LinearMap

📁 Source: Mathlib/Topology/Algebra/Module/LinearMap.lean

Statistics

Metric	Count
Definitions apply, add, addCommGroup, addCommMonoid, algebra, applyModule, codRestrict, coeLM, coeLMₛₗ, comp, copy, distribMulAction, funLike, id, inhabited, instMul, instNatCast, instSMul, monoidWithZero, mulAction, neg, one, projKerOfRightInverse, rangeRestrict, restrictScalars, restrictScalarsₗ, semiring, smulRight, smulRightₗ, sub, toLinearMap, toLinearMapRingHom, toSpanSingleton, toSpanSingletonLE, uniqueOfLeft, uniqueOfRight, zero, «term_∘L_», ContinuousLinearMapClass, ContinuousSemilinearMapClass, LinearMap, ClosedComplemented, subtypeL, strongDualPairing, topDualPairing, «term_→L[_]_», «term_→SL[_]_»	47
Theorems commute_iff, commute_iff_of_isUnit, conj_eq_of_ker_mem_invtSubmodule, conj_eq_of_range_mem_invtSubmodule, ext, ext_iff, isClosed_range, ker_eq_range, ker_mem_invtSubmodule, ker_mem_invtSubmodule_iff, range_eq_ker, range_mem_invtSubmodule, range_mem_invtSubmodule_iff, toLinearMap, add_apply, add_comp, algebraMap_apply, applyFaithfulSMul, applySMulCommClass, applySMulCommClass', apply_val_ker, cancel_left, closedComplemented_ker_of_rightInverse, coeFn_injective, coeLM_apply, coeLMₛₗ_apply, coe_add, coe_add', coe_codRestrict, coe_codRestrict_apply, coe_coe, coe_comp, coe_comp', coe_copy, coe_eq_id, coe_id, coe_id', coe_inj, coe_injective, coe_mk, coe_mk', coe_mul, coe_neg, coe_neg', coe_pow, coe_projKerOfRightInverse_apply, coe_rangeRestrict, coe_restrictScalars, coe_restrictScalars', coe_restrictScalarsₗ, coe_smul, coe_smul', coe_smulRight, coe_smulRightₗ, coe_sub, coe_sub', coe_sum, coe_sum', coe_zero, coe_zero', comp_add, comp_apply, comp_assoc, comp_finset_sum, comp_id, comp_neg, comp_smul, comp_smulₛₗ, comp_sub, comp_toSpanSingleton, comp_zero, completeSpace_eqLocus, completeSpace_ker, cont, continuous, continuousConstSMul_apply, continuousSemilinearMapClass, copy_eq, default_def, eqOn_closure_span, exists_ne_zero, ext, ext_iff, ext_on, ext_ring, ext_ring_iff, finset_sum_comp, id_apply, id_comp, instNontrivialId, intCast_apply, isCentralScalar, isClosed_ker, isComplete_ker, isIdempotentElem_toLinearMap_iff, isOpenMap_of_ne_zero, isScalarTower, ker_codRestrict, leftInverse_of_comp, map_add, map_neg, map_smul, map_smul_of_tower, map_smulₛₗ, map_sub, map_zero, mul_apply, mul_def, natCast_apply, neg_apply, neg_comp, ofNat_apply, one_apply, one_def, one_smulRight_eq_toSpanSingleton, projKerOfRightInverse_apply_idem, projKerOfRightInverse_comp_inv, range_coeFn_eq, range_smulRight_apply, restrictScalars_add, restrictScalars_neg, restrictScalars_smul, restrictScalars_sub, restrictScalars_zero, rightInverse_of_comp, smulCommClass, smulRight_apply, smulRight_comp, smulRight_comp_smulRight, smulRight_id, smulRight_one_eq_iff, smulRight_one_eq_toSpanSingleton, smulRight_one_one, smulRight_one_pow, smul_apply, smul_comp, smul_def, sub_apply, sub_apply', sub_comp, sum_apply, toContinuousAddMonoidHom_add, toContinuousAddMonoidHom_comp, toContinuousAddMonoidHom_id, toContinuousAddMonoidHom_inj, toContinuousAddMonoidHom_injective, toContinuousAddMonoidHom_neg, toContinuousAddMonoidHom_restrictScalars, toContinuousAddMonoidHom_sub, toContinuousAddMonoidHom_zero, toLinearMapRingHom_apply, toLinearMap_toSpanSingleton, toSpanSingletonLE_apply, toSpanSingletonLE_symm_apply, toSpanSingleton_add, toSpanSingleton_apply, toSpanSingleton_apply_map_one, toSpanSingleton_apply_one, toSpanSingleton_comp, toSpanSingleton_comp_toSpanSingleton, toSpanSingleton_inj, toSpanSingleton_one, toSpanSingleton_pow, toSpanSingleton_smul, toSpanSingleton_smul', toSpanSingleton_zero, uniformContinuous, zero_apply, zero_comp, toContinuousMapClass, toSemilinearMapClass, topologicalClosure_map_submodule, dualPairing_apply, exists_isClosed_isCompl, isClosed, closedComplemented_bot, closedComplemented_top, coe_subtypeL, coe_subtypeL', ker_subtypeL, range_subtypeL, subtypeL_apply, topologicalClosure_map, topDualPairing_apply	184
Total	231

