogonalProjection_apply_eq_sum, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, Filter.BoundedAtFilter.smul, NonUnitalSubalgebra.unitization_range, LieModule.LinearWeights.map_smul, SemimoduleCat.Algebra.instIsScalarTowerCarrier, instIsOrderedModule, iteratedFDerivWithin_const_smul_apply, ModuleCat.CoextendScalars.smul_apply, HasDerivAt.fun_pow, egauge_zero_left, smul_eq_zero_of_left, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, starConvex_compl_Ici, LocalizedModule.equivTensorProduct_symm_apply_tmul, MeasureTheory.Integrable.smul, ContinuousLinearMap.norm_toSpanSingleton, FormalMultilinearSeries.continuousOn_of_finite, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, TensorProduct.finsuppScalarRight_apply_tmul, Submodule.topologicalClosure_map, Submodule.toConvexCone_top, Representation.single_smul, OrderDual.instSMulPosStrictMono, LinearOrderedField.smul_Ico, Polynomial.isScalarTower, FormalMultilinearSeries.ofScalars_series_of_subsingleton, Ideal.under_smul, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, affinity_unitClosedBall, ContinuousLinearMap.flip_smul, Module.FinitePresentation.linearEquivMap_symm_apply, ContDiffMapSupportedIn.coe_smul, HasDerivAtFilter.mono, PadicInt.mahlerSeries_apply, HasFDerivAt.isBigOTVS_sub, HasDerivWithinAt.fun_pow', LieModuleHom.coe_smul, AffineSubspace.coe_smul, Module.Dual.extendRCLike_apply, ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem, MeasureTheory.integral_singleton', HasCompactSupport.hasDerivAt_convolution_right, Finsupp.coe_pointwise_smul, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, OreLocalization.oreDiv_add_char', HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, Finset.affineCombination_eq_linear_combination, HasDerivWithinAt.const_add, SameRay.pos_smul_left, Coalgebra.TensorProduct.lid_tmul, Module.Basis.constrL_apply, Module.AEval'.of_symm_X_smul, QuadraticMap.associated_apply, HasFDerivWithinAt.const_smul, ModuleFilterBasis.smul_right, MeasureTheory.ConvolutionExistsAt.integrable_swap, NormedSpace.expSeries_sum_eq, nndist_smul_le, norm_inner_eq_norm_iff, MeasureTheory.FinMeasAdditive.smul, IsLocalizedModule.finsetIntegerMultiple_image, RootPairing.weylGroup_apply_root, Real.circleAverage_eq_circleIntegral, HasFiniteFPowerSeriesOnBall.eq_partialSum, image_openSegment, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, hasDerivAt_tsum_of_isPreconnected, subset_balancedCore, Submodule.mul_mem_smul_iff, FormalMultilinearSeries.ofScalars_add, ContinuousAlternatingMap.coe_smul, ContMDiffCovariantDerivativeOn.finite_affine_combination, convexOn_dist, Filter.NeBot.smul_zero_nonneg, LinearIsometryEquiv.smul_apply, convexOn_iff_forall_pos, nnnorm_cfcₙ_nnreal_lt, inner_eq_norm_mul_iff_div, convex_Ico, Submodule.topologicalClosure_eq_self, Submodule.smul_subset_smul, SameRay.nonneg_smul_right, LinearMap.hasStrictDerivAt, real_linearMap_map_smul_complex, AffineMap.hasDerivAt_lineMap, AddMonoidHom.instSMulCommClass, fderivWithin_continuousAlternatingMap_apply_const_apply, MeasureTheory.setToFun_smul_left', ratCast_smul_eq, MeasureTheory.integral_smul, Seminorm.convexOn, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left', Subring.coe_pointwise_smul, mellinInv_eq_fourierIntegralInv, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, ProbabilityTheory.strong_law_ae, HasDerivWithinAt.fun_finset_prod, Convex.semilinear_image, Derivation.comp_aeval_eq, Algebra.Extension.Cotangent.val_smul''', HasDerivWithinAt.norm_sq, CStarModule.inner_smul_right_complex, HasGradientAtFilter.hasDerivAtFilter', ContDiffOn.const_smul, Polynomial.cauchyBound_smul, Seminorm.balanced_closedBall_zero, ValuationSubring.smul_mem_pointwise_smul_iff, zmod_smul_mem, dualTensorHom_apply, LinearEquiv.mem_fixedSubmodule_transvection_iff, HahnSeries.coeff_smul, SmoothPartitionOfUnity.contDiffAt_finsum, IsInvariantSubring.smul_mem, ContMDiffAt.smul, Mathlib.Tactic.Module.NF.add_eq_eval₃, TrivSqZeroExt.map_comp_inlAlgHom, AddMonoidAlgebra.smul_single, intervalIntegral.integral_hasDerivWithinAt_left, GeneralSchauderBasis.expansion, ofNat_smul_eq_nsmul, HasFPowerSeriesOnBall.fderiv_eq, Finsupp.weight_single, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, Seminorm.coe_restrictScalars, strictConvex_closedBall, NormedSpace.toNormSMulClass, Finset.sum_smul_const_vsub_eq_vsub_affineCombination, Quaternion.fst_imK_dualNumberEquiv_symm, midpoint_eq_smul_add, IsCovariantDerivativeOn.smul_const, Submodule.smul_le_self_of_tower, RootPairing.Equiv.root_indexEquiv_eq_smul, Asymptotics.IsLittleOTVS.zero, isBigO_rpow_top_log_smul, HasDerivAtFilter.fun_add, AffineMap.left_vsub_lineMap, SchwartzMap.smulLeftCLM_sum, midpoint_sub_right, CompactlySupportedContinuousMap.smul_apply, Submodule.smul_mem_span_smul_of_mem, AffineMap.hasDerivWithinAt_lineMap, Asymptotics.IsLittleOTVS.congr_left, ContinuousLinearMap.fderiv_of_bilinear, TestFunction.coe_smul, has_fderiv_at_filter_real_equiv, MeasureTheory.setIntegral_condExpInd, Seminorm.gaugeSeminorm_ball, MeasureTheory.Measure.addHaarScalarFactor_smul_congr, ContinuousLinearMap.nnnorm_toSpanSingleton, FixedPoints.mem_addSubmonoid, ContinuousAlternatingMap.alternatizeUncurryFin_smul, PresheafOfModules.map_smul, fderiv_mul_const', tendsto_integral_exp_smul_cocompact, Matrix.linftyOpIsBoundedSMul, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Complex.hasDerivAt_Gammaℝ_one, Ring.uniformContinuousConstSMul, ContDiffMapSupportedIn.monoCLM_eq_of_scalars, curveIntegral_segment, Module.Ray.linearEquiv_smul_eq_map, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, DualNumber.fst_eq_zero_iff_eps_dvd, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Asymptotics.isBigOTVS_iff_smallSets, Derivation.leibniz_inv, Real.fourierIntegral_continuousLinearMap_apply, smul_left_inj, LinearMap.isAlt_iff_eq_neg_flip, Submodule.adjoint_subtypeL, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, Mathlib.Tactic.LinearCombination.smul_lt_const, ConvexOn.sub, HasDerivAtFilter.sub, midpoint_mem_openSegment, gauge_norm_smul, MatrixEquivTensor.toFunBilinear_apply, InnerProductSpace.Core.cauchy_schwarz_aux, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, ContinuousLinearMap.opNorm_mul_apply, PosSMulMono.of_pos, ContinuousLinearMap.norm_smulRightL, SMulCommClass.toDistribMulActionHom_toFun, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, TrivSqZeroExt.inl_mul_inr, IsNilpotent.smul, DFinsupp.toFinsupp_smul, Asymptotics.IsBigOWith.const_smul_left, SkewMonoidAlgebra.coeff_mul_single_of_not_exists_mul, TrivSqZeroExt.fst_list_prod, AddConstMap.coe_smul, convexOn_univ_norm, DistribSMul.ext_iff, HasFDerivWithinAt.fun_smul, AffineMap.lineMap_vsub_right, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, Submodule.exists_isTorsionBy, intervalIntegral.integral_deriv_comp_smul_deriv', strictAnti_smul_left, MeasureTheory.convolution_def, QuaternionAlgebra.star_smul', ContinuousMultilinearMap.curryLeft_norm, Seminorm.ball_zero_eq_preimage_ball, lp.norm_const_smul, finsuppTensorFinsuppLid_symm_single_smul, HasCompactSupport.smul_left, Module.reflection_mul_reflection_pow_apply, Matrix.diagonal_smul, CategoryTheory.Abelian.Ext.mk₀_smul, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, SMulPosStrictMono.toSMulPosMono, MeasureTheory.Submartingale.smul_nonneg, MDifferentiableWithinAt.cle_arrowCongr, Balanced.add, ConvexOn.openSegment_subset_strict_epigraph, TensorProduct.tmul_smul, CStarModule.inner_smul_left_complex, openSegment_subset_ball_of_ne, HasFPowerSeriesWithinOnBall.prod, units_smul_eq_self_iff, NormedSpace.normalize_smul, MDifferentiableWithinAt.clm_precomp, smul_add_smul_lt_smul_add_smul, HasDerivAt.fun_add, SchwartzMap.fourierMultiplierCLM_sum, MeasureTheory.integrable_withDensity_iff_integrable_smul', HasDerivAt.neg, ContMDiffVectorBundle.continuousLinearMap, DFinsupp.mapRange_smul, IsMIntegralCurveOn.comp_mul, DenseRange.topologicalClosure_map_submodule, Prod.image_mk_segment_left, Matrix.isBoundedSMul, HasDerivAt.star, MvPolynomial.scalarRTensor_apply_tmul, Matrix.conjTranspose_inv_natCast_smul, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, RootPairing.mem_range_coroot_of_mem_range_coreflection_of_mem_range_coroot, ConvexBody.coe_smul, Polynomial.smeval_smul, Convex.combo_self_interior_subset_interior, infEDist_smul₀, Bornology.IsVonNBounded.neg, ContinuousLinearMap.continuous_restrictScalars, UniqueDiffWithinAt.dense_tangentConeAt, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, InnerProductGeometry.angle_eq_zero_iff, RootPairing.EmbeddedG2.twoShortAddLongRoot_eq, smul_add_smul_le_smul_add_smul, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, Asymptotics.IsBigOTVS.fun_add, AnalyticAt.smul, hasLineDerivAt_smul_iff, VectorField.lieBracket_const_smul_left, SameRay.sameRay_nonneg_smul_left, LinearIndependent.pair_smul_iff, neg_convexOn_iff, ENNReal.smul_top, Submodule.mem_smul_iff_inv_mul_mem, IsGaloisGroup.mulEquivCongr_apply_smul, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, Function.support_const_smul_subset, ContinuousAlternatingMap.map_piecewise_smul, mellinInv_eq_fourierInv, units_smul_eq_neg_iff, HasFPowerSeriesOnBall.uniform_geometric_approx, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_monotoneOn, Module.End.algebraMap_isUnit_inv_apply_eq_iff', ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, IsNilpotent.exp_smul, Finsupp.mapRange_smul, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, Convex.strictConvex, IsSl2Triple.mem_toLieSubalgebra_iff, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, HasDerivAtFilter.const_smul, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, NonUnitalAlgHom.coe_distribMulActionHom_mk, Submodule.mem_torsionBySet_iff, MulActionHom.coe_zero, Asymptotics.isBigOTVS_fun_neg_left, Ideal.stabilizerEquiv_symm_apply_smul, norm_smul_of_nonneg, sub_smul, VectorFourier.fourierIntegral_const_smul, HasFPowerSeriesWithinAt.fderivWithin_eq, Convex.span_tangentConeAt, inCoordinates_apply_eq₂, Asymptotics.isBigOTVS_fun_neg_right, KaehlerDifferential.tensorKaehlerEquivBase_tmul, AddSubmonoid.smul_le, ContDiffAt.contDiffAt_norm_smul, Real.fourier_real_eq, CentroidHom.smul_apply, MeasureTheory.setToFun_smul, SkewMonoidAlgebra.coeff_mul_right, FormalMultilinearSeries.id_comp', Seminorm.rescale_to_shell_zpow, FormalMultilinearSeries.ofScalars_sub, LaurentPolynomial.smeval_C, Asymptotics.IsEquivalent.smul, MeasureTheory.distribHaarChar_apply, MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_poles, prodXSubSMul.smul, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, Convex.openSegment_interior_self_subset_interior, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, Matrix.toEuclideanCLM_toLp, PiTensorProduct.liftAux.smul, Seminorm.smul_closedBall_zero, HasDerivAt.comp, AddMonoid.End.smul_apply, Seminorm.balanced_ball_zero, hasSum_fourier_series_L2, AddMonoidAlgebra.smul_apply, DualNumber.lift_inlAlgHom_eps, DifferentiableWithinAt.hasDerivWithinAt, isSMulRegular_submodule_iff_right_eq_zero_of_smul, Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNil, ZeroHom.coe_smul, mem_openSegment_of_ne_left_right, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, Ioo_smul_sphere_zero, HasFPowerSeriesOnBall.sum, Real.tendsto_integral_gaussian_smul', HasFDerivAt.comp_hasDerivAt, Mathlib.Tactic.Module.NF.eq_cons_const, Real.hasFDerivAt_fourier, LinearOrder.convexOn_of_lt, HasDerivWithinAt.mul, absorbs_iff_eventually_nhdsNE_zero, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, Antitone.convex_lt, CategoryTheory.ShortComplex.Homotopy.smul_h₀, AddMonoidAlgebra.smulCommClass_symm_self, QuadraticMap.polar_smul, fderiv_inverse, smul_sphere', SchwartzMap.smulLeftCLM_fun_neg, ClosedSubmodule.mulI_sup, two_smul, Ideal.IsPrime.smul_iff, PiLp.instNormSMulClass, MeasureTheory.setIntegral_countable, ContMDiffOn.clm_precomp, CategoryTheory.ShortComplex.Homotopy.smul_h₃, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, contDiffOn_nat_iff_continuousOn_differentiableOn, Module.Basis.isScalarTower_finsupp, CategoryTheory.ShortComplex.cyclesMap_smul, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Submodule.smul_coe_torsionBy, Fintype.not_linearIndependent_iffₛ, iteratedFDeriv_const_smul_apply', InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, map_nnrat_smul, stereoInvFun_apply, monovaryOn_iff_forall_smul_nonneg, TrivSqZeroExt.mul_left_eq_one, CompactlySupportedContinuousMap.coe_smul, SkewMonoidAlgebra.instFaithfulSMul, StrictConvexOn.translate_left, analyticAt_smul, Seminorm.restrictScalars_ball, Filter.EventuallyEq.hasDerivAt_iff, ConvexBody.coe_mk, LieAlgebra.Basis.baseSupp_apply_smul_f, InnerProductSpace.rankOne_eq_zero, egauge_le_one, Real.fourierIntegral_convergent_iff', MeasureTheory.AEFinStronglyMeasurable.const_smul, fderivWithin_continuousMultilinear_apply_const_apply, NonUnitalNonAssocRing.int_isScalarTower, LieModuleHom.smul_apply, Submodule.mem_annihilator, hasDerivAt_deriv_iff, Unitization.splitMul_injective_of_clm_mul_injective, RCLike.mul_wInner_left, Seminorm.continuous, Function.Antiperiodic.const_inv_smul₀, StrictConvexOn.translate_right, CliffordAlgebra.ι_mul_ι_mul_ι, ContinuousAlternatingMap.norm_curryLeft, Module.End.HasEigenvector.apply_eq_smul, MeasureTheory.integral_indicatorConstLp, CFC.nnrpow_map_pi, inner_map_polarization', HasStrictDerivAt.clog_real, smul_zero, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal, hasDerivAt_of_hasDerivAt_of_ne', intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, LieDerivation.ofGradingSum_of, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, MonoidAlgebra.faithfulSMul, QuadraticMap.polar_smul_left_of_tower, ContinuousLinearMapWOT.smul_apply, MeasureTheory.Measure.integral_comp_smul, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, Asymptotics.isBigOTVS_iff_isBigO, Asymptotics.IsLittleO.smul, setIntegral_withDensity_eq_setIntegral_smul₀', LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, Bornology.isVonNBounded_sub_of_nonempty, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, subset_tangentConeAt_prod_right, TrivSqZeroExt.snd_exp, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, MeasureTheory.condExpIndSMul_smul, fderivWithin_inv', KaehlerDifferential.isScalarTower_of_tower, TannakaDuality.FiniteGroup.sumSMulInv_apply, Submodule.isTorsion'_iff_torsion'_eq_top, hasDerivAt_add_const_iff, not_disjoint_segment_convexHull_triple, AlgEquiv.smul_def, MeasureTheory.Measure.hausdorffMeasure_smul₀, real_inner_div_norm_mul_norm_eq_one_iff, HahnSeries.coeff_smul', Monotone.ae_hasDerivAt, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, star_natCast_smul, ContinuousLinearMap.fderivWithin_of_bilinear, Module.Basis.smul_det, HasFPowerSeriesOnBall.compContinuousLinearMap, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonpos, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', AddMonoidAlgebra.isScalarTower, lineMap_mem_openSegment, iteratedDeriv_const_smul, Fintype.sum_single_smul, gaugeSeminorm_ball_one, LinearMap.BilinForm.smul_right_of_tower, ContinuousMultilinearMap.cons_smul, DiffContOnCl.deriv_eq_smul_circleIntegral, ContinuousLinearMap.applyFaithfulSMul, DifferentiableOn.deriv_eq_smul_circleIntegral, ContDiffMapSupportedIn.uniformSpace_eq_iInf, DomMulAct.coe_smul_addMonoidHom, Submodule.mem_span_singleton, iteratedFDerivWithin_smul_const_apply, Algebra.Generators.H1Cotangent.δAux_monomial, Mathlib.Meta.Positivity.smul_nonneg_of_nonneg_of_pos, PiTensorProduct.liftIsometry_tprodL, VectorField.mpullback_smul_apply, DualNumber.isNilpotent_iff_eps_dvd, TrivSqZeroExt.map_comp_inrHom, RootPairing.reflectionPerm_coroot, Disjoint.exists_open_convexes, UniformConvergenceCLM.continuousSMul, curveIntegral_segment_const, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, hasDerivWithinAt_one, ConvexOn.smul_concaveOn', le_egauge_smul_left, sub_smul_slope_vadd, LieRinehartAlgebra.toIsScalarTower, Algebra.Extension.instIsScalarTowerCotangent, Bundle.Trivialization.eventually_eq_localFrame_sum_coeff_smul, DualNumber.isMaximal_span_singleton_eps, HahnSeries.SummableFamily.smul_hsum, Seminorm.finset_sup_apply_lt, Convex.second_derivative_within_at_symmetric, AffineSubspace.setOf_wOppSide_eq_image2, BoxIntegral.BoxAdditiveMap.volume_apply, spinGroup.conjAct_smul_range_ι, ConvexCone.isGenerating_bot, ProbabilityTheory.HasGaussianLaw.fun_smul, ModuleCat.Derivation.d_mul, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, MeasureTheory.Integrable.toL1_smul, InnerProductSpace.rankOne_eq_rankOne_iff_comm, realPart_add_I_smul_imaginaryPart, ContinuousLinearMap.uniformContinuousConstSMul, Ideal.Quotient.smul_top, HasLineDerivAt.tendsto_slope_zero, Asymptotics.IsLittleOTVS.fst, SemilinearMapClass.map_smul_inv, HasDerivWithinAt.inner, subset_tangentConeAt_prod_left, LocalizedModule.mk_cancel_common_left, strictConvex_Ioo, ConvexBody.convex, ContinuousLinearMap.holder_smul_left, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, HahnSeries.SummableFamily.smul_support_subset_prod, sameRay_smul_left_iff, Quaternion.coe_smul, Set.smul_indicator_one_apply, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, Submodule.FG.restrictScalars_iff, Seminorm.comp_smul, IsGreatest.nnnorm_cfcₙ_nnreal, LieRinehartRing.lie_smul_eq_mul', absorbent_nhds_zero, ContMDiffAt.const_smul_section, Submodule.pointwise_smul_toAddSubmonoid, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Real.fourierIntegral_iteratedDeriv, intervalIntegral.smul_integral_comp_mul_sub, Derivation.leibniz', Derivation.leibniz_zpow, iteratedDerivWithin_smul_const, Mathlib.Tactic.Module.NF.sub_eq_eval₃, MeasureTheory.hasFDerivAt_convolution_right_with_param, InnerProductSpace.exists_of_rankOne_eq_rankOne, fderiv_pow', MeasureTheory.Lp.coeFn_smul, SkewMonoidAlgebra.sum_smul_index', ContMDiffSection.coe_smul, Asymptotics.IsLittleO.isLittleOTVS, hasDerivAt_ofNat, SchwartzMap.postcompCLM_apply, Asymptotics.IsLittleOTVS.neg_left, Ideal.tensorCotangentHom_tmul, iteratedFDerivWithin_eq_equiv_comp, Matrix.smul_kroneckerTMul, DifferentiableAt.isBigOTVS_sub, nhds_basis_balanced, Module.Quotient.mk_smul_mk, AlternatingMap.mkContinuousAlternating_norm_le, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ContDiffWithinAt.const_smul, VonNeumannAlgebra.centralizer_centralizer', FormalMultilinearSeries.mkPiRing_coeff_eq, differentialIdeal_le_iff, IsLocalizedModule.exist_integer_multiples_of_finite, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, RightPreLieAlgebra.toSMulCommClass, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, LinearMap.lsmul_flip_apply, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, IsModuleTopology.instProd, LinearIndependent.smul_left_injective, isLocalizedModule_iff, HahnEmbedding.Partial.exists_sub_mem_ball, Unitization.inr_mul, Representation.asModuleEquiv_symm_map_smul, Asymptotics.IsLittleOTVS.pi, Submodule.mem_span_iff_exists_finset_subset, LinearEquiv.transvection.apply, DualNumber.lift_smul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, SameRay.exists_pos_right, MeasureTheory.SimpleFunc.integral_eq_sum, Coalgebra.sum_counit_smul, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, iteratedDerivWithin_const_smul_field, Quaternion.imK_fst_dualNumberEquiv, Bundle.Pretrivialization.continuousLinearMap.isLinear, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonneg, HahnSeries.of_symm_smul_of_eq_mul, CFC.posPart_smul, TotallyBounded.isVonNBounded, UpperHalfPlane.hasStrictDerivAt_smul, smul_min_of_nonpos, IsSMulRegular.polynomial, NormedSpace.normalize_smul_of_pos, HahnSeries.SummableFamily.smul_toFun, Seminorm.comp_zero, ContinuousLinearMap.adjoint_inner_left, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, lift_rank_lt_rank_dual', Subring.mem_inv_pointwise_smul_iff, PointwiseConvergenceCLM.isInducing_inducingFn, KaehlerDifferential.tensorKaehlerEquiv_tmul, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, DomMulAct.coe_smul_linearMap, IsStrictOrderedRing.toIsStrictOrderedModule, Module.AEval'.X_pow_smul_of, Bornology.IsVonNBounded.image_multilinear, StarConvex.sub, groupHomology.isCycle₂_of_mem_cycles₂, LieRinehartAlgebra.Hom.map_smul_apply', Algebra.Generators.H1Cotangent.δAux_toAlgHom, ContDiffMapSupportedIn.seminorm_monoLM_le, Finsupp.linearCombination_single_index, intervalIntegral.integral_comp_smul_deriv'', Monovary.smul_add_smul_le_smul_add_smul, CochainComplex.HomComplex.Cochain.shift_smul, ContinuousLinearMap.isBoundedBilinearMap, WeakFEPair.