ContinuousLinearMap

Definitions

Name	Category	Theorems
add 📖	CompOp	169 math math: Matrix.l2_opNorm_toEuclideanCLM, mfderiv_prod_eq_add, coe_add, MeasureTheory.setToFun_add_left, HasDerivWithinAt.clm_comp, HasStrictFDerivAt.fun_mul', HasMFDerivAt.mul, HasFDerivWithinAt.continuousMultilinearMap_apply, Complex.restrictScalars_one_smulRight', HasMFDerivAt.add, fderivWithin_fun_smul, HasFDerivWithinAt.add, Matrix.cstar_nnnorm_def, HasDerivWithinAt.complexToReal_fderiv', toContinuousAddMonoidHom_add, HasFDerivWithinAt.clm_apply, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Unitization.splitMul_apply, HasFDerivAt.fun_mul, fderiv_clm_comp, HasStrictFDerivAt.mul', HasFDerivWithinAt.linear_multilinear_comp, fderiv_fun_smul, LinearIsometryEquiv.conjStarAlgEquiv_apply, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, Real.hasStrictFDerivAt_rpow_of_pos, HasFDerivWithinAt.continuousAlternatingMap_apply, HasStrictDerivAt.clm_comp, derivWithin_clm_comp, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, HasFDerivWithinAt.mul, hasFDerivWithinAt_of_bilinear, HasFDerivAt.fun_smul, fderiv_continuousAlternatingMapCompContinuousLinearMap, MeasureTheory.L1.SimpleFunc.setToL1S_add_left, comp_add, hasStrictFDerivAt_of_bilinear, Complex.hasStrictFDerivAt_cpow', HasFDerivAt.add, fderiv_continuousAlternatingMap_apply, HasFDerivAt.clm_apply, HasFDerivAt.continuousAlternatingMap_apply, fderiv_smul, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, mfderiv_prod_eq_add_comp, fderiv_of_bilinear, HasFDerivWithinAt.fun_smul, Matrix.toEuclideanCLM_toLp, Complex.hasStrictFDerivAt_cpow, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, HasFDerivWithinAt.cpow, fderivWithin_of_bilinear, DoubleCentralizer.add_fst, fderiv_mul, coprod_add, MeasureTheory.condExpInd_disjoint_union, TopModuleCat.hom_add, fderiv_fun_add, LinearIsometryEquiv.conjStarAlgEquiv_trans, HasStrictFDerivAt.rpow, fderivWithin_fun_mul', add_apply, fderiv_mul', LinearIsometryEquiv.conjStarAlgEquiv_refl, HasDerivAt.complexToReal_fderiv', restrictScalars_add, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, Complex.hasFDerivAt_cpow, DoubleCentralizer.add_snd, rayleighQuotient_add, fderivWithin_smul, mfderiv_add, HasDerivAt.clm_comp, HasStrictFDerivAt.add, Unitization.norm_eq_sup, Matrix.ofLp_toEuclideanCLM, coe_add', MeasureTheory.weightedSMul_add_measure, curveIntegral_fun_add, opNorm_add_le, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, flip_add, SchwartzMap.smulLeftCLM_add, HasMFDerivWithinAt.mul', HasFDerivAtFilter.fun_add, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, HasStrictFDerivAt.continuousAlternatingMap_apply, ContinuousAffineMap.add_contLinear, HasStrictDerivAt.complexToReal_fderiv', HasFDerivAt.mul, MeasureTheory.weightedSMul_union, fderiv_add, IsPositive.add, TemperedDistribution.smulLeftCLM_add, fderiv_fun_mul', HasFDerivAtFilter.add, HasFDerivWithinAt.clm_comp, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, HasMFDerivWithinAt.add, curveIntegralFun_add, deriv_clm_comp, fderivWithin_fun_add, MeasureTheory.weightedSMul_union', fderiv_continuousMultilinearMapCompContinuousLinearMap, LinearIsometryEquiv.symm_conjStarAlgEquiv, HasFDerivAt.fun_add, toSpanSingleton_add, ContinuousAffineMap.vadd_contLinear, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, fderivWithin_clm_comp, HasFDerivWithinAt.rpow, hasFDerivAt_uncurry_of_multilinear, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, Unitization.nnnorm_eq_sup, Matrix.toLin_finTwoProd_toContinuousLinearMap, add_compLp, HasMFDerivWithinAt.mul, HasStrictFDerivAt.clm_apply, HasStrictFDerivAt.fun_smul, HasStrictFDerivAt.cpow, fderiv_fun_mul, hasFDerivAt_of_bilinear, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, ContinuousAlternatingMap.curryLeft_add, HasFDerivWithinAt.smul, fderiv_clm_apply, HasFDerivWithinAt.fun_mul', hasStrictFDerivAt_list_prod, add_compLpL, HasFDerivWithinAt.fun_add, ContinuousAlternatingMap.alternatizeUncurryFin_add, fderivWithin_continuousAlternatingMap_apply, add_comp, HasStrictFDerivAt.mul, fderivWithin_add, HasStrictFDerivAt.fun_add, curveIntegral_add, Matrix.cstar_norm_def, HasStrictFDerivAt.fun_mul, HasFDerivWithinAt.mul', HasFDerivAt.cpow, Real.hasStrictFDerivAt_rpow_of_neg, PiTensorProduct.mapL_add, fderivWithin_mul', HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, comp_fst_add_comp_snd, HasMFDerivAt.mul', fderivWithin_clm_apply, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, HasStrictFDerivAt.clm_comp, HasFDerivAt.fun_mul', HasStrictFDerivAt.continuousMultilinearMap_apply, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, CurveIntegrable.add, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, HasFDerivAt.mul', HasFDerivAt.clm_comp, HasFDerivAt.rpow, fderivWithin_fun_mul, HasFDerivAt.smul, fderivWithin_mul, DoubleCentralizer.add_toProd, HasFDerivWithinAt.fun_mul, HasStrictFDerivAt.smul, Complex.restrictScalars_toSpanSingleton', HasFDerivAt.continuousMultilinearMap_apply
addCommGroup 📖	CompOp	158 math math: isPositive_iff_eq_sum_rankOne, Bundle.ContMDiffRiemannianMetric.contMDiff, InnerProductSpace.isPositive_rankOne_self, mulLeftRight_isBoundedBilinear, MDifferentiableOn.clm_postcomp, compSL_apply, InnerProductSpace.rankOne_one_left_eq_innerSL, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, MDifferentiableAt.cle_arrowCongr, ProbabilityTheory.covarianceBilinDual_apply', InnerProductSpace.isIdempotentElem_rankOne_self, ProbabilityTheory.covarianceBilinDual_apply, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, ContMDiffOn.clm_postcomp, ProbabilityTheory.uncenteredCovarianceBilin_apply, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, InnerProductSpace.inner_left_rankOne_apply, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, topologicalAddGroup, InnerProductSpace.rankOne_apply, precompL_apply, MDifferentiable.clm_postcomp, toSesqForm_apply_coe, finiteDimensional, hasFDerivWithinAt_of_bilinear, MDifferentiable.cle_arrowCongr, compactOperator_topologicalClosure, hasStrictFDerivAt_of_bilinear, Real.fourier_iteratedFDeriv, mulLeftRight_apply, MDifferentiableAt.clm_postcomp, hasFDerivAt_ringInverse, VectorFourier.fourierIntegral_iteratedFDeriv, InnerProductSpace.nnnorm_rankOne, InnerProductSpace.isSymmetricProjection_rankOne_self, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, NormedSpace.inclusionInDoubleDual_norm_eq, fderiv_of_bilinear, norm_smulRightL, InnerProductSpace.trace_rankOne, MDifferentiableWithinAt.cle_arrowCongr, MDifferentiableWithinAt.clm_precomp, compL_apply, isUniformAddGroup, fderiv_inverse, ContMDiffOn.clm_precomp, InnerProductSpace.adjoint_rankOne, InnerProductSpace.rankOne_eq_zero, InnerProductSpace.inner_right_rankOne_apply, fderivWithin_inv', fderivWithin_of_bilinear, NormedSpace.inclusionInDoubleDual_norm_le, InnerProductSpace.rankOne_eq_rankOne_iff_comm, precompR_apply, ProbabilityTheory.covarianceBilinDual_eq_covariance, ProbabilityTheory.covarianceBilinDual_zero, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, IsContMDiffRiemannianBundle.exists_contMDiff, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, adjointAux_apply, InnerProductSpace.rankOne_def, fderivWithin_fderivWithin_eq_of_mem_nhds, coe_flipMultilinearEquiv, TopModuleCat.hom_zsmul, fderivWithin_fderivWithin_eq_of_eventuallyEq, norm_precompR_le, IsContinuousRiemannianBundle.exists_continuous, contMDiffOn_continuousLinearMapCoordChange, InnerProductSpace.enorm_rankOne, Real.fourier_fderiv, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, iteratedFDerivWithin_two_apply', PiTensorProduct.dualSeminorms_bounded, opNorm_mulLeftRight_apply_le, ProbabilityTheory.covarianceBilinDual_self_eq_variance, PiTensorProduct.injectiveSeminorm_apply, ProbabilityTheory.covarianceBilinDual_self_nonneg, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, ContMDiffAt.clm_precomp, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, InnerProductSpace.rankOne_def', ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, MDifferentiableOn.cle_arrowCongr, MDifferentiableAt.clm_precomp, mdifferentiableOn_continuousLinearMapCoordChange, InnerProductSpace.isStarProjection_rankOne_self, hasStrictFDerivAt_ringInverse, InnerProductSpace.rankOne_comp_rankOne, InnerProductSpace.rankOne_comp, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, InnerProductSpace.isSymmetric_rankOne_self, fderiv_continuousLinearEquiv_comp, ProbabilityTheory.isPosSemidef_covarianceBilinDual, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, opNorm_mulLeftRight_apply_apply_le, TopModuleCat.hom_nsmul, norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, ProbabilityTheory.covarianceBilinDual_comm, ContMDiff.clm_postcomp, MDifferentiableWithinAt.clm_postcomp, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, MDifferentiableOn.clm_precomp, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, InnerProductSpace.toLinearMap_rankOne, iteratedFDerivWithin_two_apply, Pretrivialization.continuousOn_continuousLinearMapCoordChange, hasFDerivAt_of_bilinear, ProbabilityTheory.uncenteredCovarianceBilin_zero, norm_compSL_le, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, OrthonormalBasis.sum_rankOne_eq_id, norm_smulRightL_le, coe_symm_flipMultilinearEquiv, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, hasStrictFDerivAt_inv', iteratedFDeriv_two_apply, MDifferentiable.clm_precomp, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, opNorm_mulLeftRight_le, ContMDiffWithinAt.clm_precomp, ContMDiff.clm_precomp, ProbabilityTheory.covarianceBilinDual_of_not_memLp, NormedSpace.double_dual_bound, Real.zero_at_infty_vector_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, ProbabilityTheory.IsGaussian.charFunDual_eq', hasFDerivAt_inv', exists_continuousLinearEquiv_fderiv_symm_eq, ContMDiffWithinAt.cle_arrowCongr, apply_apply', ProbabilityTheory.covarianceBilinDual_of_not_memLp', exists_continuousLinearEquiv_fderivWithin_symm_eq, VectorFourier.fourierIntegral_fderiv, fderiv_continuousLinearEquiv_comp', smulRightL_apply_apply, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, norm_precompL_le, apply_apply, IsSymmSndFDerivWithinAt.eq, Real.fourierIntegral_iteratedFDeriv, InnerProductSpace.symm_toEuclideanLin_rankOne, ContMDiffAt.cle_arrowCongr, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, norm_smulRightL_apply, NormedSpace.dual_def, toSesqForm_apply_norm_le, PiTensorProduct.injectiveSeminorm_def, ContMDiff.cle_arrowCongr, InnerProductSpace.norm_rankOne, IsSymmSndFDerivAt.eq, fderiv_inv'
addCommMonoid 📖	CompOp	628 math math: LinearMap.det_toContinuousLinearMap, LinearMap.mkContinuous₂_norm_le', derivWithin_of_bilinear, Bundle.ContMDiffRiemannianMetric.isVonNBounded, LinearMap.mkContinuous₂_apply, isPositive_iff_eq_sum_rankOne, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, ProbabilityTheory.isGaussian_iff_gaussian_charFun, mulLeftRight_isBoundedBilinear, HasFDerivWithinAt.continuousMultilinearMap_apply, MDifferentiableOn.clm_postcomp, analyticWithinAt_bilinear, HasCompactSupport.convolution_integrand_bound_left, compSL_apply, continuous₂, SchwartzMap.integral_sesq_fourier_fourier, Real.hasFDerivAt_fourierChar_neg_bilinear_left, MeasureTheory.convolution_eq_right', hasStrictFDerivAt_list_prod_finRange', InnerProductSpace.rankOne_one_left_eq_innerSL, map_add_add, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, toLinearMap₁₂_injective, hasFDerivAt_multiset_prod, MDifferentiableAt.cle_arrowCongr, ProbabilityTheory.covarianceBilinDual_apply', ContinuousMultilinearMap.analyticAt_uncurry_of_linear, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, StrongDual.polarSubmodule_eq_setOf, ProbabilityTheory.covarianceBilinDual_apply, Real.fderiv_fourierChar_neg_bilinear_right_apply, fderivWithin_fun_pow', HasFDerivWithinAt.clm_apply, Continuous.convolution_integrand_fst, iteratedFDerivWithin_succ_eq_comp_right, innerSL_apply_apply, fderiv_multiset_prod, SchwartzMap.integral_bilin_fourierInv_eq, HasFDerivAtFilter.fun_sum, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContMDiffOn.clm_postcomp, toBilinForm_apply, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, LinearMap.adjoint_eq_toCLM_adjoint, ProbabilityTheory.uncenteredCovarianceBilin_apply, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, opNorm_lsmul_apply_le, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, fderiv_clm_comp, SchwartzMap.bilinLeftCLM_apply, fpowerSeriesBilinear_apply_zero, fderiv_continuousAlternatingMap_apply_const, coprodEquiv_apply, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, coe_restrictScalarsₗ, Differentiable.fderiv_norm_rpow, integrable_of_bilin_of_bdd_left, isometry_mul_flip, LinearMap.coe_toContinuousLinearMap', HasFDerivWithinAt.linear_multilinear_comp, CStarModule.innerSL_apply, hasDerivWithinAt_of_bilinear, Bundle.ContinuousLinearMap.vectorBundle, MeasureTheory.ConvolutionExistsAt.integrable, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, opNorm_mul_flip_apply, bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, InnerProductSpace.inner_left_rankOne_apply, HasFDerivAt.finset_prod, HasStrictFDerivAt.fun_sum, HasFDerivAt.norm_sq, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, fderiv_fun_pow', Real.integrable_prod_sub, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, sum_apply, HasFDerivAt.continuousMultilinear_apply_const, HasFDerivWithinAt.continuousAlternatingMap_apply, InnerProductSpace.rankOne_apply, fderiv_sum, NormedSpace.Dual.toWeakDual_continuous, mkOfIsCompactOperator_mem_compactOperator, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMultilinearMap.norm_smulRightL_le, precompL_apply, MDifferentiable.clm_postcomp, CStarMatrix.toCLM_injective, LinearMap.adjoint_toContinuousLinearMap, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, toSesqForm_apply_coe, HasFDerivAt.multilinear_comp, SchwartzMap.integral_bilin_fourierIntegral_eq, toLinearMap₁₂_apply, VectorFourier.fourierPowSMulRight_eq_comp, hasFDerivWithinAt_of_bilinear, HasFDerivWithinAt.multiset_prod, opNorm_mul, MDifferentiable.cle_arrowCongr, flipMultilinear_apply_apply, fderiv_continuousAlternatingMapCompContinuousLinearMap, compactOperator_topologicalClosure, SchwartzMap.integral_sesq_fourier_eq, adjointAux_norm, ProbabilityTheory.covarianceBilin_apply_basisFun_self, hasStrictFDerivAt_of_bilinear, HasStrictFDerivAt.list_prod', CStarMatrix.inner_toCLM_conjTranspose_left, Real.fourier_iteratedFDeriv, WeakDual.toStrongDual_inj, mulLeftRight_apply, Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, analyticOn_bilinear, hasStrictFDerivAt_multiset_prod, MDifferentiableAt.clm_postcomp, fderiv_continuousAlternatingMap_apply, coe_innerSL_apply, fderivWithin_finset_prod, RegularNormedAlgebra.isometry_mul', HasFDerivAt.sum, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, HasFDerivAt.clm_apply, StrongDual.toWeakDual_inj, hasFDerivAt_ringInverse, HasFDerivAt.continuousAlternatingMap_apply, WeakDual.coe_toStrongDual, VectorFourier.fourierIntegral_iteratedFDeriv, InnerProductSpace.nnnorm_rankOne, ContinuousLinearEquiv.arrowCongr_apply, toUniformConvergenceCLM_apply, flip_smul, InnerProductSpace.isSymmetricProjection_rankOne_self, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, MeasureTheory.ConvolutionExistsAt.integrable_swap, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, instLocallyConvexSpace, NormedSpace.inclusionInDoubleDual_norm_eq, SchwartzMap.smulLeftCLM_sum, fderiv_of_bilinear, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, LinearMap.toLinearMap_toContPerfPair, opNorm_mul_apply, norm_smulRightL, MeasureTheory.convolution_def, Pretrivialization.continuousLinearMapCoordChange_apply, InnerProductSpace.trace_rankOne, MDifferentiableWithinAt.cle_arrowCongr, MDifferentiableWithinAt.clm_precomp, ContMDiffVectorBundle.continuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, hasFDerivAt_norm_rpow, compL_apply, lsmul_flip_inj, summable_jacobiTheta₂_term_fderiv_iff, inCoordinates_apply_eq₂, flip_apply, ProbabilityTheory.covarianceBilin_zero, contDiffOn_stereoToFun, fderiv_inverse, ContMDiffOn.clm_precomp, bilinearRestrictScalars_apply_apply, InnerProductSpace.adjoint_rankOne, InnerProductSpace.rankOne_eq_zero, Real.fourierIntegral_convergent_iff', Bundle.ContMDiffRiemannianMetric.symm, InnerProductSpace.inner_right_rankOne_apply, SchwartzMap.pairing_apply, innerSL_inj, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, fderivWithin_inv', StrongDual.toLp_of_not_memLp, fderivWithin_of_bilinear, NormedSpace.inclusionInDoubleDual_norm_le, WeakDual.isCompact_closedBall, Convex.second_derivative_within_at_symmetric, BoxIntegral.BoxAdditiveMap.volume_apply, InnerProductSpace.rankOne_eq_rankOne_iff_comm, precompR_apply, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', ProbabilityTheory.IsGaussian.charFun_eq', fderiv_pow', ProbabilityTheory.covarianceBilinDual_eq_covariance, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, ProbabilityTheory.covarianceBilinDual_zero, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, hasStrictDerivAt_of_bilinear, ContinuousLinearEquiv.arrowCongr_symm, isBoundedBilinearMap, fderivWithin_continuousMultilinear_apply_const, continuousMultilinearCurryRightEquiv_symm_apply, coe_smulRightₗ, lsmul_apply, Bundle.ContMDiffRiemannianMetric.pos, bilinearComp_zero_right, IsContMDiffRiemannianBundle.exists_contMDiff, comp_finset_sum, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, Convex.taylor_approx_two_segment, adjointAux_apply, ProperCone.innerDual_singleton, hasFDerivAt_list_prod', InnerProductSpace.rankOne_def, coe_flipₗᵢ', stereoToFun_apply, adjointAux_inner_left, SchwartzMap.convolution_apply, hasSum_jacobiTheta₂_term_fderiv, ProbabilityTheory.covarianceBilin_comm, HasFDerivAtFilter.sum, SchwartzMap.integral_bilin_fourier_eq, ClosedSubmodule.orthogonal_eq_inter, coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, SchwartzMap.smulRightCLM_apply_apply, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, coe_restrict_scalarsL', StrongDual.polarSubmodule_eq_polar, PiTensorProduct.liftEquiv_symm_apply, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, norm_iteratedFDeriv_le_of_bilinear, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, aestronglyMeasurable_comp₂, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, StrongDual.dualPairing_apply, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, fderiv_fun_sum, LinearMap.range_toContinuousLinearMap, norm_precompR_le, hasFDerivWithinAt_pow', hasFPowerSeriesOnBall_bilinear, WeakDual.isSeqCompact_closedBall, PiTensorProduct.liftEquiv_apply, Convex.isLittleO_alternate_sum_square, deriv_of_bilinear, Orientation.areaForm'_apply, innerSLFlip_apply_apply, nnnorm_holder_apply_apply_le, bilinear_hasTemperateGrowth, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, postcomp_apply, LinearMap.coe_toContinuousLinearMap, prodMapL_apply, toSpanSingletonLE_apply, contMDiffOn_continuousLinearMapCoordChange, InnerProductSpace.enorm_rankOne, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, toLinearMap_innerSL_apply, hasFDerivAt_list_prod_finRange', ContinuousMultilinearMap.flipLinear_apply_apply, CStarMatrix.toCLM_apply_single, Real.fourier_fderiv, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, HasFDerivWithinAt.norm_sq, StrongDual.dualPairing_separatingLeft, ProperCone.dual_singleton, uncurryBilinear_apply, MeasureTheory.integral_posConvolution, VectorFourier.integral_fourierIntegral_swap, Bundle.RiemannianMetric.symm, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Unitization.norm_eq_sup, CStarMatrix.toCLM_apply_eq_sum, coeLM_apply, LinearMap.isPositive_toContinuousLinearMap_iff, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, HasFDerivAt.multiset_prod, memLp_of_bilin, toLinearMap_eq_iff_eq_toContinuousLinearMap, ProbabilityTheory.covarianceBilin_self_nonneg, HasStrictFDerivAt.continuousMultilinear_apply_const, opNorm_mulLeftRight_apply_le, analyticOnNhd_bilinear, ProbabilityTheory.covarianceBilinDual_self_eq_variance, hasStrictFDerivAt_norm_sq, fderiv_tsum, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, fderiv_pow_ring', map_sub₂, bilinearComp_apply, CStarMatrix.toCLM_apply, HasFDerivAt.continuousAlternatingMap_apply_const, ProbabilityTheory.covarianceBilinDual_self_nonneg, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, Matrix.l2_opNNNorm_def, adjointAux_adjointAux, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, ContMDiffAt.clm_precomp, ProbabilityTheory.covarianceBilin_real_self, HasMFDerivWithinAt.sum, coprodEquivL_apply_apply, flip_add, VectorFourier.fourierSMulRight_apply, ContinuousMultilinearMap.uncurryRight_apply, bilinearComp_zero, HasFDerivAt.fun_pow', ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, Real.fourier_bilin_convolution_eq, BoxIntegral.BoxAdditiveMap.toSMul_apply, CStarMatrix.mul_entry_mul_eq_inner_toCLM, le_opNorm₂, lpPairing_eq_integral, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, InnerProductSpace.rankOne_def', opNorm_mul_le, HasFDerivWithinAt.multilinear_comp, Pretrivialization.continuousLinearMap.isLinear, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, SchwartzMap.integral_sesq_fourierIntegral_eq, MeasureTheory.Integrable.convolution_integrand, ProbabilityTheory.covarianceBilin_apply_pi, SchwartzMap.integral_bilinear_laplacian_right_eq_left, isometry_mul, StrongDual.toLpₗ_apply, HasStrictFDerivAt.continuousAlternatingMap_apply, tendsto_iff_forall_eval_tendsto_topDualPairing, MeasureTheory.dist_convolution_le', fderivWithin_multiset_prod, MDifferentiableOn.cle_arrowCongr, InnerProductSpace.innerSL_norm, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, second_derivative_symmetric, ContinuousMultilinearMap.curryRight_apply, hasStrictFDerivAt_pow', MDifferentiableAt.clm_precomp, ProbabilityTheory.covarianceBilin_apply_basisFun, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, mdifferentiableOn_continuousLinearMapCoordChange, InnerProductSpace.isStarProjection_rankOne_self, LinearMap.mkContinuous₂_norm_le, hasFPowerSeriesAt_bilinear, fderiv_finset_prod, hasStrictFDerivAt_list_prod_attach', StrongDual.norm_toLpₗ_le, PiTensorProduct.mapLMultilinear_apply_apply, HasFDerivWithinAt.clm_comp, hasStrictFDerivAt_ringInverse, mul_apply', HasFDerivAt.fun_sum, InnerProductSpace.rankOne_comp_rankOne, BoxIntegral.hasIntegral_const, StrongDual.toLpₗ_of_not_memLp, hasStrictFDerivAt_finset_prod, InnerProductSpace.rankOne_comp, StrongDual.mem_polarSubmodule, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, HasFDerivWithinAt.continuousMultilinear_apply_const, InnerProductSpace.isSymmetric_rankOne_self, opNNNorm_mul, norm_iteratedFDerivWithin_le_of_bilinear, iteratedFDeriv_succ_eq_comp_right, coe_sum', fderiv_continuousLinearEquiv_comp, SchwartzMap.convolution_continuous_left, adjoint_toSpanSingleton, toBilinForm_injective, IsBoundedBilinearMap.toContinuousLinearMap_apply, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, innerSLFlip_apply, HasFDerivAt.list_prod', ProbabilityTheory.covarianceBilin_real, separatingDual_iff_injective, fderiv_continuousMultilinearMapCompContinuousLinearMap, hasFDerivAt_pow', opNorm_mulLeftRight_apply_apply_le, opNorm_lsmul_le, ProbabilityTheory.covarianceBilin_of_not_memLp, WeakDual.CharacterSpace.norm_le_norm_one, innerSL_apply_norm, Real.fourier_bilin_convolution_eq_integral, coe_restrictScalarsL, norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, fderivWithin_clm_comp, HasStrictFDerivAt.sum, fderiv_continuousMultilinear_apply_const, ProbabilityTheory.covarianceBilinDual_comm, opNNNorm_mul_flip_apply, HasMFDerivAt.prod, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, ContMDiff.clm_postcomp, fderivWithin_continuousAlternatingMap_apply_const, ContinuousLinearEquiv.arrowCongrSL_apply, MDifferentiableWithinAt.clm_postcomp, hasFDerivAt_uncurry_of_multilinear, opNorm_mul_apply_le, ProbabilityTheory.covarianceBilin_apply, BoxIntegral.integralSum_sub_partitions, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, MeasureTheory.convolutionExistsAt_iff_integrable_swap, hasFDerivAt_tsum, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, norm_bilinearRestrictScalars, coeLMₛₗ_apply, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, Unitization.nnnorm_eq_sup, bilinearComp_zero_left, Bundle.ContinuousRiemannianMetric.pos, Matrix.toLin_finTwoProd_toContinuousLinearMap, IsCoercive.continuousLinearEquivOfBilin_apply, MDifferentiableOn.clm_precomp, HasFDerivWithinAt.fun_sum, VectorFourier.integral_bilin_fourierIntegral_eq_flip, InnerProductSpace.toLinearMap_rankOne, adjointAux_inner_right, Bundle.RiemannianMetric.pos, HasStrictFDerivAt.clm_apply, continuousMultilinearCurryRightEquiv_symm_apply', ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, prodL_apply, LinearMap.isStarProjection_toContinuousLinearMap_iff, Pretrivialization.continuousOn_continuousLinearMapCoordChange, DoubleCentralizer.coe_fst, HasFDerivAt.pow', HasStrictFDerivAt.pow', hasFDerivAt_of_bilinear, ProbabilityTheory.uncenteredCovarianceBilin_zero, HasStrictFDerivAt.multiset_prod, LinearMap.toContPerfPair_apply, VectorFourier.fourierPowSMulRight_apply, SchwartzMap.convolution_flip, opNorm_flip, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, BoxIntegral.integral_const, FormalMultilinearSeries.derivSeries_eq_zero, fderivWithin_list_prod', fderiv_clm_apply, norm_compSL_le, innerSL_apply, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, InnerProductSpace.isIdempotentElem_rankOne_self_iff, fderivWithin_continuousLinearEquiv_comp, StrongDual.toLp_apply, map_smul₂, coe_flipₗᵢ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, fderivWithin_pow_ring', Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, HasFDerivWithinAt.fun_pow', HasStrictFDerivAt.continuousAlternatingMap_apply_const, toSpanSingletonLE_symm_apply, norm_smulRightL_le, coe_symm_flipMultilinearEquiv, VectorFourier.norm_fourierSMulRight_le, coe_sum, signedDist_apply, HasStrictFDerivAt.fun_pow', continuousMultilinearCurryRightEquiv_apply', flipₗᵢ'_symm, flip_zero, VectorFourier.norm_fourierPowSMulRight_le, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, VectorFourier.norm_fourierSMulRight, fderivWithin_continuousAlternatingMap_apply, toUniformConvergenceCLM_continuous, hasStrictFDerivAt_inv', HasMFDerivAt.sum, SchwartzMap.fourier_convolution_apply, TemperedDistribution.smulLeftCLM_sum, StrongDual.coe_toWeakDual, WeakDual.toStrongDual_apply, MDifferentiable.clm_precomp, Real.differentiable_fourierChar_neg_bilinear_left, ContinuousMultilinearMap.smulRightL_apply, Convex.second_derivative_within_at_symmetric_of_mem_interior, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, ContinuousLinearEquiv.arrowCongrSL_symm_apply, opNorm_mulLeftRight_le, topDualPairing_apply, ContMDiffWithinAt.clm_precomp, LinearMap.coe_toContinuousLinearMap_symm, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, Submodule.orthogonal_eq_inter, lsmul_flip_apply, compContinuousAlternatingMapCLM_apply_apply, prodₗ_apply, coprodEquiv_symm_apply, fderiv_norm_rpow, map_add₂, ContMDiff.clm_precomp, FormalMultilinearSeries.derivSeries_apply_diag, opNorm_lsmul, ProbabilityTheory.covarianceBilinDual_of_not_memLp, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, MeasureTheory.convolution_eq_swap, map_zero₂, Real.zero_at_infty_vector_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, precomp_apply, norm_holderL_le, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, analyticAt_bilinear, ProbabilityTheory.IsGaussian.charFunDual_eq', toPointwiseConvergenceCLM_apply, innerSL_apply_coe, bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, isPositive_sum, toUniformConvergenceCLM_symm_apply, hasFDerivAt_inv', MeasureTheory.AEStronglyMeasurable.convolution_integrand', map_neg₂, Matrix.l2_opNorm_def, Bundle.RiemannianMetric.continuousAt, holderL_apply_apply, MeasureTheory.AEStronglyMeasurable.convolution_integrand, norm_innerSL_le, VectorFourier.hasFDerivAt_fourierChar_smul, ContMDiffWithinAt.cle_arrowCongr, continuousMultilinearCurryRightEquiv_apply, integrable_of_bilin_of_bdd_right, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, apply_apply', ProbabilityTheory.covarianceBilinDual_of_not_memLp', fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, flipₗᵢ_symm, fderivWithin_clm_apply, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, NormedSpace.Dual.coe_toWeakDual, norm_holder_apply_apply_le, fderivWithin_sum, HasStrictFDerivAt.clm_comp, VectorFourier.fourierIntegral_fderiv, fderiv_continuousLinearEquiv_comp', smulRightL_apply_apply, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, toSpanSingletonCLE_apply_apply, HasStrictFDerivAt.continuousMultilinearMap_apply, opNNNorm_mul_apply, toSpanSingletonCLE_symm_apply, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, apply_apply, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, map_smulₛₗ₂, PiTensorProduct.mapLMultilinear_opNorm, hasFDerivAt_tsum_of_isPreconnected, instModuleFinite, fderivWithin_fun_sum, Real.fourierIntegral_iteratedFDeriv, NormedSpace.Dual.toWeakDual_inj, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, hasFDerivAt_list_prod_attach', MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, HasCompactSupport.convolution_integrand_bound_right, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, ContMDiffAt.cle_arrowCongr, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, HasFDerivAt.clm_comp, adjoint_innerSL_apply, fderiv_tsum_apply, coprodEquivL_symm_apply, HasCompactSupport.convolution_integrand_bound_right_of_subset, second_derivative_symmetric_of_eventually_of_real, toWOT_apply, norm_smulRightL_apply, DoubleCentralizer.coe_snd, fpowerSeriesBilinear_apply_one, MeasureTheory.integral_convolution, fderiv_norm_sq_apply, NormedSpace.dual_def, fderiv_norm_sq, coe_mulₗᵢ, HasFDerivWithinAt.continuousAlternatingMap_apply_const, innerSL_apply_comp, toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, coeFn_holder, CStarMatrix.norm_def, ContMDiff.cle_arrowCongr, coe_deriv₂, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, Bundle.ContinuousRiemannianMetric.isVonNBounded, HasFDerivWithinAt.sum, hasDerivAt_of_bilinear, second_derivative_symmetric_of_eventually, HasStrictFDerivAt.finset_prod, InnerProductSpace.norm_rankOne, PiTensorProduct.mapLMultilinear_toFun_apply, CStarMatrix.inner_toCLM_conjTranspose_right, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, CStarMatrix.toCLM_apply_single_apply, ContinuousMultilinearMap.uncurryRight_norm, flipAlternating_apply_apply, LinearMap.ker_toContinuousLinearMap, norm_iteratedFDerivWithin_le_of_bilinear_aux, HasFDerivWithinAt.list_prod', HasFDerivAt.continuousMultilinearMap_apply, finset_sum_comp, fderiv_inv', fderivWithin_pow', hasFDerivAt_finset_prod
algebra 📖	CompOp	26 math math: ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Unitization.splitMul_apply, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, Unitization.nnnorm_def, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, Unitization.splitMul_injective_of_clm_mul_injective, VonNeumannAlgebra.centralizer_centralizer', VonNeumannAlgebra.mem_carrier, Unitization.norm_eq_sup, DoubleCentralizer.algebraMap_snd, DoubleCentralizer.algebraMap_toProd, PositiveLinearMap.gnsStarAlgHom_apply, Algebra.IsCentral.instContinuousLinearMap, Unitization.norm_def, DoubleCentralizer.algebraMap_fst, Unitization.nnnorm_eq_sup, VonNeumannAlgebra.coe_toStarSubalgebra, Unitization.norm_splitMul_snd_sq, Unitization.splitMul_injective, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, algebraMap_apply
applyModule 📖	CompOp	5 math math: applySMulCommClass', applyFaithfulSMul, applySMulCommClass, smul_def, continuousConstSMul_apply
codRestrict 📖	CompOp	4 math math: ker_codRestrict, coe_codRestrict, coe_codRestrict_apply, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap
coeLM 📖	CompOp	2 math math: coeLM_apply, separatingDual_iff_injective
coeLMₛₗ 📖	CompOp	1 math math: coeLMₛₗ_apply
comp 📖	CompOp	366 math math: comp_neg, sum_comp_single, HasDerivWithinAt.clm_comp, SchwartzMap.lineDerivOpCLM_eq, ClosedSubmodule.comap_comap, LinearIsometryEquiv.comp_fderiv, HasFDerivWithinAt.continuousMultilinearMap_apply, compSL_apply, HasRightInverse.comp_continuousLinearEquivalence, snd_comp_inr, Continuous.clm_comp_const, Real.hasFDerivAt_fourierChar_neg_bilinear_left, coe_comp', HasRightInverse.continuousLinearEquivalence_comp, Submodule.IsOrtho.starProjection_comp_starProjection, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, SeparationQuotient.mkCLM_comp_outCLM, Differentiable.clm_comp, precompUniformConvergenceCLM_apply, LinearIsometryEquiv.comp_fderivWithin, HasFDerivWithinAt.clm_apply, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, innerSL_apply_comp_of_isSymmetric, mfderiv_comp, opNorm_comp_linearIsometryEquiv, ContinuousLinearEquiv.coe_comp_coe_symm, fderiv_clm_comp, coprod_comp_prodComm, IsConformalMap.is_complex_or_conj_linear, Differentiable.fderiv_norm_rpow, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, comp_inl_add_comp_inr, HasFDerivWithinAt.linear_multilinear_comp, Submodule.starProjection_comp_starProjection_eq_zero_iff, LinearIsometryEquiv.conjStarAlgEquiv_apply, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, HasFDerivWithinAt.comp_of_tendsto, bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, HasFDerivWithinAt.fst, isInvertible_comp_equiv, Pretrivialization.continuousLinearMap_symm_apply', HasFDerivAt.norm_sq, Continuous.clm_comp, IsInvertible.inverse_comp_of_right, ContinuousLinearEquiv.comp_hasFDerivAt_iff, IsInvertible.inverse_comp_of_left, HasFDerivWithinAt.continuousAlternatingMap_apply, HasStrictDerivAt.clm_comp, derivWithin_clm_comp, HasStrictFDerivAt.star, HasLeftInverse.comp_continuousLinearEquivalence, mfderiv_comp_of_eq, HasFDerivAt.star, isPositive_self_comp_adjoint, hasStrictFDerivAt_pi', HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, toSesqForm_apply_coe, inTangentCoordinates_eq_mfderiv_comp, HasFDerivAt.multilinear_comp, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, hasFDerivWithinAt_pi', fderivWithin_star, PointwiseConvergenceCLM.postcomp_apply, fst_comp_prod, fderiv_continuousAlternatingMapCompContinuousLinearMap, Submodule.coe_orthogonalDecomposition_symm, isEmbedding_postcomp, MeasureTheory.charFunDual_pi', smul_comp, comp_add, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, isBoundedBilinearMap_comp, ContinuousAffineMap.comp_contLinear, fderiv_continuousAlternatingMap_apply, HasFDerivAt.clm_apply, det_pi, HasFDerivAt.continuousAlternatingMap_apply, hasFDerivAt_finCons, hasFDerivWithinAt_finCons, HasFDerivWithinAt.star, HasStrictFDerivAt.fst, ContinuousOn.clm_comp, apply_norm_sq_eq_inner_adjoint_left, MeasureTheory.charFunDual_prod, HasFDerivAt.comp_hasFDerivWithinAt, mfderivWithin_comp_of_preimage_mem_nhdsWithin_of_eq, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', mfderiv_prod_eq_add_comp, mfderiv_comp_mfderivWithin, ContinuousLinearEquiv.comp_fderiv, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContinuousLinearEquiv.comp_right_fderiv, compL_apply, IsPositive.conj_adjoint, MeasureTheory.charFunDual_eq_prod_iff, exists_right_inverse_of_surjective, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, ContinuousWithinAt.clm_comp, coprod_comp_inl_inr, HasFDerivWithinAt.inner, InnerProductSpace.comp_rankOne, fderivWithin.snd, apply_norm_eq_sqrt_inner_adjoint_right, prod_ext_iff, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, inTangentCoordinates_eq, toContinuousAddMonoidHom_comp, comp_finset_sum, ContinuousLinearEquiv.coe_symm_comp_coe, inner_map_map_iff_adjoint_comp_self, ContinuousLinearEquiv.eq_toContinuousLinearMap_symm_comp, HasRightInverse.comp, isUniformInducing_postcomp, hasStrictFDerivAt_finCons, DifferentiableOn.clm_comp, fderiv_comp_fderivWithin, toSpanSingleton_comp, Submodule.coe_orthogonalDecomposition, zero_comp, ContinuousLinearEquiv.comp_coe, ContMDiffOn.clm_comp, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, hasStrictFDerivAt_piLp, isBoundedLinearMap_comp_right, ContDiffWithinAt.clm_comp, coe_comp, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, postcomp_apply, opNorm_comp_le, comp_coprod, HasFDerivWithinAt.norm_sq, hasFDerivWithinAt_piLp, MDifferentiableAt.clm_comp, HasDerivAt.clm_comp, SeparationQuotient.exists_out_continuousLinearMap, mfderivWithin_comp_of_preimage_mem_nhdsWithin, PiTensorProduct.mapL_comp, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, fderiv.snd, OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv, postcompCompactConvergenceCLM_apply, IsSelfAdjoint.conj_adjoint, ContinuousLinearEquiv.eq_comp_toContinuousLinearMap_symm, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', ProbabilityTheory.indepFun_iff_charFunDual_prod', ContinuousLinearEquiv.comp_right_fderivWithin, fderivWithin_comp_of_eq, sub_comp, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, IsInvertible.comp, isBoundedLinearMap_comp_left, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, ContDiffOn.clm_comp, LinearIsometry.norm_toContinuousLinearMap_comp, Submodule.sndL_comp_coe_orthogonalDecomposition, eventually_norm_symmL_trivializationAt_self_comp_lt, MeasureTheory.integral_continuousLinearMap_prod, fderivWithin_comp', Trivialization.continuousLinearMap_apply, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, HasFDerivAtFilter.comp, InnerProductSpace.rankOne_def', ContDiff.clm_comp, HasFDerivWithinAt.multilinear_comp, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, HasFDerivAtFilter.star, HasStrictFDerivAt.continuousAlternatingMap_apply, isInducing_postcomp, DifferentiableWithinAt.clm_comp, SeparationQuotient.postcomp_mkCLM_surjective, HasFDerivAtFilter.fst, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', fderivWithin_comp₃, HasFDerivWithinAt.snd, UniformConvergenceCLM.isUniformEmbedding_postcomp, IsContDiffImplicitAt.bijective, opENorm_comp_le, snd_comp_prod, fderivWithin_comp_of_eq', PointwiseConvergenceCLM.precomp_apply, HasFDerivWithinAt.comp, fderiv_comp, fst_comp_inl, HasFDerivAt.snd, hasFDerivWithinAt_euclidean, HasFDerivWithinAt.clm_comp, fst_comp_inr, Continuous.const_clm_comp, InnerProductSpace.rankOne_comp_rankOne, comp_smulₛₗ, isConformalMap_complex_linear_conj, InnerProductSpace.rankOne_comp, MDifferentiableWithinAt.clm_comp, hasFDerivAtFilter_finCons, PiTensorProduct.liftIsometry_comp_mapL, pi_comp, MDifferentiableOn.clm_comp, toSpanSingleton_comp_toSpanSingleton, precomp_compactConvergenceCLM_apply, HasFDerivAtFilter.snd, MeasureTheory.charFunDual_eq_pi_iff, ContinuousLinearEquiv.comp_hasFDerivAt_iff', DifferentiableAt.clm_comp, HasLeftInverse.comp, fderiv_continuousLinearEquiv_comp, deriv_clm_comp, proj_pi, smulRight_comp_smulRight, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderiv_continuousMultilinearMapCompContinuousLinearMap, HasFDerivAt.fst, inverse_comp_equiv, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, HasMFDerivAt.comp_hasMFDerivWithinAt, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, fderivWithin_clm_comp, inCoordinates_eq, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', IsIdempotentElem.range_mem_invtSubmodule_iff, IsInvertible.inverse_comp_self, opNNNorm_comp_le, comp_zero, ContinuousLinearEquiv.arrowCongrEquiv_symm_apply, ContDiffAt.clm_comp, ContinuousLinearEquiv.arrowCongrSL_apply, Pretrivialization.continuousLinearMap_apply, hasFDerivAt_uncurry_of_multilinear, IsSelfAdjoint.conj_starProjection, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, MeasureTheory.charFunDual_prod', HasFDerivWithinAt.comp_hasFDerivAt_of_eq, neg_comp, HasFDerivAt.linear_multilinear_comp, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, fderiv_comp', comp_assoc, VectorBundleCore.inCoordinates_eq, adjoint_comp, IsConformalMap.comp, IsInvertible.inverse_comp_apply_of_right, OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv, HasStrictFDerivAt.clm_apply, fderiv.fst, ContinuousLinearEquiv.arrowCongrEquiv_apply, IsPositive.orthogonalProjection_comp, MeasureTheory.charFunDual_eq_pi_iff', comp_lsmul_flip_apply, inverse_equiv_comp, LinearIsometryEquiv.comp_hasFDerivAt_iff', coprod_comp_inr, IsIdempotentElem.conj_eq_of_ker_mem_invtSubmodule, precompCompactConvergenceCLM_apply, IsPositive.adjoint_conj, PositiveLinearMap.leftMulMapPreGNS_mul_eq_comp, exist_extension_of_finiteDimensional_range, LinearIsometryEquiv.comp_hasFDerivAt_iff, inverse_eq_ringInverse, fderiv_clm_apply, fderiv_star, fderivWithin_continuousLinearEquiv_comp, Pretrivialization.continuousLinearMap_symm_apply, snd_comp_inl, FormalMultilinearSeries.compContinuousLinearMap_comp, Submodule.fstL_comp_coe_orthogonalDecomposition, IsSelfAdjoint.adjoint_conj, HasLeftInverse.continuousLinearEquivalence_comp, HasFDerivAt.comp_semilinear, id_comp, mul_def, fderivWithin.fst, MeasureTheory.charFunDual_map, pi_proj_comp, IsPositive.conj_starProjection, HasStrictFDerivAt.comp, ProbabilityTheory.variance_dual_prod, VectorBundleCore.coordChange_linear_comp, ContinuousAt.clm_comp, Real.hasFDerivAt_fourierChar_neg_bilinear_right, isUniformEmbedding_postcomp, smulRight_comp, fderivWithin_continuousAlternatingMap_apply, MeasureTheory.charFunDual_pi, add_comp, MDifferentiable.clm_comp, ContMDiff.clm_comp, coprod_comp_inl, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, ContinuousLinearEquiv.arrowCongrSL_symm_apply, ProperCone.comap_comap, comp_sub, ContinuousLinearEquiv.comp_fderivWithin, coprodEquiv_symm_apply, norm_map_iff_adjoint_comp_self, norm_adjoint_comp_self, ContMDiffWithinAt.clm_comp, IsInvertible.self_comp_inverse, TopModuleCat.hom_comp, precomp_apply, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, precomp_uniformConvergenceCLM_apply, HasMFDerivWithinAt.comp, postcompUniformConvergenceCLM_apply, Submodule.starProjection_comp_starProjection_of_le, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', apply_norm_sq_eq_inner_adjoint_right, bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, HasStrictFDerivAt.inner, HasMFDerivAt.comp, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, exists_continuousLinearEquiv_fderiv_symm_eq, isPositive_adjoint_comp_self, comp_fst_add_comp_snd, isInvertible_equiv_comp, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, HasFDerivAt.star_star, fderivWithin_clm_apply, postcomp_uniformConvergenceCLM_apply, exists_continuousLinearEquiv_fderivWithin_symm_eq, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, hasFDerivAtFilter_pi', fderivWithin_comp, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, HasStrictFDerivAt.clm_comp, HasFDerivWithinAt.comp_hasFDerivAt, fderiv_continuousLinearEquiv_comp', ContMDiffAt.clm_comp, HasStrictFDerivAt.continuousMultilinearMap_apply, IsInvertible.inverse_comp_apply_of_left, UniformConvergenceCLM.isUniformInducing_postcomp, mfderiv_comp_mfderivWithin_of_eq, isConformalMap_iff_is_complex_or_conj_linear, hasFDerivAt_pi', ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, MeasureTheory.charFunDual_eq_prod_iff', ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, HasFDerivAt.clm_comp, IsIdempotentElem.ker_mem_invtSubmodule_iff, coprodEquivL_symm_apply, LinearIsometryEquiv.comp_fderiv', postcomp_compactConvergenceCLM_apply, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap, comp_id, innerSL_apply_comp, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, comp_toSpanSingleton, mfderivWithin_comp, IsIdempotentElem.conj_eq_of_range_mem_invtSubmodule, HasFDerivAt.comp, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, lp.ext_continuousLinearMap_iff, comp_smul, comp_apply, ProbabilityTheory.indepFun_iff_charFunDual_prod, HasFDerivAt.continuousMultilinearMap_apply, finset_sum_comp, HasStrictFDerivAt.snd, hasStrictFDerivAt_euclidean, mfderivWithin_comp_of_eq
copy 📖	CompOp	2 math math: coe_copy, copy_eq
distribMulAction 📖	CompOp	10 math math: MeasureTheory.L1.setToL1_smul_left, CStarMatrix.norm_def', CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, flip_smul, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, NonUnitalAlgHom.coe_Lmul, MeasureTheory.setToFun_smul_left, PositiveLinearMap.gnsStarAlgHom_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply
funLike 📖	CompOp	1544 math math: IsLocalMaxOn.fderivWithin_nonpos, hasFDerivAt_iff_hasDerivAt, VectorBundleCore.toFiberBundleCore_coordChange, geometric_hahn_banach_open, ContinuousOn.clm_apply, ContinuousMap.toLp_inj, TopModuleCat.hom_cokerπ, sum_comp_single, Submodule.starProjection_apply_eq_isComplProjection, MeasureTheory.Lp.toTemperedDistributionCLM_apply, inner_map_map_of_mem_unitary, MeasureTheory.LpToLpRestrictCLM_coeFn, hasFPowerSeriesOnBall, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, rightInverse_of_comp, derivWithin_of_bilinear, HasStrictFDerivAt.isLittleOTVS, Bundle.ContMDiffRiemannianMetric.isVonNBounded, ContinuousLinearEquiv.equivOfInverse'_apply, TrivSqZeroExt.fstCLM_apply, MeasureTheory.condExpInd_of_measurable, cfcₙL_integral, LinearMap.mkContinuous₂_apply, le_of_opNorm_le_of_le, isPositive_iff_eq_sum_rankOne, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, isBigO_comp, ContinuousLinearEquiv.unitsEquiv_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFun, mulLeftRight_isBoundedBilinear, IsCompactOperator.clm_comp, LinearMap.mkContinuousOfExistsBound_apply, RCLike.map_apply, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, OrthonormalBasis.orthogonalProjection_eq_sum, analyticWithinAt_bilinear, MeasureTheory.aestronglyMeasurable_condExpInd, HasCompactSupport.convolution_integrand_bound_left, compSL_apply, continuous₂, RCLike.geometric_hahn_banach_point_open, fderivWithin_comp_derivWithin_of_eq, IsSelfAdjoint.quasispectrumRestricts, integral_compLp, DoubleCentralizer.star_snd, MeasureTheory.Measure.addHaar_image_continuousLinearMap, RCLike.ofRealCLM_apply, SchwartzMap.integral_sesq_fourier_fourier, Real.hasFDerivAt_fourierChar_neg_bilinear_left, coe_comp', geometric_hahn_banach_point_point, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, MeasureTheory.convolution_eq_right', RCLike.reCLM_apply, MeasureTheory.L1.setToL1_indicatorConstLp, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, RCLike.separate_convex_open_set, Convex.norm_image_sub_le_of_norm_fderivWithin_le', InnerProductSpace.rankOne_one_left_eq_innerSL, MDifferentiableAt.clm_bundle_apply, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, map_add_add, sSup_unit_ball_eq_norm, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, analyticWithinAt, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, curveIntegrable_segment, ProbabilityTheory.covarianceBilinDual_apply', sSup_unitClosedBall_eq_nnnorm, smul_apply, MeasureTheory.charFunDual_apply, IsPositive.inner_left_eq_inner_right, conformalAt_iff, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, MeasureTheory.norm_condExpL2_le, IsLocalMaxOn.hasFDerivWithinAt_nonpos, ProbabilityTheory.IsGaussian.integrable_dual, SchwartzMap.pairing_apply_apply, InnerProductSpace.isIdempotentElem_rankOne_self, MeasureTheory.weightedSMul_apply, comp_condExp_comm, Trivialization.continuousLinearMapAt_apply, geometric_hahn_banach_open_point, continuous_integral_comp_L1, isBigOWith_sub, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, ClosedSubmodule.mem_comap, TopModuleCat.hom_zero_apply, ContDiffAt.clm_apply, hasDerivAtFilter, comp_hasFiniteFPowerSeriesOnBall, Submodule.re_inner_starProjection_eq_normSq, WeakSpace.map_apply, VectorField.fderiv_apply_lieBracket, MeasureTheory.inner_condExpL2_left_eq_right, ContinuousMap.toLp_denseRange, toContinuousAddMonoidHom_add, AnalyticOnNhd.compContinuousLinearMap, integral_apply, Module.Basis.constrL_basis, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, comp_memLp, Real.fderiv_fourierChar_neg_bilinear_right_apply, Real.fourier_continuousLinearMap_apply, toWeakSpaceCLM_bijective, HasFDerivWithinAt.clm_apply, HasFPowerSeriesOnBall.unshift, Continuous.convolution_integrand_fst, ContDiffMapSupportedIn.structureMapCLM_apply, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, tangentMap_snd, iteratedDerivWithin_vcomp_two, SchwartzMap.lineDerivOp_fourier_eq, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, innerSL_apply_apply, IsInvertible.surjective, SchwartzMap.integral_bilin_fourierInv_eq, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, norm_iteratedFDerivWithin_clm_apply, innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, toBilinForm_apply, Measurable.apply_continuousLinearMap, Summable.mapL, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, map_zero, Submodule.orthogonalProjection_mem_subspace_eq_self, IsPositive.inner_nonneg_right, completeSpace_eqLocus, LinearMap.mkContinuous_apply, id_apply, HasFDerivWithinAt.hasLineDerivWithinAt, ProbabilityTheory.uncenteredCovarianceBilin_apply, TemperedDistribution.lineDerivOp_fourier_eq, FormalMultilinearSeries.derivSeries_coeff_one, Submodule.starProjection_add_starProjection_orthogonal, opNorm_lsmul_apply_le, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, fderiv_clm_comp, SchwartzMap.bilinLeftCLM_apply, intCast_apply, InnerProductSpace.toDual_symm_apply, fpowerSeriesBilinear_apply_zero, nhds_zero_eq_of_basis, MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, SmoothBumpCovering.exists_immersion_euclidean, cpolynomialAt, Submodule.starProjection_singleton, HasDerivAt.clm_apply, mfderiv_comp_apply_of_eq, comp_condExp_add_const_comm, Bundle.RiemannianMetric.isVonNBounded, measurable, ContDiffWithinAt.clm_apply, coe_smul', WithLp.sndL_apply, hasStrictFDerivAt_iff_isLittleOTVS, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, DifferentiableOn.clm_apply, ContMDiff.clm_apply, exposed_point_def, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, fderivWithin_fderivWithin, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, isBigOWith_id, integrable_of_bilin_of_bdd_left, comp_inl_add_comp_inr, fderiv_comp_deriv, norm_iteratedFDeriv_le_of_bilinear_of_le_one, ContDiffOn.clm_apply, opNNNorm_le_iff, isometry_mul_flip, BoundedContinuousFunction.evalCLM_apply, inner_gradientWithin_right, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, HasStrictFDerivAt.comp_hasStrictDerivAt, LinearMap.coe_toContinuousLinearMap', HasFDerivWithinAt.linear_multilinear_comp, isStarNormal_iff_norm_eq_adjoint, SchwartzMap.laplacianCLM_eq, CStarModule.innerSL_apply, hasDerivWithinAt_of_bilinear, isCompact_image_coe_of_bounded_of_closed_image, MeasureTheory.ConvolutionExistsAt.integrable, ProbabilityTheory.covarianceOperator_apply, algebraMapCLM_coe, ContDiffAt.laplacian_CLM_comp_left, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, coe_zero', opNorm_mul_flip_apply, ConvexOn.univ_sSup_of_countable_affine_eq, ebound, Submodule.coe_subtypeL', InnerProductSpace.inner_left_rankOne_apply, norm_iteratedFDeriv_clm_apply, TestFunction.toBoundedContinuousFunctionCLM_apply, HasLeftInverse.leftInverse_leftInverse, SchwartzMap.fderivCLM_apply, Submodule.norm_starProjection_apply_le, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, contMDiff, mdifferentiable, HasFDerivAt.norm_sq, VectorBundleCore.coordChange_self, LinearIsometry.map_starProjection', cfcL_apply, LinearIsometry.coe_toContinuousLinearMap, geometric_hahn_banach_compact_closed, eq_adjoint_iff, hasFDerivAt, Submodule.starProjection_tendsto_self, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, SchwartzMap.toLpCLM_apply, single_apply, toSpanSingleton_apply, LinearMap.IsSymmetric.directSum_decompose_apply, sum_apply, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, InnerProductSpace.rankOne_apply, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, HarmonicAt.analyticAt_complex_partial, MeasureTheory.SimpleFunc.setToSimpleFunc_const, toSpanSingleton_apply_one, MeasureTheory.weightedSMul_nonneg, cfcₙ_eq_cfcₙL_mkD, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, precompL_apply, Submodule.reflection_apply, curveIntegralFun_segment, HasDerivWithinAt.clm_apply, coe_mkOfIsCompactOperator, RCLike.geometric_hahn_banach_closed_point, InnerProductSpace.gramSchmidt_def, hasFPowerSeriesAt, SeparatingDual.exists_eq_one, fderiv_eq_deriv_mul, Submodule.starProjection_inner_eq_zero, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, toSesqForm_apply_coe, coe_algebraMapCLM, cpolynomialOn_uncurry_of_multilinear, BoxIntegral.hasIntegral_GP_pderiv, ContinuousMultilinearMap.linearDeriv_apply, SchwartzMap.integral_bilin_fourierIntegral_eq, ContinuousAffineMap.decomp, ContinuousAlternatingMap.toAlternatingMap_curryLeft, toLinearMap₁₂_apply, sSup_sphere_eq_nnnorm, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, hasFDerivWithinAt_of_bilinear, mfderivWithin_projIcc_one, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, PointwiseConvergenceCLM.postcomp_apply, ContMDiffAt.mfderiv_apply, map_sub, exists_lt_apply_of_lt_opNNNorm, hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, le_opNorm, flipMultilinear_apply_apply, equivProdOfSurjectiveOfIsCompl_apply, SchwartzMap.integral_sesq_fourier_eq, MeasureTheory.aestronglyMeasurable_condExpL2, cfcL_integrable, adjointAux_norm, MeasureTheory.L1.setToL1_smul_left, ContinuousWithinAt.clm_apply_of_inCoordinates, MDifferentiable.clm_bundle_apply₂, fderiv, MeasureTheory.L1.setToL1_zero_left, ContinuousAffineMap.coe_mk_contLinear_eq_linear, EuclideanGeometry.orthogonalProjection_apply_mem, ProbabilityTheory.covarianceBilin_apply_basisFun_self, MeasureTheory.condExpInd_nonneg, hasStrictFDerivAt_of_bilinear, fpowerSeries_apply_zero, VectorPrebundle.mk_contMDiffCoordChange, mul_apply, VectorFourier.fourierIntegral_continuousLinearMap_apply, IsInvertible.bijective, norm_iteratedFDerivWithin_comp_left, ContinuousLinearEquiv.coeFn_ofBijective, Pi.compRightL_apply, comp_memLp', map_smul_of_tower, SchwartzMap.fourier_lineDerivOp_eq, ContinuousLinearMapWOT.inducingFn_apply, norm_iteratedFDerivWithin_clm_apply_const, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, CStarMatrix.inner_toCLM_conjTranspose_left, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, ContinuousAlgHom.coe_toContinuousLinearMap, pi_apply, TemperedDistribution.fourierInv_lineDerivOp_eq, MeasureTheory.condExpL2_indicator_ae_eq_smul, exists_lt_apply_of_lt_opNorm, mfderivWithin_comp_projIcc_one, IsMIntegralCurveOn.hasDerivWithinAt, InnerProductSpace.toDualMap_apply_apply, PositiveLinearMap.leftMulMapPreGNS_apply, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', InnerProductSpace.HarmonicOnNhd.comp_CLM, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Manifold.pathELength_def, mulLeftRight_apply, Bundle.ContinuousRiemannianMetric.symm, analyticOn_bilinear, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', deriv, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, MDifferentiable.clm_bundle_apply, coe_innerSL_apply, isCompact_image_coe_closedBall, RegularNormedAlgebra.isometry_mul', isClosed_image_coe_closedBall, DoubleCentralizer.central, coe_neg', MeasureTheory.integral_condExpL2_eq, VectorBundleCore.localTriv_symm_fst, MDifferentiableWithinAt.clm_bundle_apply₂, hasFDerivAtFilter_iff_isLittleO, HasFDerivAt.clm_apply, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, hasDerivAt, hasFDerivAt_ringInverse, MeasureTheory.convolution_precompR_apply, NormedSpace.eq_zero_iff_forall_dual_eq_zero, ContinuousCohomology.I_obj_ρ_apply, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, OrthonormalBasis.orthogonalProjection_apply_eq_sum, ContinuousLinearEquiv.arrowCongr_apply, setIntegral_compLp, VectorField.fderivWithin_pullbackWithin, toUniformConvergenceCLM_apply, ContinuousAlternatingMap.curryLeft_apply_apply, contDiffPointwiseHolderAt, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, SeparationQuotient.outCLM_uniformContinuous, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, Module.Basis.constrL_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, MeasureTheory.ConvolutionExistsAt.integrable_swap, SchwartzMap.laplacianCLM_eq', VectorBundleCore.trivializationAt_coordChange_eq, apply_norm_sq_eq_inner_adjoint_left, measurable_apply₂, DifferentiableAt.fderiv_norm_self, ContDiff.continuous_fderiv_apply, fderivWithin_continuousAlternatingMap_apply_const_apply, const_apply_apply, ContinuousAt.clm_apply, EuclideanGeometry.orthogonalProjection_apply', MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, uniformContinuous, proj_apply, fderiv_of_bilinear, has_fderiv_at_filter_real_equiv, MeasureTheory.setIntegral_condExpInd, iteratedFDerivWithin_succ_apply_right, tendsto_integral_exp_smul_cocompact, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, SchwartzMap.toBoundedContinuousFunctionCLM_apply, extDeriv_apply_vectorField, curveIntegral_segment, TestFunction.postcompCLM_apply, Real.fourierIntegral_continuousLinearMap_apply, opNorm_mul_apply, norm_smulRightL, isBigO_id, MeasureTheory.L1.setToL1_eq_setToL1SCLM, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, MeasureTheory.norm_condExpL2_coe_le, Pretrivialization.continuousLinearMapCoordChange_apply, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, InnerProductSpace.trace_rankOne, isClosed_image_coe_of_bounded_of_weak_closed, NormedSpace.eq_iff_forall_dual_eq, summable, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, hasFDerivAt_norm_rpow, compL_apply, lsmul_flip_inj, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, analyticAt, Submodule.orthogonalProjection_mem_subspace_orthogonalComplement_eq_zero, inCoordinates_apply_eq₂, FourierTransform.fourierInvCLM_apply, MeasureTheory.L1.integral_def, flip_apply, tangentMapWithin_snd, Matrix.toEuclideanCLM_toLp, ContinuousCohomology.Iobj_ρ_apply, ContinuousAt.clm_apply_of_inCoordinates, HasFDerivAt.comp_hasDerivAt, contDiffOn_stereoToFun, fderiv_inverse, BoundedContinuousFunction.toLp_inj, ContinuousMultilinearMap.restrictScalarsLinear_apply, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, toSpanSingleton_apply_map_one, HilbertBasis.hasSum_orthogonalProjection, bilinearRestrictScalars_apply_apply, InnerProductSpace.adjoint_rankOne, compFormalMultilinearSeries_apply', InnerProductSpace.rankOne_eq_zero, lipschitz, Real.fourierIntegral_convergent_iff', fderivWithin_continuousMultilinear_apply_const_apply, ContinuousAffineMap.coe_linear_eq_coe_contLinear, BoundedContinuousFunction.toLp_injective, Submodule.norm_sq_eq_add_norm_sq_starProjection, Bundle.ContMDiffRiemannianMetric.symm, InnerProductSpace.inner_right_rankOne_apply, VectorField.fderiv_pullback, SchwartzMap.pairing_apply, fderivWithin_comp_derivWithin, ContinuousAlternatingMap.apply_apply, HasFPowerSeriesWithinOnBall.unshift, innerSL_inj, fderivWithin_inv', MeasureTheory.lintegral_nnnorm_condExpL2_le, StrongDual.toLp_of_not_memLp, fderivWithin_of_bilinear, MeasureTheory.L1.setToFun_eq_setToL1, SeparationQuotient.outCLM_isUniformEmbedding, ContinuousMultilinearMap.ofSubsingleton_symm_apply_apply, curveIntegral_segment_const, VectorBundleCore.localTriv_symm_apply, MeasureTheory.L1.integral_eq_setToL1, Convex.second_derivative_within_at_symmetric, BoxIntegral.BoxAdditiveMap.volume_apply, TangentBundle.trivializationAt_apply, ConvexOn.sSup_of_countable_affine_eq, TestFunction.coe_ofSupportedInCLM, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, toContinuousAddMonoidHom_zero, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, leftInverse_of_comp, norm_map_of_mem_unitary, derivWithin, analyticWithinAt_uncurry_of_multilinear, precompR_apply, HarmonicAt.differentiableAt_complex_partial, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, MeasureTheory.condExpL1CLM_indicatorConstLp, ratio_le_opNorm, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, HasStrictFDerivAt.isLittleO, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, TrivSqZeroExt.sndCLM_apply, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, MeasureTheory.L1.setToL1_add_left', Submodule.norm_orthogonalProjection_apply_le, ContinuousAffineMap.coe_mk_const_linear_eq_linear, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, ContMDiffAt.clm_apply_of_inCoordinates, InnerProductSpace.toDualMap_apply, geometric_hahn_banach_point_closed, adjoint_inner_left, hasStrictDerivAt_of_bilinear, Continuous.clm_bundle_apply, isBoundedBilinearMap, apply_norm_eq_sqrt_inner_adjoint_right, instContinuousEvalConst, VectorField.lieBracketWithin_smul_left, continuousMultilinearCurryRightEquiv_symm_apply, hasSum, lipschitz_apply, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, lsmul_apply, extDerivWithin_apply_vectorField_of_pairwise_commute, Bundle.ContMDiffRiemannianMetric.pos, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, toContinuousAddMonoidHom_comp, IsContMDiffRiemannianBundle.exists_contMDiff, iteratedFDerivWithin_comp_left, InnerProductSpace.rank_rankOne, HasRightInverse.rightInverse_rightInverse, ContMDiffAt.clm_bundle_apply, Convex.taylor_approx_two_segment, InnerProductSpace.toDual_apply_apply, adjointAux_apply, inner_map_map_iff_adjoint_comp_self, Trivialization.symmL_continuousLinearMapAt, ProbabilityTheory.IsGaussianProcess.comp_left, ContinuousMap.evalCLM_apply, ProperCone.innerDual_singleton, cpolyomialOn_uncurry_of_multilinear, ContDiffWithinAt.continuousLinearMap_comp, Continuous.clm_apply, InnerProductSpace.rankOne_def, IsLocalMinOn.hasFDerivWithinAt_nonneg, MDifferentiableAt.clm_bundle_apply₂, stereoToFun_apply, adjointAux_inner_left, coe_coe, SchwartzMap.convolution_apply, Submodule.sub_starProjection_mem_orthogonal, ConvexOn.real_univ_sSup_of_countable_affine_eq, add_apply, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, HasSum.mapL, ProbabilityTheory.covarianceBilin_comm, ContinuousMap.toLp_def, VectorField.lieBracket_fmul_left, SchwartzMap.integral_bilin_fourier_eq, HasFDerivWithinAt.lim, ClosedSubmodule.orthogonal_eq_inter, hasFDerivWithinAt_iff_hasDerivWithinAt, ProperCone.coe_comap, ContinuousOn.clm_bundle_apply₂, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, SchwartzMap.compCLMOfAntilipschitz_apply, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, hasStrictFDerivAt_iff_hasStrictDerivAt, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, MeasureTheory.L1.setToL1_smul_left', VectorField.mpullback_apply, LinearMap.IsSymmetric.toSelfAdjoint_apply, VectorField.lieBracket_eq, SchwartzMap.toTemperedDistributionCLM_apply_apply, coe_restrict_scalarsL', DoubleCentralizer.star_fst, RCLike.geometric_hahn_banach_point_point, TestFunction.coe_ofSupportedInLM, iteratedFDerivWithin_one_apply, hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, norm_iteratedFDeriv_le_of_bilinear, map_tsum, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, aestronglyMeasurable_comp₂, StrongDual.dualPairing_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, IsLocalMinOn.hasFDerivWithinAt_eq_zero, MeasureTheory.setToFun_indicator_const, ContinuousMapZero.toContinuousMapCLM_apply, IsStarNormal.adjoint_apply_eq_zero_iff, ProperCone.hyperplane_separation_point, LinearEquiv.extendOfIsometry_symm_apply, Submodule.norm_sq_eq_add_norm_sq_projection, tangentCoordChange_comp, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, hasFDerivAtFilter, Submodule.starProjection_apply, hasFPowerSeriesOnBall_bilinear, eventually_nhds_zero_mapsTo, LineDeriv.laplacianCLM_eq_sum, MeasureTheory.norm_condExpInd_apply_le, LineDeriv.iteratedLineDerivOpCLM_apply, Convex.isLittleO_alternate_sum_square, hasFDerivAt_iff_tendsto, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, deriv_of_bilinear, Orientation.areaForm'_apply, VectorBundleCore.coe_coordChange, hasFDerivAtFilter_iff_hasDerivAtFilter, innerSLFlip_apply_apply, Distribution.mapCLM_apply, bilinear_hasTemperateGrowth, IsContinuousRiemannianBundle.exists_continuous, ConvexOn.sSup_of_nat_affine_eq, postcomp_apply, Submodule.fst_orthogonalDecomposition_apply, prodMapL_apply, uncurryLeft_apply, Submodule.smul_starProjection_singleton, map_smulₛₗ, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, MDifferentiableWithinAt.clm_apply_of_inCoordinates, Complex.ofRealCLM_apply, InnerProductSpace.enorm_rankOne, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, cfcHom_real_eq_restrict, toLinearMap_innerSL_apply, SchwartzMap.pderivCLM_apply, continuousMultilinearMapOption_apply_eq_self, ContinuousMultilinearMap.apply_apply, ContinuousMultilinearMap.flipLinear_apply_apply, WeakDual.CharacterSpace.coe_toCLM, comp_hasFPowerSeriesWithinOnBall, CStarMatrix.toCLM_apply_single, lipschitzWith_of_opNorm_le, Submodule.inner_orthogonalProjection_eq_of_mem_right, IsSelfAdjoint.spectrumRestricts, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, HasFDerivWithinAt.norm_sq, lp.singleContinuousLinearMap_apply, ProbabilityTheory.HasGaussianLaw.map, ContinuousMultilinearMap.toContinuousLinearMap_apply, one_apply, uncurryBilinear_apply, mfderiv_eq, MeasureTheory.integral_posConvolution, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, Bundle.RiemannianMetric.symm, cpolynomialAt_uncurry_of_multilinear, MDifferentiableOn.clm_bundle_apply, Unitization.norm_eq_sup, ContinuousWithinAt.clm_apply, ProbabilityTheory.isGaussian_map, Matrix.ofLp_toEuclideanCLM, coe_add', CStarMatrix.toCLM_apply_eq_sum, le_of_opNorm_le, Submodule.eq_starProjection_of_mem_of_inner_eq_zero, ContDiff.comp_continuousLinearMap, MeasureTheory.Measure.map_conv_continuousLinearMap, exists_dual_vector, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst, ProbabilityTheory.IsGaussian.charFunDual_eq, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', le_opNorm_of_le, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, iteratedDeriv_vcomp_three, VectorField.fderivWithin_apply_lieBracket_of_isSymmSndFDerivWithinAt, RCLike.sqrt_map, iteratedFDerivWithin_two_apply', TopModuleCat.hom_id, NormedSpace.equicontinuous_TFAE, differentiable, Submodule.starProjection_map_apply, SpectrumRestricts.real_iff, TrivSqZeroExt.inrCLM_apply, continuousWithinAt_uncurry_of_multilinear, sSup_sphere_eq_norm, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, LinearPMap.adjointDomainMkCLM_apply, ContDiffPointwiseHolderAt.continuousLinearMap_comp, memLp_of_bilin, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, iInter_halfSpaces_eq, differentiableWithinAt, geometric_hahn_banach_closed_compact, HasFDerivWithinAt.mapsTo_tangent_cone, postcompCompactConvergenceCLM_apply, ProbabilityTheory.covarianceBilin_self_nonneg, compLeftContinuous_apply, ApproximatesLinearOn.lipschitz_sub, opNorm_mulLeftRight_apply_le, analyticOnNhd_bilinear, reApplyInnerSelf_apply, differentiableAt, sub_apply, ProbabilityTheory.covarianceBilinDual_self_eq_variance, LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, geometric_hahn_banach_open_open, iteratedFDerivWithin_succ_apply_left, hasStrictFDerivAt_norm_sq, Submodule.starProjection_unit_singleton, SchwartzMap.fourier_evalCLM_eq, LinearMap.compLeftInverse_apply_of_bdd, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, map_sub₂, QuasispectrumRestricts.real_iff, bilinearComp_apply, LinearEquiv.extendOfIsometry_apply, SchwartzMap.evalCLM_apply_apply, OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective, coe_pow, ContMDiffWithinAt.clm_bundle_apply₂, toContinuousLinearEquivOfDetNeZero_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, ContinuousMultilinearMap.compContinuousLinearMap_apply, CStarMatrix.toCLM_apply, SeparationQuotient.mk_outCLM, norm_map_tail_le, ContinuousAffineMap.map_vadd, compContinuousAlternatingMap_coe, compContinuousMultilinearMap_coe, exists_dual_vector'', FormalMultilinearSeries.compContinuousLinearMap_applyComposition, MeasureTheory.MemLp.continuousLinearMap_comp, ProbabilityTheory.IsGaussian.memLp_dual, ProbabilityTheory.covarianceBilinDual_self_nonneg, conformalFactorAt_inner_eq_mul_inner', ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, TemperedDistribution.fourier_lineDerivOp_eq, ContDiffPointwiseHolderAt.clm_apply, MeasureTheory.charFunDual_map_const_add, MeasureTheory.L1.SimpleFunc.setToL1S_const, MeasureTheory.charFunDual_map_add_const, LinearMap.extendOfNorm_eq, integrable_comp, adjointAux_adjointAux, TopModuleCat.freeMap_map, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, MeasureTheory.condExpL2_indicator_of_measurable, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, ContDiffOn.continuousOn_fderivWithin_apply, MeasureTheory.condExp_ae_eq_condExpL1CLM, LinearEquiv.extend_symm_apply, integral_comp_id_comm', coprodEquivL_apply_apply, BoundedContinuousFunction.coeFn_toLp, isBigOWith_comp, continuous_clm_apply, ContinuousLinearEquiv.skewProd_apply, hasTemperateGrowth, VectorFourier.fourierSMulRight_apply, measurable_fderiv_apply_const, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, toContinuousAddMonoidHom_injective, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, VectorBundleCore.localTriv_coordChange_eq, ContinuousMultilinearMap.uncurryRight_apply, MeasureTheory.L1.tendsto_setToL1, isVonNBounded_iff, MeasureTheory.condExpL1CLM_indicatorConst, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, ContDiffWithinAt.laplacianWithin_CLM_comp_left, Manifold.riemannianEDist_def, HasFDerivAtFilter.isLittleO, range_coeFn_eq, isVonNBounded_image2_apply, MeasureTheory.weightedSMul_smul, MeasureTheory.integral_continuousLinearMap_prod, NonlinearRightInverse.right_inv, curveIntegralFun_def', norm_extendTo𝕜'_bound, HasFDerivWithinAt.hasDerivWithinAt, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, HasGradientWithinAt.fderivWithin_apply, ContMDiffOn.clm_apply, cfc_eq_cfcL_mkD, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, contDiff_succ_iff_fderiv_apply, VectorBundleCore.localTriv_apply, LinearIsometryEquiv.coe_coe'', NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, IsPositive.re_inner_nonneg_left, extDerivWithin_apply_vectorField, measurable_comp, Real.fourier_bilin_convolution_eq, BoxIntegral.BoxAdditiveMap.toSMul_apply, ProbabilityTheory.IsGaussian.map_rotation_eq_self, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, hasFDerivWithinAt, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, CStarMatrix.mul_entry_mul_eq_inner_toCLM, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, le_opNorm₂, lpPairing_eq_integral, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, norm_iteratedFDeriv_comp_left, LinearMap.clmOfExistsBoundedImage_apply, ProbabilityTheory.covarianceOperator_inner, InnerProductSpace.rankOne_def', ContDiff.fderiv_apply, HasFDerivAt.comp_hasDerivWithinAt, fderiv_apply_one_eq_deriv, MDifferentiableAt.clm_apply_of_inCoordinates, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, HasFTaylorSeriesUpToOn.compContinuousLinearMap, SchwartzMap.integral_sesq_fourierIntegral_eq, Submodule.norm_orthogonalProjection_apply, IsPositive.inner_nonneg_left, map_add, apply_norm_eq_sqrt_inner_adjoint_left, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', fderiv_continuousMultilinear_apply_const_apply, MeasureTheory.Integrable.convolution_integrand, MeasureTheory.condExpL1CLM_lpMeas, ProbabilityTheory.HasGaussianLaw.map_fun, ContMDiffWithinAt.clm_bundle_apply, Submodule.eq_starProjection_of_mem_orthogonal, Differentiable.clm_apply, mdifferentiableWithinAt, ContMDiff.clm_bundle_apply, ProbabilityTheory.covarianceBilin_apply_pi, SchwartzMap.integral_bilinear_laplacian_right_eq_left, natCast_apply, HasFDerivAt.lim, isometry_mul, isOpen_injective, StrongDual.toLpₗ_apply, MeasureTheory.L1.setToL1_apply_coeToLp, continuous_uncurry_of_multilinear, LinearIsometry.map_starProjection, inr_apply, MeasureTheory.dist_convolution_le', ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ConvexOn.real_univ_sSup_affine_eq, toSpanSingleton_one, ContMDiff.clm_bundle_apply₂, MeasureTheory.L1.setToL1_congr_left', measurable_apply, hasFDerivAtFilter_iff_isLittleOTVS, second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Submodule.inner_orthogonalProjection_eq_of_mem_left, sSup_unit_ball_eq_nnnorm, extendTo𝕜_apply, MeasureTheory.SimpleFunc.setToSimpleFunc_indicator, HasFDerivAt.comp_hasDerivWithinAt_of_eq, ProbabilityTheory.IsGaussian.integral_dual, ContDiffWithinAt.laplacianWithin_CLM_comp_left_nhds, VectorPrebundle.exists_coordChange, continuous, MDifferentiableOn.clm_apply, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, ContDiffMapSupportedIn.postcompCLM_apply, IsContDiffImplicitAt.bijective, Submodule.eq_starProjection_of_mem_orthogonal', ProbabilityTheory.covarianceBilin_apply_basisFun, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective, algebraMapCLM_apply, iteratedFDeriv_one_apply, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFDerivAt.hasLineDerivAt, MeasureTheory.L1.setToL1_congr_left, iteratedFDeriv_succ_apply_right, hasMFDerivAt, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, fderiv_deriv, ContinuousLinearEquiv.coe_apply, HasFDerivAt.lim_real, PointwiseConvergenceCLM.precomp_apply, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, toContinuousAddMonoidHom_inj, analyticOnNhd_uncurry_of_multilinear, InnerProductSpace.isStarProjection_rankOne_self, SeparationQuotient.mk_comp_outCLM, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousLinearMapWOT.ext_dual_iff, contDiff_clm_apply_iff, hasStrictFDerivAt, oneTangentSpaceIcc_def, TrivSqZeroExt.inlCLM_apply, hasFPowerSeriesAt_bilinear, comp_analyticOn, coeFn_compLpL, sub_apply', coeFn_injective, contDiffOn_clm_apply, le_opNNNorm, fderiv_continuousAlternatingMap_apply_apply, PiTensorProduct.mapLMultilinear_apply_apply, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, HasFDerivWithinAt.clm_comp, uncurryMid_apply, isBoundedBilinearMap_apply, AEMeasurable.apply_continuousLinearMap, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', integral_comp_commSL, Complex.sqrt_map, hasStrictFDerivAt_ringInverse, mul_apply', ContDiffOn.continuousLinearMap_comp, Unitary.norm_map, Submodule.starProjection_apply_mem, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, InnerProductSpace.rankOne_comp_rankOne, geometric_hahn_banach_point_open, TestFunction.mkCLM_apply, BoxIntegral.hasIntegral_const, ContinuousMap.toLp_injective, DifferentiableAt.comp_semilinear₁, ContinuousAlternatingMap.compContinuousLinearMap_apply, PiTensorProduct.mapL_apply, ContinuousMapZero.evalCLM_apply, InnerProductSpace.rankOne_comp, StrongDual.mem_polarSubmodule, exists_dual_vector', MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, SchwartzMap.tsupport_smulLeftCLM_subset, InnerProductSpace.toMatrix_rankOne, separate_convex_open_set, cfcₙHom_real_eq_restrict, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, opNorm_le_iff, RCLike.geometric_hahn_banach_open, completion_apply_coe, InnerProductSpace.isSymmetric_rankOne_self, ContinuousMap.coe_toLp, continuousMultilinearCurryLeftEquiv_apply, ContinuousAlternatingMap.ofSubsingleton_apply_apply, precomp_compactConvergenceCLM_apply, unitary.norm_map, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContMDiffWithinAt.mfderivWithin_apply, SchwartzMap.tsupport_fderivCLM_subset, isBigOTVS_comp, NonlinearRightInverse.right_inv', integral_comp_L1_comm, intervalIntegral_apply, selfAdjointPartL_apply_coe, HasFDerivWithinAt.comp_hasDerivWithinAt, fderivWithin_continuousAlternatingMap_apply_apply, toContinuousAddMonoidHom_neg, norm_iteratedFDerivWithin_le_of_bilinear, MeasureTheory.aestronglyMeasurable_condExpL1CLM, ofNat_apply, ContDiffMapSupportedIn.seminorm_apply, VectorField.lieBracket_smul_left, rotation_apply, coe_sum', SchwartzMap.convolution_continuous_left, adjoint_toSpanSingleton, ext_iff, mfderivWithin_eq, IsExposed.eq_inter_halfSpace, continuousOn_uncurry_of_multilinear, MeasureTheory.integrable_condExpL2_indicator, tangentCoordChange_self, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, exists_mul_lt_apply_of_lt_opNNNorm, IsBoundedBilinearMap.toContinuousLinearMap_apply, AlgHom.coe_toContinuousLinearMap, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, smulRight_comp_smulRight, SchwartzMap.integralCLM_apply, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, HasStrictFDerivAt.hasStrictDerivAt, ConvexOn.real_univ_sSup_of_nat_affine_eq, neg_apply, innerSLFlip_apply, ContinuousAt.clm_bundle_apply₂, fderivWithin_derivWithin, toContinuousAddMonoidHom_restrictScalars, Trivialization.coe_continuousLinearEquivAt_eq, ProbabilityTheory.covarianceBilin_real, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', TopModuleCat.forget₂_TopCat_obj, measurable_coe, analyticOn, nndist_le_opNNNorm, SchwartzMap.lineDerivOp_fourierInv_eq, opNorm_mulLeftRight_apply_apply_le, VectorPrebundle.mk_coordChange, ConvexOn.real_sSup_of_countable_affine_eq, cfcL_integral, ContinuousMap.coeFn_toLp, MeasureTheory.L1.norm_setToL1_le_mul_norm', innerSL_apply_norm, Real.fourier_bilin_convolution_eq_integral, ContinuousWithinAt.clm_bundle_apply₂, fderivWithin, Submodule.subtypeL_apply, ContinuousAffineMap.coe_contLinear, curveIntegral_eq_intervalIntegral_deriv, fderivWithin_clm_comp, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, continuousSemilinearMapClass, ContDiffAt.continuousLinearMap_comp, HasCompactSupport.fderiv_apply, ProbabilityTheory.covarianceBilinDual_comm, ProbabilityTheory.isGaussian_iff_charFunDual_eq, opNNNorm_mul_flip_apply, compLeftContinuousBounded_apply, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, ContMDiffWithinAt.clm_apply_of_inCoordinates, ContinuousMultilinearMap.curryMid_apply, HasFDerivWithinAt.comp_hasDerivAt, SchwartzMap.compCLM_apply, ContinuousMap.toLp_comp_toContinuousMap, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure, hasFDerivAt_uncurry_of_multilinear, toContinuousAddMonoidHom_id, opNorm_mul_apply_le, smul_def, Submodule.lipschitzWith_starProjection, MDifferentiableWithinAt.clm_bundle_apply, isPositive_iff_complex, toContinuousAddMonoidHom_sub, ProbabilityTheory.covarianceBilin_apply, BoxIntegral.integralSum_sub_partitions, comp_cpolynomialOn, HasFDerivAt.linear_multilinear_comp, IsBoundedBilinearMap.deriv_apply, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, ContinuousLinearEquiv.skewProd_symm_apply, MeasureTheory.convolutionExistsAt_iff_integrable_swap, StronglyMeasurable.apply_continuousLinearMap, HasFDerivAt.hasDerivAt, isPositive_iff, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, ContinuousMultilinearMap.compContinuousLinearMapL_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, IsInvertible.inverse_apply_self, HasFDerivWithinAt.unique_on, VectorField.pullbackWithin_eq, nhds_zero_eq, PiTensorProduct.liftIsometry_apply_apply, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, Unitization.nnnorm_eq_sup, SchwartzMap.fourierTransformCLM_apply, Trivialization.symm_continuousLinearEquivAt_eq, skewAdjointPartL_apply_coe, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, MeasureTheory.Lp.constL_apply, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply, SchwartzMap.derivCLM_apply, RCLike.map_nonneg_iff, IsCoercive.continuousLinearEquivOfBilin_apply, LinearMap.toContinuousLinearMap₁_apply, TemperedDistribution.fourierTransformCLM_apply, mfderiv_comp_apply, TopModuleCat.cokerπ_surjective, Unitary.inner_map_map, VectorField.lieBracketWithin_smul_right, inner_gradientWithin_left, tsupport_fderiv_apply_subset, isConformalMap_iff, ContDiff.clm_apply, VectorFourier.integral_bilin_fourierIntegral_eq_flip, deriv_clm_apply, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, ContinuousMultilinearMap.ofSubsingleton_apply_apply, IsInvertible.inverse_comp_apply_of_right, InnerProductSpace.toLinearMap_rankOne, comp_hasFPowerSeriesOnBall, adjointAux_inner_right, isCompact_closure_image_coe_of_bounded, Bundle.RiemannianMetric.pos, HasStrictFDerivAt.clm_apply, ContMDiffAt.clm_bundle_apply₂, continuousMultilinearCurryRightEquiv_symm_apply', MeasureTheory.condExpInd_smul', isBigO_sub, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, LinearMap.norm_extendOfNorm_apply_le, MeasureTheory.L1.setToL1_add_left, Trivialization.continuousLinearMapAt_symmL, Manifold.pathELength_eq_lintegral_mfderiv_Icc, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, HasFDerivAtFilter.isLittleOTVS, ContinuousAffineMap.contLinear_map_vsub, LinearPMap.adjointDomainMkCLMExtend_apply, dimH_orthogonalProjection_le, iteratedFDerivWithin_two_apply, DoubleCentralizer.coe_fst, coprod_apply, coe_fst', Submodule.re_inner_starProjection_nonneg, OrthogonalFamily.sum_projection_of_mem_iSup, Real.fourierIntegral_continuousLinearMap_apply', TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, hasFDerivAt_of_bilinear, comp_lsmul_flip_apply, contDiffOn_succ_iff_fderiv_apply, OpenPartialHomeomorph.MDifferentiable.mfderiv_injective, LinearMap.toContPerfPair_apply, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, Submodule.starProjection_orthogonal_apply_eq_zero, VectorFourier.fourierPowSMulRight_apply, extDeriv_apply_vectorField_of_pairwise_commute, ContMDiffWithinAt.clm_apply, coe_restrictScalars', isBoundedLinearMap, opNorm_le_iff_lipschitz, SchwartzMap.convolution_flip, MeasureTheory.L1.norm_setToL1_le_mul_norm, IsLocalMaxOn.fderivWithin_eq_zero, MeasureTheory.charFunDual_dirac, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, precompCompactConvergenceCLM_apply, VectorField.mpullbackWithin_apply, coe_snd', IsCompactOperator.comp_clm, SchwartzMap.lineDerivOp_apply_eq_fderiv, conformalFactorAt_inner_eq_mul_inner, BoxIntegral.integral_const, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, differentiableOn, isPositive_iff', TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, ProperCone.mem_comap, ContinuousMultilinearMap.curryLeft_apply, ContDiffAt.laplacian_CLM_comp_left_nhds, Submodule.lipschitzWith_orthogonalProjection, norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, TopModuleCat.kerι_apply, MeasureTheory.Integrable.apply_continuousLinearMap, coe_prodMap', UniformSpace.Completion.coe_toComplL, ProperCone.hyperplane_separation_of_notMem, fderiv_clm_apply, ContinuousLinearEquiv.ofBijective_symm_apply_apply, HasFPowerSeriesWithinAt.unshift, hasFDerivAtFilter_iff_tendsto, det_smulRight, innerSL_apply, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, tendsto_birkhoffAverage_orthogonalProjection, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Submodule.norm_starProjection_apply, cfc_eq_cfcL, stereographic_apply, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, map_smul₂, Submodule.inner_starProjection_left_eq_right, PiLp.proj_apply, WeakSpace.coe_map, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, IsConformalMap.injective, Continuous.clm_bundle_apply₂, MeasureTheory.condExpInd_disjoint_union_apply, analyticOn_uncurry_of_multilinear, MeasureTheory.L1.setToL1_simpleFunc_indicatorConst, Bornology.IsVonNBounded.image, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, exists_embedding_euclidean_of_compact, coe_id', Submodule.starProjection_minimal, contMDiffWithinAt, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, dslope_comp, inl_apply, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Submodule.orthogonalProjection_orthogonal_apply_eq_zero, unit_le_opNorm, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le', Submodule.starProjection_mem_subspace_eq_self, MeasureTheory.L1.setToL1_zero_left', MeasureTheory.BoundedContinuousFunction.inner_toLp, adjoint_inner_right, exists_extension_norm_eq, DifferentiableWithinAt.clm_apply, SeparationQuotient.isEmbedding_outCLM, ContDiff.contDiff_fderiv_apply, measurable_apply', toSpanSingletonLE_symm_apply, ContDiffMapSupportedIn.postcompLM_apply, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, DifferentiableAt.clm_apply, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, SchwartzMap.tsupport_derivCLM_subset, MeasureTheory.integrable_continuousLinearMap_prod, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, ContDiffWithinAt.fderivWithin_right_apply, MeasureTheory.setToFun_const, MeasureTheory.charFunDual_map, le_of_opNorm₂_le_of_le, AddMonoidHom.coe_toRealLinearMap, Submodule.orthogonalProjectionFn_eq, iteratedFDerivWithin_clm_apply_const_apply, ContinuousAlternatingMap.toContinuousLinearMap_apply, signedDist_apply, continuousMultilinearCurryRightEquiv_apply', TemperedDistribution.lineDerivOp_fourierInv_eq, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, ProbabilityTheory.variance_dual_prod, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, isBigOTVS_fun_comp, coeFn_compLp, extendTo𝕜'_apply, isAdjointPair_inner, coe_sub', ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, ContDiffMapSupportedIn.continuous_iff_comp, smulRight_comp, cfcₙ_eq_cfcₙL, ContDiffOn.comp_continuousLinearMap, VectorFourier.norm_fourierSMulRight, smulRight_one_one, LinearEquiv.extend_apply, hasStrictFDerivAt_inv', cfcₙL_apply, Submodule.snd_orthogonalDecomposition_apply, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, MDifferentiable.clm_apply, SchwartzMap.fourier_fderivCLM_eq, integral_comp_id_comm, SchwartzMap.fourier_convolution_apply, MeasureTheory.SimpleFunc.setToSimpleFunc_const', iteratedFDeriv_two_apply, analyticOnNhd, IsLocalMaxOn.hasFDerivWithinAt_eq_zero, ContMDiffAt.clm_apply, WeakDual.toStrongDual_apply, hasMFDerivWithinAt, Real.differentiable_fourierChar_neg_bilinear_left, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, continuousMultilinearCurryLeftEquiv_symm_apply, LineDeriv.lineDerivOpCLM_apply, geometric_hahn_banach_closed_point, ContinuousMultilinearMap.smulRightL_apply, contDiff, Convex.second_derivative_within_at_symmetric_of_mem_interior, isUniformEmbedding_toUniformOnFun, exists_mul_lt_of_lt_opNorm, toWeakSpaceCLM_eq_toWeakSpace, IsLocalMinOn.fderivWithin_nonneg, Submodule.orthogonalDecomposition_apply, contMDiffOn, Convex.norm_image_sub_le_of_norm_fderiv_le', OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ, nnbound, PointwiseConvergenceCLM.evalCLM_apply, topDualPairing_apply, ContDiffMapSupportedIn.structureMapCLM_zero_injective, RCLike.iInter_halfSpaces_eq, MeasureTheory.setIntegral_condExpL1CLM, ProperCone.hyperplane_separation, cpolynomialOn, le_opENorm, continuousMultilinearCurryFin1_symm_apply, Trivialization.symmL_apply, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, coe_mul, StrongDual.mem_polar_iff, Submodule.orthogonal_eq_inter, mdifferentiableOn, MeasureTheory.eLpNorm_condExpL2_le, lsmul_flip_apply, SchwartzMap.coe_apply, ContinuousLinearEquiv.coord_self, compContinuousAlternatingMapCLM_apply_apply, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, extDerivWithin_apply, ContinuousAt.clm_bundle_apply, sSup_unitClosedBall_eq_norm, iteratedDeriv_vcomp_two, fderiv_norm_rpow, norm_map_iff_adjoint_comp_self, MeasureTheory.L1.integral_eq', Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, RCLike.geometric_hahn_banach_point_closed, ContinuousLinearEquiv.coe_coe, map_add₂, VectorField.fderivWithin_apply_lieBracket, VectorPrebundle.coordChange_apply, EuclideanGeometry.orthogonalProjection_apply, hasDerivWithinAt, FormalMultilinearSeries.derivSeries_apply_diag, iteratedFDeriv_clm_apply_const_apply, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, IsExposed.eq_inter_halfSpace', ProbabilityTheory.covarianceBilinDual_of_not_memLp, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, prod_apply, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NormedSpace.double_dual_bound, MeasureTheory.convolution_eq_swap, map_zero₂, VectorField.mlieBracketWithin_apply, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, MeasureTheory.condExpIndSMul_ae_eq_smul, iteratedFDeriv_comp_right, ContDiff.continuousLinearMap_comp, precomp_apply, cfcₙL_integrable, HasGradientAt.fderiv_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, comp_analyticOnNhd, TemperedDistribution.derivCLM_apply_apply, mfderiv_subtype_coe_Icc_one, exists_nnnorm_eq_one_lt_apply_of_lt_opNNNorm, coe_pi', postcompUniformConvergenceCLM_apply, VectorField.lieBracket_smul_right, coeFn_ofSeqClosedGraph, InnerProductSpace.HarmonicAt.comp_CLM, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, smulRight_apply, analyticAt_bilinear, inner_gradient_left, FormalMultilinearSeries.compContinuousLinearMap_apply, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', HasFDerivWithinAt.comp_hasDerivAt_of_eq, contDiffOn_fderivWithin_apply, toPointwiseConvergenceCLM_apply, apply_norm_sq_eq_inner_adjoint_right, innerSL_apply_coe, bound, StrongDual.polar_singleton, toUniformConvergenceCLM_symm_apply, MeasureTheory.ContinuousMap.inner_toLp, ConvexOn.real_sSup_of_nat_affine_eq, hasFDerivAt_inv', coe_mk', exists_continuousLinearEquiv_fderiv_symm_eq, MeasureTheory.AEStronglyMeasurable.convolution_integrand', map_neg, IsInvertible.self_apply_inverse, isOpenMap_of_ne_zero, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, integral_comp_comm, hasFDerivWithinAt_iff_tendsto, map_neg₂, coe_toContinuousAffineMap, Bundle.RiemannianMetric.continuousAt, ContinuousLinearMapWOT.continuous_dual_apply, iteratedFDeriv_comp_left, isCompact_image_coe_of_bounded_of_weak_closed, Submodule.orthogonalProjection_eq_zero_iff, holderL_apply_apply, StrongDual.mem_polar_singleton, ContMDiffOn.clm_bundle_apply, MeasureTheory.condExpL1CLM_smul, MeasureTheory.AEStronglyMeasurable.convolution_integrand, VectorFourier.hasFDerivAt_fourierChar_smul, IsInvertible.injective, Submodule.orthogonalProjection_starProjection_of_le, Real.exists_extension_norm_eq, continuousMultilinearCurryRightEquiv_apply, Submodule.coe_orthogonalProjection_apply, integrable_of_bilin_of_bdd_right, SeparationQuotient.mkCLM_apply, fderiv_comp_deriv_of_eq, apply_apply', ProbabilityTheory.covarianceBilinDual_of_not_memLp', Submodule.starProjection_apply_eq_zero_iff, SchwartzMap.fourier_convolution, AnalyticOnNhd.eval_continuousLinearMap', apply_val_ker, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, fderivWithin_clm_apply, postcomp_uniformConvergenceCLM_apply, exists_continuousLinearEquiv_fderivWithin_symm_eq, bijective_iff_dense_range_and_antilipschitz, dist_le_opNorm, FourierTransform.fourierCLM_apply, fderiv_continuousAlternatingMap_apply_const_apply, InnerProductGeometry.IsConformalMap.preserves_angle, ApproximatesLinearOn.lipschitzOnWith, isBigOTVS_id, ClosedSubmodule.coe_comap, hasStrictDerivAt, analyticAt_uncurry_of_multilinear, measurable_fderiv_apply_const_with_param, HasStrictFDerivAt.clm_comp, WithLp.fstL_apply, MeasureTheory.L1.integral_eq, smulRightL_apply_apply, continuousOn_clm_apply, toSpanSingletonCLE_apply_apply, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, IsInvertible.inverse_comp_apply_of_left, opNNNorm_mul_apply, fderivInnerCLM_apply, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, VectorBundleCore.coordChange_comp, SchwartzMap.denseRange_toLpCLM, SchwartzMap.toZeroAtInftyCLM_apply, toSpanSingletonCLE_symm_apply, Real.fderiv_fourierChar_neg_bilinear_left_apply, apply_apply, MeasureTheory.L1.setToL1_const, norm_map_removeNth_le, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, IsSymmSndFDerivWithinAt.eq, map_smulₛₗ₂, fderivWithin_restrictScalars_comp, RCLike.geometric_hahn_banach_closed_compact, ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, ContinuousOn.clm_bundle_apply, inner_gradient_right, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, derivWithin_clm_apply, Submodule.orthogonalProjection_orthogonal, MeasureTheory.L1.setToL1_lipschitz, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, TemperedDistribution.fourierTransformInvCLM_apply, MDifferentiableWithinAt.clm_apply, HasCompactSupport.convolution_integrand_bound_right, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, MeasureTheory.setToFun_eq, DifferentiableAt.lineDeriv_eq_fderiv, HasDerivAt.comp_semilinear, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, MeasureTheory.condExpL2_comp_continuousLinearMap, ConvexOn.real_sSup_affine_eq, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, AnalyticOnNhd.eval_continuousLinearMap, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, HasFDerivAt.clm_comp, adjoint_innerSL_apply, hasFDerivAt_iff_isLittleO_nhds_zero, circleAverage_comp_comm, VectorPrebundle.contMDiffCoordChange_apply, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, HasCompactSupport.convolution_integrand_bound_right_of_subset, IsPositive.re_inner_nonneg_right, postcomp_compactConvergenceCLM_apply, integral_id_map, second_derivative_symmetric_of_eventually_of_real, BoundedContinuousFunction.toLp_denseRange, MeasureTheory.condExpL2_const_inner, HasRightInverse.surjective, TemperedDistribution.laplacianCLM_apply, toWOT_apply, curveIntegralFun_def, ext_ring_iff, norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, intervalIntegral_comp_comm, contMDiffAt, zero_apply, isClosed_setOf_isCompactOperator, DoubleCentralizer.coe_snd, fpowerSeriesBilinear_apply_one, MeasureTheory.integral_convolution, le_opNorm_enorm, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, RCLike.imCLM_apply, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap, ConvexOn.univ_sSup_of_nat_affine_eq, InnerProductGeometry.ConformalAt.preserves_angle, Submodule.starProjection_tendsto_closure_iSup, domain_mvt, MeasureTheory.Lp.toTemperedDistribution_smul_eq, NormedSpace.dual_def, HasFDerivAtFilter.hasDerivAtFilter, RCLike.geometric_hahn_banach_open_open, ContinuousAlternatingMap.ofSubsingleton_symm_apply_apply, fderiv_norm_sq, coe_mulₗᵢ, isUnit_iff_bijective, MDifferentiableOn.clm_bundle_apply₂, MeasureTheory.condExpL1_eq, OrthogonalFamily.projection_directSum_coeAddHom, innerSL_apply_comp, TopModuleCat.hom_forget₂_TopCat_map, conformalAt_iff', mdifferentiableAt, toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, coeFn_holder, map_smul, coe_deriv₂, IsMIntegralCurveAt.eventually_hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, ContMDiffOn.clm_bundle_apply₂, MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving, ContinuousWithinAt.clm_bundle_apply, extDeriv_apply, mfderiv_prod_eq_add_apply, MeasureTheory.condExpL2_indicator_nonneg, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, Bundle.ContinuousRiemannianMetric.isVonNBounded, comp_toSpanSingleton, HasStrictDerivAt.clm_apply, TemperedDistribution.smulLeftCLM_apply_apply, MeasureTheory.SimpleFunc.map_setToSimpleFunc, fderiv_inner_apply, hasDerivAt_of_bilinear, second_derivative_symmetric_of_eventually, HasFDerivAt.comp_hasDerivAt_of_eq, SeparationQuotient.outCLM_injective, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, HasLeftInverse.injective, continuousAt_uncurry_of_multilinear, BoundedContinuousFunction.probCharDual_apply, InnerProductSpace.norm_rankOne, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, PiTensorProduct.mapLMultilinear_toFun_apply, CStarMatrix.inner_toCLM_conjTranspose_right, iteratedDerivWithin_vcomp_three, MDifferentiableAt.clm_apply, fderiv_eq_smul_deriv, unitary.inner_map_map, CStarMatrix.toCLM_apply_single_apply, flipAlternating_apply_apply, coeFn_compLp', MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap, algebraMap_apply, comp_apply, HasStrictFDerivAt.implicitToOpenPartialHomeomorphOfComplemented_apply, coe_completion, iteratedFDeriv_succ_apply_left, ContDiffWithinAt.fderivWithin_apply, IsSymmSndFDerivAt.eq, norm_iteratedFDerivWithin_le_of_bilinear_aux, fderiv_inv', SeparationQuotient.outCLM_isUniformInducing, coeFn_ofIsClosedGraph, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, IsLocalMinOn.fderivWithin_eq_zero, RCLike.geometric_hahn_banach_open_point, Submodule.mem_iff_norm_starProjection, Complex.reCLM_apply, ContinuousLinearEquiv.ofBijective_apply_symm_apply, continuousMultilinearCurryFin1_apply, IsCoercive.antilipschitz, LinearMap.IsSymmetric.apply_clm, IsInvertible.inverse_apply_eq, norm_iteratedFDeriv_clm_apply_const
id 📖	CompOp	113 math math: mfderiv_sumSwap, PiTensorProduct.mapL_id, snd_comp_inr, binomialSeries_eq_ordinaryHypergeometricSeries, Bundle.Trivial.symmL_trivialization, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, SeparationQuotient.mkCLM_comp_outCLM, fderiv_id, hasFDerivAt_stereoInvFunAux, RCLike.map_same_eq_id, id_apply, ContinuousLinearEquiv.coe_comp_coe_symm, adjoint_id, LinearIsometry.id_toContinuousLinearMap, hasMFDerivAt_sumSwap, Bundle.Trivial.continuousLinearMapAt_trivialization, FormalMultilinearSeries.radius_compNeg, ModelWithCorners.hasMFDerivAt, hasMFDerivAt_inr, mfderivWithin_sumInr, fderivWithin_id, NormedSpace.inclusionInDoubleDual_norm_eq, hasMFDerivWithinAt_inr, pi_proj, isPositive_id, mfderivWithin_sumInl, exists_right_inverse_of_surjective, hasFDerivAt_id, iteratedFDerivWithin_smul_const_apply, PiTensorProduct.liftIsometry_tprodL, mfderiv_sumInl, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, fderiv_pow_ring, ContinuousLinearEquiv.coe_symm_comp_coe, hasMFDerivAt_id, hasMFDerivWithinAt_id, ClosedSubmodule.comap_id, SchwartzMap.smulLeftCLM_const, hasFDerivWithinAt_pow', fderivWithin_id', SeparationQuotient.exists_out_continuousLinearMap, FormalMultilinearSeries.compContinuousLinearMap_id, OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv, hasMFDerivAt_inl, TopModuleCat.hom_id, ProperCone.map_id, fderiv_pow_ring', ContinuousLinearEquiv.coe_refl, tangentBundleCore_coordChange_model_space, hasFDerivAt_pow, hasFDerivAt_single, ModelWithCorners.hasMFDerivWithinAt, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, ClosedSubmodule.map_id, fderiv_update, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, hasStrictFDerivAt_pow', ModelWithCorners.hasMFDerivWithinAt_symm, fst_comp_inl, Submodule.starProjection_orthogonal, hasFDerivAt_update, mfderiv_sumInr, iteratedFDeriv_smul_const_apply, fderiv_id', norm_id_le, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', hasFDerivAt_pow', mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', IsInvertible.inverse_comp_self, Submodule.starProjection_top, hasFDerivAt_sub_const, toContinuousAddMonoidHom_id, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, hasFDerivAtFilter_id, isConformalMap_id, OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv, ContinuousAlternatingMap.norm_ofSubsingleton_id, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, FormalMultilinearSeries.ofScalars_comp_neg_id, fderivWithin_pow_ring', fst_prod_snd, coe_id', OrthonormalBasis.sum_rankOne_eq_id, norm_id, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, id_comp, smulRight_id, nnnorm_id, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, ProperCone.comap_id, hasStrictFDerivAt_pow, IsInvertible.self_comp_inverse, coe_eq_id, norm_id_of_nontrivial_seminorm, hasFDerivWithinAt_pow, isConformalMap_const_smul, mfderivWithin_id, coe_id, mfderivWithin_sumSwap, fderivWithin_pow_ring, hasMFDerivWithinAt_inl, fderiv_single, inverse_id, one_def, comp_id, hasStrictFDerivAt_id, hasStrictFDerivAt_sub_const, coprod_inl_inr, ContinuousMultilinearMap.norm_ofSubsingleton_id, hasFDerivWithinAt_id, mfderiv_id
inhabited 📖	CompOp	1 math math: default_def
instMul 📖	CompOp	35 math math: Matrix.l2_opNorm_toEuclideanCLM, isStarProjection_iff_isSymmetricProjection, InnerProductSpace.isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, isStarNormal_iff_norm_eq_adjoint, LinearIsometryEquiv.conjStarAlgEquiv_apply, mul_apply, Submodule.isIdempotentElem_starProjection, Matrix.toEuclideanCLM_toLp, VonNeumannAlgebra.centralizer_centralizer', LinearIsometryEquiv.conjStarAlgEquiv_trans, isIdempotentElem_toLinearMap_iff, LinearIsometryEquiv.conjStarAlgEquiv_refl, VonNeumannAlgebra.centralizer_centralizer, PiTensorProduct.mapL_mul, Matrix.ofLp_toEuclideanCLM, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, InnerProductSpace.isStarProjection_rankOne_self, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, isStarProjection_starProjection, LinearIsometryEquiv.symm_conjStarAlgEquiv, DoubleCentralizer.mul_fst, isStarProjection_iff_isIdempotentElem_and_isStarNormal, LinearMap.isStarProjection_toContinuousLinearMap_iff, InnerProductSpace.isIdempotentElem_rankOne_self_iff, isStarProjection_iff_eq_starProjection_range, VonNeumannAlgebra.mem_commutant_iff, mul_def, VonNeumannAlgebra.coe_commutant, coe_mul, isStarProjection_iff_eq_starProjection, Matrix.cstar_norm_def, DoubleCentralizer.mul_snd, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, LinearMap.IsSymmetricProjection.isStarProjection
instNatCast 📖	CompOp	4 math math: DoubleCentralizer.natCast_fst, isPositive_natCast, natCast_apply, DoubleCentralizer.natCast_snd
instSMul 📖	CompOp	329 math math: Matrix.l2_opNorm_toEuclideanCLM, HasStrictFDerivAt.log, HasStrictFDerivAt.fun_mul', HasMFDerivAt.mul, HasFDerivWithinAt.ccosh, Complex.restrictScalars_one_smulRight', HasFDerivWithinAt.ccos, Real.hasFDerivAt_fourierChar_neg_bilinear_left, hasStrictFDerivAt_exp_of_mem_ball, curveIntegral_smul, hasStrictFDerivAt_list_prod_finRange', HasStrictFDerivAt.csin, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, HasFDerivWithinAt.pow, fderivWithin_fun_smul, hasFDerivAt_multiset_prod, smul_apply, continuousSMul, Matrix.cstar_nnnorm_def, fderivWithin_csinh, HasDerivAtFilter.comp_hasFDerivAtFilter, HasDerivWithinAt.complexToReal_fderiv', fderivWithin_fun_pow', fderiv_multiset_prod, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, HasFDerivAt.fun_mul, HasDerivAt.comp_hasFDerivAt_of_eq, curveIntegralFun_smul, coe_smul', Differentiable.fderiv_norm_rpow, curveIntegrable_smul_iff, HasStrictFDerivAt.mul', fderiv_fun_pow, Complex.hasStrictFDerivAt_exp_real, fderiv_fun_smul, LinearIsometryEquiv.conjStarAlgEquiv_apply, HasStrictFDerivAt.pow, fderivWithin_sinh, HasStrictFDerivAt.const_mul, HasFDerivAt.finset_prod, smul_compLp, ContinuousAlternatingMap.curryLeft_smul, fderiv_const_smul_field, Real.hasStrictFDerivAt_rpow_of_pos, fderiv_fun_pow', HasFDerivWithinAt.csin, IsPositive.smul_of_nonneg, HasFDerivWithinAt.const_mul, HasFDerivWithinAt.fun_const_smul, HasStrictFDerivAt.const_smul, fderivWithin_ccosh, HasFDerivWithinAt.mul, fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, DoubleCentralizer.smul_toProd, HasFDerivAt.arctan, HasStrictFDerivAt.abs, HasFDerivAt.fun_smul, PiTensorProduct.mapL_smul, smul_comp, ContinuousAffineMap.smul_contLinear, HasDerivAt.comp_hasFDerivWithinAt, HasStrictFDerivAt.arsinh, HasFDerivWithinAt.exp, HasStrictFDerivAt.list_prod', fderivWithin_sin, Complex.hasStrictFDerivAt_cpow', SchwartzMap.smulLeftCLM_real_smul, HasFDerivAt.fun_const_smul, curveIntegral_fun_smul, fderiv.log, hasStrictFDerivAt_multiset_prod, fderivWithin_finset_prod, fderiv_smul, flip_smul, HasFDerivWithinAt.const_smul, NormedSpace.smul_mem_polar, ContinuousAlternatingMap.alternatizeUncurryFin_smul, fderiv_mul_const', hasStrictFDerivAt_exp, HasFDerivWithinAt.fun_smul, hasFDerivAt_norm_rpow, Matrix.toEuclideanCLM_toLp, Complex.hasStrictFDerivAt_cpow, fderiv_pow, HasFDerivAt.pow, HasFDerivWithinAt.cpow, HasStrictFDerivAt.const_cpow, HasFDerivWithinAt.csinh, HasStrictFDerivAt.cexp, HasFDerivAt.abs, HasFDerivWithinAt.abs, uniformContinuousConstSMul, HasFDerivWithinAt.mul_const, fderiv_pow', fderiv_mul, DoubleCentralizer.smul_fst, fderivWithin_cos, toSpanSingleton_smul, fderivWithin_ccos, HasStrictFDerivAt.clog, fderiv_pow_ring, LinearIsometryEquiv.conjStarAlgEquiv_trans, HasStrictFDerivAt.sqrt, HasDerivWithinAt.complexToReal_fderiv, HasStrictFDerivAt.rpow, fderivWithin_fun_mul', hasFDerivAt_list_prod', smulCommClass, fderiv_mul', fderivWithin_const_smul_of_field, HasStrictFDerivAt.ccos, HasFDerivWithinAt.cexp, LinearIsometryEquiv.conjStarAlgEquiv_refl, MeasureTheory.setToFun_smul_left, HasDerivAt.complexToReal_fderiv', HasDerivAt.complexToReal_fderiv, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, SchwartzMap.smulLeftCLM_const, Complex.hasFDerivAt_cpow, fderiv_const_smul_of_invertible, hasFDerivWithinAt_pow', HasFDerivAt.cexp, HasFDerivAt.ccos, HasFDerivWithinAt.log, HasFDerivAt.clog, fderivWithin_mul_const', fderivWithin_smul, hasFDerivAt_list_prod_finRange', Complex.restrictScalars_one_smulRight, Matrix.ofLp_toEuclideanCLM, HasFDerivAt.ccosh, fderiv_cos, hasFDerivWithinAt_comp_smul_smul_iff, fderivWithin_fun_pow, HasStrictFDerivAt.arctan, HasFDerivAtFilter.const_smul, HasFDerivAt.multiset_prod, HasFDerivAt.mul_const, HasFDerivWithinAt.mul_const', HasDerivAt.comp_hasFDerivWithinAt_of_eq, fderiv_const_mul, fderiv_exp, fderiv_arctan, HasFDerivAtFilter.fun_const_smul, fderiv_pow_ring', fderivWithin.log, HasFDerivWithinAt.sinh, instStarModuleId, hasFDerivAt_pow, HasFDerivAt.log, isVonNBounded_iff, HasFDerivAt.exp, HasFDerivAt.fun_pow', HasMFDerivWithinAt.mul', IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, fderiv_ccos, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, fderivWithin_const_smul_of_invertible, fderivWithin_exp, HasFDerivAt.const_mul, HasStrictDerivAt.complexToReal_fderiv', HasFDerivWithinAt.rpow_const, fderivWithin_multiset_prod, HasFDerivAt.mul, HasFDerivAt.sinh, hasStrictFDerivAt_pow', Complex.restrictScalars_toSpanSingleton, HasFDerivWithinAt.clog, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', HasFDerivAt.const_smul, HasFDerivAt.rpow_const, coord_norm', hasFDerivAt_exp_smul_const, HasStrictFDerivAt.const_rpow, continuousConstSMul, fderiv_finset_prod, hasStrictFDerivAt_list_prod_attach', restrictScalars_smul, HasStrictFDerivAt.cos, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, HasFDerivWithinAt.arsinh, InnerProductSpace.rankOne_comp_rankOne, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, comp_smulₛₗ, hasStrictFDerivAt_finset_prod, HasDerivWithinAt.comp_hasFDerivAt, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, HasFDerivAt.sin, HasFDerivAt.csin, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, fderiv_norm_smul, HasFDerivAt.hasFDerivAt_norm_smul, HasFDerivWithinAt.sqrt, HasFDerivWithinAt.pow', isScalarTower, fderivWithin_sqrt, HasFDerivAt.list_prod', fderivWithin_const_smul_field, fderiv_sinh, hasFDerivAt_pow', LinearIsometryEquiv.symm_conjStarAlgEquiv, HasFDerivWithinAt.const_cpow, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, HasFDerivWithinAt.arctan, HasFDerivWithinAt.rpow, HasMFDerivAt.prod, fderivWithin_csin, HasFDerivAt.cos, opNorm_smul_le, EuclideanGeometry.hasFDerivAt_inversion, HasStrictFDerivAt.fun_const_smul, fderivWithin_const_smul, HasFDerivAt.const_rpow, Matrix.toLin_finTwoProd_toContinuousLinearMap, fderiv_fun_const_smul, HasMFDerivWithinAt.mul, HasFDerivAt.arsinh, fderiv_ccosh, HasStrictFDerivAt.fun_smul, HasStrictFDerivAt.cpow, fderiv_fun_mul, HasFDerivAt.pow', HasStrictFDerivAt.pow', CurveIntegrable.smul, TopModuleCat.hom_smul, HasStrictFDerivAt.multiset_prod, HasFDerivWithinAt.smul, HasStrictFDerivAt.mul_const', IsConformalMap.smul, fderiv_sqrt, fderivWithin_list_prod', HasFDerivWithinAt.fun_mul', hasStrictFDerivAt_list_prod, fderivWithin_pow_ring', HasFDerivWithinAt.fun_pow', fderivWithin_mul_const, HasFDerivAt.mul_const', HasStrictFDerivAt.fun_pow', HasStrictFDerivAt.sin, HasFDerivWithinAt.const_rpow, fderivWithin_cosh, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, Real.hasFDerivAt_fourierChar_neg_bilinear_right, ContinuousLinearEquiv.coord_norm', Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, hasStrictFDerivAt_exp_smul_const, Complex.hasStrictFDerivAt_log_real, HasStrictFDerivAt.mul, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, toSpanSingleton_smul', fderiv_csinh, smul_compLpL, HasFDerivAt.sqrt, HasFDerivAt.csinh, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', HasStrictFDerivAt.ccosh, fderiv_norm_rpow, HasStrictFDerivAt.cosh, fderivWithin_pow, isCentralScalar, fderivWithin_fun_const_smul, hasStrictFDerivAt_pow, fderiv_comp_smul, fderivWithin_arctan, TemperedDistribution.smulLeftCLM_smul, MeasureTheory.charFun_map_eq_charFunDual_smul, Matrix.cstar_norm_def, fderiv_csin, fderiv_cosh, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, HasFDerivWithinAt.mul', HasStrictFDerivAt.sinh, HasFDerivAt.cpow, Real.hasStrictFDerivAt_rpow_of_neg, MeasureTheory.weightedSMul_smul_measure, HasStrictDerivAt.complexToReal_fderiv, fderivWithin_mul', HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, HasFDerivAt.cosh, isConformalMap_const_smul, VectorFourier.hasFDerivAt_fourierChar_smul, HasStrictFDerivAt.csinh, fderiv_const_smul_of_field, HasFDerivWithinAt.cos, coe_smul, fderiv_list_prod', HasMFDerivWithinAt.prod, fderivWithin_comp_smul, HasMFDerivAt.mul', hasFDerivAt_exp, fderivWithin_pow_ring, fderiv_const_smul, HasFDerivAt.fun_mul', HasStrictFDerivAt.mul_const, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, HasFDerivAt.mul', hasFDerivAt_list_prod_attach', HasDerivWithinAt.comp_hasFDerivAt_of_eq, HasFDerivAt.rpow, fderivWithin_fun_mul, DoubleCentralizer.smul_snd, HasFDerivAt.smul, HasFDerivWithinAt.sin, SchwartzMap.smulLeftCLM_smul, HasStrictFDerivAt.exp, fderiv_sin, hasFDerivAt_exp_of_mem_ball, const_smul_mfderiv, HasMFDerivAt.const_smul, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, fderivWithin_mul, HasFDerivWithinAt.fun_mul, HasStrictFDerivAt.smul, HasStrictFDerivAt.finset_prod, HasFDerivAt.const_cpow, HasFDerivWithinAt.cosh, comp_smul, HasStrictFDerivAt.rpow_const, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Complex.restrictScalars_toSpanSingleton', HasFDerivWithinAt.list_prod', fderivWithin_pow', hasFDerivAt_finset_prod
monoidWithZero 📖	CompOp	35 math math: ContinuousLinearEquiv.unitsEquiv_apply, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, applySMulCommClass', smulRight_one_pow, DoubleCentralizer.pow_snd, Unitary.coe_linearIsometryEquiv_apply, Unitary.linearIsometryEquiv_coe_apply, unitary.linearIsometryEquiv_coe_symm_apply, ringInverse_equiv, Unitary.coe_symm_linearIsometryEquiv_apply, isUnit_of_forall_le_norm_inner_map, applyFaithfulSMul, toSpanSingleton_pow, HasFDerivAt.iterate, isUnit_iff_isUnit_toLinearMap, Unitary.linearIsometryEquiv_coe_symm_apply, HasStrictFDerivAt.iterate, coe_pow, HasFDerivWithinAt.iterate, DoubleCentralizer.pow_toProd, applySMulCommClass, Unitary.norm_map, DoubleCentralizer.pow_fst, unitary.norm_map, ringInverse_eq_inverse, smul_def, Unitary.inner_map_map, inverse_eq_ringInverse, HasFDerivAtFilter.iterate, PiTensorProduct.mapL_pow, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, continuousConstSMul_apply, isUnit_iff_bijective, unitary.inner_map_map, unitary.linearIsometryEquiv_coe_apply
mulAction 📖	CompOp	—
neg 📖	CompOp	73 math math: comp_neg, TemperedDistribution.lineDerivOpCLM_eq, binomialSeries_eq_ordinaryHypergeometricSeries, ContinuousAffineMap.neg_contLinear, curveIntegrable_fun_neg_iff, HasFDerivAtFilter.const_sub, curveIntegral_neg, fderivWithin_const_sub, HasFDerivAtFilter.neg, FormalMultilinearSeries.radius_compNeg, TemperedDistribution.smulLeftCLM_neg, fderivWithin_fun_neg, fderiv_neg, Real.fourier_iteratedFDeriv, HasMFDerivAt.neg, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, HasFDerivWithinAt.const_sub, coe_neg', hasFDerivAt_ringInverse, VectorFourier.fourierIntegral_iteratedFDeriv, HasMFDerivWithinAt.neg, hasMFDerivAt_neg, restrictScalars_neg, HasFDerivWithinAt.abs_of_neg, HasFDerivWithinAt.neg, DoubleCentralizer.neg_snd, fderiv_inverse, SchwartzMap.smulLeftCLM_fun_neg, fderivWithin_inv', HasStrictFDerivAt.abs_of_neg, fderiv_norm_smul_neg, HasFDerivWithinAt.fun_neg, HasStrictFDerivAt.neg, Real.fourier_fderiv, HasFDerivAt.abs_of_neg, curveIntegral_fun_neg, DoubleCentralizer.neg_toProd, curveIntegralFun_neg, HasStrictFDerivAt.const_sub, fderivWithin_neg, CurveIntegrable.fun_neg, curveIntegrable_neg_iff, hasStrictFDerivAt_ringInverse, fderiv_fun_neg, Real.fourierIntegral_fderiv, fderiv_const_sub, HasFDerivAtFilter.fun_neg, SchwartzMap.smulLeftCLM_neg, toContinuousAddMonoidHom_neg, neg_apply, HasFDerivAt.fun_neg, HasStrictFDerivAt.fun_neg, neg_comp, coe_neg, HasFDerivAt.const_sub, FormalMultilinearSeries.ofScalars_comp_neg_id, HasFDerivAt.hasFDerivAt_norm_smul_neg, opNorm_neg, FormalMultilinearSeries.ofScalars_comp_neg, hasStrictFDerivAt_inv', VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, hasFDerivAt_inv', exists_continuousLinearEquiv_fderiv_symm_eq, mfderiv_neg, HasFDerivAt.neg, TopModuleCat.hom_neg, exists_continuousLinearEquiv_fderivWithin_symm_eq, VectorFourier.fourierIntegral_fderiv, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Real.fourierIntegral_iteratedFDeriv, CurveIntegrable.neg, DoubleCentralizer.neg_fst, fderiv_inv'
one 📖	CompOp	51 math math: Polynomial.fderiv, TangentBundle.continuousLinearMapAt_model_space, hasStrictFDerivAt_exp_of_mem_ball, smulRight_one_eq_toSpanSingleton, Submodule.starProjection_orthogonal', Complex.hasStrictFDerivAt_exp_real, hasStrictFDerivAt_exp_smul_const_of_mem_ball', PiTensorProduct.mapL_one, one_smulRight_eq_toSpanSingleton, Submodule.starProjection_top', hasStrictFDerivAt_exp, hasStrictFDerivAt_exp_smul_const', TangentBundle.coordChange_model_space, HasDerivWithinAt.complexToReal_fderiv, inner_map_map_iff_adjoint_comp_self, Polynomial.fderiv_aeval, HasDerivAt.complexToReal_fderiv, hasFDerivAt_exp_smul_const', Polynomial.hasFDerivAt, Complex.restrictScalars_one_smulRight, one_apply, IsMIntegralCurveAt.hasMFDerivAt, DoubleCentralizer.one_snd, Polynomial.hasFDerivAt_aeval, hasFDerivAt_exp_zero, DoubleCentralizer.one_fst, Complex.restrictScalars_toSpanSingleton, hasFDerivAt_exp_smul_const_of_mem_ball, hasFDerivAt_exp_smul_const, hasStrictFDerivAt_exp_zero_of_radius_pos, TangentBundle.symmL_model_space, Polynomial.fderivWithin_aeval, Polynomial.fderivWithin, hasStrictFDerivAt_exp_zero, Polynomial.hasFDerivWithinAt_aeval, tendsto_birkhoffAverage_orthogonalProjection, normOneClass, DoubleCentralizer.one_toProd, hasFDerivAt_exp_smul_const_of_mem_ball', hasStrictFDerivAt_exp_smul_const, Complex.hasStrictFDerivAt_log_real, norm_map_iff_adjoint_comp_self, hasFDerivAt_exp_zero_of_radius_pos, UniformCauchySeqOnFilter.one_smulRight, Polynomial.hasFDerivWithinAt, HasStrictDerivAt.complexToReal_fderiv, isPositive_one, hasFDerivAt_exp, one_def, hasFDerivAt_exp_of_mem_ball, hasStrictFDerivAt_exp_smul_const_of_mem_ball
projKerOfRightInverse 📖	CompOp	3 math math: coe_projKerOfRightInverse_apply, projKerOfRightInverse_comp_inv, projKerOfRightInverse_apply_idem
rangeRestrict 📖	CompOp	3 math math: coe_equivRange, coe_rangeRestrict, coe_linearMap_equivRange
restrictScalars 📖	CompOp	38 math math: Complex.restrictScalars_one_smulRight', isUniformEmbedding_restrictScalars, IsConformalMap.is_complex_or_conj_linear, coe_restrictScalars, coe_restrictScalarsₗ, bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, HasFDerivAt.restrictScalars, uniformContinuous_restrictScalars, restrictScalars_neg, continuous_restrictScalars, DifferentiableAt.fderiv_restrictScalars, coe_restrict_scalarsL', restrictScalars_add, curveIntegral_restrictScalars, Complex.restrictScalars_one_smulRight, HasStrictFDerivAt.restrictScalars, coe_restrictScalarsIsometry, HasFDerivWithinAt.restrictScalars, differentiableWithinAt_iff_restrictScalars, restrictScalars_sub, DifferentiableWithinAt.restrictScalars_fderivWithin, Complex.restrictScalars_toSpanSingleton, restrictScalars_zero, restrictScalars_smul, isConformalMap_complex_linear_conj, isEmbedding_restrictScalars, toContinuousAddMonoidHom_restrictScalars, norm_restrictScalars, curveIntegralFun_restrictScalars, coe_restrictScalars', differentiableAt_iff_restrictScalars, isConformalMap_complex_linear, HasFDerivAtFilter.restrictScalars, bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, isConformalMap_iff_is_complex_or_conj_linear, fderivWithin_restrictScalars_comp, curveIntegrable_restrictScalars_iff, Complex.restrictScalars_toSpanSingleton'
restrictScalarsₗ 📖	CompOp	3 math math: coe_restrictScalarsₗ, restrictScalarsIsometry_toLinearMap, coe_restrictScalarsL
semiring 📖	CompOp	39 math math: ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, PiTensorProduct.mapLMonoidHom_apply, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Unitization.splitMul_apply, DoubleCentralizer.nnnorm_def', applySMulCommClass', ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, Unitization.nnnorm_def, DoubleCentralizer.norm_def', ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, instStarOrderedRing, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, toLinearMapRingHom_apply, Unitization.splitMul_injective_of_clm_mul_injective, applyFaithfulSMul, VonNeumannAlgebra.centralizer_centralizer', VonNeumannAlgebra.mem_carrier, Unitization.norm_eq_sup, DoubleCentralizer.algebraMap_snd, DoubleCentralizer.algebraMap_toProd, PositiveLinearMap.gnsStarAlgHom_apply, Algebra.IsCentral.instContinuousLinearMap, Unitization.norm_def, applySMulCommClass, instNonnegSpectrumClassRealId, DoubleCentralizer.algebraMap_fst, smul_def, Unitization.nnnorm_eq_sup, VonNeumannAlgebra.coe_toStarSubalgebra, Unitization.norm_splitMul_snd_sq, Unitization.splitMul_injective, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, continuousConstSMul_apply, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, instStarOrderedRingRCLike, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, DoubleCentralizer.toProdMulOppositeHom_apply, algebraMap_apply
smulRight 📖	CompOp	70 math math: Polynomial.fderiv, Complex.restrictScalars_one_smulRight', smulRight_one_eq_toSpanSingleton, fderivWithin_fun_smul, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, HasDerivWithinAt.complexToReal_fderiv', intervalIntegral.fderiv_integral_of_tendsto_ae, hasStrictFDerivAt_exp_smul_const_of_mem_ball', fderiv_fun_smul, HasFDerivAt.fun_smul, one_smulRight_eq_toSpanSingleton, fderiv_smul, HasFDerivWithinAt.fun_smul, hasStrictFDerivAt_exp_smul_const', iteratedFDerivWithin_smul_const_apply, coe_smulRightₗ, InnerProductSpace.rankOne_def, Polynomial.fderiv_aeval, norm_smulRight_apply, toSpanSingleton_comp, SchwartzMap.smulRightCLM_apply_apply, HasDerivAt.complexToReal_fderiv', hasFDerivAt_exp_smul_const', intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, Polynomial.hasFDerivAt, intervalIntegral.integral_hasStrictFDerivAt, fderivWithin_smul, ContDiff.smulRight, HasFDerivWithinAt.smul_const, IsMIntegralCurveAt.hasMFDerivAt, range_smulRight_apply, Polynomial.hasFDerivAt_aeval, HasFDerivAt.smul_const, HasStrictDerivAt.complexToReal_fderiv', hasFDerivAt_exp_smul_const_of_mem_ball, hasFDerivAt_exp_smul_const, fderiv_smul_const, iteratedFDeriv_smul_const_apply, smulRight_comp_smulRight, Polynomial.fderivWithin_aeval, Polynomial.fderivWithin, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, intervalIntegral.fderivWithin_integral_of_tendsto_ae, intervalIntegral.integral_hasFDerivWithinAt, nnnorm_smulRight_apply, HasStrictFDerivAt.fun_smul, HasFDerivWithinAt.smul, ContDiffWithinAt.smulRight, Polynomial.hasFDerivWithinAt_aeval, fderivWithin_smul_const, det_smulRight, smulRight_id, smulRight_comp, hasFDerivAt_exp_smul_const_of_mem_ball', hasStrictFDerivAt_exp_smul_const, HasStrictFDerivAt.smul_const, ContDiffOn.smulRight, UniformCauchySeqOnFilter.one_smulRight, Polynomial.hasFDerivWithinAt, intervalIntegral.integral_hasFDerivAt, smulRight_apply, intervalIntegral.fderiv_integral, coe_smulRight, smulRightL_apply_apply, ContDiffAt.smulRight, isBoundedBilinearMap_smulRight, HasFDerivAt.smul, HasStrictFDerivAt.smul, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Complex.restrictScalars_toSpanSingleton'
smulRightₗ 📖	CompOp	1 math math: coe_smulRightₗ
sub 📖	CompOp	47 math math: intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, intervalIntegral.fderiv_integral_of_tendsto_ae, Submodule.starProjection_orthogonal', HasFDerivAtFilter.sub, HasFDerivAt.sub, ApproximatesLinearOn.norm_fderiv_sub_le, fderiv_fun_sub, FDerivMeasurableAux.norm_sub_le_of_mem_A, mfderiv_sub, HasFDerivWithinAt.fun_sub, fderivWithin_fun_sub, TemperedDistribution.smulLeftCLM_sub, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, ContinuousAffineMap.sub_contLinear, intervalIntegral.integral_hasStrictFDerivAt, sub_apply, HasFDerivAtFilter.fun_sub, sub_comp, fderiv_sub, restrictScalars_sub, le_def, HasStrictFDerivAt.fun_sub, DoubleCentralizer.sub_toProd, DoubleCentralizer.sub_fst, Submodule.starProjection_orthogonal, HasMFDerivAt.sub, HasFDerivWithinAt.sub, curveIntegralFun_sub, TopModuleCat.hom_sub, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, intervalIntegral.fderivWithin_integral_of_tendsto_ae, intervalIntegral.integral_hasFDerivWithinAt, toContinuousAddMonoidHom_sub, fderivWithin_sub, curveIntegral_fun_sub, coe_sub, coe_sub', DoubleCentralizer.sub_snd, SchwartzMap.smulLeftCLM_sub, comp_sub, ContinuousAffineMap.vsub_contLinear, curveIntegral_sub, intervalIntegral.integral_hasFDerivAt, CurveIntegrable.sub, intervalIntegral.fderiv_integral, HasStrictFDerivAt.sub, HasFDerivAt.fun_sub