Λ₀_eq, LinearMap.restrictScalars_self, ContinuousMultilinearMap.hasBasis_nhds_zero, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, LinearMap.extendTo𝕜_apply, RingTheory.Sequence.isWeaklyRegular_singleton_iff, HasDerivAt.sub, intervalIntegral.integral_comp_smul_deriv, SkewMonoidAlgebra.support_mul_single_eq_image, Module.piEquiv_apply_apply, HahnSeries.SummableFamily.smul_support_finite, LinearMap.BilinForm.smul_left, egauge_pi, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, Finsupp.lift_apply, ConvexOn.convex_epigraph, HasLineDerivWithinAt.smul, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, Submodule.dualCoannihilator_map_linearEquiv_flip, mdifferentiable_smul_const_section, HasStrictDerivAt.sum, Polynomial.adjSylvester_comp_sylveserMap, Finset.expect_eq_single_of_mem, FormalMultilinearSeries.apply_eq_pow_smul_coeff, fderivWithin_continuousMultilinear_apply_const, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, MeasureTheory.setIntegral_condExpIndSMul, Finset.weightedVSub_smul, totallyBounded_absConvexHull, Prod.smul_mk_zero, Asymptotics.isBigOTVS_congr, ContinuousLinearMap.toSpanSingleton_smul, MulSemiringAction.charpoly_eq_prod_smul, MeasureTheory.integrable_withDensity_iff_integrable_smul₀, AdicCompletion.AdicCauchySequence.smul_apply, inv_norm_smul_mem_unitClosedBall, Seminorm.neg_mem_ball_zero, star_ratCast_smul, Submodule.mapsTo_smul_closure, MulSemiringAction.smul_coeff_charpoly, LinearMap.isScalarTower_of_injective, Ideal.torsionOf_eq_span_pow_pOrder, ContinuousLinearEquiv.symm_smul_apply, Asymptotics.isBigOTVS_neg_right, TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply, VectorField.lieBracketWithin_smul_left, VectorField.mlieBracketWithin_const_smul_left, convex_halfSpace_ge, AffineMap.right_vsub_lineMap, Quaternion.re_fst_dualNumberEquiv, ContinuousAlternatingMap.ofSubsingletonLIE_apply, IsDivSequence.smul, ConvexOn.translate_left, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, MulSemiringActionHom.map_smul, TemperedDistribution.fourierMultiplierCLM_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, convex_list_sum, Seminorm.bound_of_continuous, ContDiff.euclidean_dist, cfcₙ_real_eq_complex, HasStrictDerivAt.smul, inner_eq_sum_norm_sq_div_four, AntivaryOn.sum_smul_le_sum_comp_perm_smul, intervalIntegral.integral_comp_add_mul, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, constFormalMultilinearSeries_apply_zero, ConvexBody.ext_iff, hasDerivAt_tsum, DifferentiableAt.fderiv_restrictScalars, starConvex_iff_forall_ne_pos, AnalyticAt.fun_smul, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, Matrix.Module.smul_def, Representation.IntertwiningMap.smul_apply, MeasureTheory.setIntegral_rnDeriv_smul, LinearIsometryEquiv.conjStarAlgEquiv_trans, FormalMultilinearSeries.radius_smul_eq, RootPairing.smul_coroot_eq_of_root_add_root_eq, traceForm_dualSubmodule_adjoin, Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, ContinuousLinearMap.bilinearComp_zero_right, SkewMonoidAlgebra.single_mul_single, DivisibleHull.instIsStrictOrderedModuleNNRat, IsContMDiffRiemannianBundle.exists_contMDiff, ConcaveOn.comp_affineMap, Unitization.isStarProjection_inr_iff, ModuleCat.smulShortComplex_g, StarConvex.zero_smul, Function.support_smul, DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul, BaireSpace.instBarrelledSpace, MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm', hasDerivAtFilter_add_const_iff, TrivSqZeroExt.inl_smul, MultilinearMap.map_update_smul_left, MvPolynomial.coeff_smul, hasDerivAt_jacobiTheta₂_fst, HomologicalComplex.units_smul_f_apply, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, DFinsupp.filter_smul, HasDerivWithinAt.scomp_of_eq, MDifferentiableAt.const_smul, SkewMonoidAlgebra.support_single_mul_eq_image, MvPowerSeries.constantCoeff_smul, CFC.nnrpow_def, VertexOperator.ncoeff_apply, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, IsSl2Triple.lie_h_e_smul, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, TrivSqZeroExt.inr_mul_inr, convex_openSegment, Convex.taylor_approx_two_segment, DiffContOnCl.const_smul, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, LinearMap.flip_bijective_iff₁, subset_balancedHull, ConvexCone.pointed_positive, VectorFourier.fourierIntegral_convergent_iff, LinearMap.flip_bijective_iff₂, WithConv.matrixToLin'StarAlgEquiv_apply, AddMonoidHom.smul_comp, IsLocalizedModule.subsingleton_iff, CompactlySupportedContinuousMap.smulc_apply, ContinuousLinearMap.adjointAux_apply, RCLike.real_smul_eq_coe_smul, IsTopologicalSemiring.toIsModuleTopology, Function.support_smul_subset_right, cfcₙ_comp_re, integral_comp_polarCoord_symm, Set.zero_mem_smul_set_iff, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, BoundedContinuousFunction.instIsScalarTower_1, IsCompactOperator.hasEigenvalue_or_mem_resolventSet, fderivWithin_fun_mul', CategoryTheory.Functor.map_smul, sup_eq_half_smul_add_add_abs_sub', Module.Basis.coe_smul, ProperCone.innerDual_singleton, VonNeumannAlgebra.coe_mk, Algebra.TensorProduct.isScalarTower_right, Filter.zero_smul_filter, Asymptotics.IsLittleO.smul_isBigO, MonotoneOn.convex_lt, HasFPowerSeriesWithinOnBall.sub, TemperedDistribution.fourierMultiplierCLM_const, HasLineDerivAt.tendsto_slope_zero_left, StrictConvexOn.add, Submodule.coe_pointwise_smul, Balanced.subset_smul, ConcaveOn.mul', ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, derivWithin_const_smul_field, StrictConvexOn.map_sum_eq_iff, Antitone.convex_ge, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, hasFDerivAt_integral_of_dominated_loc_of_lip', CliffordAlgebra.invOf_ι_mul_ι_mul_ι, ConvexCone.coe_strictlyPositive, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, Asymptotics.isLittleO_const_smul_left, DifferentiableOn.fun_const_smul, RKHS.kerFun_dense, VectorField.mpullback_const_smul, InnerProductSpace.rankOne_def, HasDerivAt.smul_const, ConvexOn.add_strictConvexOn, contDiff_const_smul, smul_vsub_vadd_mem_affineSpan_pair, HasDerivAtFilter.sub_const, smul_nonneg_of_nonpos_of_nonpos, ContinuousLinearMap.coe_flipₗᵢ', MDifferentiableAt.clm_bundle_apply₂, WeakFEPair.h_feq', star_nnrat_smul, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, uniqueDiffWithinAt_iff, SchwartzMap.convolution_apply, Polynomial.smul_mem_rootSet_iff, Submodule.IsPrincipal.mem_iff_eq_smul_generator, PointedCone.pointed_toConvexCone, fderivWithin_fderivWithin_eq_of_mem_nhds, Unitization.inr_smul, Submodule.IsLattice.smul, ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, Set.zero_mem_smul_iff, contDiff_iff_continuous_differentiable, Asymptotics.IsLittleOTVS.exists_eventuallyLE_mul_ennreal, Finsupp.instFaithfulSMulOfNonempty, hasDerivAt_const, dslope_sub_smul_of_ne, Finset.centerMass_smul_left, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Submodule.coe_tensorSpanEquivSpan_apply_tmul, Module.End.aeval_apply_of_hasEigenvector, CategoryTheory.Abelian.Ext.smul_comp, fderiv_mul', Filter.EventuallyEq.ftaylorSeriesWithin, UniformSpace.Completion.norm_toComplL, Seminorm.uniformContinuous_of_continuousAt_zero, IsRegular.smul_right_injective, fderivWithin_const_smul_of_field, Bornology.IsVonNBounded.tendsto_smallSets_nhds, Matrix.toLin_self, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, ContinuousMap.toLp_def, ContDiffAt.const_smul, OrderDual.instSMulPosReflectLE, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, instSMulDistribClassAlgEquiv, Complex.hasDerivAt_Gammaℂ_one, MulSemiringAction.smul_charpoly, VectorField.lieBracket_fmul_left, Module.Basis.SmithNormalForm.snf, Asymptotics.IsBigOTVS.snd, iteratedDerivWithin_fun_const_smul_field, sup_eq_half_smul_add_add_abs_sub, RootPairing.pairing_neg_one_neg_four_iff, SchwartzMap.integral_bilin_fourier_eq, HasFDerivWithinAt.lim, Polynomial.smeval_C, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, smul_neg, ConcaveOn.quasiconcaveOn, DifferentiableOn.clm_comp, ContDiffMapSupportedIn.monoCLM_apply, ftaylorSeriesWithin_zero, LinearMap.CompatibleSMul.finsupp_dom, ContinuousMultilinearMap.prodL_apply, Seminorm.add_comp, Finset.smul_neg, segment_eq_image, HasStrictDerivAt.mul_const, Matrix.conjTranspose_inv_ofNat_smul, InnerProductSpace.HarmonicContOnCl.const_smul, set_smul_mem_nhds_zero_iff, affinity_unitBall, convex_eball, instPosSMulStrictMono, hasFTaylorSeriesUpToOn_succ_iff_right, StrictConcaveOn.convex_gt, ContinuousOn.clm_bundle_apply₂, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, StrictConvex.add_left, Seminorm.bddAbove_iff, Matrix.IsDiag.smul, Convex.is_linear_preimage, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, LinearEquiv.map_smulₛₗ, IsGaloisGroup.faithful, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, MulActionHom.coe_sub, ModuleFilterBasis.smul_left', SchwartzMap.compCLMOfAntilipschitz_apply, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, HasDerivWithinAt.fun_neg, LinearIsometryEquiv.conjStarAlgEquiv_refl, HasDerivAt.tendsto_slope_zero_left, InnerProductSpace.laplacian_smul, MeasureTheory.setToFun_smul_left, MeasureTheory.MemLp.const_smul, HasDerivAt.complexToReal_fderiv', IsBaseChange.lift_comp, LinearMap.separatingRight_iff_flip_ker_eq_bot, AddMonoid.End.smul_def, MvPolynomial.mkDerivationₗ_monomial, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, starConvex_iff_openSegment_subset, mem_segment_iff_sameRay, derivWithin_fun_const_smul, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', ContinuousAlternatingMap.map_update_smul, eventually_singleton_add_smul_subset, MeasureTheory.L1.setToL1_smul_left', Matrix.fin_two_smul_prod, TensorProduct.finsuppScalarRight_smul, Module.Ray.units_smul_of_pos, Antivary.sum_smul_lt_sum_comp_perm_smul_iff, mem_extremePoints_iff_forall_segment, HasCompactSupport.smul_right, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, Asymptotics.IsBigOTVS.fun_symm, Submodule.mem_singleton_set_smul, Orientation.map_eq_det_inv_smul, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, Seminorm.continuousAt_zero', ContinuousLinearMap.coe_restrict_scalarsL', fderivWithin_fderivWithin_eq_of_eventuallyEq, StandardSubspace.IsCyclic, IsSMulRegular.submodule, Real.fourierIntegral_real_eq_integral_exp_smul, ConvexCone.mem_map, CochainComplex.HomComplex.Cochain.leftUnshift_smul, InnerProductSpace.laplacianWithin_smul, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2, StrongDual.polarSubmodule_eq_polar, HasDerivWithinAt.Ici_of_Ioi, Algebra.IsInvariant.orbit_eq_primesOver, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, LocallyFinite.smul_left, StrictConvex.affinity, Matrix.op_smul_eq_mul_diagonal, algebraMap_smul, Real.deriv_fourierIntegral, PiTensorProduct.liftEquiv_symm_apply, PiToModule.fromMatrix_apply_single_one, Finsupp.instSMulPosReflectLT, Algebra.Extension.CotangentSpace.map_sub_map, TestFunction.coe_ofSupportedInLM, HasStrictDerivAt.cexp, QuadraticMap.associated_toQuadraticMap, RingHom.applyFaithfulSMul, Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, extDerivWithin_fun_smul, inner_smul_real_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Asymptotics.isLittleOTVS_fun_neg_right, ftaylorSeries_fun_zero, SchauderBasis.proj_apply, TensorProduct.CompatibleSMul.smul_tmul, IsLocalizedModule.mem_ker_iff, ConvexCone.strictlyPositive_le_positive, ContDiffWithinAt.smul, HasDerivAt.add_const, cfcₙ_comp_im, Asymptotics.IsLittleOTVS.triangle, Seminorm.closedBall_finset_sup, AddSubmonoid.smul_mem_pointwise_smul, Antivary.sum_smul_le_sum_smul_comp_perm, MeasureTheory.SignedMeasure.re_toComplexMeasure, Mathlib.Tactic.ComputeDegree.natDegree_smul_le_of_le, TemperedDistribution.smulLeftCLM_sub, fromTangentSpace_mfderiv_smul', HasDerivAt.of_isLittleO, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, ZMod.algebraOfModule.proof, Seminorm.uniformSpace_eq_of_hasBasis, eq_pos_convex_span_of_mem_convexHull, SchwartzMap.postcompCLM_postcompCLM, OreLocalization.oreDiv_add_oreDiv, TensorProduct.lid_tmul, PolynomialModule.isScalarTower', IsBoundedLinearMap.smul, DualNumber.exists_mul_left_or_mul_right, SMulPosMono.of_pos, iteratedDerivWithin_scomp_eq_sum_orderedFinpartition, SModEq.smul', intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, fourierCoeff.const_smul, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, BddBelow.smul_of_nonpos, monovary_iff_forall_smul_nonneg, Unitization.inl_mul_inl, Submodule.smul_le_smul, closure_openSegment, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', HasDerivAt.sub_const, biUnion_associatedPrimes_eq_zero_divisors, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, IsLocalizedModule.map_linearCombination, hasSum_cauchyPowerSeries_integral, Convex.combo_interior_self_subset_interior, ContinuousLinearMap.aestronglyMeasurable_comp₂, MeasureTheory.Lp.instFourierSMul, SchwartzMap.smulLeftCLM_const, MeasureTheory.integral_fintype, uniformContinuousConstSMul_of_continuousConstSMul, smul_top_inf_eq_smul_of_isSMulRegular_on_quot, LinearEquiv.piRing_symm_apply, MDifferentiableAt.smul_section, ConvexCone.disjoint_hull_left_of_convex, Set.OrdConnected.convex, Asymptotics.IsBigOTVS.congr_left, Mathlib.Tactic.LinearCombination.smul_le_const, strictConvexSpace_iff, intervalIntegral.smul_integral_comp_sub_mul, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, Asymptotics.IsLittleOTVS.smul_left, Ideal.inertiaEquiv_apply_smul, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, hasDerivAt_of_tendstoUniformlyOn, Asymptotics.isLittleO_const_smul_right, Balanced.smul_mem_mono, smul_right_injective, Asymptotics.IsBigOTVS.proj, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, StarConvex.linear_image, Orientation.inner_rotation_pi_div_two_left_smul, sameRay_smul_left_iff_of_ne, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, smul_sphere, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, strictConvex_Iio, MeasureTheory.Measure.toSignedMeasure_smul, star_inv_intCast_smul, HVertexOperator.compHahnSeries_smul, HasStrictDerivAt.scomp_of_eq, DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap, HasStrictDerivAt.fun_finset_prod, ConvexCone.toPointedCone_top, fourierIntegral_eq_half_sub_half_period_translate, LinearMap.range_toContinuousLinearMap, Bornology.IsVonNBounded.of_sub_right, linearDepOn_iff, Ideal.exact_mulQuot_quotOfMul, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, fderiv_const_smul_of_invertible, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, Matrix.inner_toEuclideanCLM, Ideal.Cotangent.smul_eq_zero_of_mem, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, Subring.mem_smul_pointwise_iff_exists, hasFDerivWithinAt_pow', SkewMonoidAlgebra.instIsScalarTower, HahnModule.coeff_smul_order_add_order, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, HahnModule.of_symm_smul, hasStrictDerivAt_finCons', Submodule.mem_colon_iff_le, LinearMap.transvection.apply, isScalarTower_closedBall_ball_ball, AffineSubspace.smul_mem_smul_iff_of_isUnit, hasDerivWithinAt_taylorWithinEval_at_Icc, Set.univ_smul_nhds_zero, ContinuousLinearMap.isBoundedLinearMap_comp_right, AdjoinRoot.smul_of, Matrix.toLinearMapₛₗ₂_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Matrix.mul_mul_right, HasFPowerSeriesWithinAt.pi, MultilinearMap.freeDFinsuppEquiv_single, Module.Basis.isUnitSMul_apply, NormedSpace.isVonNBounded_iff', VonNeumannAlgebra.mem_carrier, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, TestFunction.lineDerivCLM_add, hasStrictDerivAt_finCons, PiTensorProduct.liftEquiv_apply, intervalIntegral.integral_deriv_comp_smul_deriv, Asymptotics.IsLittleOTVS.trans_isBigOTVS, WeakDual.isBounded_iff_isVonNBounded, StarAlgEquiv.ofBijective_apply, Matrix.convex_colStochastic, HasDerivWithinAt.congr_of_eventuallyEq_of_mem, Matrix.vecMul_eq_sum, has_antideriv_at_fourier_neg, hasFTaylorSeriesUpTo_top_iff', MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, Set.neg_smul, groupHomology.isBoundary₂_of_mem_boundaries₂, fderivWithin_iteratedFDerivWithin, fromTangentSpace_mfderiv_smul_apply', Convex.isLittleO_alternate_sum_square, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, HahnModule.instIsScalarTowerHahnSeries_1, rescale_to_shell, Polynomial.smul_X, mem_openSegment_add_sub, ConvexOn.map_sum_le, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, Submodule.mem_span_set, GradedMonoid.smulCommClass_right, Subspace.flip_quotDualCoannihilatorToDual_bijective, PiTensorProduct.liftAux_tprodCoeff, Polynomial.smul_sum, closure_convexHull_extremePoints, ContinuousLinearMap.deriv_of_bilinear, balanced_neg, Orientation.areaForm'_apply, HasStrictDerivAt.comp_of_eq, segment_inter_eq_endpoint_of_linearIndependent_of_ne, openSegment_eq_image, Continuous.cfcₙ_nnreal, ContinuousLinearMap.nnnorm_holder_apply_apply_le, LinearMap.toSpanSingleton_smul, TrivSqZeroExt.mul_inv_cancel, Set.Nonempty.smul_zero, Polynomial.coe_smul, AffineMap.isCentralScalar, Asymptotics.isTheta_const_smul_left, intervalIntegral.integral_smul_measure, upperBounds_smul_of_neg, signedDist_smul_of_pos, Distribution.mapCLM_apply, Matrix.mul_single_eq_updateCol_zero, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange, HasDerivAtFilter.star, isSMulRegular_of_isSMulRegular_on_submodule_on_quotient, WeakDual.CharacterSpace.toAlgHom_apply, TensorProduct.finsuppScalarRight_apply_tmul_apply, starConvex_zero_iff, Derivation.coe_comp, DFinsupp.instPosSMulStrictMono, ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule, infEdist_smul₀, Set.subsingleton_zero_smul_set, ContinuousLinearMap.bilinear_hasTemperateGrowth, IsBoundedBilinearMap.isBoundedLinearMap_deriv, Unitization.inrRangeEquiv_apply_coe_snd, Bornology.isVonNBounded_iff_smul_tendsto_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, Monotone.convex_lt, Ideal.Quotient.stabilizerHom_apply, Module.Basis.repr_symm_single, Module.reflection_reflection_iterate, TrivSqZeroExt.inv_mul_cancel, Polynomial.smul_eq_map, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, Convex.smul, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, lp.instSMulCommClassSubtypePreLpMemAddSubgroup, Subsemiring.smul_mem_pointwise_smul_iff₀, HasDerivAtFilter.scomp, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, AffineMap.lineMap_apply_module', LinearMap.flip_apply, Submodule.orthogonal_orthogonal_eq_closure, Pi.single_smul, LieRinehartRing.leibniz_smul_right', AnalyticOn.const_smul, StrictConvex.linear_preimage, isSMulRegular_iff_torsionBy_eq_bot, AffineSubspace.convex, Submodule.smul_starProjection_singleton, finsuppTensorFinsuppRid_symm_single_smul, ContinuousLinearMap.map_smulₛₗ, SMulCommClass.complexToReal, contMDiff_smul, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonpos, smul_add_one_sub_smul, PointedCone.convex, UniformFun.continuousSMul_induced_of_range_bounded, ConvexOn.neg, intervalIntegral.integral_hasStrictFDerivAt, with_gaugeSeminormFamily, CStarAlgebra.linear_combination_nonneg, ThreeGPFree.smul_set₀, fderivWithin_mul_const', Submodule.mem_span_finset', ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, NonUnitalStarSubalgebra.unitization_injective, intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right, HasDerivWithinAt.fun_smul, IsBilinearMap.toContinuousBilinearMap_apply, smul_left_injective, SkewMonoidAlgebra.domCongr_refl, right_mem_openSegment_iff, inv_natCast_smul_comm, NonUnitalSubalgebra.smul_mem', ZMod.invDFT_def', TestFunction.lineDerivOp_eq_lineDerivCLM, ConvexCone.blunt_strictlyPositive, Module.toCentroidHom_apply_toFun, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, NonUnitalStarSubalgebra.unitization_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, aestronglyMeasurable_smul_const_iff, absConvexHull_add_subset, MvPowerSeries.le_weightedOrder_smul, HasStrictDerivAt.fun_div, PartitionOfUnity.finsum_smul_mem_convex, CliffordAlgebra.foldr'_algebraMap, differentiableAt_complex_iff_differentiableAt_real, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, IsRegular.isSMulRegular, Convex.exists_forall_hasDerivWithinAt, intervalIntegral.inv_smul_integral_comp_sub_div, ConvexCone.IsGenerating.top_le_span, hasDerivWithinAt_taylor_coeff_within, UniformConvexOn.convexOn, Seminorm.iSup_apply, HasFPowerSeriesAt.hasStrictDerivAt, SchwartzMap.fourierMultiplierCLM_apply, AnalyticOn.smul, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable, DFinsupp.sigmaCurry_smul, ClosedSubmodule.mem_symplComp_iff, ContinuousAt.cfcₙ_nnreal, WithSeminorms.tendsto_nhds, MonoidAlgebra.smul_single, hasFDerivAt_list_prod_finRange', ContDiff.smulRight, not_linearIndependent_iffₒₛ, ContinuousMultilinearMap.flipLinear_apply_apply, Asymptotics.IsBigOTVS.trans_isLittleOTVS, ConvexOn.translate_right, Representation.instIsScalarTowerMonoidAlgebraAsModule, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, Module.FinitePresentation.linearEquivMap_apply, ContinuousMap.coe_smul', CochainComplex.HomComplex.δ_smul, LinearMap.hasDerivWithinAt, Finsupp.instSMulPosMono, WithSeminorms.isOpen_iff_mem_balls, CStarMatrix.toCLM_apply_single, hasSum_two_pi_I_cauchyPowerSeries_integral, Real.fourier_fderiv, convexHull_pair, Set.Subsingleton.strictConvex, rescale_to_shell_semi_normed, FormalMultilinearSeries.comp_id, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousMap.nnnorm_smul_const, smul_eq_zero_iff_left, ContinuousMap.adjoin_id_eq_span_one_union, CategoryTheory.Linear.comp_units_smul, MeasureTheory.condExp_smul, AlgebraicGeometry.StructureSheaf.smul_const, TrivSqZeroExt.invOf_eq_inv, Seminorm.const_isBounded, hasFTaylorSeriesUpTo_succ_nat_iff_right, IsCovariantDerivativeOn.leibniz, Seminorm.preimage_metric_closedBall, tangentConeAt_of_mem_nhds, SchwartzMap.compSubConstCLM_zero, ContDiffMapSupportedIn.seminorm_top_le_iff, neg_concaveOn_iff, convexOn_of_convex_epigraph, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, NonUnitalSubalgebra.instSMulCommClass, Algebra.Extension.CotangentSpace.map_cotangentComplex, LocalizedModule.mk_cancel_common_right, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, RCLike.wInner_smul_right, Complex.restrictScalars_one_smulRight, QuotSMulTop.equivQuotTensor_naturality, IsModuleTopology.isoₛₗ, ClosedSubmodule.iInf_orthogonal, Polynomial.smul_eval_smul, Asymptotics.isLittleOTVS_iff_smallSets, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, smul_add_smul_lt_smul_add_smul', MeasureTheory.smul_extend, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity', HahnEmbedding.Partial.eval_smul, HasDerivAt.clm_comp, MeasureTheory.Measure.Regular.domSMul, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, iteratedDerivWithin_scomp_three, ProperCone.dual_singleton, ContinuousLinearMap.uncurryBilinear_apply, LinearPMap.coe_smul, Algebra.TensorProduct.basisAux_tmul, StrongDual.extendRCLikeₗ_apply, HasFDerivWithinAt.smul_const, AntivaryOn.card_smul_sum_le_sum_smul_sum, Seminorm.sSup_empty, AdicCompletion.transitionMap_comp_reduceModIdeal, MeasureTheory.integral_posConvolution, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, Algebra.Extension.tensorCotangentSpace_tmul, MeasureTheory.LocallyIntegrableOn.smul_continuousOn, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, IsOpen.smul_sphere, EuclideanGeometry.Sphere.secondInter_smul, Subring.smul_closure, monovary_iff_smul_rearrangement, Module.AEval.X_pow_smul_of, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, strongConcaveOn_iff_convex, iteratedFDeriv_eq_equiv_comp, Real.smul_iInf_of_nonpos, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, MeasureTheory.condExpIndL1_smul, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, Matrix.conjTranspose_ratCast_smul, Differentiable.continuousMultilinearMapCompContinuousLinearMap, Unitization.norm_eq_sup, MonovaryOn.sum_smul_sum_le_card_smul_sum, DFinsupp.comapDomain_smul, egauge_zero_left_eq_top, LinearEquiv.toSpanNonzeroSingleton_apply, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Submodule.mem_span_insert', Matrix.ofLp_toEuclideanCLM, Ideal.coe_restrictScalars, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Fourier.fourierIntegral_const_smul, TrivSqZeroExt.inl_mul, HasDerivWithinAt.comp_hasDerivAt_of_eq, QuadraticMap.smul_apply, hasDerivAtFilter_iff_isLittleO, Absorbent.eventually_nhdsNE_zero, HasDerivAt.fun_const_smul, HasDerivAt.fun_sub, CStarMatrix.toCLM_apply_eq_sum, Set.Subsingleton.convex, Submodule.span_algebraMap_image_of_tower, HasStrictFDerivAt.restrictScalars, LinearMap.exact_smul_id_smul_top_mkQ, MeasureTheory.Measure.ae_smul_measure_iff, TwoSidedIdeal.instSMulMemClass, StarAlgEquiv.coe_ofBijective, balancedHull_add_subset, Projectivization.mk_eq_mk_iff, StarConvex.preimage_smul, MeasureTheory.Measure.instSMulCommClassDomMulActNNReal, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ConvexOn.quasiconvexOn, strictConvex_Ici, hasDerivAt_exp_smul_const, HasDerivAtFilter.add_const, Meromorphic.fun_smul, HasSum.smul, Asymptotics.isBigOTVS_neg_left, MeasureTheory.Measure.NullMeasurableSet.const_smul, Balanced.closure, MeasureTheory.eLpNormEssSup_smul_measure, affineIndependent_smul, ContDiffMapSupportedIn.locallyConvexSpace, hasFDerivWithinAt_comp_smul_smul_iff, fourierCoeff_toLp, IsLocalizedModule.mk'_cancel', ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Algebra.Generators.H1Cotangent.