toLinearMap 📖	CompOp	202 math math: TopModuleCat.hom_cokerπ, coe_add, IsIdempotentElem.isClosed_range, MeasureTheory.Measure.addHaar_image_continuousLinearMap, isSelfAdjoint_iff_isSymmetric, isStarProjection_iff_isSymmetricProjection, Complex.ofRealCLM_coe, ker_codRestrict, ImplicitFunctionData.isCompl_ker, ContinuousLinearEquiv.snd_equivOfRightInverse, IsPositive.toLinearMap, LinearMap.adjoint_eq_toCLM_adjoint, ContinuousMap.range_toLp, coe_restrictScalars, LinearMap.toContinuousLinearMap₁_coe, coe_snd, IsIdempotentElem.ext_iff, coe_inj, ProperCone.mem_map, isComplete_ker, IsIdempotentElem.toLinearMap, LinearMap.mkContinuousOfExistsBound_coe, Submodule.IsOrtho.map_iff, ImplicitFunctionData.range_leftDeriv, Submodule.range_starProjection, IsSelfAdjoint.isSymmetric, closedComplemented_ker_of_rightInverse, IsIdempotentElem.ker_mem_invtSubmodule, Complex.reCLM_coe, iInf_ker_proj, coe_equivRange, Submodule.topologicalClosure_map, InnerProductSpace.isSymmetricProjection_rankOne_self, SeparatingDual.dualMap_surjective_iff, isClosed_ker, isPositive_def, ker_closedComplemented_of_finiteDimensional_range, LinearMap.toLinearMap_toContPerfPair, IsCoercive.range_eq_top, InnerProductSpace.trace_rankOne, DenseRange.topologicalClosure_map_submodule, toLinearMapRingHom_apply, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, Matrix.linfty_opNNNorm_toMatrix, Module.Basis.coe_constrL, Submodule.range_subtypeL, coe_coprod, PiTensorProduct.mapL_coe, IsSelfAdjoint.hasEigenvector_of_isMaxOn, LinearMap.IsSymmetric.coe_toSelfAdjoint, LinearEquiv.coe_toContinuousLinearEquiv_symm, coe_codRestrict, isPositive_toLinearMap_iff, RCLike.reCLM_coe, coe_ofSeqClosedGraph, IsPositive.isSymmetric, equivRange_symm_apply, InnerProductSpace.rank_rankOne, Submodule.toLinearMap_starProjection_eq_isComplProjection, coe_coe, coe_projKerOfRightInverse_apply, IsStarNormal.ker_adjoint_eq_ker, ClosedSubmodule.orthogonal_eq_inter, isIdempotentElem_toLinearMap_iff, Submodule.coe_continuous_linearProjOfClosedCompl, coe_inr, PiTensorProduct.liftEquiv_symm_apply, IsStarNormal.orthogonal_range, IsIdempotentElem.TFAE, coe_rangeRestrict, LinearMap.range_toContinuousLinearMap, equivRange_symm_toLinearEquiv, Submodule.starProjection_isSymmetric, coe_comp, LinearMap.coe_toContinuousLinearMap, isUnit_iff_isUnit_toLinearMap, toLinearMap_innerSL_apply, coe_pi, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, coe_linearMap_equivRange, LinearIsometryEquiv.completeSpace_map, coeLM_apply, toPMap_adjoint_eq_adjoint_toPMap_of_dense, ContinuousAffineMap.coe_contLinear_eq_linear, WithLp.coe_fstL, range_smulRight_apply, toLinearMap_eq_iff_eq_toContinuousLinearMap, PointwiseConvergenceCLM.coeLMₛₗ_apply, compLeftContinuous_apply, toLinearMap_algebraMapCLM, toLinearMap_toSpanSingleton, PointwiseConvergenceCLM.coeLM_apply, ContinuousLinearEquiv.ofSubmodule'_apply, VonNeumannAlgebra.IsIdempotentElem.mem_iff, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, IsStarProjection.ext_iff, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top, Submodule.isSymmetricProjection_starProjection, LinearMap.mkContinuous_coe, isSelfAdjoint_toLinearMap_iff, VonNeumannAlgebra.IsStarProjection.mem_iff, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, ker_prod, sub_apply', PiTensorProduct.mapL_apply, LinearIsometryEquiv.submoduleMap_symm_apply_coe, Submodule.ker_subtypeL, Submodule.IsOrtho.comap_iff, InnerProductSpace.toMatrix_rankOne, ClosedSubmodule.toSubmodule_comap, InnerProductSpace.isSymmetric_rankOne_self, LinearEquiv.coe_toContinuousLinearEquiv, ProperCone.coe_map, ImplicitFunctionData.range_rightDeriv, range_mfderiv_coe_sphere, projKerOfRightInverse_comp_inv, Submodule.ker_starProjection, ContinuousMultilinearMap.ofSubsingleton_apply_toMultilinearMap, Matrix.linfty_opNorm_toMatrix, IsIdempotentElem.commute_iff_of_isUnit, coe_restrictScalarsL, Submodule.ker_orthogonalProjection, IsIdempotentElem.range_mem_invtSubmodule_iff, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, ContinuousLinearEquiv.submoduleMap_symm_apply, Complex.imCLM_coe, orthogonal_range, WithLp.coe_sndL, IsIdempotentElem.commute_iff, isPositive_iff, IsSelfAdjoint.hasEigenvector_of_isMinOn, coeLMₛₗ_apply, IsIdempotentElem.range_mem_invtSubmodule, projKerOfRightInverse_apply_idem, toAddMonoidHom_completion, coe_proj, coe_neg, InnerProductSpace.toLinearMap_rankOne, cont, closed_range_of_antilipschitz, coe_sub, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, TopModuleCat.kerι_apply, ContinuousLinearEquiv.submoduleMap_apply, IsSelfAdjoint.hasEigenvector_of_isLocalExtrOn, IsCoercive.ker_eq_bot, ker_prod_ker_le_ker_coprod, RCLike.imCLM_coe, isStarProjection_iff_eq_starProjection_range, EuclideanGeometry.orthogonalProjection_linear, ContinuousLinearEquiv.ofSubmodule'_symm_apply, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, completeSpace_ker, coe_sum, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, coe_fst, coe_inl, coe_le_coe_iff, IsStarProjection.isSymmetricProjection, coe_prodMap, AntilipschitzWith.completeSpace_range_clm, LinearMap.coe_toContinuousLinearMap_symm, Submodule.orthogonal_eq_inter, coe_injective, LinearMap.clmOfExistsBoundedImage_coe, coe_eq_id, RCLike.ofRealCLM_coe, ProbabilityTheory.isPositive_covarianceOperator, coe_smulRight, coe_mk, Submodule.starProjection_coe_eq_isCompl_projection, algebraMapCLM_toLinearMap, IsIdempotentElem.hasOrthogonalProjection_range, coe_smul, apply_val_ker, bijective_iff_dense_range_and_antilipschitz, range_coprod, coe_id, BoundedContinuousFunction.range_toLp, ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap, ContinuousLinearEquiv.fst_equivOfRightInverse, coe_ofIsClosedGraph, Submodule.coe_subtypeL, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, coe_prod, LinearMap.canLiftContinuousLinearMap, ContinuousLinearEquiv.equivOfRightInverse_symm_apply, InnerProductSpace.symm_toEuclideanLin_rankOne, IsIdempotentElem.ker_mem_invtSubmodule_iff, IsCoercive.isClosed_range, isOpen_setOf_nat_le_rank, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, orthogonal_ker, LinearMap.ker_toContinuousLinearMap, coe_zero, mkOfIsCompactOperator_to_linearMap, LinearIsometryEquiv.submoduleMap_apply_coe
toLinearMapRingHom 📖	CompOp	1 math math: toLinearMapRingHom_apply
toSpanSingleton 📖	CompOp	53 math math: toSpanSingleton_zero, Complex.restrictScalars_one_smulRight', smulRight_one_eq_toSpanSingleton, derivWithin_fderivWithin, smulRight_one_pow, hasFDerivWithinAt_inv, toSpanSingleton_apply, toSpanSingleton_apply_one, HasDerivWithinAt.hasFDerivWithinAt, one_smulRight_eq_toSpanSingleton, deriv_fderiv, norm_toSpanSingleton, nnnorm_toSpanSingleton, HasDerivAt.hasFDerivAt, toSpanSingleton_apply_map_one, hasDerivWithinAt_iff_hasFDerivWithinAt, toSpanSingleton_pow, toSpanSingleton_smul, det_toSpanSingleton, toSpanSingleton_comp, toSpanSingletonLE_apply, Complex.restrictScalars_one_smulRight, HasStrictDerivAt.hasStrictFDerivAt, toLinearMap_toSpanSingleton, hasStrictFDerivAt_inv, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, fderiv_inv, hasDerivAt_iff_hasFDerivAt, InnerProductSpace.rankOne_def', toSpanSingleton_one, Complex.restrictScalars_toSpanSingleton, toSpanSingleton_comp_toSpanSingleton, adjoint_toSpanSingleton, toSpanSingleton_derivWithin, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, toSpanSingleton_add, fderivWithin_inv, det_one_smulRight, toSpanSingleton_deriv, comp_lsmul_flip_apply, toSpanSingleton_one_eq_algebraMapCLM, smulRight_one_eq_iff, smulRight_id, smulRight_one_one, toSpanSingleton_smul', lsmul_flip_apply, hasStrictDerivAt_iff_hasStrictFDerivAt, toSpanSingleton_inj, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, hasFDerivAt_inv, adjoint_innerSL_apply, comp_toSpanSingleton, Complex.restrictScalars_toSpanSingleton'
toSpanSingletonLE 📖	CompOp	2 math math: toSpanSingletonLE_apply, toSpanSingletonLE_symm_apply
uniqueOfLeft 📖	CompOp	—
uniqueOfRight 📖	CompOp	—
zero 📖	CompOp	160 math math: toSpanSingleton_zero, TopModuleCat.hom_zero, fderivWithin_ofNat, Submodule.IsOrtho.starProjection_comp_starProjection, fderiv_intCast, fderivWithin_one, hasFDerivWithinAt_const, hasFDerivAt_one, ContinuousAffineMap.const_contLinear, fderivWithin_zero_of_not_accPt, DoubleCentralizer.zero_snd, nhds_zero_eq_of_basis, CurveIntegrable.zero, Submodule.starProjection_comp_starProjection_eq_zero_iff, coe_zero', IsLocalMax.fderiv_eq_zero, Pretrivialization.continuousLinearMap_symm_apply', hasBasis_nhds_zero, fderivWithin_intCast, HasFDerivAt.of_notMem_tsupport, fderiv_ofNat, fderivWithin_zero, hasStrictFDerivAt_natCast, hasFDerivAtFilter_ofNat, hasFDerivAtFilter_zero, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, Submodule.orthogonalProjection_bot, HasCompactSupport.fderiv, hasFDerivWithinAt_intCast, ProbabilityTheory.covarianceOperator_zero, curveIntegral_fun_zero, hasFDerivAtFilter_const, HasFDerivWithinAt.of_notMem_tsupport, IsLocalExtr.fderiv_eq_zero, hasFDerivAt_of_subsingleton, Pretrivialization.continuousLinearMapCoordChange_apply, HasStrictFDerivAt.of_notMem_tsupport, isInvertible_zero_iff, pi_eq_zero, ProbabilityTheory.covarianceBilin_zero, InnerProductSpace.rankOne_eq_zero, fderiv_one, toContinuousAddMonoidHom_zero, ProbabilityTheory.covarianceBilinDual_zero, NormedSpace.polar_ball_subset_closedBall_div, compContinuousLinearMap_zero, MeasureTheory.weightedSMul_empty, bilinearComp_zero_right, nonneg_iff_isPositive, MeasureTheory.weightedSMul_null, CurveIntegrable.fun_zero, fderiv_mem_iff, zero_comp, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, IsLocalMax.hasFDerivAt_eq_zero, eventually_nhds_zero_mapsTo, hasFDerivWithinAt_one, InnerProductSpace.continuousLinearMapOfBilin_zero, hasFDerivAt_ofNat, BoundedContinuousFunction.probCharDual_zero, hasFDerivWithinAt_zero, hasFDerivWithinAt_singleton, ContinuousAffineMap.contLinear_eq_zero_iff_exists_const, fderivWithin_zero_of_notMem_closure, hasStrictFDerivAt_zero, Submodule.starProjection_bot, fderivWithin_const, fderiv_natCast, fderiv_const, hasMFDerivAt_const, hasFDerivAt_single, isVonNBounded_iff, mfderivWithin_zero_of_not_mdifferentiableWithinAt, curveIntegralFun_fun_zero, bilinearComp_zero, inverse_zero, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, DoubleCentralizer.zero_fst, default_def, fderiv_update, hasFDerivAt_zero_of_eventually_const, hasFDerivAt_const, Asymptotics.IsBigO.hasFDerivWithinAt, mfderivWithin_const, StrongDual.polar_univ, ContinuousAlternatingMap.curryLeft_zero, fderivWithin_fun_const, hasMFDerivWithinAt_const, restrictScalars_zero, hasFDerivAt_update, fst_comp_inr, fderiv_zero_of_not_differentiableAt, opNorm_zero, curveIntegral_zero, hasBasis_nhds_zero_of_basis, tsupport_fderiv_subset, SchwartzMap.tsupport_fderivCLM_subset, opNorm_zero_iff, mfderiv_zero_of_not_mdifferentiableAt, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, hasFDerivWithinAt_natCast, fderivWithin_natCast, NormedSpace.polar_ball, MeasureTheory.L1.SimpleFunc.setToL1S_zero_left, ProbabilityTheory.covarianceBilin_of_not_memLp, comp_zero, hasStrictFDerivAt_one, NormedSpace.sInter_polar_eq_closedBall, hasFDerivAt_natCast, hasFDerivAt_intCast, fderiv_zero, nhds_zero_eq, DoubleCentralizer.zero_toProd, inverse_of_not_isInvertible, bilinearComp_zero_left, hasFDerivWithinAt_ofNat, extend_zero, StrongDual.zero_mem_polar, hasStrictFDerivAt_ofNat, ProbabilityTheory.uncenteredCovarianceBilin_zero, mfderiv_const, hasStrictFDerivAt_list_prod, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, IsLocalMin.hasFDerivAt_eq_zero, snd_comp_inl, fderivWithin_const_apply, norm_sub_le_mul_volume_of_norm_fderiv_le, NormedSpace.closedBall_inv_subset_polar_closedBall, hasFDerivAt_zero, flip_zero, isPositive_zero, hasFDerivAtFilter_natCast, jacobiTheta₂_fderiv_undef, fderiv_of_notMem_tsupport, hasStrictFDerivAt_const, IsLocalMin.fderiv_eq_zero, fderivWithin_zero_of_not_differentiableWithinAt, NormedSpace.polar_closedBall, fderivWithin_def, support_fderiv_subset, fderiv_fun_const, pi_zero, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, hasFDerivWithinAt_of_subsingleton, MeasureTheory.condExpInd_empty, hasStrictFDerivAt_intCast, ContinuousAffineMap.zero_contLinear, MeasureTheory.weightedSMul_zero_measure, IsLocalExtr.hasFDerivAt_eq_zero, fderiv_single, fderivWithin_mem_iff, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, zero_apply, ProbabilityTheory.covarianceOperator_of_not_memLp, fderiv_const_apply, Asymptotics.IsBigO.hasFDerivAt, coe_zero, curveIntegralFun_zero, hasFDerivAtFilter_intCast, hasFDerivAtFilter_one
«term_∘L_» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
add_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike add AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup	—	—
add_comp 📖	mathematical	—	comp ContinuousLinearMap add	—	ext
algebraMap_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid funLike RingHom CommSemiring.toSemiring semiring IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup RingHom.instFunLike algebraMap algebra SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction	—	IsTopologicalAddGroup.toContinuousAdd
applyFaithfulSMul 📖	mathematical	—	FaithfulSMul ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid monoidWithZero Module.toDistribMulAction semiring applyModule	—	ext
applySMulCommClass 📖	mathematical	—	SMulCommClass ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction monoidWithZero semiring applyModule	—	map_smul
applySMulCommClass' 📖	mathematical	—	SMulCommClass ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid monoidWithZero Module.toDistribMulAction semiring applyModule Semiring.toMonoidWithZero	—	map_smul SemilinearMapClass.toMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
apply_val_ker 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike Submodule SetLike.instMembership Submodule.setLike LinearMap.ker toLinearMap AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid	—	—
cancel_left 📖	—	DFunLike.coe ContinuousLinearMap funLike comp	—	—	ext
closedComplemented_ker_of_rightInverse 📖	mathematical	DFunLike.coe ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid funLike	Submodule.ClosedComplemented LinearMap.ker toLinearMap	—	RingHomInvPair.ids projKerOfRightInverse_apply_idem
coeFn_injective 📖	mathematical	—	ContinuousLinearMap DFunLike.coe funLike	—	DFunLike.coe_injective
coeLM_apply 📖	mathematical	—	DFunLike.coe LinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap addCommMonoid LinearMap.addCommMonoid module LinearMap.module LinearMap.instFunLike coeLM toLinearMap	—	—
coeLMₛₗ_apply 📖	mathematical	—	DFunLike.coe LinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap addCommMonoid LinearMap.addCommMonoid module LinearMap.module LinearMap.instFunLike coeLMₛₗ toLinearMap	—	—
coe_add 📖	mathematical	—	toLinearMap ContinuousLinearMap add LinearMap LinearMap.instAdd	—	—
coe_add' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike add Pi.instAdd AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup	—	—
coe_codRestrict 📖	mathematical	Submodule SetLike.instMembership Submodule.setLike DFunLike.coe ContinuousLinearMap funLike	toLinearMap instTopologicalSpaceSubtype Submodule.addCommMonoid Submodule.module codRestrict LinearMap.codRestrict	—	—
coe_codRestrict_apply 📖	mathematical	Submodule SetLike.instMembership Submodule.setLike DFunLike.coe ContinuousLinearMap funLike	instTopologicalSpaceSubtype Submodule.addCommMonoid Submodule.module codRestrict	—	—
coe_coe 📖	mathematical	—	DFunLike.coe LinearMap LinearMap.instFunLike toLinearMap ContinuousLinearMap funLike	—	—
coe_comp 📖	mathematical	—	toLinearMap comp LinearMap.comp	—	—
coe_comp' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike comp	—	—
coe_copy 📖	mathematical	DFunLike.coe ContinuousLinearMap funLike	copy	—	—
coe_eq_id 📖	mathematical	—	toLinearMap RingHom.id Semiring.toNonAssocSemiring LinearMap.id id	—	coe_id
coe_id 📖	mathematical	—	toLinearMap RingHom.id Semiring.toNonAssocSemiring id LinearMap.id	—	—
coe_id' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike id	—	—
coe_inj 📖	mathematical	—	toLinearMap	—	coe_injective
coe_injective 📖	mathematical	—	ContinuousLinearMap LinearMap toLinearMap	—	—
coe_mk 📖	mathematical	Continuous AddHom.toFun AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup LinearMap.toAddHom	toLinearMap	—	—
coe_mk' 📖	mathematical	Continuous AddHom.toFun AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup LinearMap.toAddHom	DFunLike.coe ContinuousLinearMap funLike LinearMap LinearMap.instFunLike	—	—
coe_mul 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike instMul	—	—
coe_neg 📖	mathematical	—	toLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap neg LinearMap LinearMap.instNeg	—	—
coe_neg' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike neg Pi.instNeg NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	—
coe_pow 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike Monoid.toNatPow MonoidWithZero.toMonoid monoidWithZero Nat.iterate	—	hom_coe_pow
coe_projKerOfRightInverse_apply 📖	mathematical	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike	Submodule SetLike.instMembership Submodule.setLike LinearMap.ker toLinearMap RingHom.id Semiring.toNonAssocSemiring instTopologicalSpaceSubtype Submodule.addCommMonoid Submodule.module projKerOfRightInverse SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	—
coe_rangeRestrict 📖	mathematical	—	toLinearMap Submodule SetLike.instMembership Submodule.setLike LinearMap.range instTopologicalSpaceSubtype Submodule.addCommMonoid Submodule.module rangeRestrict LinearMap.rangeRestrict	—	—
coe_restrictScalars 📖	mathematical	—	toLinearMap RingHom.id Semiring.toNonAssocSemiring restrictScalars LinearMap.restrictScalars	—	—
coe_restrictScalars' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike restrictScalars	—	—
coe_restrictScalarsₗ 📖	mathematical	—	DFunLike.coe LinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap addCommMonoid module LinearMap.instFunLike restrictScalarsₗ restrictScalars	—	—
coe_smul 📖	mathematical	—	toLinearMap ContinuousLinearMap instSMul LinearMap LinearMap.instSMul	—	—
coe_smul' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike instSMul Function.hasSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass	—	—
coe_smulRight 📖	mathematical	—	toLinearMap RingHom.id Semiring.toNonAssocSemiring smulRight LinearMap.smulRight NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring	—	—
coe_smulRightₗ 📖	mathematical	—	DFunLike.coe LinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap addCommMonoid module LinearMap.instFunLike smulRightₗ smulRight	—	—
coe_sub 📖	mathematical	—	toLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap sub LinearMap LinearMap.instSub	—	—
coe_sub' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike sub Pi.instSub SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	—
coe_sum 📖	mathematical	—	toLinearMap Finset.sum ContinuousLinearMap addCommMonoid LinearMap LinearMap.addCommMonoid	—	map_sum AddMonoidHom.instAddMonoidHomClass
coe_sum' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike Finset.sum addCommMonoid Pi.addCommMonoid	—	coe_sum LinearMap.coe_sum Finset.sum_congr
coe_zero 📖	mathematical	—	toLinearMap ContinuousLinearMap zero LinearMap LinearMap.instZero	—	—
coe_zero' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike zero Pi.instZero AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid	—	—
comp_add 📖	mathematical	—	comp ContinuousLinearMap add	—	ext map_add SemilinearMapClass.toAddHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
comp_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike comp	—	—
comp_assoc 📖	mathematical	—	comp	—	—
comp_finset_sum 📖	mathematical	—	comp Finset.sum ContinuousLinearMap addCommMonoid	—	ext coe_sum' Finset.sum_apply map_sum DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass Finset.sum_congr
comp_id 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids id	—	ext RingHomCompTriple.ids
comp_neg 📖	mathematical	—	comp Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap neg	—	ext map_neg DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
comp_smul 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids ContinuousLinearMap instSMul DistribMulAction.toDistribSMul AddCommMonoid.toAddMonoid	—	ext RingHomCompTriple.ids map_smul_of_tower
comp_smulₛₗ 📖	mathematical	—	comp ContinuousLinearMap instSMul DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero AddCommMonoid.toAddMonoid Module.toDistribMulAction DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike	—	ext MulActionSemiHomClass.map_smulₛₗ SemilinearMapClass.toMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
comp_sub 📖	mathematical	—	comp Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap sub	—	ext map_sub DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
comp_toSpanSingleton 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule RingHomCompTriple.ids toSpanSingleton DFunLike.coe ContinuousLinearMap funLike	—	RingHomCompTriple.ids LinearMap.comp_toSpanSingleton
comp_zero 📖	mathematical	—	comp ContinuousLinearMap zero	—	ext map_zero AddMonoidHomClass.toZeroHomClass DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
completeSpace_eqLocus 📖	mathematical	—	CompleteSpace Submodule SetLike.instMembership Submodule.setLike LinearMap.eqLocus ContinuousLinearMap UniformSpace.toTopologicalSpace funLike ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass instUniformSpaceSubtype	—	IsClosed.completeSpace_coe ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass isClosed_eq ContinuousMapClass.map_continuous ContinuousSemilinearMapClass.toContinuousMapClass
completeSpace_ker 📖	mathematical	—	CompleteSpace Submodule SetLike.instMembership Submodule.setLike LinearMap.ker toLinearMap UniformSpace.toTopologicalSpace instUniformSpaceSubtype	—	IsComplete.completeSpace_coe isComplete_ker
cont 📖	mathematical	—	Continuous AddHom.toFun AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup LinearMap.toAddHom toLinearMap	—	—
continuous 📖	mathematical	—	Continuous DFunLike.coe ContinuousLinearMap funLike	—	cont
continuousConstSMul_apply 📖	mathematical	—	ContinuousConstSMul ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid monoidWithZero Module.toDistribMulAction semiring applyModule	—	continuous
continuousSemilinearMapClass 📖	mathematical	—	ContinuousSemilinearMapClass ContinuousLinearMap funLike	—	map_add SemilinearMapClass.toAddHomClass LinearMap.semilinearMapClass LinearMap.map_smul' cont
copy_eq 📖	mathematical	DFunLike.coe ContinuousLinearMap funLike	copy	—	DFunLike.ext'
default_def 📖	mathematical	—	ContinuousLinearMap inhabited zero	—	—
eqOn_closure_span 📖	mathematical	Set.EqOn DFunLike.coe ContinuousLinearMap funLike	closure SetLike.coe Submodule Submodule.setLike Submodule.span	—	Set.EqOn.closure LinearMap.eqOn_span' continuous
exists_ne_zero 📖	—	—	—	—	ext
ext 📖	—	DFunLike.coe ContinuousLinearMap funLike	—	—	DFunLike.ext
ext_iff 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike	—	ext
ext_on 📖	—	Dense SetLike.coe Submodule Submodule.setLike Submodule.span Set.EqOn DFunLike.coe ContinuousLinearMap funLike	—	—	ext eqOn_closure_span
ext_ring 📖	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	—	LinearMap.ext_ring
ext_ring_iff 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	ext_ring
finset_sum_comp 📖	mathematical	—	comp Finset.sum ContinuousLinearMap addCommMonoid	—	ext coe_sum' Finset.sum_apply Finset.sum_congr
id_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike id	—	—
id_comp 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.right_ids id	—	ext RingHomCompTriple.right_ids
instNontrivialId 📖	mathematical	—	Nontrivial ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring	—	exists_ne DFunLike.congr_fun
intCast_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid funLike AddGroupWithOne.toIntCast Ring.toAddGroupWithOne ring SubNegMonoid.toZSMul AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	—
isCentralScalar 📖	mathematical	—	IsCentralScalar ContinuousLinearMap instSMul DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero AddCommMonoid.toAddMonoid Module.toDistribMulAction MulOpposite MulOpposite.instMonoid MulOpposite.instSemiring SMulCommClass.op_right SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass ContinuousConstSMul.op	—	SMulCommClass.op_right ContinuousConstSMul.op ext IsCentralScalar.op_smul_eq_smul
isClosed_ker 📖	mathematical	—	IsClosed SetLike.coe Submodule Submodule.setLike LinearMap.ker toLinearMap	—	continuous_iff_isClosed ContinuousMapClass.map_continuous ContinuousSemilinearMapClass.toContinuousMapClass continuousSemilinearMapClass isClosed_singleton
isComplete_ker 📖	mathematical	—	IsComplete SetLike.coe Submodule Submodule.setLike LinearMap.ker toLinearMap UniformSpace.toTopologicalSpace	—	IsClosed.isComplete isClosed_ker
isIdempotentElem_toLinearMap_iff 📖	mathematical	—	IsIdempotentElem LinearMap RingHom.id Semiring.toNonAssocSemiring Module.End.instMul toLinearMap ContinuousLinearMap instMul	—	RingHomCompTriple.ids
isOpenMap_of_ne_zero 📖	mathematical	—	IsOpenMap DFunLike.coe StrongDual DivisionSemiring.toSemiring DivisionRing.toDivisionSemiring AddCommGroup.toAddCommMonoid funLike RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule	—	exists_ne_zero IsOpenMap.of_sections Continuous.continuousAt Continuous.fun_add continuous_const Continuous.smul Continuous.sub continuous_id' sub_self zero_smul add_zero map_add SemilinearMapClass.toAddHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass map_smul SemilinearMapClass.toMulActionSemiHomClass inv_mul_cancel₀ mul_one add_sub_cancel
isScalarTower 📖	mathematical	—	IsScalarTower ContinuousLinearMap instSMul	—	ext smul_assoc
ker_codRestrict 📖	mathematical	Submodule SetLike.instMembership Submodule.setLike DFunLike.coe ContinuousLinearMap funLike	LinearMap.ker Submodule.addCommMonoid Submodule.module toLinearMap instTopologicalSpaceSubtype codRestrict	—	LinearMap.ker_codRestrict
leftInverse_of_comp 📖	mathematical	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids id	DFunLike.coe ContinuousLinearMap funLike	—	RingHomCompTriple.ids
map_add 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup	—	map_add SemilinearMapClass.toAddHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
map_neg 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	map_neg DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
map_smul 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction	—	MulActionSemiHomClass.map_smulₛₗ SemilinearMapClass.toMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
map_smul_of_tower 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike	—	LinearMap.CompatibleSMul.map_smul
map_smulₛₗ 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction RingHom Semiring.toNonAssocSemiring RingHom.instFunLike	—	LinearMap.map_smulₛₗ
map_sub 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	map_sub DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
map_zero 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid	—	map_zero AddMonoidHomClass.toZeroHomClass DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
mul_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike instMul	—	—
mul_def 📖	mathematical	—	ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring instMul comp RingHomCompTriple.ids	—	—
natCast_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike instNatCast AddMonoid.toNatSMul AddCommMonoid.toAddMonoid	—	—
neg_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike neg NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	—
neg_comp 📖	mathematical	—	comp Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap neg	—	ext
ofNat_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike AddMonoid.toNatSMul AddCommMonoid.toAddMonoid	—	—
one_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike one	—	—
one_def 📖	mathematical	—	ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring one id	—	—
one_smulRight_eq_toSpanSingleton 📖	mathematical	—	smulRight NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Semiring.toModule IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction ContinuousLinearMap RingHom.id one toSpanSingleton	—	smulRight_one_eq_toSpanSingleton
projKerOfRightInverse_apply_idem 📖	mathematical	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike	RingHom.id Semiring.toNonAssocSemiring Submodule SetLike.instMembership Submodule.setLike LinearMap.ker toLinearMap instTopologicalSpaceSubtype Submodule.addCommMonoid Submodule.module projKerOfRightInverse	—	apply_val_ker map_zero AddMonoidHomClass.toZeroHomClass DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass sub_zero
projKerOfRightInverse_comp_inv 📖	mathematical	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike	RingHom.id Semiring.toNonAssocSemiring Submodule SetLike.instMembership Submodule.setLike LinearMap.ker toLinearMap instTopologicalSpaceSubtype Submodule.addCommMonoid Submodule.module projKerOfRightInverse Submodule.zero	—	sub_self
range_coeFn_eq 📖	mathematical	—	Set.range ContinuousLinearMap DFunLike.coe funLike Set Set.instInter setOf Continuous LinearMap LinearMap.instFunLike	—	Set.ext continuous
range_smulRight_apply 📖	mathematical	—	LinearMap.range DivisionSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomSurjective.ids toLinearMap smulRight Semiring.toModule IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction Submodule.span Set Set.instSingletonSet	—	LinearMap.range_smulRight_apply
restrictScalars_add 📖	mathematical	—	restrictScalars ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring add	—	—
restrictScalars_neg 📖	mathematical	—	restrictScalars Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring neg	—	—
restrictScalars_smul 📖	mathematical	—	restrictScalars ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring instSMul DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero AddCommMonoid.toAddMonoid Module.toDistribMulAction	—	—
restrictScalars_sub 📖	mathematical	—	restrictScalars Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring sub	—	—
restrictScalars_zero 📖	mathematical	—	restrictScalars ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring zero	—	—
rightInverse_of_comp 📖	mathematical	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids id	DFunLike.coe ContinuousLinearMap funLike	—	RingHomCompTriple.ids leftInverse_of_comp
smulCommClass 📖	mathematical	—	SMulCommClass ContinuousLinearMap instSMul	—	ext SMulCommClass.smul_comm
smulRight_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike smulRight SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring	—	—
smulRight_comp 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids smulRight Semiring.toModule IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul DFunLike.coe ContinuousLinearMap NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring funLike	—	smulRight_comp_smulRight
smulRight_comp_smulRight 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids smulRight Semiring.toModule IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul DFunLike.coe ContinuousLinearMap NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring funLike	—	ext RingHomCompTriple.ids IsScalarTower.left map_smul SemilinearMapClass.toMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass
smulRight_id 📖	mathematical	—	smulRight NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Semiring.toModule IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction id toSpanSingleton	—	IsScalarTower.left
smulRight_one_eq_iff 📖	mathematical	—	toSpanSingleton	—	—
smulRight_one_eq_toSpanSingleton 📖	mathematical	—	smulRight NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Semiring.toModule IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction ContinuousLinearMap RingHom.id one toSpanSingleton	—	IsScalarTower.left
smulRight_one_one 📖	mathematical	—	toSpanSingleton DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	toSpanSingleton_apply_map_one
smulRight_one_pow 📖	mathematical	—	ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing Semiring.toModule Monoid.toNatPow MonoidWithZero.toMonoid monoidWithZero toSpanSingleton ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring	—	toSpanSingleton_pow
smul_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike instSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass	—	—
smul_comp 📖	mathematical	—	comp ContinuousLinearMap instSMul DistribMulAction.toDistribSMul AddCommMonoid.toAddMonoid	—	—
smul_def 📖	mathematical	—	ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid monoidWithZero Module.toDistribMulAction semiring applyModule DFunLike.coe funLike	—	—
sub_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike sub SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	—
sub_apply' 📖	mathematical	—	DFunLike.coe LinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid LinearMap.instFunLike LinearMap.instSub toLinearMap SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup ContinuousLinearMap funLike	—	—
sub_comp 📖	mathematical	—	comp Ring.toSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap sub	—	ext
sum_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike Finset.sum addCommMonoid	—	coe_sum' Finset.sum_apply
toContinuousAddMonoidHom_add 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousLinearMap funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass add ContinuousAddMonoidHom AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup ContinuousAddMonoidHom.instAddCommMonoid	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toContinuousAddMonoidHom_comp 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousLinearMap funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass comp ContinuousAddMonoidHom.comp	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toContinuousAddMonoidHom_id 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass id ContinuousAddMonoidHom.id	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toContinuousAddMonoidHom_inj 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousLinearMap funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass toContinuousAddMonoidHom_injective
toContinuousAddMonoidHom_injective 📖	mathematical	—	ContinuousLinearMap ContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousAddMonoidHom.toContinuousAddMonoidHom funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass Function.Injective.of_comp_iff DFunLike.coe_injective
toContinuousAddMonoidHom_neg 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass neg ContinuousAddMonoidHom NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid ContinuousAddMonoidHom.instAddCommGroup	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toContinuousAddMonoidHom_restrictScalars 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass restrictScalars	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toContinuousAddMonoidHom_sub 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup ContinuousLinearMap Ring.toSemiring AddCommGroup.toAddCommMonoid funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass sub ContinuousAddMonoidHom SubNegMonoid.toSub ContinuousAddMonoidHom.instAddCommGroup	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toContinuousAddMonoidHom_zero 📖	mathematical	—	ContinuousAddMonoidHom.toContinuousAddMonoidHom AddCommMonoid.toAddMonoid ContinuousLinearMap funLike DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom Semiring.toNonAssocSemiring RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass zero ContinuousAddMonoidHom ContinuousAddMonoidHom.instZero	—	DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass ContinuousSemilinearMapClass.toContinuousMapClass
toLinearMapRingHom_apply 📖	mathematical	—	DFunLike.coe RingHom ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring LinearMap semiring Module.End.instSemiring RingHom.instFunLike toLinearMapRingHom toLinearMap	—	—
toLinearMap_toSpanSingleton 📖	mathematical	—	toLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule toSpanSingleton LinearMap.toSpanSingleton	—	—
toSpanSingletonLE_apply 📖	mathematical	—	DFunLike.coe LinearEquiv RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids ContinuousLinearMap NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule addCommMonoid module EquivLike.toFunLike LinearEquiv.instEquivLike toSpanSingletonLE toSpanSingleton	—	RingHomInvPair.ids
toSpanSingletonLE_symm_apply 📖	mathematical	—	DFunLike.coe LinearEquiv RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids ContinuousLinearMap NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule addCommMonoid module EquivLike.toFunLike LinearEquiv.instEquivLike LinearEquiv.symm toSpanSingletonLE funLike AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	RingHomInvPair.ids
toSpanSingleton_add 📖	mathematical	—	toSpanSingleton AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule add	—	LinearMap.toSpanSingleton_add
toSpanSingleton_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike toSpanSingleton SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction	—	—
toSpanSingleton_apply_map_one 📖	mathematical	—	toSpanSingleton DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	ext_ring LinearMap.IsScalarTower.compatibleSMul' IsScalarTower.left mul_one
toSpanSingleton_apply_one 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike toSpanSingleton AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	one_smul
toSpanSingleton_comp 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule RingHomCompTriple.ids toSpanSingleton smulRight IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction	—	RingHomCompTriple.ids
toSpanSingleton_comp_toSpanSingleton 📖	mathematical	—	comp RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule RingHomCompTriple.ids toSpanSingleton ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Module.toDistribMulAction	—	smulRight_comp_smulRight ContinuousMul.to_continuousSMul
toSpanSingleton_inj 📖	mathematical	—	toSpanSingleton	—	one_smul
toSpanSingleton_one 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule funLike toSpanSingleton AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	toSpanSingleton_apply_one
toSpanSingleton_pow 📖	mathematical	—	ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing Semiring.toModule Monoid.toNatPow MonoidWithZero.toMonoid monoidWithZero toSpanSingleton ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring	—	ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring ext_ring pow_zero toSpanSingleton.congr_simp mul_one pow_succ RingHomCompTriple.ids mul_def toSpanSingleton_comp_toSpanSingleton smul_eq_mul pow_succ'
toSpanSingleton_smul 📖	mathematical	—	toSpanSingleton SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule instSMul	—	LinearMap.toSpanSingleton_smul
toSpanSingleton_smul' 📖	mathematical	—	toSpanSingleton SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule instSMul	—	toSpanSingleton_smul
toSpanSingleton_zero 📖	mathematical	—	toSpanSingleton AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule zero	—	ext_ring smul_zero
uniformContinuous 📖	mathematical	—	UniformContinuous DFunLike.coe ContinuousLinearMap UniformSpace.toTopologicalSpace AddCommGroup.toAddCommMonoid funLike	—	uniformContinuous_addMonoidHom_of_continuous DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass continuousSemilinearMapClass continuous
zero_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap funLike zero AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid	—	—
zero_comp 📖	mathematical	—	comp ContinuousLinearMap zero	—	ext

ContinuousLinearMap.IsIdempotentElem

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
commute_iff 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul	Commute Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.range RingHomSurjective.ids LinearMap.ker	—	RingHomSurjective.ids RingHomCompTriple.ids LinearMap.IsIdempotentElem.commute_iff toLinearMap
commute_iff_of_isUnit 📖	mathematical	IsUnit ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid MonoidWithZero.toMonoid ContinuousLinearMap.monoidWithZero IsIdempotentElem ContinuousLinearMap.instMul	Commute Submodule.map RingHomSurjective.ids ContinuousLinearMap.toLinearMap LinearMap.range LinearMap.ker	—	IsTopologicalAddGroup.toContinuousAdd IsUnit.map MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass RingHom.instRingHomClass RingHomSurjective.ids CanLift.prf instCanLiftUnitsValIsUnit RingHomCompTriple.ids LinearMap.IsIdempotentElem.commute_iff_of_isUnit toLinearMap
conj_eq_of_ker_mem_invtSubmodule 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.ker	ContinuousLinearMap.comp RingHomCompTriple.ids	—	RingHomCompTriple.ids ker_mem_invtSubmodule_iff
conj_eq_of_range_mem_invtSubmodule 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.range RingHomSurjective.ids	ContinuousLinearMap.comp RingHomCompTriple.ids	—	RingHomSurjective.ids RingHomCompTriple.ids range_mem_invtSubmodule_iff
ext 📖	—	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul LinearMap.range RingHomSurjective.ids ContinuousLinearMap.toLinearMap LinearMap.ker	—	—	RingHomSurjective.ids ext_iff
ext_iff 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul	LinearMap.range RingHomSurjective.ids ContinuousLinearMap.toLinearMap LinearMap.ker	—	RingHomSurjective.ids LinearMap.IsIdempotentElem.ext_iff toLinearMap
isClosed_range 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul	IsClosed SetLike.coe Submodule Submodule.setLike LinearMap.range RingHomSurjective.ids ContinuousLinearMap.toLinearMap	—	ContinuousLinearMap.isClosed_ker RingHomSurjective.ids LinearMap.IsIdempotentElem.range_eq_ker toLinearMap
ker_eq_range 📖	mathematical	IsIdempotentElem LinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid Module.End.instMul	LinearMap.ker LinearMap.range RingHomSurjective.ids LinearMap.instSub LinearMap.id	—	LinearMap.IsIdempotentElem.ker_eq_range
ker_mem_invtSubmodule 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul ContinuousLinearMap.comp RingHomCompTriple.ids	Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.ker	—	RingHomCompTriple.ids ker_mem_invtSubmodule_iff
ker_mem_invtSubmodule_iff 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul	Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.ker ContinuousLinearMap.comp RingHomCompTriple.ids	—	RingHomCompTriple.ids LinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iff toLinearMap
range_eq_ker 📖	mathematical	IsIdempotentElem LinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid Module.End.instMul	LinearMap.range RingHomSurjective.ids LinearMap.ker LinearMap.instSub LinearMap.id	—	LinearMap.IsIdempotentElem.range_eq_ker
range_mem_invtSubmodule 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul ContinuousLinearMap.comp RingHomCompTriple.ids	Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.range RingHomSurjective.ids	—	RingHomSurjective.ids RingHomCompTriple.ids range_mem_invtSubmodule_iff
range_mem_invtSubmodule_iff 📖	mathematical	IsIdempotentElem ContinuousLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.instMul	Submodule Sublattice ConditionallyCompleteLattice.toLattice CompleteLattice.toConditionallyCompleteLattice Submodule.completeLattice SetLike.instMembership Sublattice.instSetLike Module.End.invtSubmodule ContinuousLinearMap.toLinearMap LinearMap.range RingHomSurjective.ids ContinuousLinearMap.comp RingHomCompTriple.ids	—	RingHomSurjective.ids RingHomCompTriple.ids LinearMap.IsIdempotentElem.range_mem_invtSubmodule_iff toLinearMap
toLinearMap 📖	mathematical	IsIdempotentElem ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.instMul	LinearMap Module.End.instMul ContinuousLinearMap.toLinearMap	—	ContinuousLinearMap.isIdempotentElem_toLinearMap_iff

ContinuousLinearMap.Simps

Definitions

Name	Category	Theorems
apply 📖	CompOp	—

ContinuousSemilinearMapClass

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
toContinuousMapClass 📖	mathematical	—	ContinuousMapClass	—	—
toSemilinearMapClass 📖	mathematical	—	SemilinearMapClass	—	—

DenseRange

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
topologicalClosure_map_submodule 📖	mathematical	DenseRange DFunLike.coe ContinuousLinearMap ContinuousLinearMap.funLike Submodule.topologicalClosure ContinuousSMul.continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction Top.top Submodule Submodule.instTop	Submodule.map ContinuousLinearMap.toLinearMap	—	ContinuousSMul.continuousConstSMul SetLike.ext'_iff dense_image ContinuousLinearMap.continuous

StrongDual

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
dualPairing_apply 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule LinearMap.instFunLike ContinuousLinearMap ContinuousLinearMap.addCommMonoid LinearMap.addCommMonoid ContinuousLinearMap.module Algebra.to_smulCommClass Algebra.id LinearMap.module topDualPairing ContinuousLinearMap.funLike	—	topDualPairing_apply

Submodule

Definitions

Name	Category	Theorems
ClosedComplemented 📖	MathDef	9 math math: closedComplemented_top, ContinuousLinearMap.closedComplemented_ker_of_rightInverse, closedComplemented_bot, IsCompl.closedComplemented_of_isClosed, ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, ClosedComplemented.of_finiteDimensional, closedComplemented_iff_isClosed_exists_isClosed_isCompl, ClosedComplemented.of_quotient_finiteDimensional, ClosedComplemented.of_isCompl_isClosed
subtypeL 📖	CompOp	19 math math: subtypeₗᵢ_toContinuousLinearMap, coe_subtypeL', IsOrtho.orthogonalProjection_comp_subtypeL, coe_orthogonalDecomposition_symm, HasStrictFDerivAt.to_implicitFunctionOfComplemented, adjoint_subtypeL, range_subtypeL, norm_subtypeL, HasStrictFDerivAt.to_implicitFunction, ker_subtypeL, subtypeL_apply, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, adjoint_orthogonalProjection, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, orthogonalProjection_comp_subtypeL_eq_zero_iff, norm_subtypeL_le, coe_subtypeL, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap, hasFDerivAt_stereoInvFunAux_comp_coe

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
closedComplemented_bot 📖	mathematical	—	ClosedComplemented Bot.bot Submodule Ring.toSemiring AddCommGroup.toAddCommMonoid instBot	—	eq_zero_of_bot_submodule
closedComplemented_top 📖	mathematical	—	ClosedComplemented Top.top Submodule Ring.toSemiring AddCommGroup.toAddCommMonoid instTop	—	—
coe_subtypeL 📖	mathematical	—	ContinuousLinearMap.toLinearMap RingHom.id Semiring.toNonAssocSemiring Submodule SetLike.instMembership setLike instTopologicalSpaceSubtype addCommMonoid module subtypeL subtype	—	—
coe_subtypeL' 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring Submodule SetLike.instMembership setLike instTopologicalSpaceSubtype addCommMonoid module ContinuousLinearMap.funLike subtypeL LinearMap LinearMap.instFunLike subtype	—	—
ker_subtypeL 📖	mathematical	—	LinearMap.ker Submodule SetLike.instMembership setLike addCommMonoid module RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.toLinearMap instTopologicalSpaceSubtype subtypeL Bot.bot instBot	—	ker_subtype
range_subtypeL 📖	mathematical	—	LinearMap.range Submodule SetLike.instMembership setLike addCommMonoid module RingHom.id Semiring.toNonAssocSemiring RingHomSurjective.ids ContinuousLinearMap.toLinearMap instTopologicalSpaceSubtype subtypeL	—	range_subtype
subtypeL_apply 📖	mathematical	—	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring Submodule SetLike.instMembership setLike instTopologicalSpaceSubtype addCommMonoid module ContinuousLinearMap.funLike subtypeL	—	—
topologicalClosure_map 📖	mathematical	—	Submodule Preorder.toLE PartialOrder.toPreorder instPartialOrder map ContinuousLinearMap.toLinearMap topologicalClosure ContinuousSMul.continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction	—	image_closure_subset_closure_image ContinuousLinearMap.continuous

Submodule.ClosedComplemented

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exists_isClosed_isCompl 📖	mathematical	Submodule.ClosedComplemented	IsClosed SetLike.coe Submodule Ring.toSemiring AddCommGroup.toAddCommMonoid Submodule.setLike IsCompl Submodule.instPartialOrder CompleteLattice.toBoundedOrder Submodule.completeLattice	—	ContinuousLinearMap.isClosed_ker LinearMap.isCompl_of_proj
isClosed 📖	mathematical	Submodule.ClosedComplemented	IsClosed SetLike.coe Submodule Ring.toSemiring AddCommGroup.toAddCommMonoid Submodule.setLike	—	RingHomCompTriple.ids LinearMap.ker_id_sub_eq_of_proj ContinuousLinearMap.isClosed_ker

(root)