δAux_ofComp, Algebra.Extension.CotangentSpace.map_tmul_eq_tmul_map, ContinuousMultilinearMap.smul_prod_smul, CategoryTheory.Functor.mapExactFunctor_smul, smul_unitBall_of_pos, smul_lt_smul_iff_of_neg_left, HasStrictDerivAt.congr_deriv, ProbabilityTheory.hasDerivAt_complexMGF, gauge_smul_left_of_nonneg, AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff, map_real_smul, RootPairing.reflectionPerm_root, DifferentiableWithinAt.isBigOTVS_sub, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, LinearOrder.concaveOn_of_lt, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', LinearIsometryEquiv.toSpanUnitSingleton_apply, Asymptotics.IsBigOWith.smul, Asymptotics.IsLittleOTVS.congr', IsScalarTower.rat, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', Convex.translate, LinearEquiv.apply_smulCommClass, StrictConvexOn.map_sum_lt, map_inv_natCast_smul, iteratedDeriv_comp_const_smul, norm_inner_eq_norm_tfae, Real.circleAverage_def, Submodule.map₂_span_singleton_eq_map_flip, LinearPMap.mkSpanSingleton'_apply, CategoryTheory.ShortComplex.smul_τ₃, LinearMap.pi_apply_eq_sum_univ, DilationEquiv.smulTorsor_apply, FormalMultilinearSeries.changeOrigin_eval_of_finite, Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite, Module.sum_smul_eq_zero_of_isTrivialRelation, intervalIntegral.integral_smul, ZMod.dft_apply, Seminorm.map_eq_zero_of_norm_eq_zero, Algebra.TensorProduct.distribBaseChange_comp_includeLeftSubRight, sigmaFinsuppEquivDFinsupp_smul, Rep.ofDistribMulAction_ρ_apply_apply, Quaternion.fst_imJ_dualNumberEquiv_symm, exists_nonneg_right_iff_sameRay, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, iteratedFDerivWithin_two_apply', HasDerivAt.const_smul, UniqueDiffWithinAt.smul_iff, Convex.add_smul_mem, Balanced.interior, cfcₙ_tsub, deriv.scomp, balancedCoreAux_balanced, HasStrictDerivAt.add, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, inr_comp_cfcₙHom_eq_cfcₙAux, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, MeasureTheory.DominatedFinMeasAdditive.smul, StarConvex.add_left, concaveOn_univ_piecewise_Ici_of_antitoneOn_Ici_monotoneOn_Iic, hasDerivAt_taylorWithinEval_succ, CFC.monotoneOn_one_sub_one_add_inv_real, Convex.closure, Bornology.IsBounded.smul₀, MemHolder.smul, Finsupp.instPosSMulStrictMono, HVertexOperator.of_coeff_coeff, Module.Basis.mem_submodule_iff', skewAdjoint.negISMul_apply_coe, ContinuousMapZero.coe_smul, Submodule.smithNormalFormBotBasis_def, insert_endpoints_openSegment, PMF.integral_eq_tsum, not_linearIndependent_iffₛ, DiffContOnCl.circleAverage_smul_div, groupHomology.isCycle₁_of_mem_cycles₁, QuadraticAlgebra.C_mul_eq_smul, IsLocalFrameOn.eventually_eq_sum_coeff_smul, Matrix.vecMul_ofNat, lp.infty_smulCommClass, Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, intervalIntegral.integral_comp_div, Submodule.instCovariantClassHSMulLe, TensorProduct.lid'_apply_tmul, HasSum.exists_hasSum_smul_of_apply_eq_zero, Finsupp.smul_single', KaehlerDifferential.instSMulCommClassTensorProduct_1, Algebra.Extension.Cotangent.val_smul', Finsupp.weight_single_index, DiscreteConvolution.ConvolutionExistsAt.smul_convolution, HVertexOperator.coeff_inj_iff, HasFPowerSeriesAt.fderiv_eq, CategoryTheory.endomorphism_simple_eq_smul_id, Orientation.oangle_sign_smul_left, Finset.sum_Ico_by_parts, HasDerivAtFilter.scomp_of_eq, ContinuousWithinAt.cfcₙ_nnreal, ContinuousLinearMap.coe_restrictScalarsIsometry, MeasureTheory.Integrable.bdd_smul, Finsupp.linearCombination_apply, rank_eq_one_iff, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, MonoidAlgebra.smul_of, Submodule.mem_set_smul_of_mem_mem, MatrixModCat.mem_toModuleCatObj, HasDerivAt.scomp_hasDerivWithinAt_of_eq, GradedAlgHom.restrictScalars_coe_linearMap, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, ConvexBody.isBounded, VectorField.mlieBracketWithin_smul_left, Convex.combo_self, Unitization.inrRangeEquiv_apply_coe_fst, CStarMatrix.reindexₐ_apply, WeakBilin.instContinuousSMul, ContinuousLinearMap.isometry_iff_adjoint_comp_self, Finset.inv_smul_finset_distrib₀, continuousMultilinearCurryFin0_apply, smul_le_smul_iff_of_neg_left, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, AddGroup.int_smulCommClass', IsUnit.smul_eq_zero, LocalizedModule.smul'_mk, PiTensorProduct.dualSeminorms_bounded, FormalMultilinearSeries.radius_neg, Module.Flat.isSMulRegular_of_isRegular, HasFDerivWithinAt.mul_const', InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, extDeriv_smul, homeomorphUnitSphereProd_symm_apply_coe, Polynomial.isCentralScalar, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, Algebra.Extension.Cotangent.map_comp, HasDerivAt.comp_const_sub, taylorWithinEval_succ, convex_Ioo, Submodule.mulRightMap_eq_mulMap_comp, HasDerivAt.norm_sq, StarConvex.smul, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, HasDerivWithinAt.add, IsSelfAdjoint.conj_adjoint, ContinuousMultilinearMap.curryMidEquiv_apply, StrictConvexSpace.strictConvex_closedBall, Real.fourier_eq, Algebra.trace_comp_trace_of_basis, AffineMap.lineMap_vadd_apply, Mathlib.Tactic.LinearCombination.smul_lt_const_weak, HahnSeries.SummableFamily.hasFiniteSupport_smul, differentialIdeal_le_fractionalIdeal_iff, Submodule.span_set_smul, HasStrictFDerivAt.continuousMultilinear_apply_const, Asymptotics.IsLittleOTVS.sup, AddMonoid.End.isCentralScalar, ContDiffMapSupportedIn.monoLM_eq_zero, SMulPosReflectLT.toSMulPosReflectLE, sameRay_neg_smul_left_iff_of_ne, Set.OrdConnected.convex_of_chain, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, MultilinearMap.freeFinsuppEquiv_def, Filter.top_smul_nhds_zero, ConvexOn.convex_lt, Prod.openSegment_subset, WeakBilin.instIsScalarTower, Orientation.oangle_sign_smul_add_smul_smul_add_smul, DoubleCentralizer.algebraMap_snd, Finset.expect_dite_eq', Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, Convex.add, Polynomial.aeval_smul, Finsupp.smul_apply, MeasureTheory.Measure.integral_comp_mul_left, lp.instStarModuleSubtypePreLpMemAddSubgroup, AnalyticAt.analyticOrderNatAt_eq_iff, Set.indicator_smul_const, groupHomology.isBoundary₀_of_mem_coinvariantsKer, MeasureTheory.integrable_smul_const, SchauderBasis.RankOneDecomposition.basisCoeff_spec, hasFiniteFPowerSeriesOnBall_const, SkewMonoidAlgebra.coeff_mul, Module.End.smulLeft_apply, HahnModule.SMulCommClass, ZMod.invDFT_apply', iteratedFDerivWithin_succ_apply_left, HasFDerivAtFilter.fun_const_smul, Submodule.starProjection_unit_singleton, Matrix.dualNumberEquiv_symm_apply, Finset.weightedVSub_const_smul, SchwartzMap.fourier_evalCLM_eq, SkewMonoidAlgebra.smul_single, ContinuousWithinAt.integral_sub_linear_isLittleO_ae, convex_convexHull, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, DualNumber.exp_eps, Submodule.mul_smul_mul_eq_smul_mul_smul, Asymptotics.IsBigOTVS.prodMk, Polynomial.iterate_derivative_X_pow_eq_smul, KaehlerDifferential.tensorKaehlerEquiv_left_inv, DifferentiableAt.fun_const_smul, AdicCompletion.pow_smul_top_eq_ker_eval, hasDerivWithinAt_natCast, IsTopologicalSemiring.toOppositeIsModuleTopology, CliffordAlgebra.foldl_algebraMap, Orientation.oangle_sign_smul_sub_left, RatFunc.div_smul, fderiv_pow_ring', LinearMap.toSpanSingleton_apply, MvPolynomial.constantCoeff_smul, MeasureTheory.memL1_smul_of_L1_withDensity, ContinuousLinearMap.bilinearComp_apply, analyticAt_iff_analytic_fun_smul, imaginaryPart_eq_neg_I_smul_skewAdjointPart, AddSubmonoid.mem_inv_pointwise_smul_iff₀, midpoint_vsub_left, MeasureTheory.Measure.toSphere_apply', DiscreteConvolution.ConvolutionExistsAt.convolution_smul, TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOn, LieAlgebra.smulCommClass, range_cfcₙ_nnreal_eq_image_cfcₙ_real, Matrix.Module.instIsScalarTowerForall, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, Polynomial.smeval_C_mul, LinearOrderedField.smul_Ioo, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, Matrix.smul_eq_mul_diagonal, Subsemiring.center.smulCommClass_right, DiffContOnCl.smul_const, RootPairing.InvariantForm.apply_weylGroup_smul, Convex.linear_image, ContMDiffWithinAt.clm_bundle_apply₂, MeasureTheory.condExpIndL1_smul', Submodule.singleton_smul, LinearMap.conjugate_apply, Filter.Tendsto.cfcₙ_nnreal, TopologicalGroup.IsSES.integrate_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, HasDerivAt.fun_div, Submodule.toConvexCone_le_toConvexCone, tsum_const_smul'', vadd_segment, Matrix.Module.scalar_smul, mem_parallelepiped_iff, Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy, contDiff_smul_const, MeasureTheory.integral_biUnion_eq_sum_powerset, HasFTaylorSeriesUpToOn.fderivWithin, Prod.image_mk_openSegment_right, CStarMatrix.toCLM_apply, AddSubmonoid.smul_closure, Set.zero_smul_set, LieModule.lie_smul, DoubleCentralizer.algebraMap_toProd, Set.inv_smul_set_distrib₀, AddMonoidAlgebra.faithfulSMul, continuousMultilinearCurryFin0_symm_apply_apply, HasDerivWithinAt.fun_const_smul, IsSMulRegular.zero, ConcaveOn.le_map_sum, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ContinuousLinearMap.ker_self_comp_adjoint, Quaternion.fst_imI_dualNumberEquiv_symm, differentiableAt_norm_smul, exists_nontrivial_relation_sum_zero_of_not_affine_ind, FormalMultilinearSeries.id_comp, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, invOf_two_smul_add_invOf_two_smul, Real.circleAverage_eq_integral_add, isSMulRegular_algebraMap_iff, HasFPowerSeriesAt.restrictScalars, hasDerivAt_integral_of_dominated_loc_of_deriv_le, intervalIntegral.inv_smul_integral_comp_div_sub, ConcaveOn.convex_hypograph, rank_dual_eq_card_dual_of_aleph0_le_rank', ContinuousLinearMap.instStarModuleId, ContDiff.smul_const, RCLike.wInner_smul_left, Matrix.toLinearMapₛₗ₂'_apply, edist_smul₀, Absorbs.sub, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right, Seminorm.convex_ball, VectorField.mlieBracketWithin_smul_right, Convex.combo_closure_interior_subset_interior, CategoryTheory.ShiftedHom.comp_smul, PolynomialModule.eval_lsingle, MultilinearMap.map_nonempty, DoubleCentralizer.instIsCentralScalar, Subsemiring.mem_inv_pointwise_smul_iff₀, groupHomology.single_isCycle₁_iff, DFinsupp.coe_smul, HasDerivWithinAt.const_mul, ContinuousLinearMapWOT.instContinuousSMul, HasFDerivAt.continuousAlternatingMap_apply_const, CochainComplex.HomComplex.Cochain.smul_comp, Submodule.span_eq_closure, AddSubgroup.mem_smul_pointwise_iff_exists, Finset.smul_finset_neg, PiTensorProduct.injectiveSeminorm_apply, ContinuousLinearMap.isBoundedLinearMap_comp_left, PartitionOfUnity.sum_finsupport_smul_eq_finsum, Pi.instSMulPosReflectLT, LieAdmissibleAlgebra.toIsScalarTower, LinearMap.CompatibleSMul.finsupp_cod, norm_fderiv_iteratedFDeriv, IsCompact.extremePoints_nonempty, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1, TestFunction.lineDerivCLM_eq_fderivCLM, TopologicalAddGroup.IsSES.integrate_mono, HasDerivWithinAt.div, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, Bornology.IsVonNBounded.sub, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, Path.range_segment, instIsStrictOrderedModuleOfIsCancelAdd, segment_subset_Icc, convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic, TemperedDistribution.fourier_lineDerivOp_eq, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, groupHomology.inhomogeneousChains.d_single, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', Matrix.l2_opNNNorm_def, ContinuousLinearEquiv.strictConvex_image, ContinuousMultilinearMap.instIsBoundedSMul, hasDerivAtFilter_sub_const_iff, SmoothPartitionOfUnity.finsum_smul_mem_convex, spectrum.hasDerivAt_resolvent, Module.Basis.sum_toMatrix_smul_self, AdicCompletion.val_apply_mem_smul_top_iff, ContinuousLinearMap.adjointAux_adjointAux, MvPolynomial.mkDerivation_monomial, smul_nonpos_iff_neg_imp_nonneg, Finsupp.linearCombination_single, HasStrictDerivAt.const_add, realPart_I_smul, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, Submodule.exists_smul_notMem_of_rank_lt, Convex.add_smul, Ideal.coe_smul_primesOver_mk, linearIndependent_smul, Seminorm.exists_apply_eq_finset_sup, PolynomialModule.smul_apply, ContMDiffAt.clm_precomp, NonUnitalAlgHom.coe_mulHom_mk, gauge_def, MultilinearMap.coe_smul, Complex.hasDerivAt_logTaylor, TestFunction.lineDerivCLM_apply, Multiset.sum_smul, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem, Mathlib.Tactic.Module.NF.zero_sub_eq_eval, deriv_smul, nnnorm_cfcₙ_nnreal_lt_iff, Prod.image_mk_segment_right, VectorField.mpullbackWithin_smul_apply, PositiveLinearMap.gnsStarAlgHom_apply, Absorbs.add, NNReal.coe_nnqsmul, Real.fourier_iteratedDeriv, MonoidAlgebra.smul_single', MeasureTheory.Integrable.smul_of_top_left, MeasureTheory.integral_comp_rpow_Ioi, Pi.instSMulPosStrictMono, Asymptotics.IsBigOTVS.symm, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, convex_closedEBall, hasDerivAt_iff_tendsto_slope_zero, StrictConvex.affine_preimage, ConvexOn.convex_re_epigraph, IsExposed.convex, LinearMap.norm_extendTo𝕜'_apply_sq, Asymptotics.isLittleOTVS_iff_isLittleO, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, AffineSubspace.wSameSide_smul_vsub_vadd_left, TrivSqZeroExt.inv_inv, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, HasFTaylorSeriesUpToOn.hasFDerivAt, WeakFEPair.hf_zero, convex_ball, prodXSubSMul.coeff, real_inner_smul_right, groupHomology.isBoundary₂_iff, scalarSMulCLE_apply, ContinuousLinearMap.flip_add, QuadraticMap.polar_smul_left, exists_pos_left_iff_sameRay, hasFiniteFPowerSeriesAt_const, MeasureTheory.Integrable.toL1_smul', Seminorm.uniformContinuous, infDist_smul₀, Submodule.smul_mem_iff_of_isUnit, ContinuousAlternatingMap.hasBasis_nhds_zero, Orientation.oangle_sub_right_smul_rotation_pi_div_two, MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport, Bornology.isBounded_iff_isVonNBounded, Antivary.sum_smul_lt_sum_smul_comp_perm_iff, Convex.min_le_combo, monovaryOn_iff_smul_rearrangement, VectorFourier.fourierSMulRight_apply, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, ConcaveOn.translate_right, Derivation.leibniz, ContinuousLinearMap.isSelfAdjoint_iff', HasFDerivWithinAt.restrictScalars, LinearIsometry.map_smulₛₗ, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, OrthonormalBasis.equiv_apply_euclideanSpace, RootPairing.PolarizationIn_apply, Polynomial.sylvesterDeriv_updateRow, Convex.interior, StrongConcaveOn.strictConcaveOn, CochainComplex.HomComplex.Cochain.rightShift_smul, RatFunc.instIsScalarTowerPolynomial, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, LinearMap.liftQ₂_mk, Matrix.mulVec_smul, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Seminorm.coe_sSup_eq', ContinuousMultilinearMap.uncurryRight_apply, HasDerivAt.comp_const_add, ContinuousLinearMap.isVonNBounded_iff, SchwartzMap.fourierMultiplierCLM_ofReal, InnerProductSpace.Core.inner_smul_ofReal_left, Real.isScalarTower, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, differentiableWithinAt_iff_restrictScalars, IsModuleTopology.iso, NormedSpace.normalize_smul_of_neg, TrivSqZeroExt.exp_def, derivWithin_comp_mul_left, Seminorm.coe_bot, hasDerivAt_circleMap, vectorSpan_segment, ProperCone.smul_mem, derivWithin_fun_smul, ContinuousLinearMap.bilinearComp_zero, MeasureTheory.integral_fun_norm_addHaar, SkewMonoidAlgebra.coeff_mul_antidiagonal_finsum, HasFDerivAt.fun_pow', LocalizedModule.subsingleton_iff, Convex.mem_toCone, MeasureTheory.setIntegral_ge_of_const_le, HasDerivWithinAt.scomp_hasDerivAt_of_eq, imaginaryPart_apply_coe, Complex.UnitDisc.instSMulCommClass_closedBall_right, ContinuousLinearMap.isVonNBounded_image2_apply, segment_same, MulSemiringActionHom.map_one', PartitionOfUnity.continuous_finsum_smul, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, pinGroup.conjAct_smul_range_ι, LinearMap.lsmul_apply, HasMFDerivWithinAt.mul', intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, Polynomial.ofFinsupp_smul, segment_subset_closedBall_left, UnitAddTorus.hasSum_mFourier_series_L2, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, Submodule.smul_closure_subset, HasFTaylorSeriesUpToOn.shift_of_succ, CentroidHom.instSMulCommClass_1, ConvexCone.mem_add, SemimoduleCat.Algebra.instSMulCommClassCarrier, QuotSMulTop.map_exact, Representation.asModuleEquiv_symm_map_rho, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, HasDerivWithinAt.neg, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, ContinuousLinearMap.norm_extendTo𝕜'_bound, Polynomial.leadingCoeff_smul_of_smul_regular, sum_mem_ball_of_strictConvexSpace, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, Polynomial.degree_sum_eq_of_linearIndepOn, le_egauge_smul_right, ContinuousMultilinearMap.integral_apply, NonUnitalSubalgebra.unitization_apply, AddMonoidAlgebra.coeff_smul, SeminormFamily.basisSets_smul, iteratedDerivWithin_const_smul, DualNumber.lift_apply_apply, HasStrictDerivAt.smul_const, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LocalizedModule.smul_def, Submodule.span_eq_iUnion_nat, HasStrictDerivAt.sub, groupHomology.single_isCycle₂_iff, SameRay.sameRay_nonneg_smul_right, MeasureTheory.SimpleFunc.setToSimpleFunc_smul, HasFiniteFPowerSeriesOnBall.neg, ModuleTopology.eq_coinduced_of_surjectiveₛₗ, CentroidHom.instIsScalarTower_1, Basis.multilinearMap_apply_apply, HasDerivWithinAt.Ioo_of_Ioi, Finset.weightedVSubOfPoint_smul, MeasureTheory.average_union_mem_segment, lineDifferentiableWithinAt_smul_iff, Fintype.expect_ite_mem, LinearMap.convexOn, DifferentiableWithinAt.smul_const, SMulCommClass.rat', CompactlySupportedContinuousMap.instIsCentralScalar, cfcₙ_real_eq_nnreal, Submodule.le_span_singleton_iff, hasDerivAt_fourier, HahnSeries.SummableFamily.coeff_smul, Asymptotics.IsBigOTVS.congr_right, ContinuousLinearEquiv.smulLeft_apply_apply, DiffContOnCl.circleAverage_poissonKernel_smul, QuadraticMap.half_moduleEnd_apply_eq_half_smul, smul_lie, Seminorm.neg_closedBall, Complex.UnitDisc.instIsScalarTower_closedBall, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, AffineMap.lineMap_apply, Finsupp.linearCombination_unique, DistribMulAction.toLinearEquiv_apply, TrivSqZeroExt.inr_mul_inl, smul_eq_zero_iff_right, AntivaryOn.sum_smul_comp_perm_eq_sum_smul_iff, StrongDual.extendRCLikeₗᵢ_symm_apply, Asymptotics.IsThetaTVS.isBigOTVS, MultilinearMap.map_update_smul', Real.fourier_bilin_convolution_eq, BoxIntegral.BoxAdditiveMap.toSMul_apply, IsLocalizedModule.mk'_cancel_right, AntitoneOn.quasiconcaveOn, segment_eq_image', CStarMatrix.mul_entry_mul_eq_inner_toCLM, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Finsupp.isCentralScalar, Module.supportDim_quotSMulTop_succ_eq_supportDim, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, ConvexOn.smul_concaveOn, homeomorphSphereProd_symm_apply_coe, Subring.smul_mem_pointwise_smul_iff₀, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Submodule.convex, ExteriorAlgebra.toTrivSqZeroExt_ι, FormalMultilinearSeries.le_comp_radius_of_summable, ContinuousLinearMap.le_opNorm₂, ContinuousLinearMap.lpPairing_eq_integral, TrivSqZeroExt.snd_invOf, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, slope_fun_def, Seminorm.continuous_iff, HasFDerivAt.smul_const, MeasureTheory.integrable_tilted_iff, Submodule.mem_smul_pointwise_iff_exists, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀, ContinuousLinearMap.norm_uncurryMid, Submodule.torsionBy.mk_ideal_smul, Cardinal.mk_smul_set₀, TopologicalGroup.IsSES.pushforward_apply_apply, isIntegralCurveOn_comp_mul_ne_zero, Submodule.mem_span_iff_of_fintype, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, ContinuousLinearMap.uncurryLeft_norm, DualNumber.ringHom_ext_iff, star_inv_natCast_smul, TestFunction.instLineDerivLeftSMulRealTopENat, mellin_eq_fourierIntegral, mem_vectorSpan_pair_rev, PiTensorProduct.smul_tprodCoeff_aux, hasStrictDerivAt_abs_neg, HasFDerivAt.comp_hasDerivWithinAt, ContinuousLinearMap.holder_smul_right, WithSeminorms.continuous_seminorm, HasFPowerSeriesOnBall.tendstoUniformlyOn', extremePoints_closedBall_subset_sphere, HasFPowerSeriesWithinOnBall.const_smul, HVertexOperator.coeff_inj, PolynomialModule.smul_single_apply, TensorProduct.rid_tmul, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, Asymptotics.IsLittleOTVS.comp_tendsto, TrivSqZeroExt.inl_mul_inl, Subalgebra.smul_mem_pointwise_smul, Mathlib.Tactic.Module.NF.neg_eq_eval, Set.indicator_smul_const_apply, Representation.TensorProduct.rid_apply, SchwartzMap.fourierMultiplierCLM_const, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, fderivWithin_const_smul_of_invertible, Real.fourierIntegral_eq', Real.circleAverage_fun_smul, RootPairing.coroot_root_two, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, TestFunction.monoCLM_eq_of_scalars, Ideal.inertiaEquiv_symm_apply_smul, UniformConvergenceCLM.isVonNBounded_image2_apply, CategoryTheory.ShortComplex.cyclesMap'_smul, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', intervalIntegral.integral_comp_smul_deriv', EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Complex.hasSum_taylorSeries_on_emetric_ball, LinearEquiv.smulOfNeZero_apply, HasStrictDerivAt.of_notMem_tsupport, fderiv_continuousMultilinear_apply_const_apply, MeasureTheory.integrable_withDensity_iff_integrable_smul, Asymptotics.IsLittleOTVS.congr, MeasureTheory.Integrable.convolution_integrand, LieModule.exists_forall_lie_eq_smul, FormalMultilinearSeries.radius_compContinuousLinearMap_eq, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Projectivization.exists_smul_eq_mk_rep, Module.reflection_mul_reflection_pow_apply_self, DivisibleHull.qsmul_def, hasFPowerSeriesOn_cauchy_integral, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, antitone_smul_left, LinearEquiv.fixedReduce_eq_smul_iff, concaveOn_of_convex_hypograph, StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, Set.indicator_smul_apply_left, EuclideanGeometry.inversion_def, Matrix.trace_single_mul, NormedSpace.vonNBornology_eq, KaehlerDifferential.isBaseChange, Function.Periodic.const_smul₀, ConvexBody.smul_le_of_le, ConvexOn.lt_right_of_left_lt', SchwartzMap.integral_bilinear_laplacian_right_eq_left, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, KaehlerDifferential.instSMulCommClassTensorProduct, iteratedDeriv_fun_const_smul_field, DomMulAct.mk_smul_mulDistribActionHom_apply, HasFDerivAt.lim, Seminorm.comp_apply, hasDerivWithinAt_const, openSegment_eq_image_lineMap, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', intervalIntegral.integral_comp_sub_mul, multiple_mem_span_of_mem_localization_span, OrthonormalBasis.sum_repr_symm, homeomorphUnitSphereProd_apply_fst_coe, CFC.posPart_smul_of_nonneg, MultilinearMap.cons_smul, Pi.single_smul₀, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, DifferentiableWithinAt.restrictScalars_fderivWithin, isCompact_closedAbsConvexHull_of_totallyBounded, HasStrictFDerivAt.continuousAlternatingMap_apply, Orthonormal.inner_left_sum, NonUnitalSubalgebra.instSMulMemClass, Orientation.inner_smul_rotation_pi_div_two_right, MatrixEquivTensor.invFun_smul, UniformConcaveOn.concaveOn, DiscreteConvolution.AddConvolutionExistsAt.convolution_vadd, StrongDual.extendRCLikeₗ_symm_apply, HasDerivAtFilter.congr_of_eventuallyEq, HasStrictDerivAt.complexToReal_fderiv', Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric, constFormalMultilinearSeries_apply_of_nonzero, RootPairing.CoPolarization_apply, egauge_ball_one_le_of_one_lt_norm, cfcₙ_comp_smul, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', Matrix.linftyOpNormSMulClass, finsuppTensorFinsuppRid_single_tmul_single, Real.circleAverage_smul, LieModule.shiftedGenWeightSpace.coe_lie_shiftedGenWeightSpace_apply, star_qsmul, Subalgebra.inclusion.isScalarTower_right, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, WithLp.normSMulClassSeminormedAddCommGroupToProd, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, VectorField.lieBracket_const_smul_right, Module.preReflection_apply, Asymptotics.isBigOTVS_pi, SkewMonoidAlgebra.sum_smul_index, DFinsupp.instPosSMulReflectLE, Derivation.smul_apply, PiLp.smul_apply, TrivSqZeroExt.hasSum_expSeries_of_smul_comm, DifferentiableWithinAt.clm_comp, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Matrix.blockDiagonal_smul, MDifferentiableOn.cle_arrowCongr, PiLp.normSMulClassSeminormedAddCommGroupToPi, Polynomial.degree_smul_of_isRightRegular_leadingCoeff, MeasureTheory.uniformIntegrable_average, LinearIsometryEquiv.strictConvex_image, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', CochainComplex.HomComplex.Cochain.