Definitions

Name	Category	Theorems
ContinuousLinearMapClass 📖	MathDef	5 math math: LinearMap.continuousLinearMapClassOfFiniteDimensional, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, AlgHom.instContinuousLinearMapClassOfAlgHomClass, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, WeakDual.CharacterSpace.instContinuousLinearMapClass
ContinuousSemilinearMapClass 📖	CompData	5 math math: ContinuousSemilinearEquivClass.continuousSemilinearMapClass, SemilinearIsometryClass.toContinuousSemilinearMapClass, ContinuousLinearMap.continuousSemilinearMapClass, UniformConvergenceCLM.instContinuousSemilinearMapClass, ContinuousLinearMapWOT.instContinuousLinearMapClass
LinearMap 📖	CompData	5744 math math: AdicCompletion.of_surjective_iff, ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, Polynomial.fderiv, CliffordAlgebra.unop_reverseOp, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂, Pi.comul_eq_adjoint, DFinsupp.coprodMap_apply, MvPolynomial.pUnitAlgEquiv_symm_monomial, MvPowerSeries.coeff_zero_eq_constantCoeff_apply, LinearMap.det_toContinuousLinearMap, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, Polynomial.support_monomial, TensorProduct.finsuppRight_apply, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, CuspFormClass.qExpansion_isBigO, DFinsupp.comul_single, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, TensorProduct.mapInclIsometry_apply, IsSymmetricAlgebra.lift_eq, MvPowerSeries.hasSubst_def, Ideal.toCotangent_to_quotient_square, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, LinearMap.comp_toSpanSingleton, LinearMap.isSymm_zero, KaehlerDifferential.kerCotangentToTensor_toCotangent, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, Finset.weightedVSub_sdiff, Rep.resCoindHomEquiv_apply_hom, RootPairing.InvariantForm.apply_reflection_reflection, MvPolynomial.dvd_monomial_one_iff_exists, CliffordAlgebra.contractRight_algebraMap_mul, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr, LinearMap.restrictScalars_toMatrix, Submodule.starProjection_apply_eq_isComplProjection, Lagrange.interpolate_one, StarModule.decomposeProdAdjointL_symm_apply, Orientation.kahler_map_complex, ModuleCat.hom_zero, Algebra.normalizedTrace_map, RootPairing.rootForm_self_smul_coroot, CliffordAlgebra.toBaseChange_reverse, StarModule.selfAdjointPart_add_skewAdjointPart, ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, Polynomial.taylor_eval, AlgHom.coe_toLinearMap, ContinuousLinearMap.coe_add, Bialgebra.comulAlgHom_apply, TensorProduct.forall_vanishesTrivially_iff_forall_fg_rTensor_injective, LieDerivation.IsKilling.ad_mem_ker_killingForm_ad_range_of_mem_orthogonal, LinearMap.apply_symm_toPerfPair_self, LinearMap.SeparatingRight.toMatrix₂', PowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, ModuleCat.forget_preservesLimits, Matrix.toLinAlgEquiv_one, Bialgebra.comul_natCast, Finsupp.linearCombination_apply_of_mem_supported, LinearMap.inl_map_mul, PowerSeries.hasSum_aeval, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, RootPairing.RootPositiveForm.algebraMap_rootLength, Finset.weightedVSubOfPoint_map, Algebra.SubmersivePresentation.cotangentComplexAux_injective, SemimoduleCat.Hom.hom₂_apply, MeasureTheory.OuterMeasure.map_iInf, LinearMap.baseChange_eq_ltensor, Module.Flat.iff_lTensor_exact', Module.Basis.det_comp_basis, LinearMap.charpoly_def, Lagrange.eval_iterate_derivative_eq_sum, LinearEquiv.congrRight₂_refl, MonomialOrder.sPolynomial_leadingTerm_mul', iSupIndep.dfinsupp_lsum_injective, LinearMap.BilinForm.dualSubmoduleParing_spec, Polynomial.eraseLead_monomial, SymmetricAlgebra.lift_ι_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, CommRingCat.KaehlerDifferential.map_d, Submodule.FG.rTensor.directedSystem, Derivation.apply_eval_eq, ModuleCat.MonoidalCategory.braiding_hom_apply, PiTensorProduct.lift_reindex, Rep.coe_linearization_obj_ρ, MvPowerSeries.coeff_zero_eq_constantCoeff, LinearMap.BilinForm.zero_right, dot_self_cross, Finset.affineCombination_vsub, CliffordAlgebra.contractRight_algebraMap, Submodule.coe_continuous_linearProjOfClosedCompl', DFinsupp.lsum_lsingle, Matrix.toLin_kronecker, Lagrange.interpolate_eq_of_values_eq_on, Matrix.toLin'_symm, Orthonormal.inner_left_finsupp, ModuleCat.restrictScalars.map_apply, MvPolynomial.totalDegree_monomial, AlgEquiv.moduleEndSelfOp_apply_apply, Polynomial.derivative_X_sq, Matrix.SeparatingLeft.toBilin', LinearMap.detAux_def'', RootPairing.posRootForm_posForm_apply_apply, QuadraticMap.smul_toBilin, ModuleCat.forget₂_reflectsLimitsOfSize, TensorProduct.LieModule.liftLie_apply, PowerSeries.coeff_mul_one_sub_of_lt_order, LinearMap.BilinForm.dualSubmoduleToDual_apply_apply, IsLocalizedModule.liftOfLE_apply, Polynomial.smeval_monomial_mul, PiTensorProduct.lift.tprod, LinearMap.toAddMonoidHom_coe, Coalgebra.lTensor_counit_comul, CliffordAlgebra.contractRight_eq, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, LinearMap.toMatrixAlgEquiv'_mul, LinearMap.BilinForm.toMatrix_toBilin, Pretrivialization.linearMapAt_def_of_notMem, Submodule.comap_zero, Module.Basis.end_repr_apply, LinearMap.IsSymmetric.inner_map_polarization, Complex.coe_realPart, Polynomial.ofFn_zero, Algebra.Presentation.differentials.comm₁₂_single, CategoryTheory.Functor.mapExtLinearMap_toAddMonoidHom, Submodule.linearProjOfIsCompl_apply_left, MvPowerSeries.coeff_zero, LinearMap.coe_toSeminorm, MvPowerSeries.weightedOrder_monomial, Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker, AdicCompletion.mk_zero_of, MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum, LinearMap.adjoint_adjoint, Matrix.SeparatingRight.toLinearMap₂, LinearIsometry.coe_toLinearMap, PowerSeries.coeff_mul_of_lt_order, LinearMap.IsReflective.regular, taylorWithin_succ, LinearMap.BilinForm.symmCompOfNondegenerate_left_apply, PolyEquivTensor.toFunBilinear_apply_eq_sum, LinearMap.BilinForm.dualSubmoduleToDual_injective, Rep.MonoidalClosed.linearHomEquiv_symm_hom, MeasureTheory.Measure.addHaar_image_continuousLinearMap, groupCohomology.isoCocycles₁_hom_comp_i_apply, DFinsupp.lsingle_apply, Seminorm.continuous_of_continuous_comp, LinearMap.instIsTorsionFree, Module.Presentation.cokernelSolution_var, LinearMap.coe_mk, Polynomial.monomial_eq_monomial_iff, LinearMap.inr_apply, RootPairing.Polarization_apply, PolynomialModule.comp_single, PolynomialModule.map_lsingle, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_same, Polynomial.coeff_derivative, LinearMap.funLeft_id, LinearIsometryEquiv.coe_ofLinearIsometry_symm, PowerSeries.coeff_of_lt_order_toNat, PiTensorProduct.liftAlgHom_apply, groupCohomology.mem_cocycles₂_def, BilinForm.toMatrix_symm, PowerSeries.constantCoeff_subst, ExteriorAlgebra.ι_eq_algebraMap_iff, PowerSeries.WithPiTopology.continuous_coeff, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, SimpleGraph.lapMatrix_toLinearMap₂', LinearMap.coe_compAlternatingMap, LinearMap.pow_mulRight, groupHomology.coinfNatTrans_app, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, PowerSeries.coeff_mul_C, Module.FaithfullyFlat.iff_exact_iff_lTensor_exact, RootPairing.coroot_eq_polarizationEquiv_apply_root, IsGroupLikeElem.comul_eq_tmul_self, LinearMap.compAlternatingMap_apply, ModuleCat.forget_preservesLimitsOfSize, groupCohomology.d₂₃_hom_apply, Algebra.PreSubmersivePresentation.cotangentComplexAux_apply, MvPolynomial.degrees_monomial, LinearMap.Nondegenerate.congr, LinearMap.prodMap_one, CliffordAlgebraQuaternion.j_quaternionBasis, ExteriorAlgebra.ι_inj, dotProductEquiv_symm_apply, groupHomology.d₁₀_single_one, addMonoidHomLequivNat_symm_apply, DirectSum.component.of, Polynomial.hasseDeriv_zero', LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, Matrix.separatingRight_toLinearMap₂'_iff, LinearMap.baseChange_smul, realPart_idem, MvPolynomial.one_def, Algebra.Generators.H1Cotangent.δAux_mul, Complex.kahler, CliffordAlgebra.changeForm_comp_changeForm, CliffordAlgebra.mul_ι_mul_ι_of_isOrtho, MvPowerSeries.coeff_mul_monomial, LinearMap.convMul_def, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, Finsupp.restrictDom_apply, Lagrange.eval_interpolate_not_at_node', Complex.areaForm, QuadraticMap.sum_polar_sub_repr_sq, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, ModuleCat.forget₂PreservesColimitsOfSize, Matrix.det_smul_inv_mulVec_eq_cramer, LinearMap.map_add, LinearMap.zero_apply, Ideal.toCotangent_eq, CStarModule.innerₛₗ_apply, Module.Flat.toAlgebra_injective, Submodule.mulMap_tmul, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, Polynomial.derivWithin_aeval, Matrix.UnitaryGroup.toGL_mul, Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd, Finset.weightedVSubOfPoint_apply, PowerSeries.coeff_rescale, LinearMap.ker_eq_top, Profinite.NobelingProof.injective_πs', MvPolynomial.scalarRTensor_apply_monomial_tmul, AffineMap.hasDerivAtFilter, MvPolynomial.homogeneousComponent_eq_zero', QuadraticMap.canLift, Polynomial.derivative_intCast_mul, LinearMap.lTensor_sub, LinearMap.injective_iff_surjective_of_finrank_eq_finrank, Polynomial.toMatrix_sylvesterMap', LaurentPolynomial.comul_T, DirectSum.coe_toModule_eq_coe_toAddMonoid, Matrix.toLinearMapRight'_mul, eval_minpolyDiv_self, Algebra.normalizedTrace_surjective, LinearMap.IsPositive.ne_zero_iff, ContinuousLinearMap.toLinearMap₁₂_injective, Submodule.exists_fg_le_eq_rTensor_inclusion, Algebra.normalizedTrace_eq_of_finiteDimensional, Polynomial.disjoint_ker_aeval_of_isCoprime, SkewPolynomial.monomial_add, LinearMap.isPositive_adjoint_comp_self, LinearMap.BilinForm.IsAlt.neg_eq, Rep.diagonalSuccIsoFree_inv_hom_single, LinearMap.BilinMap.polar_toQuadraticMap, PolynomialModule.smul_def, LinearMap.mapMatrix_zero, LinearMap.isAdjointPair_iff_comp_eq_compl₂, LinearMap.IsPerfPair.bijective_left, MonomialOrder.degree_monomial, Module.End.isNilpotent_restrict_genEigenspace_nat, CategoryTheory.Functor.coe_mapLinearMap, Module.End.IsNilpotent.mapQ, LinearMap.exact_zero_iff_surjective, Matrix.separatingRight_toLinearMap₂_iff, Matrix.cramer_transpose_row_self, AdicCompletion.map_val_apply, PowerSeries.coeff_expand_mul, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, Representation.repOfTprodIso_apply, LinearMap.GeneralLinearGroup.congrLinearEquiv_refl, LinearMap.coe_semilinearMap, Polynomial.derivative_C_mul, ModuleCat.freeHomEquiv_apply, AffineSubspace.map_pointwise_vadd, Matrix.spectrum_toEuclideanLin, eval₂_minpolyDiv_self, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, LinearMap.rTensor_comm, Derivation.coe_to_linearMap_comp, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, RootPairing.Hom.root_weightMap, addMonoidHomLequivInt_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, ModuleCat.forget₂AddCommGroup_preservesLimitsOfSize, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Polynomial.iterate_derivative_zero, IsBaseChange.basis_repr_comp_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, LinearMap.range_neg, PiTensorProduct.ofDirectSumEquiv_tprod_lof, Submodule.linearMap_eq_zero_iff_of_eq_span, Trivialization.continuousLinearMapAt_apply, Module.Basis.toDual_linearCombination_left, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, PowerSeries.catalanSeries_coeff, AddMonoidHom.toZModLinearMap_injective, Module.Basis.constr_comp, Polynomial.card_rootSet_le_derivative, LinearEquiv.congrRight_symm, PowerSeries.coeff_X_mul_largeSchroderSeries, realPart_ofReal, Module.Basis.constr_symm_apply, LinearMap.mapMatrixLinear_apply, LightCondensed.forget_obj_val_map, Submodule.comap_neg, LinearMap.BilinForm.toMatrixAux_eq, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, PowerSeries.coeff_trunc, Algebra.Extension.H1Cotangent.equiv_apply, PolynomialModule.eval_map, LieModule.trace_toEnd_eq_zero_of_mem_lcs, CliffordAlgebra.involute_prod_map_ι, Polynomial.derivative_mul, IsAdjoinRootMonic.coeff_apply, PowerSeries.trunc_mul_trunc, Module.Relations.Solution.surjective_π_iff_span_eq_top, Matrix.toLinearMap₂'_comp, groupHomology.d₃₂_single, PiTensorProduct.lift_reindex_symm, DirectLimit.Module.of_f, Finset.weightedVSubOfPoint_insert, MeasureTheory.OuterMeasure.comap_map, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U, Module.FaithfullyFlat.lTensor_injective_iff_injective, ExteriorAlgebra.lift_symm_apply, Rep.coindToInd_of_support_subset_orbit, PiTensorProduct.map_reindex_symm, RootPairing.root_coroot_two, Representation.finsupp_apply, ModuleCat.extendScalarsId_hom_app_one_tmul, MvPolynomial.X_pow_eq_monomial, LinearMap.toMatrix_apply', Polynomial.opRingEquiv_op_monomial, Polynomial.natDegree_monomial_le, Module.Flat.iff_rTensor_preserves_injective_linearMap, Module.Presentation.directSum_var, LinearMap.llcomp_apply, LinearMap.toMatrix₂_mul, LinearMap.BilinForm.smul_left_of_tower, groupHomology.mapCycles₁_comp_apply, Orientation.kahler_comp_rightAngleRotation', groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, LinearMap.le_ker_iff_comp_subtype_eq_zero, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, AddMonoidAlgebra.comul_single, Module.Basis.dualBasis_coord_toDualEquiv_apply, PowerSeries.trunc_X_pow_self_mul, Matrix.repr_toLin, FDRep.endRingEquiv_symm_comp_ρ, AdicCompletion.of_ofAlgEquiv_symm, LieModule.traceForm_eq_sum_genWeightSpaceOf, Lagrange.derivative_nodal, CliffordAlgebra.even.lift.aux_mul, LocalizedModule.restrictScalars_map_eq, Representation.Coinvariants.mk_inv_tmul, LinearMap.polar_eq_iInter, PolynomialModule.map_smul, Submodule.linearProjOfIsCompl_apply_right, MvPowerSeries.coeff_pow, Polynomial.monomial_mem_lifts, Module.DirectLimit.map_apply_of, Polynomial.taylor_mul, RootPairing.Equiv.id_coweightMap_apply, ModuleCat.ι_coprodIsoDirectSum_hom_apply, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero, Finsupp.linearCombination_id_surjective, LinearMap.tensorKer_tmul, LinearMap.toMatrixAlgEquiv_comp, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearMap.det_mulLeft, TensorProduct.sum_tmul_basis_right_injective, ModuleCat.restrictScalarsComp'App_hom_apply, Subspace.dualLift_of_subtype, Submodule.mem_colon', LinearMap.IsPositive.re_inner_nonneg_right, Ideal.map_pi, RootPairing.Hom.comp_coweightMap_apply, PresheafOfModules.epi_iff_surjective, RootPairing.EmbeddedG2.shortAddLongRoot_shortRoot, Polynomial.sum_bernoulli, Finset.affineCombination_sdiff_sub, LinearMap.compRight_apply, LightCondensed.ihomPoints_symm_comp, Representation.asAlgebraHom_single, Trivialization.linearMapAt_symmₗ, Polynomial.C_mul_X_eq_monomial, Matrix.liftLinear_single, LinearMap.IsSymmetric.im_inner_self_apply, imaginaryPart_I_smul, LinearEquiv.coe_mk, Pi.counit_coe_dFinsupp, RootPairing.Equiv.coweightEquiv_symm_coweightMap, traceForm_nondegenerate_tfae, LinearPMap.mk_apply, CategoryTheory.whiskering_linearCoyoneda, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, Algebra.trace_eq_of_ringEquiv, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Subspace.dualRestrict_comp_dualLift, PowerSeries.coeff_of_lt_order, MvPowerSeries.constantCoeff_subst, Orientation.areaForm_le, LinearMap.BilinForm.congr_apply, Rep.indToCoindAux_self, LinearMap.id'_coe, TensorAlgebra.toTrivSqZeroExt_ι, Representation.asGroupHom_apply, LieModule.traceForm_eq_sum_finrank_nsmul', DomMulAct.smul_linearMap_apply, LinearMap.mul_apply_apply, eval₂_minpolyDiv_of_eval₂_eq_zero, MvPolynomial.divMonomial_add_modMonomial, LinearMap.BilinForm.toMatrix_compRight, LinearMap.det_pi, LinearMap.fst_comp_inr, ModuleCat.AlternatingMap.postcomp_apply, RootPairing.rootSpan_dualAnnihilator_le_ker_rootForm, LinearMap.ext_ring_op_iff, Submodule.mapQ_apply, LinearMap.adjoint_innerₛₗ_apply, LinearMap.continuousLinearMapClassOfFiniteDimensional, LinearMap.BilinMap.toQuadraticMap_add, Polynomial.hasseDeriv_one', Polynomial.derivative_comp_one_sub_X, SemimoduleCat.instReflectsIsomorphismsAddCommMonCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, PolynomialModule.comp_smul, LinearPMap.neg_graph, TensorAlgebra.ι_comp_lift, LinearEquiv.domMulActCongrRight_symm_apply, ContinuousLinearMap.toBilinForm_apply, WittVector.IsocrystalHom.frob_equivariant, MvPolynomial.eval₂Hom_monomial, Coalgebra.sum_map_tmul_counit_eq, Polynomial.derivative_pow_eq_zero, LinearMap.adjoint_eq_toCLM_adjoint, LinearMap.BilinForm.IsNonneg.nonneg, MvPolynomial.homogeneousComponent_of_mem, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, PowerSeries.coeff_succ_mul_X, LinearMap.IsPosSemidef.add, LinearIndependent.linearCombination_repr, ModuleCat.linearIndependent_shortExact, PolynomialModule.aeval_equivPolynomial, Profinite.NobelingProof.coe_πs, Rep.coe_res_obj_ρ, TensorAlgebra.adjoin_range_ι, LeftInvariantDerivation.left_invariant', Coalgebra.sum_tmul_counit_eq, MvPolynomial.homogeneousComponent_mem, DFinsupp.subtypeDomainLinearMap_apply, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, Submodule.factor_mk, MvPowerSeries.coeff_monomial_mul, LinearMap.det_zero, LinearEquiv.conjAlgEquiv_symm_apply_apply, Matrix.toLinearMap₂_toMatrix₂, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, LinearMap.toMatrix_one, ModuleCat.monoidalClosed_uncurry, QuaternionAlgebra.imIₗ_apply, LinearMap.IsReflective.smul_coroot, QuotSMulTop.equivTensorQuot_naturality, Module.Basis.mk_repr, Polynomial.roots_monomial, MvPowerSeries.coeff_X_pow, LinearMap.submoduleComap_apply_coe, LinearMap.intrinsicStar_mulRight, LinearMap.compl₂_apply, LinearMap.default_def, MvPolynomial.support_monomial, CliffordAlgebraDualNumber.equiv_symm_eps, LinearMap.IsReflective.apply_self_mul_coroot_apply, MeasureTheory.OuterMeasure.restrict_trim, Finset.weightedVSubOfPoint_congr, MonoidAlgebra.antipode_single, Polynomial.aeval_iterate_derivative_of_ge, Module.Flat.ker_lTensor_eq, MvPolynomial.monomial_finsupp_sum_index, KaehlerDifferential.cotangentComplexBaseChange_tmul, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, SpecialLinearGroup.mem_center_iff_spec, Rep.diagonalHomEquiv_symm_apply, Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span, cross_cross, Matrix.separatingRight_toBilin_iff, Polynomial.derivative_expand, Polynomial.derivative_sum, Polynomial.isCoveringMapOn_eval, IsBaseChange.of_fintype_basis_eq, MvPolynomial.mul_def, Matrix.spectrum_toLpLin, ExteriorAlgebra.ι_eq_zero_iff, Complex.reLm_coe, Polynomial.derivative_pow_succ, LinearMap.prodMap_add, LinearMap.ofIsCompl_smul, LieModuleHom.coe_mk, CondensedMod.isDiscrete_tfae, RootPairing.InvariantForm.pairing_mul_eq_pairing_mul_swap, IsSymmetricAlgebra.equiv_apply, sum_smul_minpolyDiv_eq_X_pow, Polynomial.derivative_ofNat, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, Submodule.quotDualCoannihilatorToDual_apply, IsSMulRegular.linearMap_subsingleton_of_mem_annihilator, LinearIndependent.of_isLocalizedModule_of_isRegular, Submodule.injective_inclusionSpan, Polynomial.monomial_one_one_eq_X, LinearMap.toAddMonoidHom_mulLeft, CategoryTheory.Linear.comp_apply, LinearMap.BilinForm.toMatrix'_symm, Coalgebra.coassoc_symm_apply, QuadraticMap.polarBilin_prod, Matrix.cramer_row_self, Span.repr_def, AffineMap.hasDerivWithinAt, Polynomial.Splits.eval_derivative, Submodule.dualPairing_apply, MeasureTheory.VectorMeasure.mapₗ_apply, NonUnitalAlgHom.coe_lmul_eq_mul, LeftInvariantDerivation.left_invariant, Matrix.toLin_mul_apply, LinearMap.sub_comp, LinearMap.prodMap_apply, Polynomial.derivative_smul, LinearMap.tensorEqLocusEquiv_apply, toMatrix_distrib_mul_action_toLinearMap, groupCohomology.coe_mapCocycles₁, LinearMap.domRestrict'_apply, PowerSeries.gaussNorm_monomial, groupHomology.mem_cycles₂_iff, LinearMap.smul_comp, ModuleCat.Iso.homCongr_eq_arrowCongr, MvPowerSeries.X_pow_eq, Polynomial.Splits.monomial, LieDerivation.coe_sub_linearMap, PiToModule.fromEnd_apply, ModuleCat.CoextendScalars.smul_apply', TensorPower.gMul_eq_coe_linearMap, CStarMatrix.mapₗ_reindexₐ, LinearAlgebra.FreeProduct.mul_injections, RatFunc.laurent_algebraMap, Polynomial.iterate_derivative_eq_factorial_smul_sum, ContinuousAlternatingMap.compContinuousLinearMapₗ_apply, LinearMap.lTensor_id_apply, LinearMap.BilinForm.IsRefl.groupSMul, LinearMap.BilinForm.toMatrix'_apply, ContinuousLinearMap.coe_restrictScalarsₗ, Polynomial.iterate_derivative_X_add_pow, Finsupp.sum_smul_index_linearMap', LinearMap.BilinMap.toQuadraticMapAddMonoidHom_apply, linearIndependent_iff_injective_finsuppLinearCombination, groupCohomology.d₁₂_hom_apply, Module.FaithfullyFlat.lTensor_exact_iff_exact, Representation.IntertwiningMap.toLinearMap_injective, Module.End.id_pow, LinearMap.BilinForm.SeparatingRight.toMatrix, AdicCompletion.incl_apply, AdicCompletion.map_ext'_iff, AdicCompletion.ofTensorProduct_surjective_of_finite, MeasureTheory.Measure.comapₗ_eq_comap, RootPairing.Hom.root_weightMap_apply, LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero', LinearEquiv.congrRight₂_apply, PresheafOfModules.pushforward_map_app_apply, cross_self, eval_minpolyDiv_of_aeval_eq_zero, Module.Basis.mk_coord_apply_eq, Polynomial.derivative_X, TensorProduct.map_add_right, CliffordAlgebra.contractRight_mul_ι, groupCohomology.coboundariesToCocycles₁_apply, SpecialLinearGroup.mem_center_iff, Polynomial.sumIDeriv_map, Module.FaithfullyFlat.lTensor_bijective_iff_bijective, Matrix.Nondegenerate.toLinearMap₂, rTensor_injective_iff_lcomp_surjective, MvPolynomial.smul_monomial, Representation.directSum_apply, Algebra.Extension.h1Cotangentι_injective, TensorProduct.gradedMul_assoc, CliffordAlgebra.op_reverse, LinearMap.inl_injective, Lagrange.eval_interpolate_not_at_node, AffineBasis.linear_eq_sumCoords, LieModule.lowerCentralSeries_one_inf_center_le_ker_traceForm, Polynomial.mirror_monomial, Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff, AnalyticOnNhd.eval_linearMap', FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, CliffordAlgebra.reverse_involute_commute, LinearMap.compPMap_apply, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same, Matrix.intrinsicStar_toLin', LinearMap.le_rank_iff_exists_linearIndependent, Polynomial.dvd_iterate_derivative_pow, QuaternionAlgebra.imKₗ_apply, IsLocalizedModule.liftOfLE_mk', PresheafOfModules.sections_property, Submodule.FG.lTensor.directedSystem, Polynomial.coeffs_monomial, LinearMap.coe_toContinuousLinearMap', KaehlerDifferential.polynomialEquiv_D, LinearMap.BilinMap.toQuadraticMap_zero, SemimoduleCat.Iso.homCongr_eq_arrowCongr, minpoly_algHom_toLinearMap, Polynomial.ofFn_eq_sum_monomial, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, Module.Basis.coe_mkFinConsOfLE, Matrix.coe_mulVecLin, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Matrix.mulVecLin_apply, Submodule.comap_le_comap_smul, PowerSeries.coeff_ne_zero_C, IsLocalizedModule.iso_symm_apply, QuadraticMap.toBilinHom_apply, ExteriorAlgebra.liftAlternating_ι_mul, LinearMap.tensorKer_coe, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, Module.Relations.Solution.surjective_fromQuotient_iff_surjective_π, Real.vector_fourierIntegral_eq_integral_exp_smul, TensorProduct.map_map, RootPairing.Hom.id_coweightMap_apply, RootPairing.coPolarization_apply_eq_zero_iff, PresheafOfModules.toSheafify_app_apply', Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, Module.End.mapsTo_restrict_maxGenEigenspace_restrict_of_mapsTo, LinearMap.toMatrixOrthonormal_reindex, Polynomial.abc, LinearMap.toMatrixAlgEquiv_toLinAlgEquiv, Fintype.linearIndependent_iff', QuadraticMap.add_linMulLin, HahnSeries.embDomainLinearMap_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, Algebra.TensorProduct.piRightHom_mul, Module.le_rank_iff_exists_linearMap, LinearMap.intrinsicStar_toSpanSingleton, Finsupp.linearCombination_zero_apply, QuadraticMap.associated_eq_self_apply, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, QuadraticMap.toMatrix'_comp, Representation.IntertwiningMap.coe_mul, LinearMap.trace_mul_cycle, Submodule.map_span_le, BoundedContinuousFunction.toContinuousMapLinearMap_apply, Module.exists_smul_eq_zero_and_mk_eq, Submodule.val_mulMap'_tmul, LinearMap.isUnit_iff_range_eq_top, Matrix.GeneralLinearGroup.coe_toLin, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, Finset.weightedVSub_apply_const, LinearMap.lTensor_smul, LinearMap.fst_surjective, ContinuousAlternatingMap.toAlternatingMapLinear_apply, TestFunction.continuous_iff_continuous_comp, LinearMap.ker_localizedMap_eq_localized'_ker, Polynomial.Splits.eval_root_derivative, exteriorPower.alternatingMapLinearEquiv_ιMulti, ModuleCat.forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, TensorProduct.directSum_lof_tmul_lof, IsLocalizedModule.iso_apply_mk, KaehlerDifferential.kerToTensor_apply, RatFunc.laurent_div, Submodule.coe_subtypeL', Finsupp.mem_span_iff_linearCombination, star_dotProduct_toMatrix₂_mulVec, RootPairing.root_coroot_eq_pairing, IsLocalFrameOn.coeff_apply_of_mem, IsBaseChange.linearMapLeftRightHom_comp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange, QuadraticModuleCat.forget₂_map_associator_inv, AffineMap.slope_comp, Finset.weightedVSubOfPoint_indicator_subset, selfAdjointPart_comp_subtype_skewAdjoint, setBasisOfLinearIndependentOfCardEqFinrank_repr_apply, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, MvPowerSeries.monomial_mem_nonzeroDivisors, LocallyConstant.toContinuousMapLinearMap_apply, Algebra.Presentation.differentials.hom₁_single, Profinite.NobelingProof.Products.max_eq_eval, LocalizedModule.divBy_apply, TensorProduct.AlgebraTensorModule.lTensor_id, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, Algebra.Generators.exists_presentation_of_basis_cotangent, Bialgebra.counitBialgHom_apply, instNontrivialLinearMapId, zero_prodMap_dualTensorHom, LinearMap.sum_repr_mul_repr_mulₛₗ, SemimoduleCat.hom_zsmul, Polynomial.derivative_monomial, TensorProduct.AlgebraTensorModule.rTensor_one, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerₛₗ_apply_apply, LinearMap.ringLmapEquivSelf_symm_apply, groupCohomology.cocycles₂.d₂₃_apply, LinearMap.lTensor_surj_iff_rTensor_surj, LinearMap.liftBaseChange_one_tmul, groupCohomology.d₀₁_hom_apply, RootPairing.self_comp_coPolarization_eq_corootForm, QuadraticMap.associated_rightInverse, Polynomial.aeval_sumIDeriv, Representation.ofMulAction_apply, DirectSum.lmap_apply, Matrix.toBilin_symm, AddMonoidHom.toRatLinearMap_injective, Rep.linearization_single, LinearMap.spectrum_toMatrix', Profinite.NobelingProof.Products.eval_πs, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd, LieModule.trace_toEnd_genWeightSpace, Bialgebra.counitAlgHom_apply, Polynomial.sumIDeriv_C, Polynomial.Chebyshev.T_derivative_eq_U, Real.smul_map_diagonal_volume_pi, Algebra.traceMatrix_apply, SemimoduleCat.hom_nsmul, MvPowerSeries.coeff_mul_right_one_sub_of_lt_weightedOrder, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, Polynomial.coeff_taylor_natDegree, groupHomology.d₃₂_single_one_thd, LinearMap.mulLeft_zero_eq_zero, toMatrix_rotation, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, LinearMap.BilinForm.sum_right, ModuleCat.hom_surjective, LinearMap.eventually_iSup_ker_pow_eq, LinearMap.separatingRight_congr_iff, LinearMap.rTensor_id_apply, Module.eval_apply_injective, LieAlgebra.IsKilling.ker_traceForm_eq_bot_of_isCartanSubalgebra, IsSelfAdjoint.selfAdjointPart_apply, le_comap_range_lTensor, Matrix.diagLinearMap_apply, LinearMap.polar_singleton, Matrix.diagonalLinearMap_apply, LieModule.shiftedGenWeightSpace.toEnd_eq, Ideal.finsuppTotal_apply_eq_of_fintype, ConcaveOn.comp_linearMap, groupHomology.isoCycles₁_inv_comp_iCycles_apply, Polynomial.aeval_iterate_derivative_self, StarModule.decomposeProdAdjointL_apply, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, strongRankCondition_iff_forall_not_injective, TensorProduct.liftAux_tmul, RootPairing.RootPositiveForm.zero_lt_posForm_iff, QuotSMulTop.equivTensorQuot_naturality_mk, RootPairing.toLinearMap_apply_CoPolarization, LinearMap.BilinForm.ext_iff_of_isSymm, LieDerivation.inner_apply_apply, Submodule.IsCompl.projection_apply_left, dot_cross_self, ModuleCat.forget₂_addCommGrp_essSurj, surjective_of_nonzero_of_finrank_eq_one, groupCohomology.map_H0Iso_hom_f_apply, MeasureTheory.Lp.compMeasurePreservingₗ_apply, LieModule.Cohomology.twoCochain_alt, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, groupCohomology.d₁₂_comp_d₂₃_apply, PointedCone.coe_map, Matrix.toLpLin_mul_same, groupCohomology.H0IsoOfIsTrivial_inv_apply, Polynomial.toFinsupp_monomial, CliffordAlgebra.toProd_ι_tmul_one, PresheafOfModules.congr_map_apply, Polynomial.coe_monomial, tensorIteratedFDerivTwo_eq_iteratedFDeriv, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity, Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective, CliffordAlgebra.changeForm_self_apply, PowerSeries.aeval_eq_sum, PresheafOfModules.freeYonedaEquiv_symm_app, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom, Representation.apply_sub_id_partialSum_eq, Rep.finsuppToCoinvariantsTensorFree_single, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, PolyEquivTensor.toFunAlgHom_apply_tmul, groupCohomology.eq_d₂₃_comp_inv_apply, PiTensorProduct.mul_assoc, PolynomialLaw.exists_lift', HahnSeries.SummableFamily.lsum_apply, LinearMap.toMatrix_baseChange, groupCohomology.eq_d₁₂_comp_inv_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, Coalgebra.sum_counit_tmul_eq, Finset.weightedVSub_map, Representation.asAlgebraHom_def, PresheafOfModules.restrictScalarsObj_map, PolynomialLaw.toFun_eq_rTensor_φ_toFun', QuadraticMap.linMulLin_apply, LinearMap.transvection.comp_of_left_eq_apply, groupHomology.chains₁ToCoinvariantsKer_surjective, TensorProduct.adjoint_map, MeasureTheory.OuterMeasure.comap_iInf, LinearMap.GeneralLinearGroup.generalLinearEquiv_to_linearMap, LinearMap.IsContPerfPair.bijective_left, Algebra.trace_eq_of_algEquiv, LinearEquiv.domMulActCongrRight_apply, Rep.coinvariantsTensorFreeLEquiv_symm_apply, CliffordAlgebra.contractRight_comm, LinearMap.submoduleMap_coe_apply, Orientation.map_eq_neg_iff_det_neg, TrivSqZeroExt.map_inr, Matrix.coe_vecMulLinear, LinearMap.coprod_zero_right, CliffordAlgebra.EquivEven.reverse_e0, CStarMatrix.toCLM_injective, MvPolynomial.monomial_zero, Polynomial.monomial_mul_C, LinearMap.trace_eq_matrix_trace_of_finset, LinearMap.adjoint_toContinuousLinearMap, Polynomial.X_pow_eq_monomial, Matrix.SeparatingLeft.toLinearMap₂', Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, LinearMap.rTensor_comp_flip_mk, TensorProduct.dualDistrib_apply_comm, LinearMap.BilinForm.IsAlt.eq_of_add_add_eq_zero, Finsupp.llift_apply, ExteriorAlgebra.liftAlternating_comp, Representation.Coinvariants.mk_tmul_inv, Algebra.isIntegral_trace, CharacterModule.curry_apply_apply, LinearMap.map_sub₂, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, Matrix.sum_cramer, ContinuousLinearMap.IsIdempotentElem.toLinearMap, ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape, finrank_algHom, signedDist_linear_apply_apply, mem_vectorSpan_iff_eq_weightedVSub, SpecialLinearGroup.mem_range_toGeneralLinearGroup_iff, Module.Basis.toDualEquiv_apply, CliffordAlgebra.changeFormAux_changeFormAux, ModuleCat.forget_reflectsLimitsOfSize, Function.Exact.iff_of_ladder_linearEquiv, Fintype.bilinearCombination_apply_single, LinearMap.BilinForm.nondegenerate_toMatrix_iff, Matrix.derivative_det_one_add_X_smul, LinearMap.coe_inr, LinearMap.toMatrixₛₗ₂'_symm, IsGroupLikeElem.antipode_antipode, LinearMap.coe_smul, Ideal.range_mul', PositiveLinearMap.coe_toLinearMap, Module.FaithfullyFlat.iff_zero_iff_rTensor_zero, CliffordAlgebra.ι_mul_ι_comm, PowerSeries.binomialSeries_coeff, dotProductEquiv_apply_apply, LinearMap.rank_diagonal, LinearPMap.adjointAux_unique, LinearMap.ker_localizedMap_eq_localized₀_ker, QuotSMulTop.map_comp_mkQ, Polynomial.derivative_rootMultiplicity_of_root, RootPairing.injOn_dualMap_subtype_span_root_coroot, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, AlgEquiv.pow_toLinearMap, SemimoduleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, TensorProduct.directLimitRight_tmul_of, LinearMap.sub_mem_ker_iff, Ideal.finsuppTotal_apply, ContinuousAlternatingMap.toAlternatingMap_curryLeft, RootPairing.disjoint_corootSpan_ker_corootForm, TensorProduct.flip_mk_surjective, LinearMap.smul_apply, LinearMap.rTensor_tmul, LinearMap.separatingRight_toMatrix₂'_iff, Matrix.toEuclideanLin_apply, Submodule.biSup_eq_range_dfinsupp_lsum, Rep.resCoindAdjunction_unit_app_hom_hom, CliffordAlgebra.changeForm.add_proof, Polynomial.taylor_injective, ContinuousLinearMap.toLinearMap₁₂_apply, groupCohomology.mem_cocycles₁_def, LinearMap.IsPositive.isPositive_smul_iff, Polynomial.iterate_derivative_mul_X, Algebra.toMatrix_lmul_eq, LieModule.traceForm_eq_zero_of_isNilpotent, LinearMap.toMatrixAlgEquiv'_id, isAdjointPair_toLinearMap₂, HahnSeries.single.linearMap_apply, MvPowerSeries.monomial_mem_nonzeroDivisorsLeft, LinearEquiv.congrLeft_symm_apply, CliffordAlgebra.ι_sq_scalar, LieModule.Cohomology.d₂₃_apply, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, Representation.Coinvariants.le_comap_ker, LinearMap.id_apply, AddMonoidHom.toNatLinearMap_injective, ModuleCat.endRingEquiv_symm_apply_hom, LinearMap.BilinForm.sub_left, Algebra.intTrace_eq_of_isLocalization, BialgHom.coe_linearMap_injective, exteriorPower.alternatingMapLinearEquiv_symm_map, LieIdeal.coe_killingCompl_top, PowerSeries.coeff_subst, Polynomial.sumIDeriv_eq_self_add, Submodule.span_range_inclusion_restrictScalars_eq_top, SemimoduleCat.forget_obj, LinearMap.restrictScalars_apply, Algebra.trace_algebraMap, Polynomial.self_sub_monomial_natDegree_leadingCoeff, AffineMap.map_vadd', LinearMap.det_baseChange, Rep.homEquiv_apply_hom, QuadraticForm.tmul_tensorMap_apply, HahnEmbedding.Partial.truncLT_mem_range_extendFun, Polynomial.iterate_derivative_X, ModN.basis_apply_eq_mkQ, Module.Flat.out, LinearMap.coprod_zero_left, ExteriorAlgebra.ιMulti_succ_apply, Orientation.rightAngleRotation_def, Matrix.liftLinear_singleLinearMap, LieModule.Cohomology.d₁₂_apply_apply, Polynomial.eval₂_monomial, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, LinearMap.smulRight_apply, FiniteDimensional.mem_span_of_iInf_ker_le_ker, Module.AEval'.X_smul_of, LinearMap.isUnit_iff_isUnit_det, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotent, LinearMap.IsSymmetricProjection.sub_of_range_le_range, PowerSeries.coeff_coe, TensorProduct.AlgebraTensorModule.map_smul_left, Matrix.liftLinear_comp_singleLinearMap, LinearMap.ofIsComplProd_apply, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, LinearMap.mul_apply', SemimoduleCat.MonoidalCategory.tensorHom_tmul, LocalizedModule.divBy_mul_by, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, LinearMap.toMatrix_symm, Matrix.toBilin_apply, ModuleCat.forget_preservesMonomorphisms, LinearMap.range_mkQ_comp, LinearMap.toMatrix₂'_compl₁₂, groupCohomology.mapCocycles₂_comp_i_apply, AffineMap.const_linear, Module.Relations.surjective_toQuotient, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MvPolynomial.monomial_eq_monomial_iff, RootPairing.flip_comp_polarization_eq_rootForm, Polynomial.derivative'_apply, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, Module.End.ringHomEndFinsupp_apply_apply, LinearMap.prodEquiv_apply, Profinite.NobelingProof.Products.eval_πs', Polynomial.mem_support_derivative, MvPowerSeries.coeff_X, LinearMap.ker_eq_bot, Module.Relations.Solution.IsPresentation.linearMapEquiv_apply, PowerSeries.eq_shift_mul_X_pow_add_trunc, Polynomial.monomial_pow, Representation.ofMulAction_single, Module.Basis.toLin_toMatrix, Submodule.linearProjOfIsCompl_apply_right', ModuleCat.MonoidalCategory.associator_hom_apply, groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, MvPolynomial.eval₂_mul_monomial, MvPolynomial.weightedHomogeneousComponent_zero, LinearMap.flip_injective_iff₁, Matrix.toLinearEquivRight'OfInv_symm_apply, RootPairing.Hom.id_weightMap_apply, ContinuousAffineMap.coe_mk_contLinear_eq_linear, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, SModEq.map, Pi.counit_eq_adjoint, ConvexCone.coe_map, Module.FaithfullyFlat.lTensor_surjective_iff_surjective, Rep.norm_comm_apply, LinearMap.BilinForm.coeFnAddMonoidHom_apply, CategoryTheory.Linear.leftComp_apply, LinearMap.ker_smul', LinearMap.toMatrixOrthonormal_apply_apply, IsLocalizedModule.map_linearMap_of_isLocalization, Submodule.coe_isComplEquivProj_symm_apply, MvPolynomial.homogeneousComponent_C_mul, CliffordAlgebra.EquivEven.ι_eq_v_add_smul_e0, AdicCompletion.pi_apply_coe, Matrix.toLin'_mul_apply, Orientation.areaForm_to_volumeForm, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, Polynomial.toLaurent_C_mul_T, MeasureTheory.OuterMeasure.map_apply, Polynomial.card_roots_le_derivative, Matrix.toLinearMapₛₗ₂'_single, LieAlgebra.bracket_ofTwoCocycle, LinearMap.exact_subtype_mkQ, Representation.ofDistribMulAction_apply_apply, Algebra.Extension.Cotangent.val_mk, Matrix.nondegenerate_toBilin'_iff, Representation.coinvariantsFinsuppLEquiv_apply, TensorProduct.AlgebraTensorModule.restrictScalars_curry, ModuleCat.HasColimit.colimitCocone_ι_app, LinearMap.trace_eq_contract_of_basis', PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, LinearMap.id_coe, Submodule.linearDisjoint_iff, LinearMap.BilinForm.congr_comp, LinearMap.toMatrixAlgEquiv_apply, LinearMap.IsSymmetric.coe_re_inner_self_apply, Lagrange.eq_interpolate_iff, LocalizedModule.lift'_mk, Polynomial.derivative_eval, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, Algebra.traceForm_apply, CliffordAlgebra.changeFormEquiv_symm, LinearMap.BilinForm.apply_dualBasis_left, LinearMap.range_le_bot_iff, ContinuousLinearMapWOT.inducingFn_apply, QuadraticMap.add_toBilin, DFinsupp.injective_pi_lapply, CStarMatrix.inner_toCLM_conjTranspose_left, Orientation.areaForm_neg_orientation, Module.exists_finite_presentation, LinearMap.toMatrix'_toLin', ModuleCat.MonoidalCategory.tensorHom_tmul, PolynomialModule.monomial_smul_single, MultilinearMap.curryRight_apply, IntermediateField.LinearDisjoint.trace_algebraMap, groupHomology.d₂₁_single_inv_mul_ρ_add_single, Submodule.toLocalized₀_apply_coe, MvPolynomial.weightedDecomposition.decompose'_apply, LinearMap.add_apply, CliffordAlgebra.changeForm.zero_proof, RootPairing.ker_copolarization_eq_ker_corootForm, LinearMap.range_toAddSubmonoid, QuadraticModuleCat.forget₂_map, TensorProduct.toMatrix_assoc, LinearMap.applyₗ'_apply_apply, Submodule.mem_map, LinearMap.commute_mulLeft_right, Matrix.toLinearMap₂'_apply', PresheafOfModules.Derivation.postcomp_d_apply, Pretrivialization.linearMapAt_eq_zero, Module.FaithfullyFlat.zero_iff_rTensor_zero, RootPairing.exists_ge_zero_eq_rootForm, Representation.instIsTrivialSubtypeMemSubgroupSubmoduleInvariantsCompLinearMapIdSubtypeToInvariants, MvPolynomial.expand_monomial, ModuleCat.forget₂_addCommGroup_full, LinearMap.sumOfConjugatesEquivariant_apply, Polynomial.X_pow_smul_rTensor_monomial, Finset.weightedVSubOfPoint_vadd, PiToModule.fromEnd_injective, isCompactOperator_iff_isCompact_closure_image_ball, LinearMap.coe_lTensorHom, Module.Basis.mk_coord_apply_ne, KaehlerDifferential.mapBaseChange_tmul, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, Module.DirectLimit.quotMk_of, SkewPolynomial.monomial_def, MvPolynomial.monomial_mul_mem_coeffsIn, PresheafOfModules.sectionsMap_coe, MvPowerSeries.coeff_monomial_same, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq, LinearMap.toMatrix_id, Polynomial.smul_monomial, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, LinearMap.transvection.comp_of_right_eq_apply, NNRealRMK.lintegral_rieszMeasure, groupHomology.d₁₀_comp_coinvariantsMk_apply, LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec, Orientation.kahler_eq_zero_iff, LinearMap.eq_adjoint_iff_basis_left, LinearMap.BilinForm.isNonneg_def, MvPowerSeries.hasSum_aeval, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.ρ_hom, LinearMap.baseChange_one, Rep.diagonalSuccIsoFree_inv_hom_single_single, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, ProperCone.mem_dual, MvPowerSeries.weightedOrder_monomial_of_ne_zero, groupCohomology.H1IsoOfIsTrivial_inv_apply, Algebra.Generators.H1Cotangent.δAux_C, Polynomial.iterate_derivative_X_sub_pow, LinearMap.instSMulCommClass, LinearEquiv.coe_toLinearMap_mul, QuadraticMap.associated_prod, Pretrivialization.coe_linearMapAt, LinearMap.isIdempotentElem_iff_eq_isCompl_projection_range_ker, LinearMap.IsSymmetricProjection.isIdempotentElem, ConvexCone.coe_comap, LinearIndependent.repr_eq_single, SemimoduleCat.ofHom₂_hom_apply_hom, CliffordAlgebra.star_def', LieModuleHom.coe_toLinearMap, PowerSeries.coeff_inv_aux, MvPowerSeries.X_pow_dvd_iff, PresheafOfModules.map_comp_apply, MeasureTheory.OuterMeasure.restrict_iInf, MeasureTheory.OuterMeasure.comap_apply, MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero, PowerSeries.degree_trunc_lt, IsAdjoinRootMonic.basis_repr, Module.Baer.ExtensionOf.is_extension, LinearMap.toMatrix_transpose, Representation.leftRegular_norm_eq_zero_iff, LinearMap.toMatrix₂_toLinearMapₛₗ₂, MeasureTheory.VectorMeasure.restrictₗ_apply, ModuleCat.biprodIsoProd_inv_comp_snd_apply, LinearMap.identityMapOfZeroModuleIsZero, MvPowerSeries.coeff_mul_prod_one_sub_of_lt_order, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange_residueField, PresheafOfModules.pushforward_map_app_apply', PowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, LieIdeal.mem_killingCompl, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, Orientation.areaForm_swap, ContinuousLinearMap.holderₗ_apply_apply, LinearMap.smul_compMultilinearMap, HopfAlgebra.sum_mul_antipode_eq_smul, Algebra.Extension.subsingleton_h1Cotangent, Matrix.mulVecLin_add, ext_inner_map, LinearMap.trace_smulRight, LinearMap.convOne_apply, AdicCompletion.factor_eval_eq_evalₐ, Module.Relations.Solution.fromQuotient_toQuotient, AddMonoidAlgebra.counit_single, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, Pi.intrinsicStar_comul_commSemiring, Algebra.Generators.exists_presentation_of_free_cotangent, MvPolynomial.X_mul_pderiv_monomial, LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, Matrix.toLinAlgEquiv_mul, LinearMap.range_zero, QuadraticAlgebra.imₗ_apply, HahnEmbedding.Seed.strictMono_coeff, LinearMap.det_mulRight, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, MvPowerSeries.coeff_index_single_X, PowerSeries.WithPiTopology.uniformContinuous_coeff, MeasureTheory.OuterMeasure.restrict_ofFunction, Module.one_le_rank_iff, IsLocalizedModule.fromLocalizedModule.bij, LieDerivation.coe_neg_linearMap, LinearMap.nonneg_iff_isPositive, Lagrange.interpolate_eq_sum, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, LieDerivation.coe_smul_linearMap, Algebra.Extension.CotangentSpace.map_tmul, Submodule.quotientQuotientEquivQuotientAux_mk, Orientation.kahler_swap, Matrix.toLinearMap₂'Aux_single, groupCohomology.H2π_comp_map_apply, Matrix.vecMulBilin_apply, Orientation.det_rotation, MvPowerSeries.LinearTopology.mem_basis_iff, Coalgebra.comm_comul, Module.Relations.Solution.IsPresentation.linearEquiv_apply, MvPowerSeries.subst_monomial, LinearMap.IsSymmetric.inner_map_self_eq_zero, LinearMap.mk₂'ₛₗ_apply, cross_anticomm, OrthonormalBasis.prod_apply, Submodule.subtype_apply, KaehlerDifferential.span_range_map_derivation_of_isLocalization, Ideal.powQuotSuccInclusion_apply_coe, LaurentPolynomial.antipode_T, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Rep.ihom_ev_app_hom, SemimoduleCat.MonoidalCategory.whiskerRight_apply, IsBaseChange.endHom_toMatrix, Representation.Coinvariants.sub_mem_ker, MeasureTheory.OuterMeasure.map_iInf_comap, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, Ideal.range_mul, ModuleCat.homLinearEquiv_symm_apply, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, IsAdicComplete.of_liftRingHom, Algebra.discr_powerBasis_eq_norm, LinearMap.BilinForm.sum_left, ModuleCat.hom_smul, LinearMap.surjective_iff_ne_zero, GradedTensorProduct.mul_def, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, Module.Flat.iff_lTensor_preserves_injective_linearMap, MvPolynomial.weightedHomogeneousComponent_eq_zero', PowerSeries.coeff_zero_one, QuadraticForm.polarBilin_tmul, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, Finset.weightedVSubOfPoint_filter_of_ne, orzechProperty_iff, ModuleCat.uliftFunctorForgetIso_hom_app, MvPowerSeries.coeff_of_lt_order, QuadraticMap.Ring.polarBilin_pi, RootPairing.toLinearMap_apply_apply_Polarization, Orientation.map_eq_iff_det_pos, LinearMap.BilinForm.Nondegenerate.congr, Rep.MonoidalClosed.linearHomEquivComm_hom, Polynomial.map_monomial, rieszContentAux_image_nonempty, isGroupLikeElem_iff, PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sq, SemimoduleCat.homLinearEquiv_apply, ModuleCat.smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, TensorProduct.equivFinsuppOfBasisLeft_symm, LinearMap.isClosedEmbedding_of_injective, Submodule.comap_smul, LinearMap.flip_surjective_iff₁, LinearMap.tensorEqLocus_coe, TensorAlgebra.toExterior_ι, AlternatingMap.alternatizeUncurryFin_apply, LinearMap.span_preimage_le, Submodule.mem_comap, LinearMap.dfinsuppSum_apply, LinearMap.IsPositive.inner_nonneg_left, LinearMap.toAddMonoidHom'_apply, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, TensorProduct.curry_injective, Matrix.toLinearMap₂'_apply, Profinite.NobelingProof.GoodProducts.smaller_factorization, matPolyEquiv_coeff_apply_aux_1, LinearMap.funLeft_surjective_of_injective, LinearMap.mem_submoduleImage_of_le, Submodule.mulLeftMap_apply, lTensorHomEquivHomLTensor_apply, LinearMap.BilinForm.separatingLeft_toMatrix'_iff, TensorProduct.finsuppScalarRight_apply, Algebra.FormallySmooth.iff_injective_lTensor_residueField, ModularGroup.lcRow0Extend_symm_apply, LinearMap.extendScalarsOfIsLocalizationEquiv_apply, rank_lt_rank_dual', AdicCompletion.sumInv_apply, LinearMap.det_def, Polynomial.derivative_X_sub_C_sq, MvPolynomial.homogeneousComponent_isHomogeneous, Module.Relations.Solution.ofQuotient_var, LinearMap.trace_mul_comm, LinearMap.trace_eq_contract, Orientation.kahler_comp_rightAngleRotation, LinearMap.toKerLocalized_isLocalizedModule, FiniteField.algebraMap_trace_eq_sum_pow, ModuleCat.CoextendScalars.smul_apply, CliffordAlgebra.changeFormAux_apply_apply, Submodule.isOpenQuotientMap_mkQ, LinearMap.rTensor_sub, Submodule.factor_eq_factor, DirectSum.coeLinearMap_of, AdicCompletion.sum_lof, LinearEquiv.arrowCongr_symm_apply, Representation.single_smul, Polynomial.smeval.linearMap_apply, LinearMap.trace_eq_sum_inner, Polynomial.eval_derivative_of_splits, MvPolynomial.sum_homogeneousComponent, LinearMap.BilinForm.not_nondegenerate_zero, Derivation.coe_neg_linearMap, Module.Relations.Solution.IsPresentation.linearMapEquiv_symm_apply, DirectSum.coeLinearMap_eq_dfinsuppSum, AffineEquiv.linear_equivUnitsAffineMap_symm_apply, Module.FinitePresentation.linearEquivMap_symm_apply, exists_basis_of_pairing_ne_zero, RootPairing.polarizationIn_Injective, LinearMap.isUnit_iff_ker_eq_bot, Algebra.IsEpi.injective_lift_mul, LinearMap.restrictScalarsₗ_apply, LinearMap.exists_antilipschitzWith, Matrix.isNilpotent_toLin'_iff, divRadical_dvd_derivative, ModuleCat.exteriorPower.desc_mk, MvPolynomial.coe_monomial, LinearMap.trace_one, PresheafOfModules.unit_map_one, LinearMap.span_inl_union_inr, Module.AEval'.of_symm_X_smul, CliffordAlgebra.reverse_involute, TensorAlgebra.equivFreeAlgebra_symm_ι, selfAdjoint.imaginaryPart_coe, homTensorHomEquiv_apply, QuadraticMap.associated_apply, Polynomial.aeval_add_of_sq_eq_zero, monomial_mem_adjoin_monomial, MvPowerSeries.X_def, Polynomial.derivativeFinsupp_apply_toFun, ExteriorAlgebra.GradedAlgebra.ι_sq_zero, MvPolynomial.C_apply, ModuleCat.HasColimit.colimitCocone_pt_isModule, LinearMap.detAux_def, Polynomial.deriv_aeval, IsModuleTopology.continuous_bilinear_of_pi_fintype, TensorProduct.mk_apply, MeasureTheory.Measure.comapₗ_apply, IsLocalizedModule.finsetIntegerMultiple_image, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, CliffordAlgebra.star_def, LinearMap.isCompl_iSup_ker_pow_iInf_range_pow, Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero, IsLocalFrameOn.coeff_congr, ExteriorAlgebra.lift_comp_ι, Profinite.NobelingProof.πs'_apply_apply, AlternatingMap.alternatizeUncurryFin_add, MeasureTheory.OuterMeasure.map_comap_le, Polynomial.ofFinsupp_single, Matrix.toLinearEquiv'_symm_apply, MvPowerSeries.ext_iff, LinearMap.BilinForm.IsSymm.eq, AffineMap.linear_injective_iff, LinearMap.hasStrictDerivAt, AddMonoidAlgebra.lsingle_apply, LinearMap.BilinForm.mul_toMatrix'_mul, CategoryTheory.preadditiveYoneda_obj, Matrix.toLin_symm, SemimoduleCat.forget₂_obj_moduleCat_of, TensorProduct.mapOfCompatibleSMul_surjective, LinearMap.toMatrixAlgEquiv_id, Polynomial.le_trailingDegree_monomial, Polynomial.iterate_derivative_derivative_mul_X_sq, MvPolynomial.single_eq_monomial, LinearMap.det_eq_one_of_not_module_finite, Finset.weightedVSub_empty, Rep.standardComplex.εToSingle₀_comp_eq, Convex.semilinear_image, Derivation.comp_aeval_eq, CliffordAlgebraQuaternion.k_quaternionBasis, MeasureTheory.Measure.mapₗ_congr, Module.Flat.iff_rTensor_injective, LieModule.Weight.coe_coe, Representation.prod_apply_apply, LinearMap.baseChange_pow, CompactlySupportedContinuousMap.coe_toRealLinearMap, SeparatingDual.dualMap_surjective_iff, Representation.tprod_apply, InnerProductGeometry.norm_toLp_symm_crossProduct, dualTensorHom_apply, BilinForm.mul_toMatrix_mul, isNoetherian_linearMap_pi, FunOnFinite.continuous_linearMap, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Module.Invertible.rTensorEquiv_apply_apply, Rep.coindVEquiv_symm_apply_coe, LinearMap.localized'_range_eq_range_localizedMap, exists_extension_of_le_sublinear, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, lTensorHomEquivHomLTensor_toLinearMap, MeasureTheory.OuterMeasure.map_le_restrict_range, LinearMap.trace_comp_eq_mul_of_commute_of_isNilpotent, PowerSeries.trunc_trunc_mul_trunc, Module.Basis.linearMap_apply, Module.FinitePresentation.exists_lift_of_isLocalizedModule, LinearMap.intrinsicStar_mul', PowerSeries.coeff_invOfUnit, Matrix.toLinearMap₂_compl₁₂, LinearAlgebra.FreeProduct.