shift_units_smul, Algebra.Extension.contangentEquiv_tmul, Unitization.norm_def, convex_uIcc, ContMDiff.clm_bundle_apply₂, ModuleTopology.eq_coinduced_of_surjective, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, Ideal.quotOfMul_surjective, Real.iteratedDeriv_fourier, map_natCast_smul, SchwartzMap.eLpNorm_le_seminorm, MDifferentiableAt.smul, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, HasStrictDerivAt.const_smul, StrictConvex.add, HasDerivAt.fun_sum, hasFDerivAtFilter_iff_isLittleOTVS, MeasureTheory.setIntegral_rnDeriv_smul', FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, TensorProduct.finsuppScalarLeft_apply_tmul_apply, TrivSqZeroExt.snd_pow_of_smul_comm, second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonneg, ContinuousMultilinearMap.curryRight_apply, CategoryTheory.Abelian.Ext.comp_smul, Ideal.pointwise_smul_eq_comap, Distribution.dsupport_smulLeftCLM_subset, MeasureTheory.eLpNorm_const_smul_le, ArithmeticFunction.mul_smul', DFinsupp.instPosSMulMono, MonoidAlgebra.smul_apply, Balanced.absorbs_self, CategoryTheory.Linear.comp_smul, star_nnqsmul, HasFPowerSeriesOnBall.uniform_geometric_approx', image_segment, intervalIntegral.smul_integral_comp_mul_left, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul, AddMonoidHom.coe_smul, ZeroAtInftyContinuousMap.instSMulCommClass, Function.support_const_smul_of_ne_zero, ContinuousLinearMap.extendTo𝕜_apply, Submodule.starConvex, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, PowerSeries.coeff_smul, Module.AEval.of_symm_X_smul, MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct, HasFDerivAt.comp_hasDerivWithinAt_of_eq, Convex.gauge_le, convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Ici, Derivation.leibniz_of_mul_eq_one, matrixEquivTensor_apply_symm, smul_floorDiv_le, uniformConcaveOn_zero, AffineSubspace.mem_affineSpan_insert_iff, ConvexCone.pointed_zero, ZeroHom.smul_apply, LieModule.traceForm_eq_sum_finrank_nsmul, LieAlgebra.Basis.baseSupp_apply_smul_e, Seminorm.closedBall_eq_emptyset, Convex.strictConvex', egauge_le_of_smul_mem, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, LinearMap.det_restrictScalars, hasStrictFDerivAt_pow', convex_Icc, IsBoundedSMul.of_enorm_smul_le, ContinuousLinearMap.applySMulCommClass, strictConvex_Ioc, LinearMap.flip_injective_iff₂, RestrictScalars.ringEquiv_map_smul, AddSubmonoid.smul_mem_pointwise_smul_iff₀, ContinuousLinearMap.norm_extendTo𝕜', InnerProductGeometry.angle_smul_smul, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, RestrictScalars.lsmul_apply_apply, IsIntegralClosure.range_le_span_dualBasis, HahnModule.coeff_single_zero_smul, Matrix.toLin_apply, IsStarProjection.inr, Asymptotics.IsLittleOTVS.fun_symm, HasDerivAtFilter.const_add, smul_sub, HasDerivWithinAt.of_notMem_tsupport, StrictConvex.preimage_smul, not_linearIndependent_iff_finsupp, MDifferentiableAt.clm_precomp, ModelWithCorners.convex_range, ContDiffMapSupportedIn.postcompCLM_apply, SchwartzMap.compSubConstCLM_comp, HasDerivWithinAt.mono_of_mem_nhdsWithin, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, ContinuousAlternatingMap.curryLeft_zero, RootPairing.reflection_dualMap_eq_coreflection, Matrix.Module.smul_apply, IsLeftCancelMulZero.toFaithfulSMul_opposite, DualNumber.coe_lift_symm_apply, ContDiffBump.integral_normed_smul, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, MultilinearMap.freeFinsuppEquiv_apply, Orientation.oangle_sign_smul_right, Module.Basis.constr_apply_fintype, Finsupp.mapRange_smul', fwdDiff_smul, Asymptotics.IsTheta.isThetaTVS, LieSubmodule.Quotient.isCentralScalar, AddMonoidAlgebra.liftMagma_apply_apply, Finsupp.coe_smul, ContinuousAlternatingMap.cons_smul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, inhomogeneousCochains.d_hom_apply, ZMod.dft_dft, SmoothBumpFunction.contMDiff_smul, Quaternion.imJ_snd_dualNumberEquiv, HasDerivWithinAt.Ioi_of_Ioo, HasDerivWithinAt.fun_mul, DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap, AbsConvex.closure, Polynomial.coeff_smul, Filter.Tendsto.zero_smul_isBoundedUnder_le, fderiv_fun_mul', TrivSqZeroExt.liftEquivOfComm_apply, Finset.centerMass_segment', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFDerivAt.const_smul, AdicCompletion.pow_smul_top_le_ker_eval, NormedSpace.expSeries_sum_eq_rat, Submodule.top_le_span_range_iff_forall_exists_fun, HasFPowerSeriesWithinAt.prod, HasDerivWithinAt.pow', LinearPMap.map_smul, Polynomial.support_smul, ContMDiffMap.coe_smul, Set.neg_smul_set, LinearMap.concaveOn, MulSemiringActionHom.map_mul', Derivation.instIsCentralScalar, IsLocalizedModule.exists_integer_multiple, ContinuousLinearMap.adjoint_comp_self_injective_iff, Convex.is_linear_image, FormalMultilinearSeries.leftInv_coeff_one, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul', Module.Basis.smul_eq_map, MultilinearMap.smulRight_apply, Submodule.singleton_set_smul, PosSMulReflectLT.toPosSMulReflectLE, SkewMonoidAlgebra.support_mul_single_subset, sameRay_iff_inv_norm_smul_eq, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, AddMonoidHom.instIsCentralScalar, Asymptotics.IsThetaTVS.symm, Polynomial.aeval_apply_smul_mem_of_le_comap', BoxIntegral.integral_smul, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH, AddMonoidAlgebra.liftNC_smul, Submodule.exists_smith_normal_form_of_rank_eq, MeasureTheory.L1.setToL1_smul, zero_smul, hasFPowerSeriesAt_pi_iff, IsEllDivSequence.smul, MeasureTheory.eLpNorm'_const_smul, IsBaseChange.iff_lift_unique, smul_zpow₀', MeasureTheory.Lp.coeFn_lpSMul, Unitization.inr_mul_inl, QuadraticMap.canLift', ProbabilityTheory.integral_tilted_mul_eq_mgf, MeasureTheory.integral_simpleFunc_larger_space, Antitone.convex_gt, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, finrank_eq_one_iff', ContDiffBump.apply, TrivSqZeroExt.isUnit_inv_iff, CStarMatrix.smul_mul, Seminorm.ball_zero_absorbs_ball_zero, Module.Basis.smulTower'_apply, Submodule.pointed_toConvexCone, Orientation.oangle_sign_add_smul_left, Submodule.span_range_update_sub_smul, Submodule.topologicalClosure_mem_invtSubmodule, HasFDerivAt.lim_real, OrderDual.instSMulPosMono, Matrix.kronecker_ofNat, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, exists_open_convex_of_notMem, lp.coeFn_smul, smul_upperBounds_subset_lowerBounds_smul, InnerProductSpace.isStarProjection_rankOne_self, MulSemiringAction.charpoly_eq, StrictConvex.smul, ProperCone.relative_hyperplane_separation, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, affineSegment_eq_segment, DomMulAct.mk_smul_linearMap_apply, ContinuousAffineMap.coe_smul, Quaternion.snd_imK_dualNumberEquiv_symm, strictConvex_Ico, HasFPowerSeriesAt.hasFDerivAt, StrictConvex.linearIsometry_preimage, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, ConcaveOn.openSegment_subset_strict_hypograph, DistribSMul.smul_add, ConvexCone.coe_positive, Bornology.IsVonNBounded.extend_scalars, ContinuousMultilinearMap.smul_apply, analyticAt_iff_analytic_smul, Asymptotics.IsBigOTVS.congr, DFinsupp.isScalarTower, Matrix.mulVec_eq_sum, LinearEquiv.smul_apply, instInvertibleReprₛ, Submodule.range_powSMulQuotInclusion, StrongDual.extendRCLikeₗᵢ_apply, UniformConcaveOn.strictConcaveOn, Subalgebra.inclusion.faithfulSMul, HasDerivAt.ofReal_comp, HasFPowerSeriesWithinOnBall.compContinuousLinearMap, ContinuousOn.cfcₙ_nnreal', DFinsupp.sigmaUncurry_smul, DivisibleHull.qsmul_of_nonneg, LinearMap.mkContinuous₂_norm_le, MeasurableSet.const_smul₀, CochainComplex.HomComplex.Cochain.units_smul_v, IsBilinearMap.smul_left, MvPowerSeries.le_order_smul, SkewMonoidAlgebra.coeff_mul_single, HomologicalComplex.smul_f_apply, IsLocalizedModule.smul_inj, FormalMultilinearSeries.zero_radius, smul_unitBall, IsLocalization.linearMap_compatibleSMul, IsCompactOperator.smul_unit_iff, intervalIntegral.integral_const_of_cdf, Algebra.Extension.H1Cotangent.val_smul, DifferentiableWithinAt.const_smul, PolynomialModule.instIsScalarTower, NonUnitalAlgHom.toFun_eq_coe, WithSeminorms.congr_equiv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Matrix.detp_smul_adjp, intervalIntegral.integral_const', TrivSqZeroExt.inv_neg, MeasureTheory.condExp_smul_of_aestronglyMeasurable_left, VertexOperator.ext_iff, StrictConcaveOn.map_sum_eq_iff', Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral, hasStrictDerivAt_const, nnnorm_smul_le, Set.smul_mem_center, SkewMonoidAlgebra.support_mul, DistribMulAction.toAddEquiv_apply, PosSMulMono.toSMulPosMono, Derivation.coe_smul, intervalIntegral.integral_smul_deriv_eq_deriv_smul, Finset.inv_op_smul_finset_distrib₀, ContinuousLinearMap.self_comp_adjoint_injective_iff, Module.algebraMap_end_apply, hasStrictFDerivAt_list_prod_attach', Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsLocalizedModule.iso_symm_apply_aux, HasStrictDerivAt.scomp, Orientation.oangle_sub_left_smul_rotation_pi_div_two, HasFPowerSeriesWithinAt.restrictScalars, tangentConeAt_real_subset_isRCLikeNormedField, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, integral_withDensity_eq_integral_toReal_smul, ZLattice.covolume.tendsto_card_div_pow', WithCStarModule.instContinuousSMul, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, MeasureTheory.Lp.instIsCentralScalar, fderiv_continuousAlternatingMap_apply_apply, Matrix.scalar_comm_iff, SchwartzMap.hasDerivAt, HasDerivWithinAt.fun_sub, Module.End.mem_eigenspace_iff, lp.single_smul, Seminorm.inf_apply, TrivSqZeroExt.sndHom_comp_map, PiTensorProduct.mapLMultilinear_apply_apply, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, Units.neg_smul, HasFDerivWithinAt.clm_comp, AddMonoid.End.smulCommClass, ContinuousLinearMap.evalL_apply, AddMonoidAlgebra.smul_single', LinearPMap.supSpanSingleton_apply_smul_self, CategoryTheory.Functor.map_units_smul, isBoundedBilinearMap_apply, FormalMultilinearSeries.analyticOnNhd, ContinuousLinearEquiv.map_smulₛₗ, Submodule.mem_span_range_iff_exists_fun, Unitization.nnreal_cfcₙ_eq_cfc_inr, exteriorPower.presentation_relation, NonUnitalSeminormedRing.isBoundedSMul, StarConvex.add_smul_sub_mem, hasDerivAtFilter_iff_tendsto, AddMonoid.End.applyFaithfulSMul, Matrix.single_mul_eq_updateRow_zero, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, convex_hyperplane, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, CStarModule.inner_smul_left_real, Polynomial.iterate_derivative_smul, HasStrictDerivAt.comp, HVertexOperator.ext_iff, Finset.weightedVSubOfPoint_apply_const, PosSMulMono.toPosSMulStrictMono, InnerProductSpace.HarmonicOnNhd.const_smul, hasStrictFDerivAt_ringInverse, KaehlerDifferential.map_compDer, OrderDual.instSMulPosReflectLT, MeasureTheory.setIntegral_indicatorConstLp, InnerProductSpace.HarmonicContOnCl.fun_const_smul, LinearMap.liftBaseChange_tmul, ContinuousLinearMap.mul_apply', NonUnitalSeminormedRing.isBoundedSMulOpposite, starConvex_singleton, AffineSubspace.wOppSide_smul_vsub_vadd_right, fromTangentSpace_mfderiv_smul, TrivSqZeroExt.map_comp_map, CStarMatrix.reindexₐ_symm, ContDiff.smul, Unitization.IsIdempotentElem.inr, ConcaveOn.add, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, signedDist_smul, LieModule.Cohomology.smul_apply_apply, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_pos, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, smulAddHom_apply, MeasureTheory.convolution_lsmul_swap, Orientation.oangle_add_right_smul_rotation_pi_div_two, TestFunction.mkCLM_apply, FixedPoints.smul_polynomial, PolyEquivTensor.toFunBilinear_apply_apply, Ideal.IsPrime.smul, LinearEquiv.apply_smulCommClass', HasDerivAtFilter.comp_of_eq, Module.End.instSMulCommClass', TrivSqZeroExt.inr_smul, Orientation.inner_smul_rotation_pi_div_two_left, lp.instIsCentralScalarSubtypePreLpMemAddSubgroup, hasDerivAtFilter_finCons', Asymptotics.IsBigOTVS.eventually_smallSets, MeasureTheory.Supermartingale.smul_nonpos, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Matrix.ofNat_mulVec, TensorProduct.smul_tmul', ContinuousMap.toLp_injective, StrictConcaveOn.map_sum_eq_iff, TestFunction.fderivCLM_eq_of_scalars, midpoint_vsub_right, setIntegral_withDensity_eq_setIntegral_smul, IsLocalizedModule.mk'_smul_mk', ConcaveOn.translate_left, Function.Antiperiodic.const_smul₀, Module.End.instIsScalarTower, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, StrictConvexOn.convex_lt, hasDerivWithinAt_finCons', AffineMap.coe_lineMap, mellin_comp_rpow, ProbabilityTheory.integral_poissonMeasure, TrivSqZeroExt.instL1IsBoundedSMul, VectorField.mpullbackWithin_const_smul_apply, Finsupp.toDFinsupp_smul, IsAddUnit.smul_left, MeasureTheory.Submartingale.sum_smul_sub', Asymptotics.Filter.Tendsto.isBigOTVS_one, StarConvex.preimage_add_left, antivaryOn_iff_smul_rearrangement, MulActionHom.coe_neg, TestFunction.lineDerivCLM_eq_of_scalars, convex_RCLike_iff_convex_real, PointedCone.mem_span_set, Representation.norm_ofDistribMulAction_eq, Module.End.HasUnifEigenvector.apply_eq_smul, MultilinearMap.freeFinsuppEquiv_single, IsFractionRing.stabilizerHom_apply_apply_mk, intervalIntegral.smul_integral_comp_mul_add, dotProduct_smul, IsIntegralCurveAt.comp_mul_ne_zero, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Module.AEval.X_smul_of, Convex.combo_closure_interior_mem_interior, InnerProductSpace.rankOne_comp, CochainComplex.HomComplex.Cochain.rightShift_units_smul, Prod.instSMulPosStrictMono, Module.End.apply_smulCommClass, Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Finset.sum_range_by_parts, Asymptotics.IsTheta.const_smul_left, CliffordAlgebra.invOf_ι, DifferentiableWithinAt.fun_smul, Asymptotics.isLittleOTVS_comm, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, Rep.leftRegularHom_hom_single, HasDerivWithinAt.scomp, lp.instIsScalarTowerPreLp, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, TrivSqZeroExt.snd_pow_of_smul_comm', Asymptotics.IsLittleOTVS.snd, hasFPowerSeriesWithinAt_pi_iff, CircleIntegrable.const_fun_smul, IsLocalizedModule.exists_of_eq, MeasureTheory.eLpNorm_const_smul, hasDerivWithinAt_comp_mul_left_smul_iff, Ideal.restrictScalars_mul, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, Matrix.vecMul_diagonal_const, hasDerivAt_iff_isLittleO_nhds_zero, inner_smul_right, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, QuadraticMap.toFun_smul, SchwartzMap.tsupport_smulLeftCLM_subset, DFinsupp.instSMulPosReflectLT, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, HasFDerivWithinAt.continuousMultilinear_apply_const, Bornology.IsVonNBounded.vadd, LinearMap.equivariantProjection_apply, cfcₙHom_real_eq_restrict, Complex.UnitDisc.instSMulCommClass_circle_right, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, LinearMap.polar_AbsConvex, smul_floorDiv, vadd_openSegment, MeasureTheory.ComplexMeasure.im_apply, LinearMap.IsPerfPair.bijective_right, PiTensorProduct.liftIsometry_comp_mapL, iteratedFDeriv_smul_const_apply, FractionalIdeal.den_mul_self_eq_num, HasStrictDerivAt.fun_const_smul, MeasureTheory.Measure.addHaar_smul_of_nonneg, add_smul, HasDerivWithinAt.congr_deriv, CochainComplex.HomComplex.Cochain.rightUnshift_smul, Seminorm.continuous_iSup, RootPairing.pairingIn_one_four_iff, MeasureTheory.Lp.instIsBoundedSMul, RootPairing.Equiv.instSMulCommClassAut, InnerProductSpace.isSymmetric_rankOne_self, AddSubgroup.smul_mem_pointwise_smul, Orientation.oangle_smul_right_of_neg, CeilDiv.ceilDiv_gc, ContinuousLinearMap.toSpanSingleton_comp_toSpanSingleton, Seminorm.ball_smul_ball, IsSMulRegular.of_flat_of_isBaseChange, ContinuousMap.coe_toLp, Real.fourierIntegral_convergent_iff, SkewMonoidAlgebra.smul_sum, skewAdjointPart_apply_coe, continuousMultilinearCurryLeftEquiv_apply, SkewMonoidAlgebra.coeff_mul_single_one, IsIntegralCurveAt.hasDerivAt, convex_stdSimplex, linearIndependent_add_smul_iff, MonoidAlgebra.GroupSMul.linearMap_apply, ContinuousMapZero.instSMulCommClass', MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff, Seminorm.coe_sSup_eq, Ideal.smul_mem_pointwise_smul, ConvexBody.nonempty, MeasureTheory.integral_rnDeriv_smul, Asymptotics.IsBigOTVS.rfl, fourierCoeff_eq_intervalIntegral, Seminorm.bddBelow_range_add, NonUnitalSubalgebra.instSMulCommClass', CStarAlgebra.conjugate_le_norm_smul', Asymptotics.IsLittleOTVS.bot, IsSemisimpleModule.exists_end_algEquiv, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, RootPairing.weylGroup.ofIdx_smul, ContinuousLinearMap.isBigOTVS_comp, ContDiffAt.smul_const, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, Module.supportDim_le_supportDim_quotSMulTop_succ, AnalyticAt.exists_eq_sum_add_pow_mul, QuotSMulTop.equivQuotTensor_naturality_mk, inner_sum_smul_sum_smul_of_sum_eq_zero, hammingNorm_smul_le_hammingNorm, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, WithLp.smul_fst, iteratedDerivWithin_comp_const_smul, StrictConvexSpace.extremePoints_closedBall_eq_sphere, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Rat.instIsScalarTowerRight, Complex.taylorSeries_eq_on_eball, MeasureTheory.Measure.map_addHaar_smul, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, ContinuousLinearMap.intervalIntegral_apply, Function.noZeroSMulDivisors, span_fourierLp_closure_eq_top, smul_finsum', selfAdjointPartL_apply_coe, HasFDerivWithinAt.comp_hasDerivWithinAt, PMF.integral_eq_sum, MeasureTheory.average_add_measure, hasDerivAt_intCast, Seminorm.absorbent_ball_zero, IsRegular.smul_eq_zero_iff_right, PiTensorProduct.liftIsometry_symm_apply, Derivation.tensorProductTo_mul, IsCompactOperator.smul_iff₀, fderivWithin_continuousAlternatingMap_apply_apply, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, Matrix.diagonal_kronecker, RootPairing.pairingIn_neg_one_neg_four_iff, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonpos, Polynomial.smeval_at_zero, RestrictScalars.addEquiv_symm_map_smul_smul, IsBilinearMap.smul_right, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, PowerSeries.constantCoeff_smul, FormalMultilinearSeries.leftInv_comp, Polynomial.natDegree_smul_le, LieModule.smul_lie, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Submodule.span_range_update_add_smul, ValuationSubring.ofPrime_scalar_tower, IsLocalization.smul_mem_iff, Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, HasFPowerSeriesAt.const_smul, iteratedFDeriv_succ_eq_comp_right, Complex.re_qsmul, ContinuousMultilinearMap.changeOriginSeries_support, WeakFEPair.functional_equation₀, DiscreteConvolution.AddConvolutionExistsAt.vadd_convolution, CFC.nnrpow_le_nnrpow, Finsupp.linearCombination_comp_addSingleEquiv, convex_multiset_sum, Real.tendsto_integral_cexp_sq_smul, Asymptotics.isBigOTVS_fun_comm, TrivSqZeroExt.algebraMap_eq_inl, ContDiffMapSupportedIn.seminorm_apply, AddMonoidHom.smul_apply, AffineSubspace.sSameSide_smul_vsub_vadd_right, Matrix.toLinAlgEquiv_apply, WithSeminorms.tendsto_nhds_atTop, Submodule.mem_smul_top_iff, aemeasurable_withDensity_iff, derivWithin_const_smul, HasFDerivAt.isThetaTVS_sub, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, DifferentiableAt.clm_comp, SubmodulesRingBasis.leftMul, Fintype.not_linearIndependent_iff, DistribMulActionHom.map_zero', Monovary.sum_smul_comp_perm_lt_sum_smul_iff, MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff, QuadraticMap.weightedSumSquares_apply, CochainComplex.HomComplex.Cochain.smul_v, ODE.hasDerivWithinAt_picard_Icc, Module.support_quotSMulTop, signedDist_smul_of_neg, MeasureTheory.lpNorm_const_smul, VectorField.lieBracket_smul_left, DualNumber.range_inlAlgHom_sup_adjoin_eps, Submodule.smul_one_eq_span, ContinuousLinearMap.rotation_apply, Real.iteratedFDeriv_fourier, Seminorm.smul_closedBall_subset, Submodule.span_singleton_smul_eq, circleAverage_sub_sub_inv_smul_of_differentiable_on, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, TopologicalAddGroup.IsSES.pushforward_def, DoubleCentralizer.algebraMap_fst, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, Submodule.mem_span_image_finset_iff_exists_fun, deriv_clm_comp, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, Submodule.mem_annihilator_span, Bornology.IsVonNBounded.of_topologicalSpace_le, DifferentiableAt.fun_smul, circleIntegral.integral_smul_const, ContDiffMapSupportedIn.structureMapCLM_top_apply, inner_smul_real_left, Submodule.span_smul, Balanced.zero_insert_interior, DistribMulActionHom.map_add', Submodule.map_pointwise_smul, Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card, IsLocalization.map_eq_toLinearMap_mapₐ, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, Real.hasDerivAt_Gamma_one_half, IsClosed.balancedCore, toSpanSingleton_derivWithin, Asymptotics.IsBigOTVS.triangle, fderiv_norm_smul, IsOrderedModule.of_smul_nonneg, isMIntegralCurveAt_comp_mul_ne_zero, ContinuousLinearMap.isEmbedding_restrictScalars, lowerBounds_smul_of_neg, Finsupp.support_smul, spectrum.hasFDerivAt_resolvent, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, HasFDerivAt.hasFDerivAt_norm_smul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, Finsupp.instPosSMulMono, smul_ceilDiv, HasFiniteFPowerSeriesOnBall.eq_partialSum', VectorField.mlieBracket_const_smul_left, exists_lt_of_gauge_lt, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, CategoryTheory.ShortComplex.homologyMap'_smul, StarModule.complexToReal, AffineSubspace.smul_mem_smul_iff, IsScalarTower.to_smulCommClass, HasDerivAt.comp_hasDerivWithinAt, Complex.wedgeIntegral_add_wedgeIntegral_eq, IsMIntegralCurve.comp_mul, MeasureTheory.Integrable.smul_essSup, IsBoundedBilinearMap.toContinuousLinearMap_apply, Module.annihilator_eq_bot, isSMulRegular_of_ker_lsmul_eq_bot, Bornology.isVonNBounded_sub, ModuleFilterBasis.smul', MatrixModCat.isScalarTower_toModuleCat, HasFDerivWithinAt.curveIntegral_segment_source, ModuleCat.restrictScalars.smul_def, LinearIndependent.sum_smul_of_nondegenerate, Subsemiring.coe_pointwise_smul, HasFPowerSeriesOnBall.pi, Submodule.toSubMulAction_strictMono, HasFPowerSeriesWithinOnBall.fderivWithin_eq, jacobson_density, nhds_basis_closed_balanced, Finsupp.instIsScalarTowerForall, ContinuousMultilinearMap.piₗᵢ_symm_apply, ray_pos_smul, Matrix.instIsScalarTowerForall, convex_parallelepiped, HasDerivAt.scomp, ContDiffMapSupportedIn.structureMapLM_top_apply, ContinuousLinearMap.ker_adjoint_comp_self, AnalyticAt.analyticOrderAt_ne_top, DFinsupp.comapDomain'_smul, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, CochainComplex.HomComplex.Cochain.comp_units_smul, ContinuousLinearMap.smulRight_comp_smulRight, balancedCoreAux_subset, iteratedDerivWithin_fun_const_smul, Submodule.mem_span_pair, Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable, Matrix.toLinearMap₂_apply, Filter.Tendsto.isVonNBounded_range, HasDerivAt.const_mul, Real.hasFDerivAt_fourierIntegral, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, CompactlySupportedContinuousMap.coe_smulc, HasDerivWithinAt.congr, SchwartzMap.integralCLM_apply, IsCovariantDerivativeOn.add_one_form, Submodule.set_smul_eq_iSup, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, PolynormableSpace.withSeminorms', DistribSMul.toAddMonoidHom_apply, ConvexBody.isClosed, hasDerivAt_one, HasDerivAtFilter.fun_neg, SameRay.exists_nonneg_left, MultilinearMap.freeDFinsuppEquiv_apply, CliffordAlgebra.forall_mul_self_eq_iff, LinearMap.IsSymmetric.apply_eigenvectorBasis, IsOpen.strictConvex_iff, RootPairing.coroot_root_eq_pairing, Matrix.Module.single_smul, hasFDerivAt_iff_isLittleOTVS, Polynomial.map_smul, Representation.smul_tprod_one_asModule, CFC.nnrpow_eq_nnrpow_pi, IsBoundedSMul.of_nnnorm_smul_le, DomMulAct.instSMulCommClassAddMonoidHom_1, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, AnalyticAt.const_smul, smul_nonneg_iff, KaehlerDifferential.kerTotal_mkQ_single_smul, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, ContinuousAt.clm_bundle_apply₂, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, Polynomial.degree_smul_le, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, ZMod.map_smul, Algebra.Generators.repr_CotangentSpaceMap, ContinuousMultilinearMap.isVonNBounded_image2_apply, DividedPowerAlgebra.dp_sum_smul, hasLineDerivAt_iff_tendsto_slope_zero, MultilinearMap.piFamily_smul, Ideal.mem_iInf_smul_pow_eq_bot_iff, HasFDerivAt.list_prod', MeasureTheory.SignedMeasure.singularPart_smul_nnreal, Function.Even.smul_odd, ProbabilityTheory.strong_law_Lp, separatingDual_iff_injective, fderivWithin_const_smul_field, Pi.openSegment_subset, fderiv_continuousMultilinearMapCompContinuousLinearMap, deriv_fun_const_smul, MeasureTheory.integral_const, LinearEquiv.isSMulRegular_congr', Module.Basis.smulTower_apply, Function.Antiperiodic.const_smul, LinearMap.map_smul₂, IsLocalizedModule.isScalarTower_module, AffineMap.homothety_apply, HasDerivWithinAt.smul_const, HahnModule.orderTop_vAdd_le_orderTop_smul, CStarAlgebra.star_left_conjugate_le_norm_smul, LinearMap.intrinsicStarModule, DifferentiableOn.smul, contDiff_nat_iff_continuous_differentiable, hasFDerivAt_pow', ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, sameRay_smul_right_iff_of_ne, absorbent_ball, MeasureTheory.Lp.simpleFunc.coe_smul, Seminorm.zero_or_exists_apply_eq_finset_sup, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, Module.End.span_orbit_mem_invtSubmodule, StarConvex.affinity, hasDerivAt_abs, LinearMap.IsContPerfPair.bijective_right, HasFiniteFPowerSeriesOnBall.add, MeasureTheory.Lp.smul_def, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, iteratedDeriv_comp_const_sub, Submodule.coe_smul, LaurentPolynomial.smeval_single, ContinuousLinearMap.opNorm_lsmul_le, LinearMapClass.map_smul, Seminorm.ball_comp, FixedBy.intermediateField_mem_iff, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.mkContinuousMultilinear_norm_le, WithLp.instProdNormSMulClass, le_floorDiv_iff_mul_le, RootPairing.polarizationEquiv_symm_apply_coroot, ContDiffMapSupportedIn.monoCLM_eq_zero, StrictConvex.sum_mem_interior, DualNumber.commute_eps_left, Matrix.vecMul_natCast, KaehlerDifferential.isLocalizedModule, MulSemiringAction.toAlgEquiv_apply, hasDerivAt_natCast, IsMprojection.Mnorm, smul_vsub_rev_mem_vectorSpan_pair, HasDerivAtFilter.fun_sub, TrivSqZeroExt.kerIdeal_sq, RingHom.smul_def, ContinuousMap.coeFn_toLp, Seminorm.rescale_to_shell, AffineSubspace.direction_affineSpan_pair_le_iff_exists_smul, HasDerivWithinAt.union, gaugeRescale_def, Matrix.smul_mul, ConvexBody.isCompact, Real.hasDerivAt_Gamma_one, Convex.toCone_isLeast, segment_translate_image, ArithmeticFunction.smul_map, Real.fourier_bilin_convolution_eq_integral, Derivation.map_aeval, IsGaloisGroup.coe_quotient_smul, closedBall_normSeminorm, Complex.coe_smul, SchauderBasis.RankOneDecomposition.exists_coeff, ContinuousWithinAt.clm_bundle_apply₂, range_cfcₙ_nnreal_subset, Matrix.smul_eq_mulVec, ContinuousLinearMap.coe_restrictScalarsL, ModuleFilterBasis.smul_left, MemHolder.nnHolderNorm_smul, Matrix.detp_smul_add_adjp, Convex.combo_interior_self_mem_interior, HasDerivWithinAt.add_const, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, MeasureTheory.Integrable.integral_smul, lp.mem_lp_const_smul, Matrix.star_dotProduct_gram_mulVec, Bornology.IsVonNBounded.of_add_left, OpenPartialHomeomorph.univUnitBall_apply, LocalizedModule.instIsScalarTower, ContinuousLinearMap.norm_compL_le, Seminorm.continuousAt_zero_of_forall, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, EulerSine.antideriv_cos_comp_const_mul, Unitization.instIsStarNormal, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, Module.isTorsionBySet_quotient_iff, fderivWithin_clm_comp, integralClosure.coe_smul, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, sameRay_neg_smul_right_iff_of_ne, meromorphicOrderAt_smul_of_ne_zero, HasDerivWithinAt.congr_set, Submodule.mem_smul_span, Matrix.normSMulClass, Bornology.isVonNBounded_add, Nonneg.instIsOrderedModule, DualNumber.algHom_ext_iff, HasFPowerSeriesAt.sub, MvPolynomial.support_smul_eq, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, MeasureTheory.Lp.instSMulCommClass, BoxIntegral.integralSum_smul, taylor_integral_remainder_aux, OrderDual.instIsOrderedModule, Finset.centerMass_segment, Finsupp.sum_option_index_smul, OrthogonalFamily.range_linearIsometry, isIntegralCurve_comp_mul_ne_zero, TensorProduct.finsuppScalarLeft_apply_tmul, Real.tendsto_integral_exp_smul_cocompact, mellin_convergent_iff_norm, RestrictScalars.isScalarTower, MeasureTheory.setIntegral_tilted', fderiv_continuousMultilinear_apply_const, HasDerivWithinAt.smul, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq, Mathlib.Tactic.LinearCombination.smul_const_lt, ContinuousOn.integral_sub_linear_isLittleO_ae, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, MeasureTheory.L1.SimpleFunc.integral_smul, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one, iteratedDerivWithin_smul, NonUnitalStarSubalgebra.instSMulCommClass', ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, ContinuousLinearMap.opNNNorm_mul_flip_apply, HasDerivWithinAt.fun_pow, PiTensorProduct.smul_tprodCoeff', HasDerivWithinAt.finset_prod, cfc_smul, smul_le_smul_of_nonpos_left, IsNilpotent.exp_eq_sum, Nonneg.instNonUnitalContinuousFunctionalCalculus, ConvexOn.sub_strictConcaveOn, HasFPowerSeriesOnBall.hasFDerivAt, egauge_eq_zero_iff, SMulPosReflectLE.toSMulPosReflectLT, HasDerivWithinAt.mono, Orientation.oangle_smul_smul_self_of_nonneg, AddSubmonoid.smul_subset_smul, Algebra.Extension.Cotangent.val_smul, MeromorphicNFAt.smul_analytic, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, zero_mem_absConvexHull, Submodule.powSMulQuotInclusion_mk, ContinuousMultilinearMap.curryMid_apply, AntitoneOn.quasilinearOn, smul_neg_iff_of_pos_left, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, inv_smul_lt_iff_of_neg, HasFDerivWithinAt.comp_hasDerivAt, SchwartzMap.compCLM_apply, AddSubgroup.smul_mem_pointwise_smul_iff₀, convex_Ici, Finset.weightedVSub_eq_linear_combination, TemperedDistribution.fourierMultiplierCLM_apply_apply, Module.Basis.map_orientation_eq_det_inv_smul, ClosedSubmodule.sInf_orthogonal, AlternatingMap.coeFn_smul, intervalIntegral.fderivWithin_integral_of_tendsto_ae, concaveOn_iff_pairwise_pos, HasDerivAt.mul, ContinuousMap.toLp_comp_toContinuousMap, Function.HasTemperateGrowth.smul, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Bornology.IsVonNBounded.add, HasStrictFDerivAt.isBigOTVS_sub, rescale_to_shell_zpow, ConvexCone.mem_zero, ContMDiff.clm_postcomp, Asymptotics.IsLittleOTVS.tendsto_inv_smul, PolynomialModule.eval_apply, LieAlgebra.isScalarTower, balanced_closedBall_zero, integrableOn_peak_smul_of_integrableOn_of_tendsto, TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent, instSMulCommClass_sphere_ball_ball, Finset.neg_smul_finset, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, ModelWithCorners.convex_range', MeasureTheory.Lp.smul_comm, Submodule.smul_mem_iff, Module.End.baseChangeHom_apply_apply, isBoundedBilinearMap_smul, fderivWithin_continuousAlternatingMap_apply_const, ConcaveOn.map_add_sum_le, NonUnitalAlgHom.map_mul', smul_inv₀, EulerSine.antideriv_sin_comp_const_mul, LinearMap.map_smul, Matrix.isDiag_smul_one, Module.End.instSMulCommClass, mapsTo_tangentConeAt_pi, Finset.sum_smul_sum_eq_sum_perm, strictConvex_singleton, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, Finsupp.comapDomain_smul, ContinuousLinearMap.norm_restrictScalars, Asymptotics.IsLittleOTVS.isBigOTVS, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, coe_normSeminorm, Submodule.restrictScalars.isScalarTower, DFinsupp.single_smul, Module.reflection_mul_reflection_zpow_apply_self, ConvexCone.coe_add, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, Finsupp.instSMulPosStrictMono, parallelepiped_eq_sum_segment, MDifferentiableWithinAt.clm_postcomp, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, WeakDual.instContinuousSMul, convex_Iio, Matrix.toLinAlgEquiv_self, boole_smul, RootPairing.coreflection_apply, convex_halfSpace_gt, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, HasDerivWithinAt.const_sub, Matrix.isAddUnit_detp_smul_mul_adjp, LocallyFinite.smul_right, Algebra.Extension.tensorCotangentInvFun_smul_mk, ContDiffBump.convolution_eq_right, ContinuousMultilinearMap.map_update_smul, TemperedDistribution.instFourierInvSMul, sameRay_neg_smul_right_iff, MeasureTheory.AEEqFun.Integrable.smul, ExistsContDiffBumpBase.w_def, HasDerivWithinAt.const_smul, MeasureTheory.Measure.setIntegral_comp_smul, ValuationSubring.coe_pointwise_smul, ContDiffOn.smul, mem_vectorSpan_pair, ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity, WeakFEPair.hf_modif_FE, HasDerivWithinAt.hasDerivAt, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, ContinuousLinearMap.opNorm_mul_apply_le, deriv_smul_const, intervalIntegral.integral_hasFDerivWithinAt, HasFPowerSeriesAt.tendsto_partialSum, Complex.ofReal_qsmul, TopologicalGroup.IsSES.pushforward_mono, ContinuousLinearMap.smul_def, ContinuousLinearMap.orthogonal_range, NormedDivisionRing.toNormSMulClass, Antitone.quasilinearOn, HasFiniteFPowerSeriesAt.add, Matrix.conjTranspose_intCast_smul, HasFPowerSeriesAt.hasDerivAt, TensorProduct.AlgebraTensorModule.lift_apply, hasDerivWithinAt_congr_set', Finsupp.mem_span_range_iff_exists_finsupp, Module.Finite.toModuleEnd_moduleEnd_surjective, smul_div₀', ContinuousLinearMap.isThetaTVS_comp, DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul, StrictConcaveOn.neg, fourierIntegral_half_period_translate, ediam_smul₀, CategoryTheory.ShiftedHom.map_smul, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, AddCommMonoid.nat_isScalarTower, ContinuousLinearMap.opNorm_smul_le, tendsto_smul_congr_of_tendsto_left_cobounded_of_isBoundedUnder, StrictConvexSpace.sphere_subset_extremePoints_closedBall, TestFunction.fderivCLM_apply_of_gt, MeasureTheory.withDensitySMulLI_apply, Asymptotics.isLittleOTVS_congr, HasStrictFDerivAt.isThetaTVS_sub, hasDerivWithinAt_const_add_iff, convexHull_toCone_isLeast, ConvexCone.IsGenerating.span_eq_top, MeasureTheory.Measure.addHaar_nnreal_smul, ContinuousLinearMap.spectralRadius_eq_nnnorm, Complex.taylorSeries_eq_on_emetric_ball, finsuppTensorFinsuppLid_apply_apply, EuclideanGeometry.hasFDerivAt_inversion, HahnModule.zero_smul', MeasureTheory.convolutionExistsAt_iff_integrable_swap, dist_div_norm_sq_smul, mem_segment_iff_wbtw, torusIntegral_smul, PolyEquivTensor.toFunBilinear_apply_eq_smul, WithConv.symm_matrixToLin'StarAlgEquiv_apply, AddGroup.int_smulCommClass, ConcaveOn.neg, VectorField.mpullback_smul, hasDerivAt_ofReal_cpow_const, Monovary.sum_comp_perm_smul_eq_sum_smul_iff, Monovary.sum_comp_perm_smul_le_sum_smul, Submodule.factorPow_comp_powSMulQuotInclusion, CliffordAlgebraDualNumber.equiv_ι, Derivation.leibniz_pow, convex_iff_div, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType, hasDerivAt_norm_rpow, ContinuousLinearMap.spectrum_eq, HasStrictFDerivAt.fun_const_smul, IsLocalizedModule.smul_injective, TrivSqZeroExt.snd_map, Subring.center.smulCommClass_left, Ideal.mem_torsionOf_iff, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem, smul_algebra_smul_comm, fderivWithin_const_smul, concaveOn_univ_piecewise_Iic_of_monotoneOn_Iic_antitoneOn_Ici, smul_neg_of_pos_of_neg, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, Submodule.mem_span_triple, Matrix.instSMulCommClassForall, HasStrictDerivAt.fun_sub, HasDerivWithinAt.star, Submodule.mem_torsionBy_iff, Matrix.kroneckerTMul_smul, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, Matrix.trace_mul_single, Ideal.smul_bot, TensorProduct.smul_tmul_smul, Module.Invertible.instFaithfulSMul, Seminorm.smul_closedBall_preimage, HasFDerivWithinAt.unique_on, MeromorphicOn.extract_zeros_poles, CategoryTheory.Free.lift_map_single, ProbabilityTheory.IsGaussianProcess.smul, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, ContinuousLinearMap.norm_bilinearRestrictScalars, ContinuousLinearMap.nhds_zero_eq, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HasDerivAt.sum, ProbabilityTheory.covarianceBilin_map, zero_mem_tangentConeAt, SchwartzMap.instFourierSMul, CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, HasFPowerSeriesOnBall.prod, MonoidAlgebra.smulCommClass_symm_self, Unitization.nnnorm_eq_sup, Orientation.two_zsmul_oangle_smul_right_self, Finsupp.sum_smul_index_semilinearMap', MvPowerSeries.instIsScalarTower, SchwartzMap.fourierTransformCLM_apply, HasFDerivAt.curveIntegral_segment_source', LinearEquiv.isSMulRegular_congr, HasFPowerSeriesWithinOnBall.neg, selfAdjointPart_apply_coe, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, Seminorm.bound_of_shell_sup, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Finset.expect_univ, WeakSpace.instContinuousSMul, intervalIntegral.integral_deriv_smul_deriv_comp, AlgEquiv.moduleEndSelfOp_symm_apply, TensorProduct.directSumRight'_restrict, ConcaveOn.mul, skewAdjointPartL_apply_coe, Finset.weightedVSub_apply, Polynomial.smeval_monomial, ContinuousLinearMap.bilinearComp_zero_left, HasStrictDerivAt.finCons, ContinuousLinearMap.nnnorm_smulRight_apply, mem_tangentConeAt_of_openSegment_subset, RootPairing.pairing_neg_one_neg_four_iff', hasFPowerSeriesWithinOnBall_pi_iff, HasDerivAt.fun_smul, hasDerivAt_zero, Convex.add_smul_sub_mem_interior', SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, IsLocalizedModule.mk'_smul, CStarModule.inner_mul_inner_swap_le, HasFDerivWithinAt.isLittleOTVS, ConvexOn.sup, Multiset.pow_smul_esymm, mellin_const_smul, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, ContMDiffOn.const_smul_section, LinearIndependent.units_smul, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, Seminorm.gauge_ball, FreeLieAlgebra.Rel.smulOfTower, NormedSpace.exp_smul, Fintype.sum_smul_sum, MeasureTheory.integral_fun_fst, right_mem_segment, SmoothPartitionOfUnity.contMDiff_finsum_smul, hasDerivWithinAt_inter', MeasureTheory.pdf.integrable_pdf_smul_iff, Seminorm.coe_comp, LinearMap.map_smulₛₗ, HahnSeries.SummableFamily.sum_vAddAntidiagonal_eq, DirectSum.GAlgebra.smul_def, HasDerivWithinAt.scomp_hasDerivAt, MDifferentiableOn.clm_precomp, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, VectorField.lieBracketWithin_smul_right, AddSubmonoid.mem_inv_pointwise_smul_iff, DualNumber.commute_eps_right, ConvexOn.mul_concaveOn, StrictConvexOn.sup, fderiv_fun_const_smul, QuaternionAlgebra.coe_smul, hasDerivAt_exp_smul_const_of_mem_ball', Finset.zero_smul_finset, extremePoints_convexHull_subset, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, LinearEquiv.isScalarTower, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, StarConvex.is_linear_preimage, Polynomial.smul_C, gauge_lt_eq', deriv_comp_mul_left, Submodule.mem_span_image_finset_iff_exists_fun', hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, Module.End.mem_genEigenspace_one, intervalIntegral.integral_hasDerivAt_right, hasFTaylorSeriesUpToOn_succ_iff_left, HasDerivWithinAt.mul_const, LinearOrderedField.smul_Ici, mem_segment_iff_div, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Absorbs.neg_neg, MonotoneOn.quasiconcaveOn, HasCompactSupport.hasDerivAt_convolution_left, SkewMonoidAlgebra.isScalarTower_self, IsSMulRegular.not_zero, DistribSMul.toLinearMap_apply, HasDerivWithinAt.cexp, Balanced.starConvex, DualNumber.instIsLocalRing, VectorFourier.integral_bilin_fourierIntegral_eq_flip, smul_inv_le_iff_of_neg, Ideal.pointwise_smul_le_pointwise_smul_iff, deriv_clm_apply, Module.End.apply_faithfulSMul, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, CFC.monotone_sqrt, HasFPowerSeriesWithinOnBall.add, exposedPoints_subset_extremePoints, Module.isTorsionBy_quotient_iff, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK, Finset.centerMass_pair, contDiff_smul, exists_maximal_linearIndepOn, AffineMap.hasStrictDerivAt, Finset.smul_sum, ConvexBody.iInter_smul_eq_self, IsGaloisGroup.smul_eq_self, InnerProductSpace.toLinearMap_rankOne, openSegment_translate_preimage, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, HasDerivWithinAt.Ioi_of_Ici, Module.reflection_mul_reflection_zpow_apply, ContinuousLinearMap.adjointAux_inner_right, HasDerivWithinAt.Ioi_iff_Ioo, VectorField.mpullback_mfderivWithin_apply_smul, VectorField.mpullbackWithin_const_smul, MeromorphicOn.smul, Seminorm.finset_sup_smul, Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real, Complex.taylorSeries_eq_on_ball, TemperedDistribution.instLineDerivSMulComplex, StrictConcaveOn.translate_left, CStarAlgebra.conjugate_le_norm_smul, HasStrictFDerivAt.clm_apply, ContMDiffAt.clm_bundle_apply₂, Nat.cast_smul_eq_nsmul, ContDiffMapSupportedIn.fderivLM_apply, smul_lowerBounds_subset_upperBounds_smul, Seminorm.isBounded_sup, norm_midpoint_lt_iff, LinearMap.prodMap_smul, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LinearMap.trace_tensorProduct, continuousMultilinearCurryRightEquiv_symm_apply', AntitoneOn.convex_ge, MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', NormedSpace.expSeries_sum_eq_div, Summable.tsum_smul_const, Homotopy.smul_hom, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, Convex.add_smul_mem_interior', LinearEquiv.mem_stabilizer_fixedSubmodule, measurable_smul_const, AffineSubspace.wSameSide_smul_vsub_vadd_right, Polynomial.toFinsupp_smul, WeakFEPair.functional_equation, MeasureTheory.Submartingale.sum_smul_sub, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, LinearEquiv.map_smul, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, HahnModule.one_smul', convex_Ioc, Submodule.smul_torsionBy, intervalIntegral.integral_comp_smul_deriv''', TrivSqZeroExt.fst_map, HasDerivWithinAt.fun_add, LinearMap.BilinForm.smul_right, LinearMap.isStarProjection_toContinuousLinearMap_iff, CategoryTheory.Limits.IsColimit.ι_smul, Matrix.Semiring.isScalarTower, MeromorphicOn.divisor_smul, Matrix.natCast_mulVec, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, IsLinearMap.isLinearMap_smul, LocalizedModule.mk'_smul_mk, Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, HasFDerivAtFilter.isLittleOTVS, Representation.ofModule_asAlgebraHom_apply_apply, Submodule.smul_le, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, iteratedDerivWithin_eq_equiv_comp, Matrix.convex_rowStochastic, MvPowerSeries.coeff_smul, HasDerivAt.const_add, slope_sub_smul, iteratedFDerivWithin_two_apply, Matrix.conjTranspose_ofNat_smul, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, extDerivWithin_smul, AddAction.automorphize_smul_left, Derivation.compAEval_eq, ContDiffMapSupportedIn.seminorm_postcompLM_le, Ideal.Quotient.smulCommClass', MeasureTheory.integrable_smul_iff, CategoryTheory.MonoidalLinear.smul_whiskerRight, Derivation.tensorProductTo_tmul, IsExtreme.convex_diff, MeasureTheory.integral_countable, DoubleCentralizer.coe_fst, HasStrictFDerivAt.fun_smul, HahnModule.of_smul, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul, Polynomial.aeval_endomorphism, smul_inv_lt_iff_of_neg, CompactlySupportedContinuousMap.toReal_smul, Derivation.map_smul, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, norm_cfcₙ_one_sub_one_add_inv_lt_one, Seminorm.closedBall_bot, LocallyConvexSpace.convex_open_basis_zero, Submodule.adjoint_orthogonalProjection, CategoryTheory.MonoidalLinear.whiskerLeft_smul, Filter.HasBasis.isBigOTVS_iff, MeasureTheory.Integrable.fun_smul, Real.sInf_smul_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, HasFDerivAt.pow', IsCompactOperator.smul, continuousOn_cfcₙ_nnreal, Function.Odd.smul_even, HasStrictFDerivAt.pow', ContDiffWithinAt.smul_const, surjOn_extremePoints_image, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, Convex.smul_mem_of_zero_mem, Real.fourierIntegral_continuousLinearMap_apply', CurveIntegrable.smul, BoxIntegral.Integrable.smul, RootPairing.rootFormIn_self_smul_coroot, Finsupp.smul_eq, LinearEquiv.smul_def, Finset.centroid_pair, TopModuleCat.hom_smul, isMIntegralCurveOn_comp_mul_ne_zero, ContinuousLinearMap.hasFDerivAt_of_bilinear, starConvex_iff_forall_pos, Submodule.tensorToSpan_apply_tmul, lp.infty_isScalarTower, FormalMultilinearSeries.min_radius_le_radius_add, hasStrictDerivAt_one, FormalMultilinearSeries.ofScalars_comp_neg_id, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, MeasureTheory.HasFiniteIntegral.smul, LinearOrderedField.smul_Ioi, RootPairing.corootForm_self_smul_root, HasDerivWithinAt.of_isLittleO, TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_apply_tmul, StrongDual.extendRCLike_apply, ContinuousLinearMap.closed_range_of_antilipschitz, tendsto_integral_comp_smul_smul_of_integrable, Matrix.frobeniusNormSMulClass, MonoidAlgebra.liftNC_smul, HasDerivAt.div_const, strictConvex_iff_div, HasDerivAt.scomp_of_eq, VonNeumannAlgebra.coe_toStarSubalgebra, LieAlgebra.SemiDirectSum.smul_eq_mk, BddAbove.smul_of_nonpos, lie_eq_smul, SeminormFamily.basisSets_singleton_mem, Ideal.ofList_cons_smul, Module.AEval.of_aeval_smul, Absorbs.zero, Finset.centerMass_eq_of_sum_1, Pi.single_smul', Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, ContDiffMapSupportedIn.continuous_iff_comp_order_le, Mathlib.Tactic.Module.NF.sub_eq_eval₂, TensorialAt.mkHom₂_apply, ConvexCone.disjoint_hull_right_of_convex, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, TopologicalAddGroup.IsSES.integral_inducedMeasure, IsScalarTower.complexToReal, HasFPowerSeriesAt.pi, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, StrictConcaveOn.add_concaveOn, smul_ball, Subalgebra.instIsScalarTowerSubtypeMem, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', map_intCast_smul, AddAut.mulLeft_apply_apply, IntervalIntegrable.continuousOn_smul, Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, SameRay.exists_pos, VectorFourier.fourierPowSMulRight_apply, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, finsuppTensorFinsuppRid_apply_apply, Module.Basis.repr_sum_self, SameRay.smul, inner_eq_norm_mul_iff_real, HasDerivAt.cexp, ContinuousAlternatingMap.prodLIE_apply, Finsupp.linearCombination_option, MeasureTheory.Submartingale.smul_nonpos, SkewMonoidAlgebra.support_single_mul_subset, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, image_extremePoints, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, Summable.smul_const, MeasureTheory.Lp.simpleFunc.toLp_smul, LieAlgebra.IsKilling.chainLength_smul, IsEllSequence.smul, segment_eq_image_lineMap, sub_smul_slope, dist_smul₀, convexCombination_eq_sum, concaveOn_iff_forall_pos, ftaylorSeries_zero, PadicInt.mahlerEquiv_apply, Module.Basis.toMatrix_smul_left, Submodule.span_singleton_eq_range, CentroidHom.instIsCentralScalar, SchwartzMap.convolution_flip, Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul, HasDerivWithinAt.isLittleO, Matrix.diagonal_const_mulVec, ContinuousLinearMap.opNorm_flip, LieRinehartAlgebra.Hom.map_smul_apply, Module.Basis.parallelepiped_map, Seminorm.bound_of_shell_smul, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, Filter.Tendsto.integral_sub_linear_isLittleO_ae, FormalMultilinearSeries.radius_compContinuousLinearMap_le, MeasureTheory.distribHaarChar_eq_div, hasDerivWithinAt_derivWithin_iff, IsCompactOperator.smul_isUnit_iff, hasDerivAt_sub_const_iff, midpoint_mem_segment, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, hammingNorm_smul, LinearMap.smulRightₗ_apply_apply, HasDerivAt.div, Complex.isometryOfOrthonormal_apply, IsConformalMap.smul, Matrix.vecMulVec_mul_vecMulVec, AddSubgroup.coe_pointwise_smul, intervalIntegral.smul_integral_comp_mul_right, HasDerivWithinAt.pow, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity, Matrix.dualNumberEquiv_apply, MeasureTheory.eLpNorm'_const_smul_le, intervalIntegral.integral_comp_div_add, ConvexCone.isGenerating_top, ConvexBody.zero_mem_of_symmetric, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, CategoryTheory.Pretriangulated.Triangle.smul_hom₃, Complex.hasDerivAt_Gamma_one, TemperedDistribution.fourierMultiplierCLM_sum, LinearMap.restrictScalars_extendScalarsOfIsLocalization, SkewMonoidAlgebra.instSMulCommClass, intervalIntegral.integral_smul_const, FormalMultilinearSeries.derivSeries_eq_zero, InnerProductSpace.laplacianWithin_smul_nhds, AntitoneOn.quasiconvexOn, QuotientGroup.automorphize_smul_left, TestFunction.lineDerivCLM_smul, Unitization.instStarModule, Algebra.Generators.H1Cotangent.δ_eq_δAux, ContDiffWithinAt.smulRight, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, HasDerivWithinAt.congr_of_eventuallyEq, HasDerivAtFilter.isEquivalent_sub, AddSubmonoid.coe_pointwise_smul, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ContinuousLinearMap.star_eq_adjoint, SchwartzMap.integral_fourier_smul_eq, Real.dimH_segment, FormalMultilinearSeries.comp_rightInv, IsSMulRegular.skewMonoidAlgebra_iff, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable, IsBaseChange.equiv_tmul, Polynomial.fwdDiff_iter_degree_eq_factorial, ContinuousMultilinearMap.curryLeft_apply, ValuationSubring.mem_smul_pointwise_iff_exists, Finset.centerMass_smul, Monotone.quasiconvexOn, Submodule.mem_toConvexCone, AffineSpace.asymptoticNhds_eq_smul, smul_max_of_nonpos, HasStrictDerivAt.fun_neg, ContDiffAt.fun_smul, HasFPowerSeriesWithinAt.neg, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, RootPairing.pairing_smul_coroot_eq, Function.Antiperiodic.smul, Bornology.IsVonNBounded.closure, HasFDerivAt.hasFDerivAt_norm_smul_neg, SkewMonoidAlgebra.coeff_mul_antidiagonal_of_finset, QuotSMulTop.map_comp, finsuppTensorFinsuppLid_single_tmul_single, Asymptotics.isThetaTVS_comm, Ideal.pointwise_central_scalar, fderivWithin_list_prod', AlternatingMap.mkContinuousLinear_norm_le, FreeLieAlgebra.instIsCentralScalar, ProperCone.hyperplane_separation_of_notMem, ConvexOn.mul', SkewMonoidAlgebra.instIsCentralScalar, MeasureTheory.charFun_map_smul_comp, fderiv_clm_apply, DualNumber.eps_pow_two, ContinuousAlternatingMap.curryLeftLI_apply, smul_pos_iff_of_neg_left, ContMDiffWithinAt.const_smul_section, ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasis, ContinuousLinearEquiv.smul_apply, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, HasFDerivWithinAt.fun_mul', ContinuousLinearMap.norm_compSL_le, TestFunction.monoCLM_apply, ContinuousAlternatingMap.instIsCentralScalar, fderivWithin_smul_const, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, Balanced.neg, ContDiffMapSupportedIn.withSeminorms, cfc_smul_id, Polynomial.rootSet.coe_smul, ConvexCone.mem_strictlyPositive, AnalyticOn.fun_const_smul, MeasureTheory.withDensityᵥ_smul, wbtw_or_wbtw_smul_vadd_of_nonneg, ContDiffAt.exists_eventually_eq_hasDerivAt, ContinuousLinearEquiv.continuousSMul, DivisibleHull.qsmul_of_nonpos, TopologicalAddGroup.IsSES.pushforward_mono, Bornology.isVonNBounded_vadd, star_mul_self_sub_self_mul_star, MeasureTheory.integrable_comp_smul_iff, MeasureTheory.distribHaarChar_mul, derivWithin_fun_const_smul', convex_halfSpace_le, Convex.openSegment_closure_interior_subset_interior, mem_openSegment_of_gauge_lt_one, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ, cfcₙ_nnreal_eq_real, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, Matrix.trace_smul, ConvexOn.convex_strict_epigraph, HasFDerivWithinAt.isBigOTVS_sub, LinearOrderedField.smul_Ioc, DirectSum.support_smul, convexHull_isClosed, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, iteratedDeriv_const_smul_field, Seminorm.absorbent_closedBall, SemilinearEquivClass.map_smulₛₗ, IsMIntegralCurveAt.comp_mul_ne_zero, CategoryTheory.NatTrans.app_smul, inf_eq_half_smul_add_sub_abs_sub, InnerProductSpace.isIdempotentElem_rankOne_self_iff, HasDerivAt.tendsto_slope_zero, fderivWithin_continuousLinearEquiv_comp, ContinuousMultilinearMap.toUniformOnFun_toFun, Quaternion.re_snd_dualNumberEquiv, Ideal.pointwise_smul_toAddSubgroup, sub_mem_posTangentConeAt_of_openSegment_subset, MulSemiringAction.toAlgHom_apply, IsLocalization.instCompatibleSMulLocalizationOfIsScalarTower, Submodule.span_singleton_mul, div_le_egauge_ball, TrivSqZeroExt.algebraMap_eq_inlHom, hasDerivAtFilter_pi, stereographic_apply, tsupport_smul_subset_right, Asymptotics.IsThetaTVS.trans, Orientation.rotation_apply, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, ContinuousSMul.of_basis_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, SameRay.norm_smul_eq, Representation.leftRegular_norm_apply, segment_subset_uIcc, Matrix.cons_vecMulVec, TensorProduct.liftAux.smul, Set.smul_zero_subset, inner_map_polarization, not_linearIndepOn_finset_iff, UniformConvergenceCLM.instContinuousConstSMul, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, AddMonoid.End.isScalarTower, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Matrix.cons_vecMul, Real.iteratedFDeriv_fourierIntegral, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonneg, SMulPosMono.toSMulPosStrictMono, Mathlib.Tactic.Module.NF.eval_smul, StieltjesFunction.measure_smul, MeasureTheory.Lp.coe_LpSubmodule, Submodule.exists_of_finrank_lt, Bornology.isVonNBounded_insert, Algebra.Generators.CotangentSpace.map_toComp_injective, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, StieltjesFunction.ae_hasDerivAt, InnerProductSpaceable.innerProp, Continuous.clm_bundle_apply₂, MeasureTheory.withDensityᵥ_rnDeriv_smul, FormalMultilinearSeries.ofScalars_series_eq_zero, CochainComplex.HomComplex.Cochain.leftShift_units_smul, differentiableWithinAt_smul_iff, Antivary.sum_smul_comp_perm_eq_sum_smul_iff, Asymptotics.IsLittleOTVS.mono, fderivWithin_pow_ring', ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, LocalizedModule.mk_smul_mk, ConvexCone.mem_hull_of_convex, LinearEquiv.coord_apply_smul, FormalMultilinearSeries.changeOrigin_eval, VertexOperator.ncoeff_of_coeff, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, LinearMap.toSeminorm_ball_zero, Polynomial.smul_mem_rootSet_iff_of_isUnit, AffineMap.homothety_def, convex_doublyStochastic, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, DFinsupp.isCentralScalar, ExteriorAlgebra.liftAlternating_algebraMap, Finsupp.smul_apply_addAction, StrictConvex.add_smul_sub_mem, inner_smul_left_eq_smul, Finset.expect_dite_eq, StrongConvexOn.strictConvexOn, DifferentiableOn.const_smul, Convex.sum_mem, CategoryTheory.Free.lift_map, midpoint_sub_left, Submodule.mem_span_set', ContinuousLinearMap.reApplyInnerSelf_smul, ConcaveOn.smul', NonUnitalCStarAlgebra.toIsScalarTower, MeasureTheory.integral_indicator_const, Asymptotics.IsThetaTVS.trans_isLittleOTVS, ConcaveOn.smul, VertexOperator.ncoeff_eq_zero_of_lt_order, Set.indicator_const_smul_apply, IsSelfAdjoint.adjoint_conj, Asymptotics.IsBigOTVS.trans_isThetaTVS, Bornology.IsVonNBounded.image, not_linearIndependent_iff, enorm_smul_le, Matrix.vecMulVec_cons, closedAbsConvexHull_eq_closure_absConvexHull, MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff, RootPairing.pairing_smul_root_eq, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, Set.zero_mem_smul_set, HasDerivAt.inner, HasFPowerSeriesAt.prod, TensorProduct.lidOfCompatibleSMul_tmul, midpoint_vsub, LinearMap.toSeminorm_apply, gc_floorDiv_smul, LinearIndependent.units_smul_iff, linearDepOn_iffₛ, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, Complex.hasDerivAt_Gamma_one_half, convex_sum, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonneg, CFC.sqrt_le_sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Real.smul_iSup_of_nonneg, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ZMod.invDFT_def, skewAdjoint.smul_mem, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, lineDeriv_smul, ContinuousMap.smul_apply', MeasureTheory.integrable_rnDeriv_smul_iff, AlternatingMap.mkContinuousAlternating_norm_le_max, LinearMap.map_smul', Polynomial.eval_smul, OrthonormalBasis.sum_rankOne_eq_id, ProbabilityTheory.strong_law_ae_simpleFunc_comp, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, hasDerivAt_finCons', HasStrictDerivAt.hasDerivAt, segment.lift, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Asymptotics.IsLittleOTVS.trans, absorbs_iff_eventually_nhds_zero, Finsupp.support_smul_eq, RootPairing.Equiv.reflection_smul, StrictConvex.add_smul_mem, HahnModule.support_smul_subset_vadd_support, Matrix.cons_vecMul_cons, isScalarTower_sphere_ball_ball, TensorProduct.equivFinsuppOfBasisRight_symm, TensorProduct.AlgebraTensorModule.ker_mapOfCompatibleSMul, GradedMonoid.isScalarTower_right, HasFPowerSeriesWithinAt.add, Antivary.card_smul_sum_le_sum_smul_sum, SMulWithZero.zero_smul, ContDiffMapSupportedIn.fderivCLM_apply_of_le, inf_eq_half_smul_add_sub_abs_sub', ContinuousLinearMap.adjoint_inner_right, Real.tendsto_integral_gaussian_smul, map_nnratCast_smul, HVertexOperator.compHahnSeries_coeff, LinearMap.liftBaseChange_comp, IsSMulRegular.subsingleton_linearMap_iff, LieDerivation.smul_apply, HasFDerivWithinAt.fun_pow', StarAlgEquiv.ofInjective'_apply, Module.Basis.orientation_unitsSMul, ConvexOn.comp_affineMap, IntervalIntegrable.integral_smul, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, groupHomology.isBoundary₀_iff, StrictConvex.convex, HasStrictFDerivAt.continuousAlternatingMap_apply_const, VectorFourier.fourierIntegral_comp_add_right, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, ContDiffMapSupportedIn.postcompLM_apply, DFinsupp.instSMulPosReflectLE, Submodule.mem_colon_singleton, UnitAddTorus.span_mFourier_closure_eq_top, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, ZeroHom.instIsScalarTower, Convex.combo_le_max, MeasureTheory.withDensityᵥ_smul', AlgEquiv.apply_faithfulSMul, differentiableAt_iff_restrictScalars, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, smul_mem_asymptoticCone_iff, Mathlib.Tactic.Module.NF.add_eq_eval, MonoidAlgebra.isScalarTower_self, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, DirectSum.smul_apply, intervalIntegral.integral_deriv_smul_comp''', Filter.Tendsto.cesaro_smul, Algebra.Extension.Hom.sub_tmul, StrictConvex.preimage_add_right, LinearEquiv.reduce_mk, deriv_fun_const_smul_field, Convex.combo_self_interior_mem_interior, Matrix.ofNat_kronecker, SubMulAction.val_neg, NNRat.instIsScalarTowerRight, tendsto_integral_exp_inner_smul_cocompact, QuadraticMap.polar_smul_right_of_tower, CategoryTheory.Linear.instEpiHSMulHomOfInvertible, Matrix.vecMulVec_mulVec, StrictConvex.linear_image, MellinConvergent.const_smul, Finset.centroid_pair_fin, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, MeasureTheory.Measure.addHaarScalarFactor_domSMul, inner_smul_right_eq_smul, NonUnitalAlgHom.coe_mk, Polynomial.faithfulSMul, ProperCone.pointed_toConvexCone, ConvexCone.Pointed.of_nonempty_of_isClosed, smul_pos, StarConvex.is_linear_image, QuadraticMap.apply_linearCombination, RingAut.apply_faithfulSMul, IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul, MulAction.automorphize_smul_left, DualNumber.exp_smul_eps, AddSubmonoid.smul_mem_pointwise_smul_iff, SchwartzMap.integral_smul_laplacian_right_eq_left, StrictConvexOn.convexOn, gc_smul_ceilDiv, ContinuousMultilinearMap.smulRight_apply, StrictConcaveOn.add_const, tsum_smul_tsum, Set.OrdConnected.strictConvex, TrivSqZeroExt.map_inl, FormalMultilinearSeries.radius_prod_eq_min, imaginaryPart_smul, CliffordAlgebra.foldr_algebraMap, Quaternion.snd_imI_dualNumberEquiv_symm, LaurentPolynomial.smeval_C_mul_T_n, OrthonormalBasis.coe_equiv_euclideanSpace, StrongDual.im_extendRCLike_apply, VectorFourier.fourierIntegral_probChar, ModuleCat.restrictScalars.smul_def', SkewMonoidAlgebra.coeff_mul_left, Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass, Mathlib.Tactic.Module.NF.eq_const_cons, openSegment_same, QuaternionAlgebra.star_smul, MonoidAlgebra.ofCoeff_smul, Seminorm.preimage_metric_ball, NonUnitalCommCStarAlgebra.toSMulCommClass, LocallyConvexSpace.convex_basis, Submodule.smul_mem_span_smul', HasFDerivAt.mul_const', Set.smul_neg, MvPolynomial.derivation_C_mul, essSup_smul_measure, mem_segment_add_sub, IsCyclic.mulAutMulEquiv_symm_apply_apply, Module.toAddMonoidEnd_apply_apply, Orientation.two_zsmul_oangle_smul_left_self, ContinuousLinearMap.le_of_opNorm₂_le_of_le, AddSubgroup.mem_inv_pointwise_smul_iff₀, Fourier.fourierIntegral_def, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, NonUnitalStarSubalgebra.instIsScalarTower, Complex.IsExactOn.with_val_at, LinearMap.rid_comp_lTensor, HahnSeries.SummableFamily.hsum_smulFamily, ContinuousMultilinearMap.currySum_apply, exists_convex_convex_compl_subset, Submodule.mem_colon, NormSMulClass.toIsBoundedSMul, Ideal.Quotient.smulCommClass, Matrix.Module.diagonal_const_smul, MeasureTheory.ComplexMeasure.re_apply, FormalMultilinearSeries.ofScalars_comp_neg, SeminormedSpace.Core.norm_smul, Seminorm.comp_mono, HasDerivAt.pow', Unitization.norm_splitMul_snd_sq, SameRay.sameRay_pos_smul_right, HasStrictFDerivAt.fun_pow', CentroidHom.coe_smul, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, le_egauge_ball_one, ConcaveOn.left_lt_of_lt_right', Coalgebra.lTensor_counit_comp_comul, TestFunction.instLineDerivSMulTopENat, rank_eq_zero_iff, Finsupp.smul_sum, NonUnitalSubalgebra.instIsScalarTowerSubtypeMem, TemperedDistribution.lineDerivOp_fourierInv_eq, QuotientAddGroup.automorphize_smul_left, fourierCoeffOn_eq_integral, MeasureTheory.SimpleFunc.integral_const, Submodule.smul_span, CompactConvergenceCLM.continuousSMul, mfderiv_smul, HasFiniteFPowerSeriesOnBall.hasFDerivAt, hasStrictDerivAt_zero, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousLinearMap.isBigOTVS_fun_comp, Orientation.oangle_sign_smul_add_smul_right, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, Coalgebra.TensorProduct.rid_tmul, Pi.image_update_segment, HasDerivAtFilter.finCons, Finset.sum_smul_vsub_const_eq_weightedVSub, MeasureTheory.integral_deriv_smul_comp_Ioi, le_egauge_of_forall_ne_zero, IsBoundedSMul.of_norm_smul_le, Finset.sum_smul_vsub_const_eq_affineCombination_vsub, realPart_apply_coe, convex_of_nonneg_surjective_algebraMap, FormalMultilinearSeries.coeff_iterate_fslope, QuotSMulTop.map_apply_mk, HasFPowerSeriesAt.eq_zero, AbsolutelyContinuousOnInterval.fun_smul, Matrix.cramer_smul, Matrix.represents_iff', ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, deriv_const_smul', ContDiffMapSupportedIn.fderivCLM_apply, DualNumber.lift_apply_inl, intervalIntegral.integral_comp_mul_right, hasStrictDerivAt_exp_smul_const_of_mem_ball', IsSMulRegular.not_zero_iff, tangentConeAt_subset_zero, ContinuousLinearMap.extendTo𝕜'_apply, LocalizedModule.smul_eq_iff_of_mem, TestFunction.fderivCLM_apply, Matrix.conjTranspose_rat_smul, MeasureTheory.integral_concaveOn_of_integrand_ae, ContinuousLinearMap.isAdjointPair_inner, LinearMap.coe_smulRight, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, EuclideanGeometry.dist_smul_vadd_eq_dist, PolynomialModule.monomial_smul_apply, posSMulMono_iff_posSMulStrictMono, MeasureTheory.integral_singleton, intervalIntegral.integral_comp_div_sub, SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply, isSelfAdjoint_smul_of_mem_skewAdjoint, Submodule.setSemiring_smul_def, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, bddBelow_smul_iff_of_pos, complexOfReal_hasDerivAt, ConvexBody.hausdorffDist_coe, LieSubmodule.exists_smul_add_of_span_sup_eq_top, MeasureTheory.integral_comp_smul_deriv_Ioi, not_linearIndepOn_finset_iffₛ, Convex.starConvex_iff, openSegment_subset_Ioo, Convex.add_smul_sub_mem, IsLocalRing.ResidueField.residue_smul, HVertexOperator.coeff_comp, DifferentiableAt.smul_const, StrictConvexOn.add_const, convexHull_smul, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, Finset.sum_Ioc_by_parts, Complex.re_nnqsmul, Real.fourier_continuousMultilinearMap_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h, Unitization.splitMul_injective, LaurentPolynomial.smul_eq_C_mul, WeakFEPair.f_modif_aux1, MDifferentiableAt.smul_const_section, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, collinear_iff_exists_forall_eq_smul_vadd, MeasureTheory.Lp.smul_assoc, ContDiffMapSupportedIn.continuous_iff_comp, Asymptotics.IsTheta.const_smul_right, ContinuousLinearMap.smulRight_comp, QuaternionAlgebra.im_smul, Algebra.normalizedTrace_trans, DualNumber.lift_op_smul, ContMDiffOn.smul_section_of_tsupport, Seminorm.uniformContinuous', HasStrictDerivAt.div_const, HasStrictDerivAt.fun_mul, autEquivRootsOfUnity_apply_rootOfSplit, ContMDiffWithinAt.smul_section, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, TrivSqZeroExt.mul_right_eq_one, UniformConvergenceCLM.instUniformContinuousConstSMul, fderivWithin_continuousAlternatingMap_apply, ContinuousMultilinearMap.instIsCentralScalar, IsBaseChange.comp, smul_mem_asymptoticCone, absConvexHull_eq_convexHull_balancedHull, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, ProbabilityTheory.hasDerivAt_mgf, HasFPowerSeriesAt.eq_zero_of_eventually, SkewMonoidAlgebra.coeff_mul_single_aux, SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply, NormedSpace.norm_smul_normalize, Set.OrdConnected.starConvex, Derivation.apply_aeval_eq', smul_add_smul_le_smul_add_smul', HVertexOperator.coeff_apply_apply, div_le_egauge_closedBall, StrictConcaveOn.add, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, hasStrictFDerivAt_inv', MeasureTheory.Integrable.smul_prod, LinearMap.mem_span_iff_bound, Representation.asModuleEquiv_map_smul, homeomorphSphereProd_apply_fst_coe, ContinuousOn.cfcₙ_nnreal, WithSeminorms.partial_sups, Convex.lift, ConcaveOn.sub, SameRay.exists_pos_left, HasDerivAt.scomp_hasDerivWithinAt, Set.indicator_smul_left, MeasureTheory.Lp.toTemperedDistribution_apply, Finset.smul_expect, SchwartzMap.smulLeftCLM_sub, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, HasStrictDerivAt.add_const, wbtw_or_wbtw_smul_vadd_of_nonpos, Subring.smul_mem_pointwise_smul, Module.Basis.smul_apply, ConvexCone.salient_positive, Bornology.IsVonNBounded.smul_tendsto_zero, intervalIntegral.integral_hasStrictDerivAt_right, strongConvexOn_zero, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, fromModuleCatToModuleCatLinearEquiv_apply, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, Asymptotics.isBigO_const_smul_left, ConvexBody.hausdorffEDist_coe, Fintype.linearCombination_apply_single, LinearEquiv.symm_smul_apply, HVertexOperator.of_coeff_apply, smul_eq_zero_of_right, MDifferentiableOn.smul_section, MeasureTheory.SimpleFunc.integral_eq, integral_withDensity_eq_integral_toReal_smul₀, SchwartzMap.fourier_convolution_apply, Seminorm.smul_ball_zero, Complex.hasStrictFDerivAt_log_real, Fintype.linearCombination_apply, mem_openSegment_iff_div, MvPolynomial.totalDegree_smul_le, Real.iteratedDeriv_fourierIntegral, Asymptotics.isBigOTVS_map, Projectivization.generalLinearGroup_smul_def, iteratedFDeriv_two_apply, starConvex_compl_Iic, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, PointedCone.mem_toConvexCone, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, MeasureTheory.setIntegral_finset, real_inner_smul_left, ContDiffAt.smul, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, TemperedDistribution.smulLeftCLM_sum, Finsupp.pointwise_smul_support_finite, intervalIntegral.integral_hasStrictDerivAt_left, StrictConvex.sub, MeasureTheory.SimpleFunc.integral_smul, Asymptotics.IsBigOTVS.neg_left, bddAbove_smul_iff_of_pos, ModuleCat.Algebra.instSMulCommClassCarrier, antivaryOn_iff_forall_smul_nonpos, Module.End.apply_isScalarTower, gauge_smul, ConvexCone.isGenerating_bot_iff, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, MDifferentiable.clm_precomp, InnerProductSpace.laplacian_smul_nhds, HahnModule.coeff_smul_left, Polynomial.scaleRoots_zero, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, ConvexBody.hausdorffEdist_coe, ContDiffMapSupportedIn.fderivLM_apply_of_le, sameRay_smul_right_iff, Pi.segment_subset, MultilinearMap.mkPiRing_apply, IsLocalizedModule.eq_iff_exists, fderiv_norm_smul_pos, Fintype.expect_ite_eq', CFC.sqrt_map_pi, Convex.strictConvex_of_isOpen, FormalMultilinearSeries.le_radius_pi, Polynomial.smul_eval, AffineSpace.asymptoticNhds_eq_smul_vadd, HahnModule.coeff_smul_right, continuousMultilinearCurryLeftEquiv_symm_apply, MultilinearMap.map_smul_univ, WithLp.unitization_mul, TwoSidedIdeal.instSMulMemClassMulOpposite, UnitAddTorus.mFourierCoeff_eq_integral, FixedPoints.smul, IsUnit.integrable_smul_iff, hasDerivAt_exp_smul_const', CategoryTheory.ShortComplex.smul_τ₁, TrivSqZeroExt.exp_def_of_smul_comm, DoubleCentralizer.instStarModule, HasStrictDerivAt.finset_prod, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, Matrix.smul_single, smul_nonpos_of_nonneg_of_nonpos, ContinuousMultilinearMap.smulRightL_apply, MonoidAlgebra.isCentralScalar, NNReal.instIsStrictOrderedModule, StrictConcaveOn.concaveOn, Representation.smul_one_tprod_asModule, CStarAlgebra.star_right_conjugate_le_norm_smul, smul_nonneg_iff_pos_imp_nonneg, Convex.second_derivative_within_at_symmetric_of_mem_interior, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, NNReal.instContinuousMapZero.UniqueHom, iteratedDerivWithin_scomp_two, exists_pos_left_iff_sameRay_and_ne_zero, CochainComplex.HomComplex.Cochain.comp_smul, sameRay_neg_smul_left_iff, LieSubalgebra.instIsScalarTowerSubtypeMem, lp.norm_const_smul_le, TestFunction.instContinuousSMulReal, MeasureTheory.integral_comp_mul_left_Ioi, Asymptotics.IsLittleOTVS.congr_right, Polynomial.smulCommClass, ContinuousMap.norm_smul_const, iteratedFDeriv_succ_eq_comp_left, ContinuousMapZero.toNNReal_neg_smul, IsSMulRegular.zero_iff_subsingleton, Submodule.smul_mem_smul, antivary_iff_forall_smul_nonpos, Finsupp.sum_smul_index_addMonoidHom, ContinuousLinearMap.smul_compLpL, MeasureTheory.Measure.addHaarScalarFactor_smul_congr', VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, Submodule.instSMulCommClass_1, MeasureTheory.SimpleFunc.map_integral, LinearOrderedField.smul_Iic, infinite_range_add_smul_iff, Polynomial.qsmul_eq_C_mul, ContDiffMapSupportedIn.fderivLM_apply_of_gt, IsLocalizedModule.smul_mem_finsetIntegerMultiple_span, HasDerivAt.hasDerivAtFilter, Convex.sub, cfcₙ_const_mul, AffineMap.homothety_add, SkewPolynomial.instSMulCommClass, CategoryTheory.ShortComplex.smul_τ₂, AddMonoid.End.coe_smul, HasDerivAt.comp_hasDerivWithinAt_of_eq, ContinuousLinearMap.opNorm_mulLeftRight_le, ConvexOn.mul, Polynomial.natDegree_sum_eq_of_linearIndepOn, gauge_smul_left, Finset.sum_smul_vsub_eq_affineCombination_vsub, MeasureTheory.measure_smul_setAverage, ClosedSubmodule.orthogonal_closure, DualNumber.lift_comp_inlHom, ModuleFilterBasis.smul, AntivaryOn.sum_smul_le_sum_smul_comp_perm, AlgHom.linearMapMk_toAddHom, MeasureTheory.Integrable.comp_smul, LinearMap.toSeminormFamily_apply, MonoidAlgebra.isScalarTower, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, SMulPosReflectLT.of_pos, ContDiffMapSupportedIn.structureMapCLM_zero_injective, Seminorm.ball_finset_sup_eq_iInter, LinearMap.lflip_symm, HasFDerivWithinAt.curveIntegral_segment_source', ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, Module.Basis.opNNNorm_le, Polynomial.evalEval_smul, Derivation.leibniz_div_const, TrivSqZeroExt.inl_mul_eq_smul, ContMDiffWithinAt.clm_precomp, Polynomial.mirror_smul, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Convex.exists_mem_add_smul_eq, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, HasDerivAtFilter.comp, QuadraticAlgebra.C_smul, DualNumber.algHom_ext'_iff, MeasureTheory.Integrable.fourier_smul, LinearMap.coe_toContinuousLinearMap_symm, Matrix.mulVec_single, IsCompactOperator.smul_iff, hasStrictFDerivAt_list_prod', finsum_smul', right_sub_midpoint, balancedHull.balanced, Submodule.torsionBySet.mk_smul, continuousMultilinearCurryFin1_symm_apply, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, HasStrictDerivAt.fun_add, Convex.toCone_eq_sInf, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, FixedPoints.smulCommClass', balancedCore_zero_mem, intervalIntegral.integral_comp_mul_add, HasSum.smul_const, Set.smul_mem_centralizer, FormalMultilinearSeries.radius_pi_le, DualNumber.ideal_trichotomy, NonUnitalStarAlgHom.coe_mk, HasDerivAt.comp_of_eq, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, VectorFourier.integral_fourierIntegral_smul_eq_flip, AffineSubspace.sOppSide_smul_vsub_vadd_left, Complex.integral_boundary_rect_of_differentiableOn_real, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, smul_vsub_mem_vectorSpan_pair, Orientation.inner_smul_rotation_pi_div_two_smul_left, Submodule.mem_annihilator_span_singleton, Module.reflection_apply, CategoryTheory.Functor.linear_iff, hasDerivAt_iff_tendsto, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, ConvexCone.coe_hull_of_convex, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, Prod.instSMulPosReflectLT, HasStrictFDerivAt.smul_const, SchwartzMap.coe_apply, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, IsInvariantSubfield.smul_mem, sub_smul_dslope, ConvexOn.smul', PointedCone.dual_eq_comap_dual_eval, UniformOnFun.continuousSMul_submodule_of_image_bounded, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, SkewPolynomial.instIsScalarTower, le_floorDiv_iff_smul_le, LinearMap.trace_comp_comm, MeasureTheory.condExp_bot', WeakSpace.instIsScalarTower, Subbimodule.smul_mem, SchwartzMap.smulLeftCLM_ofReal, StarConvex.sub', Orientation.oangle_smul_right_of_pos, DualNumber.inr_eq_smul_eps, norm_iteratedFDeriv_smul_le, KaehlerDifferential.instIsScalarTowerTensorProduct_1, Function.Periodic.const_smul, realPart_smul, exists_eq_smul_of_parallel, ContDiffAt.differentiableAt_iteratedFDeriv, TrivSqZeroExt.inv_zero, SMulCommClass.nnrat, abs_real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivAt.hasFDerivAt_norm_smul_pos, MeasureTheory.Integrable.smul_const, Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn, Finsupp.faithfulSMul, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, Monotone.convex_le, ContinuousMultilinearMap.nnnorm_smulRight, HasDerivAt.finset_prod, Ring.uniformContinuousConstSMul_op, isClosedMap_smul₀, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, zero_mem_tangentConeAt_iff, ContDiffOn.smulRight, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, Convex.subset_toCone, LinearIsometryEquiv.map_smul, DualNumber.eps_mul_eps, MeasureTheory.lpMeasToLpTrim_smul, RootPairing.pairing_one_four_iff, MvPolynomial.rTensor_apply, disjoint_interior_extremePoints, MDifferentiableOn.smul_section_of_tsupport, MeasureTheory.integral_finset, TwoSidedIdeal.coe_smul, ConcaveOn.mul_convexOn, Mathlib.Meta.Positivity.smul_nonneg_of_pos_of_nonneg, ContinuousLinearMap.norm_adjoint_comp_self, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, Pi.evalStarAlgHom_apply, Orientation.inner_smul_rotation_pi_div_two_smul_right, hasDerivWithinAt_intCast, MeasureTheory.integral_bilinear_hasDerivAt_eq_sub, Convex.add_smul_sub_mem_interior, Asymptotics.IsBigO.const_smul_self, ContinuousAt.integral_sub_linear_isLittleO_ae, CircleIntegrable.out, PolynomialModule.monomial_smul_lsingle, ContMDiff.clm_precomp, birkhoffAverage_apply_sub_birkhoffAverage, IsLinearTopology.tendsto_smul_zero, locallyConvexSpace_iff_zero, TensorProduct.Algebra.moduleAux_apply, ContinuousLinearMap.continuousConstSMul_apply, HasFPowerSeriesWithinAt.compContinuousLinearMap, ContinuousLinearMap.isCentralScalar, ContinuousMultilinearMap.norm_smulRight, LSeries_hasDerivAt, ConcaveOn.lt_right_of_left_lt', Real.hasDerivAt_fourierIntegral, fderivWithin_fun_const_smul, Antivary.sum_smul_le_sum_comp_perm_smul, IntervalIntegrable.smul, SameRay.sameRay_pos_smul_left, Antitone.quasiconcaveOn, ContinuousMapZero.elemental_eq_top, ContinuousLinearEquiv.strictConvex_preimage, DividedPowerAlgebra.dp_smul, SkewMonoidAlgebra.coeff_smul, CategoryTheory.ShortComplex.rightHomologyMap'_smul, LinearMap.BilinMap.polarBilin_toQuadraticMap, Mathlib.Tactic.LinearCombination.smul_const_le, ContinuousLinearMap.hasDerivWithinAt, Submodule.Convex.semilinear_range, Antivary.sub_smul_sub_nonpos, AddMonoidAlgebra.ofCoeff_smul, Mathlib.Tactic.Module.NF.sub_eq_eval, LinearPMap.smul_apply, HasDerivWithinAt.comp_of_eq, FormalMultilinearSeries.derivSeries_apply_diag, CFC.negPart_smul, Seminorm.coe_iSup_eq, StrictConvex.preimage_add_left, SameRay.exists_nonneg_right, lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup, ClosedSubmodule.symplComp_sup, DistribMulActionSemiHomClass.toMulActionSemiHomClass, ContinuousMapZero.toNNReal_smul, fderiv_comp_smul, groupCohomology.isCocycle₂_of_mem_cocycles₂, LinearMap.map_smul_inv, Asymptotics.IsLittleOTVS.add, convex_vadd, ContinuousLinearMap.opNorm_lsmul, IsLocalizedModule.map_integerMultiple, Seminorm.zero_comp, LinearOrderedField.smul_Icc, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, Submodule.mem_set_smul, FormalMultilinearSeries.norm_changeOriginSeriesTerm, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Seminorm.continuous_of_continuousAt_zero, left_mem_openSegment_iff, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, LeftPreLieAlgebra.toIsScalarTower, Polynomial.eval₂_smul, finsum_smul, TrivSqZeroExt.instIsScalarTower, Subsemiring.smul_closure, VectorField.lieBracketWithin_const_smul_right, ContinuousMapZero.instIsScalarTower', HasGradientAt.hasDerivAt, Matrix.intCast_mulVec, ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, StrictConvexOn.add_convexOn, Algebra.FormallyUnramified.comp_sec, HasFTaylorSeriesUpTo.zero_eq', AffineSubspace.setOf_sOppSide_eq_image2, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, Filter.ZeroAtFilter.smul, Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, ConvexBody.coe_add, ContinuousAlternatingMap.map_smul_univ, map_rat_smul, Finsupp.linearCombination_comapDomain, fourierCoeffOn.const_smul, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, Function.Odd.smul_odd, ModuleCat.smulShortComplex_X₃_isModule, inv_smul_le_iff_of_neg, MeasureTheory.convolution_eq_swap, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Real.fourierInv_eq, Module.Basis.opNorm_le, UniformCauchySeqOnFilter.one_smulRight, isConformalMap_complex_linear, mulInvariantVectorField_smul, hasDerivAt_const_add_iff, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonpos, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', Convex.translate_preimage_left, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ValuationSubring.smul_mem_pointwise_smul, Projectivization.mk_eq_mk_iff', InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, MeasureTheory.Measure.euclideanHausdorffMeasure_smul₀, WithSeminorms.continuous_iff_continuous_comp, WeakDual.seminormFamily_apply, MeasureTheory.condExpIndSMul_ae_eq_smul, HasFTaylorSeriesUpTo.fderiv, concaveOn_iff_convex_hypograph, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, PosSMulReflectLE.toPosSMulReflectLT, Seminorm.ball_finset_sup, DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul, ConvexOn.add, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, mem_tangentConeAt_of_add_smul_mem, neg_strictConcaveOn_iff, StarAlgEquiv.ofLeftInverse'_symm_apply, IsRegular.smul_right_inj, IsModuleTopology.instPi, Submodule.span_smul_span, ContinuousLinearMap.norm_holderL_le, SmoothPartitionOfUnity.contMDiff_smul, Polynomial.isScalarTower_right, gaugeSeminorm_lt_one_of_isOpen, Asymptotics.IsLittleOTVS.fun_add, PolynormableSpace.withSeminorms, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, interval_average_eq, hasFDerivWithinAt_iff_isLittleOTVS, TensorProduct.AlgebraTensorModule.range_lTensor_idealMap, Finsupp.smul_single_one, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, segment_subset_closure_openSegment, gaugeSeminormFamily_ball, Mathlib.Tactic.Module.NF.add_eq_eval₂, ConvexOn.add_const, HahnModule.instIsTorsionFree, mdifferentiable_smul_section, isSMulRegular_iff_ker_lsmul_eq_bot, SubMulAction.neg_mem_iff, HasFDerivWithinAt.mul', PresheafOfModules.germ_ringCat_smul, rank_le_one_iff, QuadraticMap.polarSym2_map_smul, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, SchwartzMap.instFourierInvSMul, Seminorm.comp_smul_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, TemperedDistribution.derivCLM_apply_apply, gauge_lt_eq, groupCohomology.isCoboundary₂_of_mem_coboundaries₂, AffineBasis.linear_combination_coord_eq_self, TorusIntegrable.function_integrable, RootPairing.smul_coroot_eq_of_root_eq_smul, AffineSubspace.setOf_wSameSide_eq_image2, Submodule.coe_toSubMulAction, MeasureTheory.Supermartingale.smul_nonneg, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, hasDerivWithinAt_Ici_of_tendsto_deriv, spectrum.hasDerivAt_resolvent_const_left, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson, LinearMap.hasDerivAt, Submodule.smulMemClass, CategoryTheory.ShortComplex.rightHomologyMap_smul, MDifferentiableWithinAt.smul, Module.Basis.sum_equivFun, IsCovariantDerivativeOn.affine_combination, egauge_smul_right, MeasureTheory.weightedSMul_smul_measure, VectorField.lieBracket_smul_right, midpoint_vsub_midpoint_same_left, TensorProduct.piScalarRightHom_tmul, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, HasFDerivAtFilter.restrictScalars, Balanced.smul_eq, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, convex_halfSpace_lt, intervalIntegral.integral_hasFDerivAt, LinearMap.flip_surjective_iff₂, Subalgebra.pointwise_smul_toSubmodule, HasFiniteFPowerSeriesOnBall.fderiv_eq, ConvexOn.pow, Bialgebra.mul_compr₂_comul, smul_closedBall, PointedCone.to_isOrderedModule, ContMDiffOn.smul, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, IsLocalFrameOn.coeff_sum_eq, IsBaseChange.linearMapRight, Finset.zero_smul_finset_subset, Complex.hasDerivAt_log_sub_logTaylor, PointedCone.mem_hull_set, TestFunction.lineDerivCLM_apply_of_gt, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real, WithSeminorms.isVonNBounded_iff_seminorm_bounded, DualNumber.snd_mul, ContinuousLinearMap.smulRight_apply, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, intervalIntegral.fderiv_integral, right_vsub_midpoint, MeasureTheory.IntegrableOn.continuousOn_smul_of_subset, SkewMonoidAlgebra.coeff_single_mul_aux, intervalIntegral.integral_unitInterval_deriv_eq_sub, RootPairing.reflection_apply, ContinuousLinearMap.analyticAt_bilinear, cfcₙ_smul, integral_withDensity_eq_integral_smul₀, Complex.ofReal_nnqsmul, IsModuleFiltration.toGradedSMul, HasFDerivWithinAt.comp_hasDerivAt_of_eq, HasFPowerSeriesAt.hasStrictFDerivAt, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, HasDerivWithinAt.comp_hasDerivAt, AnalyticOnNhd.fun_const_smul, QuadraticMap.coeFn_smul, MeasureTheory.integral_prod_smul, Set.add_smul_subset, QuotSMulTop.map_id, convex_closed_sInter, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AddMonoidHom.smulLeft_apply, Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Submodule.map_dualCoannihilator_linearEquiv_flip, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, Module.Basis.constr_apply, fderivWithin_mul', AffineSubspace.sSameSide_smul_vsub_vadd_left, Derivation.leibniz_invOf, hasStrictDerivAt_exp_smul_const_of_mem_ball, Module.Baer.ExtensionOfMaxAdjoin.eqn, Finset.zero_smul_subset, smul_neg_iff_of_neg_left, ContMDiff.const_smul_section, AddMonoidHom.instIsScalarTower, HasDerivWithinAt.fun_sum, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, Ideal.map_pointwise_smul, lp.instSMulCommClassPreLp, Ideal.smul_mem_pointwise_smul_iff, Real.hasDerivAt_Gamma_nat, Orientation.oangle_smul_right_self_of_nonneg, HolderWith.smul, Convex.affinity, TopologicalGroup.IsSES.integrate_mono, LinearPMap.supSpanSingleton_apply_mk, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, NormedAddGroupHom.coe_smul, TensorProduct.toLinearMap_symm_rid, hasDerivAt_pi, smul_zero, strictConvex_uIoc, MeasureTheory.ContinuousMap.inner_toLp, convexOn_const, HasDerivAt.of_notMem_tsupport, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, RestrictScalars.isCentralScalar, MeasureTheory.integrable_fun_norm_addHaar, integral_bilinear_fderiv_right_eq_neg_left_of_integrable, CategoryTheory.Linear.toCatCenter_apply_app, skewAdjoint.I_smul_neg_I, Derivation.linearEquiv_coe_comp, hasFDerivAt_inv', ModuleCat.sMulCommClass_mk, PowerSeries.smul_eq_C_mul, Matrix.vecMul_cons, SeminormFamily.basisSets_mem, LinearMap.flip_flip, Polynomial.smul_X_eq_monomial, Submodule.powSMulQuotInclusion_injective, HasDerivAt.fun_mul, Finset.zero_mem_smul_iff, HasStrictDerivAt.const_sub, hasDerivWithinAt_finCons, TensorProduct.AlgebraTensorModule.coe_rTensor, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, PresheafOfModules.germ_smul, CFC.abs_smul, exists_continuousLinearEquiv_fderiv_symm_eq, HasDerivAt.smul, FormalMultilinearSeries.rightInv_coeff, Seminorm.absorbent_ball, Matrix.vecMul_intCast, Meromorphic.smul, Convex.mem_toCone', Unitization.inl_smul, TensorialAt.mkHom₂_apply_eq_extend, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Module.Basis.dvd_coord_smul, tangentConeAt_eq_univ, Orientation.oangle_sign_smul_add_smul_left, Matrix.Module.smul_def', tendsto_integral_comp_smul_smul_of_integrable', IsLinearMap.map_smul, LinearMap.map_smulₛₗ₂, SModEq.smul, Convex.affine_preimage, not_linearIndepOn_finset_iffₒₛ, isClosedMap_smul_left, Asymptotics.IsBigOTVS.mono, Asymptotics.IsLittleOTVS.proj, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, LinearMap.dualCoannihilator_range_eq_ker_flip, ContDiffOn.differentiableOn_iteratedFDerivWithin, MeasureTheory.average_union_mem_openSegment, PosSMulStrictMono.toSMulPosStrictMono, ConcaveOn.add_strictConcaveOn, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, ZMod.instIsScalarTower, Real.fourierInv_eq', RestrictScalars.addEquiv_symm_map_algebraMap_smul, Asymptotics.IsBigOTVS.trans, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div', ConvexBody.coe_nsmul, HasFiniteFPowerSeriesOnBall.sub, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, ConvexCone.mem_toPointedCone, ModuleCat.isScalarTower_of_algebra_moduleCat, mem_segment_translate, TensorProduct.lift_mk_compr₂, Convex.convexJoin, RootPairing.CoPolarizationIn_apply, HasStrictDerivAt.neg, MellinConvergent.cpow_smul, Finset.smul_zero_subset, MatrixEquivTensor.toFunAlgHom_apply, ContDiffOn.fun_smul, Real.fourierIntegral_deriv, Seminorm.closedBall_comp, ContinuousLinearMap.holderL_apply_apply, FormalMultilinearSeries.comp_rightInv_aux2, CFC.negPart_smul_of_nonneg, Matrix.mulVec_cons, TrivSqZeroExt.mul_inv_rev, Algebra.Extension.CotangentSpace.map_comp, Module.Basis.units_smul_span_eq_top, Finset.Nonempty.smul_zero, MeasureTheory.hasFiniteIntegral_smul_iff, MeasureTheory.integral_fun_snd, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, fwdDiff_smul_const, ZLattice.covolume.tendsto_card_div_pow'', Asymptotics.isLittleOTVS_insert, IsScalarTower.restrictScalars, AdicCompletion.ofPowSMul_val_apply, isClosedEmbedding_smul_left, MeasureTheory.integrable_fun_smul_iff, ModuleCat.Algebra.instIsScalarTowerCarrier, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, real_inner_smul_self_right, Submodule.smul_mem_iff'', hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, dist_smul_add_one_sub_smul_le, ConvexOn.comp_linearMap, MeromorphicAt.smul, Finsupp.smul_single, SeminormFamily.basisSets_iff, VectorFourier.hasFDerivAt_fourierChar_smul, Ideal.coe_smul_primesOver, MeasureTheory.LocallyIntegrableOn.continuousOn_smul, Finset.neg_smul, ConvexCone.IsReproducing.sub_eq_univ, LinearMap.IsAdjointPair.smul, Matrix.vecMul_smul, NonUnitalStarAlgHom.map_star', Real.fourierIntegral_real_eq, ContMDiffWithinAt.cle_arrowCongr, Matrix.scalar_commute_iff, fderiv_const_smul_of_field, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, groupHomology.single_isCycle₁_of_mem_fixedPoints, HasLineDerivAt.smul, OrthonormalBasis.sum_repr', Finset.expect_ite_eq, continuousMultilinearCurryRightEquiv_apply, Seminorm.convex_closedBall, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, HasDerivAt.comp_add_const, Bornology.isVonNBounded_of_smul_tendsto_zero, Module.Presentation.tautologicalRelations_relation, Module.End.HasEigenvector.pow_apply, ContDiffMapSupportedIn.structureMapLM_zero_apply, nnnorm_cfcₙ_nnreal_le, FixedPoints.mem_intermediateField_iff, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, MeasureTheory.average_union, Ideal.exists_map_eq_of_isGalois, OpenPartialHomeomorph.univUnitBall_symm_apply, Module.p_pow_smul_lift, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countable, convex_zero, Subring.smul_mem_pointwise_smul_iff, concaveOn_const, AnalyticOnNhd.const_smul, DifferentiableOn.hasDerivAt, Seminorm.continuous_of_forall, Bornology.sUnion_isVonNBounded_eq_univ, StarConvex.add_right, LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmodule, finrank_eq_one_iff_of_nonzero', SchwartzMap.integral_smul_deriv_right_eq_neg_left, QuadraticMap.polar_smul_right, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcₙ_nnreal, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left', Matrix.smul_eq_diagonal_mul, smul_inv'', intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Orientation.two_zsmul_oangle_smul_smul_self, ContMDiffAt.smul_section, fderiv_list_prod', SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, Module.Basis.unitsSMul_apply, intervalIntegral.integral_deriv_smul_comp'', SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, UnitAddTorus.span_mFourierLp_closure_eq_top, fderivWithin_comp_smul, Orientation.rotation_symm_apply, nnratCast_smul_eq, strictConvex_Ioi, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Orthonormal.inner_right_fintype, MultilinearMap.snoc_smul, NonUnitalStarSubalgebra.instSMulCommClass, LinearEquiv.smul_refl, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, HasFPowerSeriesAt.compContinuousLinearMap, MvPolynomial.scalarRTensor_apply_tmul_apply, Asymptotics.IsBigOTVS.refl, LieSubalgebra.instSMulMemClass, convex_closedConvexHull, WeakFEPair.f_modif_aux2, cfcₙ_comp_const_mul, Asymptotics.isTheta_const_smul_right, continuousOn_cfcₙ_nnreal_setProd, Prod.smul_zero_mk, fderivWithin_clm_apply, IsLocalizedModule.mk'_cancel, Algebra.trace_comp_trace, exists_continuousLinearEquiv_fderivWithin_symm_eq, MulActionHom.coe_add, ProbabilityTheory.HasIndepIncrements.smul, eHolderNorm_smul, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', mellin_cpow_smul, AlternatingMap.mkContinuousLinear_norm_le_max, FormalMultilinearSeries.rightInv_coeff_one, QuotSMulTop.mem_annihilator, Module.Basis.sum_repr, fderiv_continuousAlternatingMap_apply_const_apply, Differentiable.smul_const, WithLp.instProdIsBoundedSMul, RootPairing.coreflection_apply_coroot, ZMod.dft_const_smul, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, Ideal.Quotient.isScalarTower_right, LieDerivation.ofGrading_apply_apply, Submodule.toSubMulAction_one, DFinsupp.subtypeDomain_smul, absorbs_neg_neg, ContinuousLinearMap.isBigOTVS_id, PointedCone.instCanLiftConvexConeToConvexConePointed, MeasureTheory.condExpIndL1Fin_smul', ContinuousLinearMap.norm_holder_apply_apply_le, lipschitzWith_smul, ClosedSubmodule.symplComp_inf, intervalIntegral.integral_deriv_smul_comp, MeasureTheory.LocallyIntegrable.smul, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, UniformConvergenceCLM.isVonNBounded_iff, DualNumber.instIsPrincipalIdealRing, Algebra.Generators.CotangentSpace.map_ofComp_surjective, MvPolynomial.support_smul, Absorbent.vadd_absorbs, absorbent_ball_zero, Asymptotics.IsBigOTVS.fst, edist_smul_le, SMulCommClass.nnrat', DFinsupp.smul_sum, Matrix.mul_adjp_add_detp, RootPairing.Equiv.instSMulCommClassMulOppositeAut, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, List.smul_sum, constFormalMultilinearSeries_apply_succ, StrictConvex.vadd, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, StrictConvexOn.sub, FormalMultilinearSeries.continuousOn, ZMod.smul_mem, Mathlib.Tactic.Module.NF.smul_eq_eval, HasStrictFDerivAt.clm_comp, ZMod.dft_smul_const, ProbabilityTheory.Kernel.integral_withDensity, Orientation.oangle_sign_smul_sub_right, AlgebraicGeometry.structureSheafInType.smul_apply, Finsupp.isScalarTower, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, LieAlgebra.of_symm_smul, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, Submodule.basis_of_pid_aux, Submodule.span_singleton_eq_span_singleton, MonotoneOn.nnnorm_cfcₙ, Projectivization.smul_mk, Representation.IntertwiningMap.coe_smul, Function.Odd.const_smul, VectorFourier.fourierIntegral_fderiv, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, Convex.finsum_mem, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, KaehlerDifferential.map_liftBaseChange_smul, WeakFEPair.Λ_residue_zero, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', LieSubalgebra.instIsCentralScalarSubtypeMem, Seminorm.continuous_iff_continuous_comp, PartitionOfUnity.continuous_smul, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, gaugeRescale_smul, constFormalMultilinearSeries_zero, StarConvex.add, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, Asymptotics.IsBigOTVS.of_egauge_le_mul, Asymptotics.IsLittleOTVS.symm, threeGPFree_smul_set₀, Real.fourierIntegralInv_eq, Convex.thickening, HasStrictFDerivAt.continuousMultilinearMap_apply, Submodule.instSMulCommClassSubtypeMemTorsion', cfcₙ_const_mul_id, Asymptotics.IsBigO.isBigOTVS, Int.cast_smul_eq_zsmul, IsScalarTower.nnrat, CliffordAlgebra.contractLeftAux_apply_apply, isSMulRegular_iff_right_eq_zero_of_smul, taylor_within_apply, Asymptotics.isLittleOTVS_neg_left, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top, AddMonoidAlgebra.isCentralScalar, LinearIsometryEquiv.toContinuousLinearEquiv_smul, Function.Antiperiodic.const_inv_smul, ContinuousLinearMap.opNNNorm_mul_apply, le_comap_range_rTensor, LaurentPolynomial.instIsScalarTowerPolynomial, ContinuousMultilinearMap.curryFinFinset_apply, LieRinehartAlgebra.LieRinehartRing.lie_smul_eq_mul, ContDiffAt.smulRight, Unitization.inrRangeEquiv_symm_apply, HasSum.const_smul, Affine.Simplex.ninePointCircle_center, Convex.add_smul_mem_interior, TestFunction.injective_toBoundedContinuousFunctionCLM, Submodule.le_traceDual_iff_map_le_one, VertexOperator.coeff_eq_ncoeff, derivWithin_smul_const, FormalMultilinearSeries.changeOriginSeriesTerm_bound, HasDerivWithinAt.sum, MeasureTheory.integral_smul_measure, Fintype.not_linearIndependent_iffₒₛ, convex_Ioi, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, Antivary.sum_mul_lt_sum_mul_comp_perm_iff, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, Asymptotics.IsLittleOTVS.of_tendsto_div, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, smul_pos_of_neg_of_neg, ContinuousLinearMap.norm_precompL_le, HasFTaylorSeriesUpToOn.restrictScalars, Differentiable.smul, isConformalMap_iff_is_complex_or_conj_linear, ZMod.dft_def, starConvex_iff_div, ProbabilityTheory.integral_poissonMeasure', HasDerivAtFilter.neg, IsArithFrobAt.conj, ContinuousLinearMap.apply_apply, ConcaveOn.sub_strictConvexOn, AbsolutelyContinuousOnInterval.smul, egauge_zero_right, Module.Presentation.tautological_relation, Asymptotics.isThetaTVS_iff_isTheta, Finsupp.mapDomain_smul, Algebra.Extension.CotangentSpace.map_comp_apply, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, Real.fourierIntegral_continuousMultilinearMap_apply', AddMonoid.nat_smulCommClass, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, GroupWithZero.toNoZeroSMulDivisors, HVertexOperator.comp_apply, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, PiTensorProduct.mapLMultilinear_opNorm, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, hasDerivWithinAt_inter, fderivWithin_restrictScalars_comp, isSMulRegular_of_range_eq_ker, Seminorm.uniformContinuous_of_forall', PiLp.instIsBoundedSMul, hasFPowerSeriesAt_iff', StarConvex.neg, Matrix.diagonal_comp_single, CategoryTheory.ShiftedHom.smul_comp, StrictConvex.smul_mem_of_zero_mem, Real.fourier_eq', IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, hasDerivAt_exp_smul_const_of_mem_ball, Module.IsTorsionBy.mk_smul, Polynomial.eval_smul', LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, RingTheory.Sequence.isRegular_cons_iff', Real.fourierIntegral_iteratedFDeriv, hasMellin_const_smul, Algebra.Extension.CotangentSpace.map_comp_cotangentComplex, star_rat_smul, deriv_const_smul_field, NonUnitalCStarAlgebra.toSMulCommClass, mem_convexJoin, HasFDerivAt.mul', DirectSum.instIsScalarTower, WeakFEPair.Λ_residue_k, convex_iff_forall_pos, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, WithSeminorms.hasBasis_ball, ContDiff.fun_smul, Convex.openSegment_interior_closure_subset_interior, Monovary.sum_smul_sum_le_card_smul_sum, smul_add, exteriorPower.presentation.relations_relation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, Orientation.rotationAux_apply, Fourier.fourierIntegral_comp_add_right, derivWithin_clm_apply, Finset.sum_smul_sum, smul_finsum, Quaternion.fst_re_dualNumberEquiv_symm, TrivSqZeroExt.mem_kerIdeal_iff_inr, SchwartzMap.fourierMultiplierCLM_smul, MeasureTheory.MemLp.toLp_const_smul, QuadraticMap.basisRepr_apply, Set.Finite.isVonNBounded, slope_def_module, fwdDiff_iter_const_smul, openSegment_subset_union, smul_right_inj, IsBaseChange.endHom_comp, HasStrictDerivAt.congr_of_eventuallyEq, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_div, IsSMulRegular.of_isLocalizedModule, Quaternion.imI_snd_dualNumberEquiv, cfcₙ_smul_id, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, MeasureTheory.IntegrableOn.smul_continuousOn_of_subset, Algebra.forall_mem_adjoin_smul_eq_self_iff, AddMonoidAlgebra.smulCommClass_self, HasCompactSupport.convolution_integrand_bound_right, bddAbove_smul_iff_of_neg, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, MonovaryOn.smul_add_smul_le_smul_add_smul, integral_comp_pi_polarCoord_symm, CategoryTheory.ShiftedHom.mk₀_smul, Matrix.smul_mulVec, SkewPolynomial.smul_monomial, Submodule.mem_span_insert, DirectSum.decompose_smul, Asymptotics.isBigOTVS_comm, Submodule.toConvexCone_bot, Seminorm.finset_sup_le_sum, HasDerivAt.comp_semilinear, IsLocalizedModule.isInteger_smul, convexJoin_singleton_right, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, IsSMulRegular.of_ne_zero, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, HasDerivAt.clog_real, HasDerivAt.comp_sub_const, ModuleFilterBasis.smul_right', MeasureTheory.charFun_map_smul, convexHull_eq_self, convex_closedBall, intervalIntegral.integral_deriv_smul_deriv_comp', Algebra.Extension.Cotangent.ker_mk, ContMDiffAt.cle_arrowCongr, VertexOperator.coeff_eq_zero_of_lt_order, groupHomology.isBoundary₁_iff, IsLocalizedModule.mk'_cancel_left, Matrix.op_smul_eq_vecMul, convexOn_iff_convex_epigraph, HasFDerivAt.clm_comp, Polynomial.smul_comp, ContinuousLinearMap.adjoint_innerSL_apply, IsGaloisGroup.commutes, SameRay.pos_smul_right, StrictConvexOn.map_sum_eq_iff', Set.zero_smul_set_subset, sameRay_iff_norm_smul_eq, LSeries.hasDerivAt_term, TrivSqZeroExt.mul_inl_eq_op_smul, gaugeSeminorm_toFun, Ideal.pointwise_smul_toAddSubmonoid, Finset.expect_ite_eq', polyEquivTensor_symm_apply_tmul_eq_smul, IsBoundedBilinearMap.smul_right, Asymptotics.isLittleOTVS_pi, Module.finrank_eq_zero_iff, Bundle.Pretrivialization.continuousLinearMapCoordChange_apply, DifferentiableWithinAt.smul, IsOrderedRing.toIsOrderedModule, ContDiffMapSupportedIn.structureMapLM_apply, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, LieDerivation.instSMulBase, Matrix.kronecker_diagonal, derivWithin_const_smul', Convex.mem_smul_of_zero_mem, isBoundedLinearMap_prod_multilinear, Module.reflection_mul_reflection_mul_reflection_pow_apply_self, LinearEquiv.reduce_mkQ, Orthonormal.inner_sum, Module.End.algebraMap_isUnit_inv_apply_eq_iff, ContDiff.const_smul, HasCompactSupport.convolution_integrand_bound_right_of_subset, DFinsupp.mk_smul, hasStrictDerivAt_of_hasDerivAt_of_continuousAt, Finsupp.weight_apply, HasStrictDerivAt_ofNat, Function.Periodic.const_inv_smul₀, Real.fourier_smul_convolution_eq, Module.reflection_mul_reflection_mul_reflection_zpow_apply_self, PointedCone.smul_mem, lipschitzGroup.conjAct_smul_range_ι, balancedCore_eq_iInter, ConcaveOn.convex_gt, AntitoneOn.convex_lt, HasFiniteFPowerSeriesAt.comp, Submodule.exists_smith_normal_form_of_le, Subring.mem_inv_pointwise_smul_iff₀, second_derivative_symmetric_of_eventually_of_real, hasDerivWithinAt_iff_tendsto, lp.instIsScalarTowerSubtypePreLpMemAddSubgroup, Convex.convexIndependent_extremePoints, balancedHull_convexHull_subseteq_absConvexHull, ContDiffAt.hasStrictDerivAt', tsupport_smul_subset_left, StrictConvex.mem_smul_of_zero_mem, MeasureTheory.integral_countable', finrank_le_one_iff, TemperedDistribution.laplacianCLM_apply, isBigO_rpow_zero_log_smul, Seminorm.finset_sup_apply_le, ConvexBody.coe_smul', IsLocalization.mem_span_iff, Monovary.sub_smul_sub_nonneg, PresheafOfModules.Sheafify.SMulCandidate.h, HasDerivAt.star_conj, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, Wbtw.mem_segment, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, DFinsupp.support_smul, Bornology.IsVonNBounded.insert, groupCohomology.isCoboundary₁_of_mem_coboundaries₁, Subsemiring.mem_inv_pointwise_smul_iff, segment_inter_eq_endpoint_of_linearIndependent_sub, IsLocalizedModule.mk'_eq_iff, NonUnitalStarSubalgebra.instIsScalarTower', Seminorm.continuousAt_zero, ftaylorSeriesWithin_fun_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, Submodule.torsionBy.mk_smul, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, Submodule.mem_torsion'_iff, upperBounds_smul_of_pos, HasFDerivAt.smul, Real.deriv_fourier, CStarAlgebra.exists_sum_four_nonneg, RootPairing.EmbeddedG2.threeShortAddLongRoot_eq, CategoryTheory.Linear.smul_comp, Mathlib.Tactic.LinearCombination.smul_const_lt_weak, cfcₙ_complex_eq_real, Submodule.toSubMulAction_injective, CategoryTheory.Pretriangulated.Triangle.smul_hom₁, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, smul_inv₀', LinearIndependent.pair_add_smul_add_smul_iff, KaehlerDifferential.instIsScalarTowerTensorProduct_2, DoubleCentralizer.coe_snd, MemHolder.smul_iff, ContinuousLinearMap.opNorm_le_bound₂, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, MeasureTheory.integral_convolution, Seminorm.closedBall_finset_sup_eq_iInter, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, PosSMulMono.of_smul_nonneg, CategoryTheory.ShortComplex.leftHomologyMap_smul, IsLocalRing.spanFinrank_eq_finrank_quotient, Seminorm.comp_add_le, DivisibleHull.nnqsmul_mk, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, Polynomial.mkDerivation_apply, Ideal.mem_inv_pointwise_smul_iff, RightDerivMeasurableAux.le_of_mem_A, Representation.TensorProduct.lid_apply, toZeroHom_apply, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, TrivSqZeroExt.snd_expSeries_of_smul_comm, ContinuousMultilinearMap.norm_curryMid, Submodule.smul_mem, zero_mem_tangentCone, ContinuousAffineMap.instIsCentralScalar, CategoryTheory.ShortComplex.opcyclesMap'_smul, TopologicalAddGroup.IsSES.integrate_apply, aestronglyMeasurable_withDensity_iff, Affine.Simplex.points_vsub_eulerPoint, hasDerivAt_of_tendstoUniformlyOnFilter, Ideal.pointwise_smul_def, Submodule.starProjection_tendsto_closure_iSup, MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff, LieSubalgebra.smul_mem, InnerProductGeometry.angle_smul_left_of_pos, AddMonoidHom.mapMatrix_smul, SMulCommClass.rat, domain_mvt, MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, TrivSqZeroExt.inv_inr, MeasureTheory.Lp.toTemperedDistribution_smul_eq, SchwartzMap.laplacian_eq_fourierMultiplierCLM, Asymptotics.IsBigOTVS.pi, egauge_le_of_smul_mem_of_ne, HasFDerivAt.isLittleOTVS, HVertexOperator.coeff_of_coeff, Prod.instPosSMulStrictMono, IsAddUnit.smul_right, MeasureTheory.Lp_toLp_restrict_smul, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, const_smul_mfderiv, Filter.EventuallyEq.hasDerivAtFilter_iff, Seminorm.smul_le_smul, HasMFDerivAt.const_smul, HasDerivAtFilter.fun_sum, IsCovariantDerivativeOn.finite_affine_combination, Mathlib.Meta.Positivity.smul_nonneg_of_pos_of_pos, Matrix.blockDiagonal'_smul, NonUnitalCommCStarAlgebra.toIsScalarTower, MeasureTheory.condExp_bot_ae_eq, map_inv_intCast_smul, FormalMultilinearSeries.hasFPowerSeriesOnBall, KaehlerDifferential.mulActionBaseChange_smul_tmul, ModuleFilterBasis.continuousSMul, ContinuousLinearMap.coe_mulₗᵢ, deriv_fun_const_smul', LinearMap.BilinForm.apply_smul_sub_smul_sub_eq, TensorProduct.instIsCentralScalar, balancedCoreAux_empty, Function.Periodic.const_inv_smul, MDifferentiableOn.clm_bundle_apply₂, Seminorm.sSup_apply, Real.smul_iInf_of_nonneg, Module.isTorsionBy_quotient_element_smul, Seminorm.ball_bot, SkewMonoidAlgebra.coeff_single_mul, egauge_pi', Asymptotics.IsBigO.smul_isLittleO, left_sub_midpoint, HasFDerivWithinAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.innerSL_apply_comp, Module.Finite.of_isComplemented_codomain, Balanced.smul_mono, CategoryTheory.ShortComplex.leftHomologyMap'_smul, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, hasDerivAt_abs_pos, mem_convexAddSubmonoid, ite_zero_smul, midpoint_vsub_midpoint_same_right, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Algebra.lsmul_coe, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Affine.Simplex.centroid_vsub_eq, Orientation.oangle_smul_left_of_pos, openSegment.lift, HilbertBasis.hasSum_repr_symm, PosSMulStrictMono.toPosSMulReflectLT, ContinuousLinearMap.map_smul, CStarMatrix.norm_def, ContinuousAlternatingMap.smulRight_apply, AlternatingMap.instIsCentralScalar, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_deriv₂, IsMIntegralCurveAt.eventually_hasDerivAt, openSegment_subset_iff_segment_subset, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, RestrictScalars.smul_def, ContMDiffOn.clm_bundle_apply₂, inner_smul_left, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', TrivSqZeroExt.eq_smul_exp_of_invertible, QuadraticAlgebra.coe_smul, Submodule.restrictScalars_self, DomMulAct.mk_smul_addMonoidHom_apply, Set.inv_op_smul_set_distrib₀, balanced_iff_neg_mem, DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, Seminorm.continuous_of_le, mem_segment_sub_add, AddSubmonoid.mem_smul_pointwise_iff_exists, ContinuousLinearMap.adjoint_adjoint, StrictConvexOn.sub_concaveOn, HasCompactSupport.hasFDerivAt_convolution_left, TrivSqZeroExt.map_id, Submodule.flip_quotDualCoannihilatorToDual_injective, Algebra.Extension.H1Cotangent.map_comp, LinearMap.lflip_apply, HolderWith.smul_iff, SkewMonoidAlgebra.liftNC_smul, MeasureTheory.Integrable.smul_of_top_right, Unitization.isStarNormal_inr, Bundle.ContinuousRiemannianMetric.isVonNBounded, MonovaryOn.sub_smul_sub_nonneg, IsBaseChange.linearMapLeftRightHom_comp, HasDerivWithinAt.finCons, HasStrictDerivAt.clm_apply, IsLocalizedModule.fromLocalizedModule'_smul, TemperedDistribution.smulLeftCLM_apply_apply, HasDerivAt.congr_deriv, HasDerivAt.tendsto_slope_zero_right, Submodule.toSubMulAction_mono, WithSeminorms.hasBasis_zero_ball, Finset.sum_smul_vsub_eq_weightedVSub_sub, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, DFinsupp.instSMulPosStrictMono, ContinuousLinearMap.hasDerivAt_of_bilinear, Circle.norm_smul, ConvexOn.map_add_sum_le, locallyConvexSpace_iff_exists_convex_subset_zero, second_derivative_symmetric_of_eventually, uniformConvexOn_zero, Convex.mem_extremePoints_iff_convex_diff, HasFDerivAt.comp_hasDerivAt_of_eq, VectorField.lieBracketWithin_const_smul_left, mellin_comp_mul_left, DifferentiableOn.fun_smul, convexOn_iff_pairwise_pos, Convex.combo_affine_apply, convex_segment, vadd_left_mem_affineSpan_pair, Finsupp.linearCombination_onFinset, MeasureTheory.SignedMeasure.im_toComplexMeasure, HasDerivAtFilter.const_sub, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, left_vsub_midpoint, Module.Basis.groupSMul_apply, LinearMap.IsRefl.ker_flip, AnalyticAt.hasStrictDerivAt, BoxIntegral.unitPartition.tag_mem_smul_span, Asymptotics.IsThetaTVS.refl, Asymptotics.IsLittleO.const_smul_left, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, AffineMap.coe_homothety, ContMDiff.smul_section, Continuous.cfcₙ_nnreal', Filter.EventuallyEq.hasDerivWithinAt_iff, Seminorm.neg_mem_closedBall_zero, HahnModule.single_zero_smul_eq_smul, NonUnitalStarAlgHom.mk_coe, intervalIntegral.inv_smul_integral_comp_add_div, AlgebraicGeometry.Scheme.Modules.map_smul, SeminormFamily.basisSets_smul_left, InnerProductSpace.norm_rankOne, MeasureTheory.Measure.ae_smul_measure_eq, Ideal.stabilizerEquiv_apply_smul, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, Complex.hasDerivAt_Gamma_nat, Pi.noZeroSMulDivisors, RestrictScalars.addEquiv_map_smul, hasFDerivAt_integral_of_dominated_loc_of_lip, smul_eq_zero, tendsto_smul_comp_nat_floor_of_tendsto_nsmul, ArchimedeanClass.mk_smul, Submodule.pointwiseCentralScalar, Antivary.sum_comp_perm_smul_eq_sum_smul_iff, Submodule.smul_coe, PiTensorProduct.mapLMultilinear_toFun_apply, IsLocalizedModule.eq_zero_iff, VectorField.mlieBracket_smul_right, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, CStarMatrix.inner_toCLM_conjTranspose_right, FixedBy.subfield_mem_iff, HasDerivAtFilter.fun_const_smul, instSMulMemClassHomogeneousSubmodule, LinearIsometryEquiv.map_smulₛₗ, MeasureTheory.integral_sum_dirac, real_inner_I_smul_self, AnalyticWithinAt.smul, Seminorm.closedBall_smul_closedBall, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, balancedCore_subset_balancedCoreAux, Orthonormal.inner_right_sum, mellin_comp_mul_right, IsLocalizedModule.surj, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, PointedCone.dual_singleton, RingFilterBasis.SubmodulesBasis.smul, convexOn_norm, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, bernsteinApproximation.apply, LinearMap.sum_repr_mul_repr_mul, fderiv_eq_smul_deriv, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, StrictConvex.add_right, CStarMatrix.toCLM_apply_single_apply, Finset.zero_mem_smul_finset, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Submodule.instIsScalarTower, LinearMap.ker_toContinuousLinearMap, groupCohomology.isCocycle₁_of_mem_cocycles₁, PointedCone.salient_iff_inter_neg_eq_singleton, MeasureTheory.integral_sum_dirac_eq_tsum, Submodule.span_smul_of_span_eq_top, Polynomial.C_smul_derivation_apply, exists_pos_right_iff_sameRay_and_ne_zero, closedConvexHull_isClosed, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, ContinuousSMul.induced, PointedCone.toConvexCone_injective, HasDerivAt.mul_const, HasStrictDerivAt.fun_smul, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀, Matrix.smul_mat_empty, Monotone.convex_gt, Nonneg.instIsStrictOrderedModule, ContinuousLinearMap.algebraMap_apply, LinearEquiv.apply_faithfulSMul, Representation.leftRegularMapEquiv_symm_apply_toFun, Seminorm.uniformity_eq_of_hasBasis, AlgEquiv.apply_smulCommClass, MeasureTheory.average_eq, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, MDifferentiableWithinAt.smul_section, ContMDiffOn.smul_section, StarConvex.linear_preimage, TensorProduct.liftAux.smulₛₗ, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, WithSeminorms.finset_sups, LinearEquiv.conjAlgEquiv_ext_iff, MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOn, Submodule.restrictScalars_map, hasDerivWithinAt_sub_const_iff, Convex.linear_preimage, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, TensorProduct.restrictScalar_directSumRight, intervalIntegral.smul_integral_comp_add_mul, Complex.restrictScalars_toSpanSingleton', AffineSubspace.sOppSide_smul_vsub_vadd_right, HasFDerivWithinAt.list_prod', HasFDerivAt.continuousMultilinearMap_apply, Complex.hasSum_taylorSeries_on_eball, ofMul_uzpow, exists_smul_eq_of_finrank_eq_one, Quaternion.imK_snd_dualNumberEquiv, Module.Flat.isSMulRegular_of_nonZeroDivisors, fderiv_inv', MeasureTheory.Measure.integral_comp_inv_mul_right, ContinuousLinearMapWOT.ext_inner_iff, Besicovitch.SatelliteConfig.exists_normalized_aux3, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, NormedSpace.exp_eq_expSeries_sum, TwoSidedIdeal.coe_mop_smul, Convex.asymptoticCone, Monovary.sum_smul_comp_perm_eq_sum_smul_iff, PolynomialModule.eval_single, VectorField.mlieBracket_const_smul_right, norm_inner_div_norm_mul_norm_eq_one_iff, Valuation.HasExtension.instIsScalarTowerInteger, le_smul_ceilDiv, Submodule.disjoint_span_singleton'', HasStrictDerivAt.star, ProbabilityTheory.integral_tilted_mul_eq_cgf, FormalMultilinearSeries.comp_assoc, Set.indicator_smul_apply, egauge_smul_left, MeasureTheory.Measure.addHaar_smul, HasFPowerSeriesWithinAt.comp, IsLocalizedModule.mk'_sub_mk', ContinuousSMul.of_nhds_zero, MeasureTheory.hasSum_integral_sum_dirac, MeasureTheory.L1.SimpleFunc.setToL1S_smul, autEquivRootsOfUnity_smul, fderivWithin_pow', Algebra.Extension.Cotangent.val_smul'', Mathlib.Tactic.ComputeDegree.coeff_smul, balanced_zero, continuousMultilinearCurryFin1_apply, locallyConvexSpace_iff_exists_convex_subset, RootPairing.reflection_apply_root, LineDifferentiableAt.smul, StarConvex.mem_smul, IsLocalizedModule.injective_iff_isRegular, star_intCast_smul, RootPairing.reflectionPerm_eq_iff_smul_coroot, LinearMap.dualAnnihilator_ker_eq_range_flip, TensorialAt.smul, HilbertBasis.finite_spans_dense, Derivation.apply_aeval_eq, Module.notMem_support_iff', smul_dotProduct, AffineSubspace.smul_span, MeasureTheory.setIntegral_const, HasStrictDerivAt.fun_pow, norm_combo_lt_of_ne, Matrix.GeneralLinearGroup.fin_two_smul_prod, Ideal.mulQuot_injective, Subsemiring.center.smulCommClass_left, LinearIsometry.adjoint_comp_self, Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun, ConvexCone.mem_comap bridge: BoxIntegral.hasIntegralIndicatorConst
toZeroHom 📖	CompOp	1 math math: toZeroHom_apply

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
smul_zero 📖	mathematical	—	toSMul	—	—
toZeroHom_apply 📖	mathematical	—	DFunLike.coe ZeroHom ZeroHom.funLike toZeroHom toSMul	—	—

ZeroHom

Definitions

Name	Category	Theorems
smulZeroClass 📖	CompOp	—

(root)

Definitions

Name	Category	Theorems
DistribSMul 📖	CompData	—
MulActionWithZero 📖	CompData	—
SMulZeroClass 📖	CompData	—
instSMulZeroClass 📖	CompOp	17 math math: IsGaloisGroup.smul_mem_of_normal, NumberField.RingOfIntegers.instSMulDistribClass, Normal.minpoly_eq_iff_mem_orbit, ValuationSubring.mem_inv_pointwise_smul_iff, ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem, ValuationSubring.smul_mem_pointwise_smul_iff, IsGaloisGroup.mulEquivCongr_apply_smul, instSMulDistribClassAlgEquiv, smul_zpow₀', IsGaloisGroup.coe_quotient_smul, ValuationSubring.coe_pointwise_smul, smul_div₀', IsGaloisGroup.smul_eq_self, ValuationSubring.mem_smul_pointwise_iff_exists, IsLocalRing.ResidueField.residue_smul, ValuationSubring.smul_mem_pointwise_smul, smul_inv₀'

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
boole_smul 📖	mathematical	—	SMulZeroClass.toSMul SMulWithZero.toSMulZeroClass MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass MulActionWithZero.toSMulWithZero MulOne.toOne MulOneClass.toMulOne MulZeroOneClass.toMulOneClass	—	ite_smul one_smul zero_smul
ite_zero_smul 📖	mathematical	—	SMulZeroClass.toSMul SMulWithZero.toSMulZeroClass MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass MulActionWithZero.toSMulWithZero	—	ite_smul zero_smul
left_ne_zero_of_smul 📖	—	—	—	—	smul_eq_zero_of_left
right_ne_zero_of_smul 📖	—	—	—	—	smul_eq_zero_of_right
smul_add 📖	mathematical	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero DistribSMul.toSMulZeroClass AddZero.toAdd	—	DistribSMul.smul_add
smul_div₀' 📖	mathematical	—	SMulZeroClass.toSMul MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass GroupWithZero.toMonoidWithZero instSMulZeroClass DivInvMonoid.toDiv GroupWithZero.toDivInvMonoid	—	div_eq_mul_inv smul_mul' smul_inv₀'
smul_eq_zero_iff_eq 📖	mathematical	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul DivInvMonoid.toMonoid Group.toDivInvMonoid	—	inv_smul_smul smul_zero
smul_eq_zero_of_left 📖	mathematical	—	SMulZeroClass.toSMul SMulWithZero.toSMulZeroClass	—	zero_smul
smul_eq_zero_of_right 📖	mathematical	—	SMulZeroClass.toSMul	—	smul_zero
smul_inv₀ 📖	mathematical	—	InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid GroupWithZero.toDivisionMonoid SMulZeroClass.toSMul MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass GroupWithZero.toMonoidWithZero SMulWithZero.toSMulZeroClass MulActionWithZero.toSMulWithZero	—	eq_or_ne zero_smul inv_zero smul_zero inv_eq_of_mul_eq_one_left smul_mul_smul_comm IsScalarTower.left inv_mul_cancel₀ one_smul
smul_inv₀' 📖	mathematical	—	SMulZeroClass.toSMul MulZeroClass.toZero MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass GroupWithZero.toMonoidWithZero instSMulZeroClass InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid GroupWithZero.toDivisionMonoid	—	inv_zero smul_zero eq_inv_of_mul_eq_one_right smul_mul' mul_inv_cancel₀ MulDistribMulAction.smul_one
smul_ite_zero 📖	mathematical	—	SMulZeroClass.toSMul	—	smul_zero
smul_ne_zero_iff_ne 📖	—	—	—	—	smul_eq_zero_iff_eq
smul_neg 📖	mathematical	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid AddGroup.toSubtractionMonoid	—	eq_neg_of_add_eq_zero_left smul_add neg_add_cancel smul_zero
smul_sub 📖	mathematical	—	SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass SubNegMonoid.toSub	—	sub_eq_add_neg smul_add smul_neg
smul_zero 📖	mathematical	—	SMulZeroClass.toSMul	—	SMulZeroClass.smul_zero
zero_smul 📖	mathematical	—	SMulZeroClass.toSMul SMulWithZero.toSMulZeroClass	—	SMulWithZero.zero_smul

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