ι_apply, AffineMap.smul_linear, Finsupp.lcoeFun_apply, Module.Finite.exists_nat_not_surjective, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, LinearEquiv.mem_dilatransvections_iff_rank, ModuleCat.imageIsoRange_inv_image_ι_apply, Polynomial.C_mul_X_pow_eq_monomial, PiTensorProduct.ofDirectSumEquiv_symm_lof_tprod, basisOfLinearIndependentOfCardEqFinrank_repr_apply, ExteriorAlgebra.liftAlternating_ιMulti, MonomialOrder.leadingTerm_monomial, MvPowerSeries.WithPiTopology.continuous_coeff, linearIndependent_algHom_toLinearMap', AdicCompletion.map_comp_apply, CondensedMod.isDiscrete_iff_isDiscrete_forget, PowerSeries.trunc_mul_C, Representation.IntertwiningMap.isIntertwiningMap_of_mem_center, CliffordAlgebra.changeForm_ι_mul, PresheafOfModules.map_smul, LieModule.traceForm_lieSubalgebra_mk_right, Matrix.cramer_apply, LinearMap.lsum_apply, FGModuleCat.FGModuleCatEvaluation_apply, ModuleCat.epi_iff_surjective, Matrix.toLinearMapₛₗ₂'_symm, Module.Basis.forall_coord_eq_zero_iff, LinearMap.localized'_ker_eq_ker_localizedMap, Submodule.mem_annihilator', Module.Relations.Solution.postcomp_var, LinearMap.mk₂_apply, LinearMap.iterateFrobenius_def, CliffordAlgebra.changeForm_self, LinearMap.isAlt_iff_eq_neg_flip, RootPairing.PolarizationIn_eq, RootPairing.RootPositiveForm.exists_eq, AdicCompletion.AdicCauchySequence.map_zero, LinearMap.toLinearMap_toContPerfPair, TensorProduct.AlgebraTensorModule.rTensor_comp, PresheafOfModules.Monoidal.tensorObj_map_tmul, LinearMap.snd_comp_inl, LinearMap.coe_restrictScalars, Module.Basis.trace_traceDual_mul, PowerSeries.hasSum_of_monomials_self, Polynomial.monomial_eq_zero_iff, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, coevaluation_apply_one, CliffordAlgebraQuaternion.i_quaternionBasis, MatrixEquivTensor.toFunBilinear_apply, LinearMap.isSymmetric_adjoint_mul_self, Representation.isProj_averageMap, ModuleCat.exteriorPower.map_mk, AffineMap.decomp', IsBaseChange.transvection, MvPowerSeries.le_lexOrder_iff, LinearMap.toBilin'Aux_toMatrixAux, RootPairing.Equiv.weightMap_weightEquiv_symm, lipschitzGroup.conjAct_smul_ι_mem_range_ι, IsTensorProduct.map_map, Finset.weightedVSub_weightedVSubVSubWeights, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, IsLocalRing.map_tensorProduct_mk_eq_top, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, Module.Dual.eval_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Representation.coinvariantsTprodLeftRegularLEquiv_apply, ModuleCat.id_apply, LinearMap.toMatrix₂_compl₂, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, SameRay.map, Finset.weightedVSubOfPoint_sdiff, DFinsupp.sum_mapRange_index.linearMap, groupCohomology.infNatTrans_app, InnerProductSpace.trace_rankOne, MonomialOrder.span_leadingTerm_eq_span_monomial, Ideal.pi_mkQ_surjective, rTensorHomEquivHomRTensor_apply, LinearMap.trace_eq_contract_apply, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, ExteriorAlgebra.liftAlternatingEquiv_apply, RCLike.imLm_coe, LinearMap.instIsCentralScalar, dualTensorHomEquivOfBasis_symm_cancel_right, LinearMap.toPMap_apply, MonomialOrder.span_leadingTerm_eq_span_monomial₀, groupCohomology.d₁₂_apply_mem_cocycles₂, LinearMap.GeneralLinearGroup.ofLinearEquiv_inv, IsModuleTopology.continuous_of_linearMapₛₗ, Matrix.toLpLin_symm_pow, Module.Invertible.embAlgebra_injective, ModuleCat.hom_inv_apply, Polynomial.mkDerivation_one_eq_derivative', TensorProduct.map_add_left, spinGroup.units_involute_act_eq_conjAct, IsAdicComplete.of_lift, Polynomial.derivative_X_add_C, IsLocalization.tensorProduct_isLocalizedModule, Submodule.coe_linearProjOfIsCompl_apply, Submodule.inclusion_apply, TensorAlgebra.lift_symm_apply, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, RootPairing.rootForm_root_self, IsLocalizedModule.is_universal, MvPowerSeries.monomial_mem_nonzeroDivisorsRight, ModuleCat.monoidalClosed_curry, IsTensorProduct.map_pow, Polynomial.hermite_succ, groupCohomology.d₀₁_apply_mem_cocycles₁, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, LinearMap.proj_apply, IsBaseChange.det_endHom, ContinuousLinearMap.toLinearMapRingHom_apply, LinearMap.polyCharpolyAux_map_eval, AlternatingMap.curryLeft_apply_apply, Matrix.toLinearMapₛₗ₂'_aux_eq, IsLocalizedModule.mapExtendScalars_apply_apply, stdSimplex.map_coe, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, LinearMap.BilinForm.isRefl_zero, MvPolynomial.C_mul_X_eq_monomial, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, LinearEquiv.det_symm_mul_det, PowerSeries.coeff_derivativeFun, KaehlerDifferential.linearMapEquivDerivation_apply_apply, Submodule.surjective_tensorToSpan, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, LinearMap.mulLeft_eq_zero_iff, PolyEquivTensor.toFunLinear_mul_tmul_mul, Representation.Coinvariants.mk_self_apply, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, Polynomial.hermite_eq_iterate, AffineMap.continuous_iff, Polynomial.hasseDeriv_comp, Rep.indToCoindAux_fst_mul_inv, Module.preReflection_preReflection, MvPowerSeries.coeff_index_single_self_X, QuadraticMap.comp_apply, Matrix.linfty_opNNNorm_toMatrix, MvPowerSeries.WithPiTopology.as_tsum, MeasureTheory.OuterMeasure.isometry_comap_mkMetric, inCoordinates_apply_eq₂, KaehlerDifferential.tensorKaehlerEquivBase_tmul, Module.Basis.coe_constrL, ModuleCat.exteriorPower.iso₀_hom_apply, MeasureTheory.OuterMeasure.map_comap, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.applyAsHom_comm_apply, HahnSeries.coe_truncLTLinearMap, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, QuadraticMap.toQuadraticMap_associated, TensorProduct.map_map_assoc_symm, MvPolynomial.bind₂_monomial, IsLocalizedModule.fromLocalizedModule.inj, Module.Invertible.bijective_curry, Algebra.traceForm_toMatrix, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, LinearMap.trace_eq_zero_of_mapsTo_ne, ModuleCat.restrictScalarsId'App_hom_apply, groupCohomology.subtype_comp_d₀₁_apply, MvPolynomial.monomialOneHom_apply, Module.Basis.coe_sumCoords_of_fintype, LinearMap.coprod_apply, realPart.norm_le, LinearMap.comp_zero, SheafOfModules.pushforwardComp_inv_app_val_app, Submodule.span_range_inclusion_eq_top, cross_anticomm', spinGroup.conjAct_smul_ι_mem_range_ι, LinearMap.mul_eq_one_comm, Matrix.toLin_scalar, TensorProduct.instDirectedSystemCoeLinearMapIdRTensor, Submodule.image_span_subset_span, LeftInvariantDerivation.evalAt_coe, ModuleCat.FilteredColimits.forget_preservesFilteredColimits, Polynomial.iterate_derivative_natCast_mul, Module.rank_linearMap, groupCohomology.H2π_eq_iff, DirectSum.sigmaLcurry_apply, LinearMap.adjoint_rTensor, toBilin'Aux_toMatrixAux, IsSimpleModule.toSpanSingleton_surjective, MvPolynomial.coeff_homogeneousComponent, LinearMap.IsPositive.add, LieModule.coe_genWeightSpaceOf_zero, LinearMap.adjoint_inner_right, TensorAlgebra.equivFreeAlgebra_ι_apply, BilinForm.dotProduct_toMatrix_mulVec, LinearMap.BilinForm.tensorDistrib_tmul, AdjoinRoot.mk_leftInverse, CliffordAlgebra.coe_toEven_reverse_involute, Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, TensorProduct.AlgebraTensorModule.mk_apply, LinearMap.toMvPolynomial_add, LinearMap.trace_transpose', Polynomial.natTrailingDegree_monomial, MvPowerSeries.WithPiTopology.uniformContinuous_coeff, ContinuousAffineMap.coe_linear_eq_coe_contLinear, LinearMap.comp_apply, LinearMap.IntrinsicStar.starLinearEquiv_eq_arrowCongr, IsTensorProduct.equiv_symm_apply, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, Projectivization.cross_mk_of_cross_ne_zero, Matrix.toLpLin_one, Module.Basis.trace_mul_traceDual, LinearIsometry.lTensor_apply, CliffordAlgebra.ι_mul_ι_mul_ι, Polynomial.eval_monomial_one_add_sub, groupCohomology.cocycles₂_map_one_snd, inner_map_polarization', LinearMap.mul'_apply, LinearMap.map_neg, RootPairing.InvariantForm.exists_apply_eq_or, ModuleCat.homAddEquiv_symm_apply_hom, Rep.coinvariantsTensorFreeLEquiv_apply, SchwartzMap.pairing_apply, MvPolynomial.monomial_left_inj, Finsupp.leftInverse_lcomapDomain_mapDomain, Module.Dual.transpose_apply, LinearMap.det_prodMap, LinearMap.BilinForm.compLeft_injective, Polynomial.map_taylor, LinearMap.isPosSemidef_iff_posSemidef_toMatrix, MvPolynomial.X_dvd_monomial, RootPairing.zero_le_rootForm, groupHomology.toCycles_comp_isoCycles₁_hom_apply, subset_tangentConeAt_prod_right, TannakaDuality.FiniteGroup.sumSMulInv_apply, TensorProduct.AlgebraTensorModule.rTensor_tmul, RootPairing.Equiv.comp_coweightMap_apply, Representation.mem_invariants_iff_of_forall_mem_zpowers, Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, spinGroup.involute_act_ι_mem_range_ι, CategoryTheory.Functor.mapExtLinearMap_coe, Derivation.mapCoeffs_monomial, MeasureTheory.ae_ae_add_linearMap_mem_iff, RootPairing.Equiv.weightEquiv_apply, Module.FaithfullyFlat.rTensor_exact_iff_exact, IsLocalizedModule.map_comp', MvPowerSeries.monomial_zero_eq_C, MvPowerSeries.coeff_inv, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, LaurentSeries.derivative_iterate_coeff, QuadraticMap.toBilin_apply, Finsupp.linearCombination_linear_comp, linearIndependent_algHom_toLinearMap, TensorAlgebra.lift_ι_apply, Matrix.singleLinearMap_apply, MeasureTheory.OuterMeasure.restrict_univ, Module.Basis.repr_eq_iff, KaehlerDifferential.linearMapEquivDerivation_symm_apply, PowerSeries.eval₂_eq_tsum, MvPolynomial.C_mul_monomial, LinearMap.neg_apply, Algebra.normalizedTrace_intermediateField, LinearMap.BilinForm.smul_right_of_tower, LinearMap.BilinForm.tensorDistribEquiv_apply, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Representation.ofQuotient_coe_apply, linearIndependent_toLinearMap, Algebra.Generators.H1Cotangent.exact_map_δ, Matrix.piLp_ofLp_toEuclideanLin, Algebra.Generators.H1Cotangent.δAux_monomial, LinearMap.coe_fst, LinearMap.BilinForm.toMatrix_apply, RootPairing.Hom.coweightHom_injective, MvPolynomial.vars_monomial, Polynomial.modByMonicHom_apply, Algebra.trace_isNilpotent_of_isNilpotent, MvPolynomial.pow_idealOfVars_eq_span, LieAlgebra.killingForm_apply_eq_zero_of_mem_rootSpace_of_add_ne_zero, RootPairing.reflectionPerm_coroot, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, TensorProduct.map₂_apply_tmul, CliffordAlgebra.adjoin_range_ι, LieSubmodule.traceForm_eq_zero_of_isTrivial, CliffordAlgebra.changeFormEquiv_apply, PowerBasis.constr_pow_algebraMap, LinearMap.dualProd_apply_apply, AnalyticOnNhd.eval_linearMap, lieEquivMatrix'_apply, PresheafOfModules.mono_iff_surjective, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, PowerSeries.trunc_X_of, LinearMap.map_zero, BilinForm.toMatrix_toBilin, AlgHom.toLinearMap_apply, SemimoduleCat.MonoidalCategory.tensorLift_tmul, LinearMap.toFun_eq_coe, IsLocalizedModule.linearEquiv_apply, Polynomial.derivative_X_pow_succ, LinearMap.isSymm_def, CliffordAlgebra.EquivEven.neg_e0_mul_v, Representation.mem_invariants, Matrix.mulVecLin_zero, LinearMap.quotientInfEquivSupQuotient_apply_mk, KaehlerDifferential.kerTotal_mkQ_single_add, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, FunOnFinite.linearMap_apply_apply, LinearMap.BilinForm.IsRefl.smul, LinearMap.intrinsicStar_zero, ProbabilityTheory.gaussianReal_map_linearMap, realPart_add_I_smul_imaginaryPart, LinearMap.BilinForm.IsNonneg.add, Rep.indToCoindAux_comm, MeasureTheory.Measure.map_def, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, Module.DirectLimit.congr_symm_apply_of, subset_tangentConeAt_prod_left, LinearEquiv.funCongrLeft_apply, Submodule.localized'_span, LinearMap.compr₂_apply, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, LinearMap.minpoly_toMatrix', LinearMap.BilinForm.IsPosSemidef.smul, Seminorm.comp_smul, MvPolynomial.bind₂_monomial_one, Derivation.leibniz', Polynomial.degree_monomial_le, LinearMap.trace_prodMap, Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd, LinearMap.liftBaseChangeEquiv_symm_apply, Fintype.bilinearCombination_apply, Polynomial.coeff_monomial_of_ne, Algebra.TensorProduct.equivFinsuppOfBasis_apply, CompactlySupportedContinuousMap.toRealLinearMap_apply, LinearMap.compQuadraticMap_polar, Polynomial.derivative_X_sub_C_pow, LinearMap.toMatrix₂_comp, exteriorPower.map_apply_ιMulti_family, LinearMap.range_eq_bot, LinearMap.restrictScalars_smul, Lagrange.degree_interpolate_erase_lt, LinearEquiv.conj_exact_iff_exact, Algebra.isNilpotent_trace_of_isNilpotent, LinearMap.lsmul_flip_apply, groupHomology.cyclesIso₀_comp_H0π_apply, LinearMap.toAddMonoidHom_injective, Algebra.TensorProduct.opAlgEquiv_apply, ContinuousAffineMap.coe_mk_const_linear_eq_linear, Bialgebra.counit_surjective, isLocalizedModule_iff, LinearMap.deriv, Matrix.SeparatingRight.toLinearMap₂', Algebra.Extension.Hom.sub_one_tmul, killingForm_eq_zero_of_mem_zeroRoot_mem_posFitting, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, GradedAlgebra.proj_recompose, Module.Basis.repr_linearCombination, groupHomology.eq_d₃₂_comp_inv_apply, Submodule.apply_coe_mem_map, SpecialLinearGroup.det_eq_one, PowerSeries.order_monomial, Coalgebra.sum_counit_smul, LinearMap.isClosed_range_coe, TensorProduct.lift.tmul', Module.DirectLimit.of_f, PointedCone.mem_dual, Submodule.mem_iSup_iff_exists_dfinsupp, Submodule.map₂_map_left, CondensedMod.epi_iff_surjective_on_stonean, IsSelfAdjoint.skewAdjointPart_apply, MvPowerSeries.coeff_homogeneousComponent, KaehlerDifferential.exact_mapBaseChange_map, PowerSeries.monomial_mul_monomial, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, LinearMap.pow_eq_aeval_mod_charpoly, LinearMap.prodEquiv_symm_apply, LinearMap.BilinForm.add_left, Seminorm.comp_zero, LinearMap.zero_compMultilinearMap, LinearMap.toSpanSingleton_apply_one, LinearMap.tensorProductEnd_apply, lift_rank_lt_rank_dual', LinearMap.snd_eq_coprod, PointwiseConvergenceCLM.isInducing_inducingFn, Matrix.toLpLin_pow, KaehlerDifferential.tensorKaehlerEquiv_tmul, DomMulAct.coe_smul_linearMap, TensorProduct.inner_mapIncl_mapIncl, Module.AEval'.X_pow_smul_of, LinearMap.trace_eq_contract', RootPairing.toLinearMap_apply_PolarizationIn, Algebra.Generators.H1Cotangent.δAux_toAlgHom, Module.finrank_linearMap, AlgEquiv.toLinearMap_injective, Finsupp.linearCombination_single_index, Polynomial.derivWithin, fdifferential_apply, KaehlerDifferential.D_apply, MeasureTheory.OuterMeasure.map_iInf_le, CliffordAlgebra.EquivEven.e0_mul_v_mul_e0, CliffordAlgebraComplex.ofComplex_I, InnerProductSpace.AlgebraOfCoalgebra.mul_def, LinearMap.BilinForm.separatingRight_toMatrix'_iff, LinearMap.extendTo𝕜_apply, Matrix.isUnit_toLin'_iff, HahnEmbedding.IsPartial.truncLT_mem_range, Module.piEquiv_apply_apply, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T, RootPairing.EmbeddedG2.long_eq_three_mul_short, LinearMap.BilinForm.smul_left, Finsupp.lift_apply, LinearIndependent.linearCombinationEquiv_apply_coe, Submodule.dualCoannihilator_map_linearEquiv_flip, Polynomial.adjSylvester_comp_sylveserMap, Polynomial.exists_iterate_derivative_eq_factorial_smul, innerₗ_apply, Finset.weightedVSub_smul, TensorAlgebra.toClifford_ι, RootPairing.GeckConstruction.trace_toEnd_eq_zero, Polynomial.monomial_injective, Matrix.toLin'_mul, Polynomial.taylor_eq_zero, MonoidAlgebra.lsingle_apply, IsArtinian.range_smul_pow_stabilizes, Submodule.iSup_eq_range_dfinsupp_lsum, ModularGroup.lcRow0Extend_apply, TensorProduct.gradedComm_tmul_of_zero, LinearMap.isNilpotent_toMatrix_iff, LinearMap.BilinForm.lieInvariant_iff, LieModule.Cohomology.twoCochain_skew, Module.Relations.Solution.directSum_var, AffineMap.vadd_linear, LocallyConstant.evalₗ_apply, LinearMap.BilinForm.dotProduct_toMatrix_mulVec, Lagrange.degree_interpolate_lt, ModuleCat.inv_hom_apply, Module.End.rTensorAlgHom_apply_apply, LinearMap.det_eq_det_toMatrix_of_finset, LieModule.traceForm_comm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, Algebra.linearMap_apply, ModuleCat.forget₂AddCommGroup_preservesLimits, LinearMap.toMatrix_reindexRange, ExteriorAlgebra.liftAlternating_apply_ιMulti, ContinuousLinearMap.coe_smulRightₗ, Module.Flat.iff_lTensor_exact, PolynomialLaw.exists_lift, LinearMap.toMvPolynomial_zero, MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict, QuadraticAlgebra.reₗ_apply, LaurentSeries.derivative_apply, groupHomology.mapCycles₁_id_comp_apply, LinearMap.ker_toAddSubmonoid, LinearMap.vecCons_apply, RatFunc.laurentAux_div, Matrix.ofLp_toLpLin, traceForm_dualSubmodule_adjoin, Module.range_piEquiv, DirectSum.lof_eq_of, polyEquivTensor_symm_apply_tmul, LinearMap.IsSymmetric.continuous, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, Ideal.quotientToQuotientRangePowQuotSucc_mk, MvPowerSeries.weightedHomogeneousComponent_of_lt_weightedOrder_eq_zero, Matrix.toBilin'_symm, StarModule.decomposeProdAdjoint_symm_apply, PresheafOfModules.presheaf_map_apply_coe, MvPowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, PiTensorProduct.piTensorHomMap_tprod_tprod, PowerSeries.eq_X_mul_shift_add_const, Submodule.coe_inclusion, MvPowerSeries.coeff_subst, CoalgHomClass.counit_comp_apply, Rep.ofMulDistribMulAction_ρ_apply_apply, LinearMap.isSymmetric_sum, MeasureTheory.OuterMeasure.comap_top, LinearMap.toMatrix_smulBasis_left, IsAdjoinRootMonic.modByMonicHom_map, RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs, VertexOperator.ncoeff_apply, Module.Dual.transpose_comp, Polynomial.derivativeFinsupp_apply_apply, LinearMap.GeneralLinearGroup.toLinearEquiv_inv, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, LinearMap.BilinForm.isSymm_iff_flip, Polynomial.sup_aeval_range_eq_top_of_isCoprime, Module.Basis.prod_apply, RootPairing.corootForm_apply_apply, LinearMap.flip_bijective_iff₁, Polynomial.taylor_apply, Submodule.comap_coe, LinearMap.flip_bijective_iff₂, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, Algebra.Extension.Cotangent.mk_eq_zero_iff, Rep.instIsTrivialCarrierVModuleCatOfCompLinearMapIdρ, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, LinearMap.BilinForm.mem_dualSubmodule, LinearMap.det_toLin', CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Polynomial.iterate_derivative_comp_one_sub_X, LinearMap.mapMatrixModule_apply, Algebra.Presentation.differentials.surjective_hom₁, DirectSum.lmap_eq_map, LinearPMap.apply_comp_inclusion, DFinsupp.filterLinearMap_apply, DirectSum.coe_congr_linearEquiv, TensorAlgebra.lift_comp_ι, LieSubmodule.toEnd_comp_subtype_mem, Matrix.kroneckerMapBilinear_apply_apply, LaurentSeries.powerSeriesPart_coeff, LinearMap.minpoly_dvd_charpoly, PowerBasis.trace_gen_eq_nextCoeff_minpoly, LinearMap.SeparatingRight.congr, Ideal.pi_tensorProductMk_quotient_surjective, Matrix.rank_eq_finrank_range_toLin, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, CliffordAlgebra.invOf_ι_mul_ι_mul_ι, Matrix.toLinearMapRight'_mul_apply, Polynomial.degree_derivative_lt, BilinForm.toMatrix_comp, TensorProduct.nnnorm_map, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_ne, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, CliffordAlgebra.EvenHom.contract, Polynomial.derivative_natCast_mul, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, ModuleCat.mono_iff_injective, Module.Basis.linearCombination_dualBasis, Ideal.mapCotangent_toCotangent, PiTensorProduct.norm_eval_le_injectiveSeminorm, ContinuousLinearMap.coe_coe, SchwartzMap.convolution_apply, Module.Flat.iff_lTensor_preserves_injective_linearMap', Algebra.Generators.Cotangent.surjective_map_ofComp, ModuleCat.forget₂_obj, Polynomial.fderiv_aeval, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one, transpose_dualTensorHom, AffineMap.linearMap_vsub, MvPolynomial.coeff_monomial_mul, LinearMap.coe_proj, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, Matrix.toLin_mul, Rep.indResAdjunction_counit_app_hom_hom, FDRep.hom_hom_action_ρ, CliffordAlgebra.map_apply_ι, LinearMap.lTensor_neg, Matrix.toLin_pow, LieSubmodule.mem_baseChange_iff, QuadraticMap.associated_tmul, Submodule.FG.lTensor.directLimit_apply', TensorProduct.directSumLeft_tmul_lof, Algebra.Generators.H1Cotangent.exact_δ_map, PowerSeries.coeff_invUnitsSub, Module.Free.linearMap, SemimoduleCat.hom_inv_apply, SkewPolynomial.monomial_zero_one, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Derivation.liftKaehlerDifferential_comp, Representation.FiniteCyclicGroup.coinvariantsKer_eq_range, Matrix.toLin_self, Rep.coindToInd_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, Module.Finite.linearMap, groupHomology.mapCycles₁_comp_i_apply, CliffordAlgebra.ι_mul_ι_add_swap, DirectSum.lieAlgebraComponent_apply, AlternatingMap.ofSubsingleton_apply_apply, SheafOfModules.pushforwardCongr_hom_app_val_app, RootPairing.Hom.comp_weightMap_apply, Polynomial.valuation_inv_monomial_eq_valuation_X_zpow, Polynomial.sum_monomial_index, Module.DirectLimit.linearEquiv_of, Polynomial.derivativeFinsupp_derivative, Complex.det_conjAe, Finsupp.lsum_single, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, MvPolynomial.dvd_monomial_iff_exists, AlgCat.forget₂Module_preservesLimitsOfSize, LinearMap.BilinForm.neg_left, ModuleCat.comp_apply, mulRightLinearMap_zero_eq_zero, AlgHom.toKerIsLocalization_apply, LinearMap.BilinForm.sum_repr_mul_repr_mul, Orientation.kahler_neg_orientation, PowerSeries.prod_monomial, ModuleCat.restrictScalarsCongr_hom_app, AdicCompletion.coe_eval, LinearMap.separatingLeft_toMatrix₂'_iff, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, KaehlerDifferential.mapBaseChange_surjective, AffineMap.neg_linear, PowerSeries.coeff_succ_C, Polynomial.sum_monomial_eq, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, TannakaDuality.FiniteGroup.leftRegular_apply, Module.FaithfullyFlat.iff_zero_iff_lTensor_zero, ContinuousMap.coeFnLinearMap_apply, ContinuousLinearMap.isIdempotentElem_toLinearMap_iff, LeftInvariantDerivation.left_invariant'', groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CliffordAlgebra.contractLeft_contractLeft, LinearMap.pi_apply, TensorProduct.algebraMap_gradedMul, trace_eq_finrank_mul_minpoly_nextCoeff, PowerSeries.trunc_trunc_mul, Matrix.cramer_zero, hasEigenvector_toLin'_diagonal, LinearMap.lcomp_apply, Matrix.GeneralLinearGroup.toLin'_apply, LinearMap.mapMatrixModule_id_apply, Representation.apply_bijective, CategoryTheory.whiskering_linearYoneda, LinearMap.separatingRight_iff_flip_ker_eq_bot, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, MvPolynomial.mkDerivationₗ_monomial, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, LinearMap.toMatrixAlgEquiv'_apply, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, Submodule.FG.rTensor.directLimit_apply, LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, TensorProduct.directLimitLeft_rTensor_of, LinearMap.IsSymmetric.toSelfAdjoint_apply, MeasureTheory.Lp.constₗ_apply, LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrict, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, LinearMap.BilinForm.IsAlt.self_eq_zero, Polynomial.degree_derivative_eq, Polynomial.C_mul_monomial, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, LinearMap.intrinsicStar_comp', Polynomial.natDegree_hasseDeriv_le, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, ModuleCat.FilteredColimits.M.mk_map, ContinuousLinearMapWOT.isInducing_inducingFn, groupCohomology.π_comp_H0Iso_hom_apply, IsTensorProduct.equiv_apply, Matrix.vecMulLinear_apply, Matrix.toLinearMapₛₗ₂'_toMatrix', LinearMap.continuous_of_isContPerfPair, LinearMap.pi_eq_zero, ConvexCone.mem_map, Bialgebra.comul_algebraMap, LinearMap.toMatrix'_algebraMap, isNoetherian_linearMap, LinearMap.ext_iff, Matrix.cramer_reindex, Submodule.inclusionSpan_apply_coe, groupHomology.coe_mapCycles₂, TensorProduct.counit_tmul, PiTensorProduct.liftEquiv_symm_apply, PiToModule.fromMatrix_apply_single_one, LocalizedModule.coe_map_eq, Representation.linHom_apply, MvPolynomial.sum_weightedHomogeneousComponent, Algebra.Extension.CotangentSpace.map_sub_map, QuadraticMap.associated_toQuadraticMap, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, MvPowerSeries.HasSubst.coeff_zero, LinearMap.dualMap_injective_iff, LinearMap.isPositive_natCast, Algebra.normalizedTrace_eq_of_fininteDimensional, CategoryTheory.whiskering_linearCoyoneda₂, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, MeasureTheory.OuterMeasure.map_map, AlternatingMap.curryLeft_apply_toMultilinearMap, LieModule.isNilpotent_toEnd_of_isNilpotent₂, Polynomial.as_sum_range, SkewPolynomial.monomial_zero_right, MeasureTheory.SignedMeasure.re_toComplexMeasure, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, Module.reflection_mul_reflection_pow, groupHomology.H1π_comp_map_apply, CoalgHom.coe_mk, BilinearForm.toMatrixAux_eq, CliffordAlgebra.contractLeft_ι_mul, QuadraticMap.two_nsmul_associated, RootPairing.rootForm_reflection_reflection_apply, Submodule.IsPrincipal.generator_submoduleImage_dvd_of_mem, LieHom.lie_apply, CliffordAlgebra.comp_ι_sq_scalar, RootPairing.posRootForm_posForm_pos_of_ne_zero, Matrix.SeparatingLeft.toBilin, Matrix.charpoly_toLin, LinearMap.inr_injective, LinearEquiv.toLinearMap_injective, FGModuleCat.FGModuleCatCoevaluation_apply_one, Module.Basis.coe_sumCoords_eq_finsum, LinearMap.toMatrixOrthonormal_symm_apply, LinearMap.map_dfinsuppSumAddHom, Derivation.compAlgebraMapL_apply_apply, LinearEquiv.congrLeft_apply, IsLocalizedModule.map_linearCombination, LinearMap.BilinMap.baseChange_tmul, Module.Flat.eqLocus_lTensor_eq, Subspace.dualRestrict_leftInverse, StrongDual.dualPairing_apply, LinearMap.intrinsicStar_rTensor, LinearMap.semilinearMapClass, HopfAlgebra.sum_antipode_mul_eq_smul, LinearMap.BilinForm.IsPosSemidef.add, LinearEquiv.piRing_symm_apply, Module.DirectLimit.congr_apply_of, MeasureTheory.OuterMeasure.restrict_empty, trace_eq_trace_adjoin, CliffordAlgebra.even.lift_ι, LinearMap.toMatrix_mulVec_repr, Module.charP_end, LinearMap.BilinForm.zero_left, Submodule.IsCompl.projection_eq_self_iff, LinearMap.toMatrix_innerₛₗ_apply, Module.Basis.ofIsLocalizedModule_apply, QuadraticMap.associated_left_inverse', KaehlerDifferential.map_surjective_of_surjective, LieModule.Cohomology.mem_twoCochain_iff, Submodule.mkQ_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, LinearMap.funLeft_injective_of_surjective, TensorProduct.lift.tmul, AffineMap.hasDerivAt, Matrix.toLin_apply_eq_zero_iff, MvPolynomial.modMonomial_add_divMonomial, StarConvex.linear_image, MonomialOrder.span_leadingTerm_eq_span_monomial', TensorProduct.lTensorHomToHomLTensor_apply, IsLocalizedModule.mapEquiv_apply, Algebra.PreSubmersivePresentation.jacobian_eq_det_aevalDifferential, Polynomial.det_taylorLinearEquiv_toLinearMap, IsTensorProduct.map_one, Matrix.nondegenerate_toBilin_iff, Coalgebra.sum_counit_tmul_map_eq, LinearMap.range_toContinuousLinearMap, Ideal.exact_mulQuot_quotOfMul, MvPolynomial.decompose'_apply, LinearMap.BilinForm.isSymm_neg, LieModule.Weight.coe_toLinear_eq_zero_iff, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, Matrix.toLin'_reindex, MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable, LinearMap.transvection.apply, PowerSeries.IsRestricted.isRestricted_iff, LinearMap.BilinForm.toDual_def, CliffordAlgebra.contractRight_mul_algebraMap, MeasureTheory.OuterMeasure.map_ofFunction, Matrix.PosSemidef.toLinearMap₂'_zero_iff, groupHomology.π_comp_H0Iso_hom_apply, LinearMap.BilinForm.toMatrix'_compLeft, Matrix.toLinearMapₛₗ₂_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, IsLocalizedModule.fromLocalizedModule_mk, Polynomial.monomial_mul_X, MeasureTheory.OuterMeasure.map_comap_of_surjective, Finsupp.lcomapDomain_apply, Polynomial.rootSet_derivative_subset_convexHull_rootSet, Polynomial.mapAlgHom_monomial, groupCohomology.eq_d₀₁_comp_inv_apply, LinearMap.BilinForm.dualBasis_repr_apply, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, MultilinearMap.map_add_sub_map_add_sub_linearDeriv, PiTensorProduct.liftEquiv_apply, MvPowerSeries.coeff_one, LinearMap.smul_lTensor, Polynomial.iterate_derivative_X_pow_eq_natCast_mul, LinearMap.lsmul_injective, ModuleCat.MonoidalCategory.tensorLift_tmul, Profinite.NobelingProof.Products.eval_πs_image', Module.IsReflexive.bijective_dual_eval', TensorProduct.intrinsicStar_map, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, Polynomial.natDegree_taylor, Unitization.sndHom_apply, Polynomial.degree_taylor, LinearMap.smulRight_apply_eq_zero_iff, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, span_range_eq_top_iff_surjective_fintypeLinearCombination, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, ExteriorAlgebra.liftAlternating_one, PolynormableSpace.induced, Subspace.flip_quotDualCoannihilatorToDual_bijective, LinearMap.isSelfAdjoint_iff', Derivation.commutator_coe_linear_map, Submodule.apply_mem_map₂, Orientation.areaForm'_apply, MvPolynomial.monomial_one_mul_cancel_left_iff, Finsupp.mapRange.linearMap_apply, pinGroup.conjAct_smul_ι_mem_range_ι, DirectSum.linearEquivFunOnFintype_lof, groupCohomology.cocycles₁_map_inv, Module.Basis.end_apply, Rep.freeLiftLEquiv_apply, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors, LinearMap.add_comp, Module.End.ringEquivEndFinsupp_apply_apply_apply, LinearMap.toSpanSingleton_smul, TensorProduct.rTensor_injective_of_forall_vanishesTrivially, PowerSeries.coeff_mk, Submodule.set_smul_eq_map, MvPolynomial.coe_basisMonomials, Polynomial.hasFDerivAt, MultilinearMap.curryMid_apply_apply, PresheafOfModules.surjective_of_epi, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, RingHom.toKerIsLocalization_apply, Matrix.Nondegenerate.toBilin, PowerSeries.sub_const_eq_X_mul_shift, LinearMap.coe_range, SemimoduleCat.MonoidalCategory.tensorμ_apply, LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, Derivation.coe_comp, LinearMap.IsPositive.isSelfAdjoint, ModuleCat.adj_homEquiv, LinearMap.toMatrix'_apply, LinearMap.mem_span_iff_continuous_of_finite, MvPolynomial.monomial_mem_pow_idealOfVars_iff, Matrix.toLpLin_toLp, PowerSeries.coeff_largeSchroderSeries, Representation.finsuppToCoinvariants_single_mk, MvPowerSeries.coeff_mul_right_one_sub_of_lt_order, apply_eq_dotProduct_toMatrix₂_mulVec, AlgHom.toLinearMap_injective, LinearEquiv.mem_dilatransvections_iff_finrank, LinearMap.coe_toContinuousLinearMap, Rep.indToCoindAux_mul_fst, LinearMap.BilinForm.separatingRight_toMatrix_iff, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, LinearMap.flip_apply, LinearMap.mulLeft_apply, TensorProduct.finsuppLeft_apply, LinearMap.ext_ring_iff, MvPolynomial.irreducible_sumSMulX, LinearMap.BilinForm.SeparatingLeft.toMatrix', RootPairing.Equiv.comp_weightMap_apply, TensorProduct.mapBilinear_apply, Lagrange.eq_interpolate, Subalgebra.LinearDisjoint.trace_algebraMap, LightCondensed.forget_map_val_app, MvPowerSeries.coeff_expand_smul, finsetBasisOfTopLeSpanOfCardEqFinrank_repr_apply, LinearMap.finiteDimensional', ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, PiTensorProduct.dualDistribInvOfBasis_apply, LinearMap.kerComplementEquivRange_apply_coe, Representation.asAlgebraHom_single_one, CStarAlgebra.linear_combination_nonneg, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, LinearMap.quotientInfEquivSupQuotient_injective, linearIndependent_inl_union_inr', ModuleCat.piIsoPi_inv_kernel_ι_apply, Submodule.map₂_eq_span_image2, Polynomial.separable_def', ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, Rep.ihom_obj_ρ_apply, Orthonormal.inner_finsupp_eq_sum_right, Matrix.ker_toLin_eq_bot, FourierTransform.fourierInvₗ_apply, Polynomial.derivative_of_natDegree_zero, TensorProduct.AlgebraTensorModule.dualDistrib_apply, Representation.finsupp_single, ContinuousLinearMap.toLinearMap_innerSL_apply, RootPairing.Hom.coroot_coweightMap, CliffordAlgebra.GradedAlgebra.ι_apply, LinearMapClass.ker_eq_bot, CondensedMod.hom_naturality_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, star_mul_self_add_self_mul_star, GradedTensorProduct.auxEquiv_mul, Fintype.linearIndependent_iff'ₛ, LinearMap.IsSymmetric.adjoint_eq, LinearMap.isPositive_sum, HahnSeries.ofPowerSeries_apply_coeff, MvPowerSeries.eval₂_eq_tsum, Submodule.lTensorOne'_tmul, RootPairing.CoPolarizationIn_eq, Module.FinitePresentation.linearEquivMap_apply, LinearMap.hasDerivWithinAt, MvPowerSeries.homogeneousComponent_of_lt_order_eq_zero, Algebra.Generators.cotangentRestrict_bijective_of_isCompl, MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination, CStarMatrix.toCLM_apply_single, Module.Relations.map_single, ModuleCat.lof_coprodIsoDirectSum_inv_apply, Submodule.span_preimage_eq, Polynomial.Splits.taylor, pow_mulLeftLinearMap, LinearMap.BilinMap.isSymm_iff_eq_flip, Submodule.rTensorOne'_tmul_one, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, LinearMap.llcomp_apply', imaginaryPart.norm_le, AffineBasis.det_smul_coords_eq_cramer_coords, LinearIndependent.map', ModuleCat.Derivation.desc_d, LinearMap.BilinForm.zero_apply, Prod.comul_apply, reesAlgebra.monomial_mem, TannakaDuality.FiniteGroup.equivApp_inv, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative, Algebra.Extension.CotangentSpace.map_cotangentComplex, QuadraticModuleCat.forget₂_map_associator_hom, MvPolynomial.coeff_sumSMulX, PresheafOfModules.injective_of_mono, ContinuousLinearMapWOT.isEmbedding_inducingFn, LinearMap.linearIndependent_iff, QuotSMulTop.equivQuotTensor_naturality, AddMonoidHom.coe_toNatLinearMap, LinearMap.smulRightₗ_apply, LinearMap.IsNonneg.smul, Submodule.rTensorOne'_tmul, PowerSeries.derivativeFun_coe, CliffordAlgebra.reverse.map_mul, IsLocalizedModule.mapEquiv_symm_apply, MvPowerSeries.le_weightedOrder_subst, ModuleCat.free_ε_one, LinearMap.toMatrix'_symm, Polynomial.coeff_monomial, Module.Invertible.rTensor_injective_iff, LinearMap.IsSymmetric.isSymmetric_smul_iff, LinearMap.injective_of_comp_eq_id, AdicCompletion.of_bijective_iff, groupCohomology.norm_ofAlgebraAutOnUnits_eq, MvPowerSeries.monomial_zero_eq_C_apply, TensorProduct.AlgebraTensorModule.map_add_left, LinearMap.mapMatrix_smul, RootPairing.algebraMap_rootFormIn, KaehlerDifferential.derivationQuotKerTotal_apply, InnerProductGeometry.norm_ofLp_crossProduct, TensorProduct.AlgebraTensorModule.uncurry_apply, TensorProduct.map_comm, Module.DirectLimit.exists_of, LinearMap.coe_sum, Pretrivialization.linearMapAt_apply, mulRightLinearMap_eq_zero_iff, Differential.mapCoeffs_monomial, AlternatingMap.domCoprod'_apply, ExteriorAlgebra.ι_sq_zero, Polynomial.taylor_coeff_zero, MonomialOrder.monic_monomial, PowerSeries.monomial_zero_eq_C, groupCohomology.mem_cocycles₂_iff, LinearMap.polyCharpolyAux_map_eq_charpoly, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Submodule.LinearDisjoint.injective, DirectSum.lmap_surjective, Submodule.baseChange_eq_span, linearMap_toMatrix_mul_basis_toMatrix, TrivSqZeroExt.liftEquiv_apply, CliffordAlgebra.isUnit_ι_iff, LinearMap.mem_submoduleImage, LinearMap.add_compMultilinearMap, Submodule.dualCopairing_apply, Module.dualPairing_apply, LinearMap.iterateKer_coe, Polynomial.mul_eq_sum_sum, PowerSeries.monomial_pow, Polynomial.mkDerivationEquiv_apply, Derivation.liftKaehlerDifferential_comp_D, LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, CStarMatrix.toCLM_apply_eq_sum, TensorProduct.AlgebraTensorModule.coe_lTensor, LinearMap.BilinForm.isNonneg_zero, LinearMap.exact_smul_id_smul_top_mkQ, Coalgebra.rTensor_counit_comp_comul, LinearMap.toMatrix_transpose_apply, LinearMap.BilinForm.IsSymm.sub, isCompactOperator_iff_image_closedBall_subset_compact, PowerSeries.eq_X_pow_mul_shift_add_trunc, PresheafOfModules.pushforward_obj_map_apply, Polynomial.iterate_derivative_C, toMatrix_dualTensorHom, SemimoduleCat.homAddEquiv_apply, PowerSeries.trunc_trunc_of_le, PolynomialModule.comp_apply, LinearEquiv.arrowCongr_apply, LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot, MulOpposite.coe_opLinearEquiv_toLinearMap, MonomialOrder.sPolynomial_def, ContinuousLinearMap.coeLM_apply, groupHomology.d₂₁_comp_d₁₀_apply, DirectSum.lmap_lof, IsLocalizedModule.mk'_cancel', ContinuousAlternatingMap.toContinuousMultilinearMapLinear_apply, exteriorPower.alternatingMapLinearEquiv_apply_ιMulti, Algebra.Generators.H1Cotangent.δAux_ofComp, Polynomial.taylor_X_pow, RootPairing.isCompl_rootSpan_ker_rootForm, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, CliffordAlgebra.changeForm_ι_mul_ι, groupHomology.mapCycles₂_comp_apply, Module.Relations.Quotient.linearMap_ext_iff, TensorProduct.AlgebraTensorModule.homTensorHomMap_apply, RootPairing.reflectionPerm_root, LinearMap.isPositive_toContinuousLinearMap_iff, Matrix.range_toLin', LinearMap.prodMapLinear_apply, LinearIndependent.span_repr_eq, MeasureTheory.OuterMeasure.map_iSup, Submodule.map₂_span_singleton_eq_map_flip, LinearMap.pi_apply_eq_sum_univ, RootPairing.rootForm_self_eq_zero_iff, LinearMap.linearIndependent_iff_of_disjoint, ModularFormClass.qExpansion_coeff, Submodule.prodEquivOfIsCompl_symm_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, PiTensorProduct.piTensorHomMap_tprod_eq_map, Rep.ofDistribMulAction_ρ_apply_apply, LinearEquiv.skewProd_symm_apply, Submodule.injective_tensorToSpan, MvPolynomial.as_sum, LinearMap.dualMap_apply', LinearMap.mul_toMatrix', Matrix.liftLinear_apply, Rep.linearization_η_hom_apply, LinearMap.det_eq_zero_iff_ker_ne_bot, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, MonomialOrder.leadingCoeff_monomial, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, ModuleCat.smulNatTrans_apply_app, exteriorPower.ιMultiDual_apply_ιMulti, MvPolynomial.monomial_add_single, Algebra.normalizedTrace_algebraMap_apply_eq_self, PiTensorProduct.lift_comp_reindex, LinearMap.ext_iff₂, CliffordAlgebra.EquivEven.neg_v_mul_e0, pow_mulRightLinearMap, Submodule.natAbs_det_equiv, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, LinearMap.coe_prod, LinearMap.dualMap_bijective_iff, HVertexOperator.of_coeff_coeff, PiTensorProduct.map₂_tprod_tprod, LinearMap.star_eq_adjoint, skewAdjoint.negISMul_apply_coe, Polynomial.toFn_zero, LinearMap.instLieModule, IsLocalizedModule.mk'_one, Module.Basis.sum_dual_apply_smul_coord, LinearMap.compMultilinearMapₗ_apply, Polynomial.ofFn_zero', Matrix.mul_adjugate_apply, Polynomial.derivative_C_mul_X, IsLocalFrameOn.eventually_eq_sum_coeff_smul, LieDerivation.coe_zero_linearMap, LinearEquiv.conjRingEquiv_apply_apply, LinearMap.toMatrix_smulBasis_right, Matrix.toLpLin_symm_id, Polynomial.eval_iterate_derivative_rootMultiplicity, Polynomial.lcoeff_apply, Polynomial.iterate_derivative_derivative_mul_X, Module.Basis.toDual_eq_repr, Polynomial.Chebyshev.add_one_mul_self_mul_T_eq_poly_in_T, Matrix.range_toLin_eq_top, Trivialization.coe_linearMapAt, AlternatingMap.curryLeft_zero, LinearMap.coe_toAffineMap, Unitization.inrHom_apply, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm, LinearAlgebra.FreeProduct.identify_one, Matrix.toLin_finTwoProd_apply, Submodule.mapQ_eq_factor, ModuleCat.forget_reflectsLimits, CliffordAlgebra.reverse_prod_map_ι, TannakaDuality.FiniteGroup.equivApp_hom, MeasureTheory.OuterMeasure.restrict_iSup, ModuleCat.uliftFunctorForgetIso_inv_app, FDRep.char_linHom, TensorProduct.map_smul_right, PowerSeries.coeff_exp, HVertexOperator.coeff_inj_iff, LinearMap.BilinForm.dualBasis_eq_iff, Matrix.isPositive_toEuclideanLin_iff, Finsupp.linearCombination_apply, PointedCone.mem_map, addMonoidEndRingEquivInt_apply, FreeAlgebra.toTensor_ι, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, Polynomial.iterate_derivative_eq_zero, FourierTransform.fourierₗ_apply, AffineMap.map_vadd, LinearMap.uncurryMid_apply, RootPairing.polarizationEquiv_apply, Polynomial.hasseDeriv_coeff, Matrix.toBilin'Aux_single, LieModule.lie_traceForm_eq_zero, IsLocalizedModule.map_mk', exteriorPower.pairingDual_ιMulti_ιMulti, LinearMap.lTensor_mul, Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors, LinearEquiv.isUnit_det', Polynomial.monomial_zero_one, Polynomial.hasseDeriv_mul, ExteriorAlgebra.map_apply_ι, LinearMap.mul_toMatrix₂, PointwiseConvergenceCLM.coeLMₛₗ_apply, Module.algebraMap_end_eq_smul_id, PowerSeries.trunc_one_left, groupHomology.H2π_eq_iff, MonomialOrder.monic_monomial_one, MvPowerSeries.isHomogeneous_iff_eq_homogeneousComponent, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, ExteriorAlgebra.ι_leftInverse, ProbabilityTheory.integral_linearMap_gaussianReal, LinearMap.ker_eq_range_of_comp_eq_id, LinearMap.mem_range_self, QuadraticMap.discr_comp, Module.Basis.linearMap_repr_apply, exteriorPower.alternatingMapLinearEquiv_comp_ιMulti, MvPolynomial.monomial_eq_zero, LinearMap.coe_dfinsuppSum, AlgEquiv.toLinearMapHom_apply_apply, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, LinearMap.lsmul_eq_DistribMulAction_toLinearMap, groupHomology.H1AddEquivOfIsTrivial_single, Module.eval_apply_eq_zero_iff, MvPolynomial.eval_monomial, LaurentSeries.hasseDeriv_comp_coeff, MvPolynomial.coeff_coe, LinearMap.coeFn_sum, AdicCompletion.map_mk, groupCohomology.mem_cocycles₁_iff, imaginaryPart_realPart, Ideal.quotientToQuotientRangePowQuotSucc_surjective, IsModuleTopology.continuous_bilinear_of_finite_left, LinearMap.lsum_single, MvPolynomial.coeff_monomial_mul', PiTensorProduct.map_mul, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, PresheafOfModules.unitHomEquiv_apply_coe, Algebra.Generators.cotangentCompAwaySec_apply, LieModule.trace_comp_toEnd_genWeightSpace_eq, MvPolynomial.monomial_mem_coeffsIn, LinearMap.IsProj.top, LinearMap.nondegenerate_congr_iff, Matrix.sum_cramer_apply, TensorProduct.gradedMul_one, Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff, RatFunc.laurentAux_algebraMap, MvPowerSeries.coeff_trunc', CliffordAlgebra.contractLeft_comm, DirectSum.ext_component_iff, CompactlySupportedContinuousMap.integralLinearMap_apply, LinearMap.le_def, ModuleCat.FreeMonoidal.εIso_inv_freeMk, PowerSeries.sub_const_eq_shift_mul_X, Module.End.smulLeft_apply, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, AdjoinRoot.modByMonicHom_mk, Matrix.traceLinearMap_apply, Matrix.UnitaryGroup.coe_toGL, FractionalIdeal.mem_dual, Finset.weightedVSub_const_smul, LinearMap.toMatrix'_mul, MvPowerSeries.coeff_zero_mul_X, groupHomology.isoCycles₂_hom_comp_i_apply, IsBaseChange.end, LinearMap.coe_compMultilinearMap, Algebra.trace_self_apply, LinearMap.adjoint_toSpanSingleton, LinearMap.lcomp_apply', CliffordAlgebra.ofBaseChange_tmul_ι, mul_basis_toMatrix, LinearMap.GeneralLinearGroup.congrLinearEquiv_apply, Finsupp.linearCombination_embDomain, CliffordAlgebra.reverse_reverse, Polynomial.iterate_derivative_X_pow_eq_smul, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, Module.dualProdDualEquivDual_apply_apply, MvPowerSeries.coeff_inv_aux, trace_eq_sum_roots, RootPairing.zero_le_posForm, LinearMap.injective_iff_surjective, Submodule.quotientPi_apply, CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero, Polynomial.linearIndependent_powers_iff_aeval, Polynomial.Chebyshev.derivative_U_eval_one, LinearMap.BilinForm.sub_apply, IsLocalizedModule.rTensor, LinearMap.toSpanSingleton_apply, Rep.coinvariantsShortComplex_f, SheafOfModules.pushforwardCongr_inv_app_val_app, killingForm_apply_apply, LinearMap.inl_eq_prod, imaginaryPart_eq_neg_I_smul_skewAdjointPart, LinearMap.trace_id, LinearMap.toMatrix_algebraMap, Algebra.trace_trace, LinearMap.spectrum_toMatrix, AdicCompletion.ofAlgEquiv_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, PowerBasis.constr_pow_gen, Polynomial.monomial_one_eq_iff, LaurentPolynomial.leval_apply, LinearMap.BilinForm.congr_refl, StandardEtalePresentation.toSubmersivePresentation_jacobian, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule, IsBaseChange.equiv_symm_apply, Function.Exact.inr_fst, LinearMap.IsSymmetric.natCast, LinearMap.SeparatingRight.toMatrix₂, MvPowerSeries.coeff_weightedHomogeneousComponent, Module.Finite.of_isComplemented_domain, Matrix.isUnit_toLin_iff, RootPairing.InvariantForm.apply_weylGroup_smul, Convex.linear_image, Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic, Subspace.quotAnnihilatorEquiv_apply, skewAdjointPart_comp_subtype_selfAdjoint, LinearMap.conjugate_apply, PowerSeries.HasSubst.monomial', Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, ModuleCat.RestrictionCoextensionAdj.unit'_app, Matrix.diagonal_toLin', LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, Module.isTorsionBySet_iff_subseteq_ker_lsmul, CStarMatrix.toCLM_apply, Polynomial.coeff_monomial_zero_mul, Module.End.mem_genEigenspace_top, Submodule.coe_mulMap_comp_eq, Bialgebra.counit_natCast, TensorProduct.AlgebraTensorModule.curry_apply, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, LinearMap.isPositive_self_comp_adjoint, Algebra.TensorProduct.mul_one, IsAdjoinRootMonic.ext_elem_iff, Matrix.charpoly_toLin', LinearMap.BilinForm.toMatrix_symm, Lagrange.iterate_derivative_interpolate, Polynomial.taylorAlgHom_apply, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, LinearMap.BilinMap.toQuadraticMap_smul, Representation.norm_comp_self, Matrix.toLinearMap₂'_toMatrix', Polynomial.pow_sub_dvd_iterate_derivative_pow, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, Module.DirectLimit.map_id, rank_dual_eq_card_dual_of_aleph0_le_rank', Submodule.isIdempotentElemEquiv_apply_coe, Matrix.toLinearMapₛₗ₂'_apply, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, Polynomial.hasFDerivAt_aeval, PolynomialModule.eval_lsingle, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply, IsLocalizedModule.map_apply, sectionOfRetractionKerToTensorAux_prop, Module.End.genEigenspace_one, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, ModuleCat.free_η_freeMk, Module.Flat.iff_lTensor_injective, Matrix.toLin'_pow, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, LinearMap.pi_ext_iff, Algebra.trace_eq_zero_of_not_exists_basis, LinearMap.range_eq_top, IsSymmetricAlgebra.equiv_symm_apply, PositiveLinearMap.toLinearMap_injective, LieModule.Cohomology.mem_twoCocycle_iff, CliffordAlgebra.ofBaseChangeAux_ι, Ideal.ker_tensorProductMk_quotient, MvPowerSeries.coeff_apply, rank_dual_eq_card_dual_of_aleph0_le_rank, Finset.affineCombination_apply, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, LinearMap.BilinForm.SeparatingLeft.toMatrix, Bialgebra.comul_mul, Derivation.liftKaehlerDifferential_unique_iff, PiTensorProduct.map_one, PowerSeries.constantCoeff_divXPowOrder, AffineMap.linear_surjective_iff, LocallyConstant.comapₗ_apply_apply, TensorProduct.AlgebraTensorModule.mapBilinear_apply, LinearMap.BilinMap.toQuadraticMapLinearMap_apply, SemimoduleCat.MonoidalCategory.braiding_hom_apply, Matrix.toLinAlgEquiv'_apply, groupHomology.inhomogeneousChains.d_single, PowerSeries.monomial_eq_mk, Matrix.l2_opNNNorm_def, Polynomial.natDegree_derivative_le, TensorProduct.piRightHom_tmul, LinearMap.lTensor_comm, RootPairing.rootForm_apply_apply, LieModule.traceForm_eq_zero_of_isTrivial, LinearMap.apply_toPerfPair_flip, MvPowerSeries.coeff_trunc, ModuleCat.exteriorPower.iso₁_hom_apply, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, apply_eq_star_dotProduct_toMatrix₂_mulVec, MvPolynomial.mkDerivation_monomial, LinearMap.aeval_eq_aeval_mod_charpoly, LinearMap.toMatrix_mul, BialgHom.coe_toLinearMap, Subrepresentation.apply_mem_toSubmodule, Finsupp.linearCombination_single, realPart_I_smul, LinearMap.det_map, Module.Presentation.CokernelData.π_lift, TwoSidedIdeal.subtype_injective, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, LinearMap.toMatrix₂_compl₁₂, LinearMap.BilinForm.IsSymm.smul, RootPairing.Equiv.bijective_weightMap, LinearMap.hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, SemimoduleCat.MonoidalCategory.braiding_inv_apply, Matrix.minpoly_toLin', QuadraticForm.tensorDistrib_tmul, selfAdjoint.realPart_unitarySelfAddISMul, IsLocalizedModule.linearEquiv_symm_apply, ExteriorAlgebra.ι_add_mul_swap, LinearMap.equivProdOfSurjectiveOfIsCompl_apply, MvPolynomial.rename_monomial, lift_rank_lt_rank_dual, Representation.coind'_apply_apply, LinearMap.eq_adjoint_iff, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, LinearMap.coprod_comp_prod, TensorProduct.map_one, GradedTensorProduct.mulHom_apply, LinearMap.toSpanSingleton_eq_zero_iff, BilinForm.toMatrix_compRight, LinearMap.BilinForm.nondegenerate_toMatrix'_iff, Polynomial.wronskianBilin_apply, Module.DirectLimit.linearEquiv_symm_mk, LinearMap.toMatrix₂_toLinearMap₂, LinearMap.detAux_def', Orthonormal.inner_right_finsupp, MultilinearMap.fromDirectSumEquiv_lof, TensorProduct.directSumRight_tmul_lof, LinearMap.toMatrix_transpose_apply', MvPowerSeries.eq_zero_iff_forall_coeff_eq_zero_and, Submodule.IsPrincipal.generator_map_dvd_of_mem, CliffordAlgebra.changeForm_one, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, AffineIsometry.norm_map, CliffordAlgebra.lift_symm_apply, WithSeminorms.equicontinuous_TFAE, Module.Invertible.rTensor_bijective_iff, LinearMap.eqOn_span_iff, LinearMap.toMatrix'_intrinsicStar, MultilinearMap.domCoprod'_apply, LinearMap.BilinForm.congr_congr, Submodule.linearMap_eq_iff_of_span_eq_top, LinearMap.finiteDimensional, TrivSqZeroExt.inrHom_apply, LinearMap.isPosSemidef_zero, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, LinearMap.map_rTensor, Submodule.coe_isComplEquivProj_apply, PowerSeries.trunc_C, Algebra.PreSubmersivePresentation.aevalDifferential_single, cross_apply, MvPolynomial.isWeightedHomogeneous_monomial, LinearMap.isPositive_iff_complex, IsBaseChange.toDual_comp_apply, IsBaseChange.linearMapLeftRightHom_toMatrix, Polynomial.sumIDeriv_apply, RootPairing.PolarizationIn_apply, Submodule.injective_subtype, LinearMap.BilinForm.isAlt_zero, LinearMap.BilinForm.toMatrixAux_apply, Polynomial.sylvesterDeriv_updateRow, Submodule.linearProjOfIsCompl_isCompl_projection, MeasureTheory.OuterMeasure.comap_mono, LinearIsometry.toLinearMap_injective, PiTensorProduct.mapMultilinear_apply, LinearMap.mem_ker, Module.Flat.iff_rTensor_exact', MeasureTheory.Measure.addHaar_image_linearMap, IsLocalFrameOn.coeff_apply_of_notMem, LinearMap.BilinForm.isAdjointPair_iff_eq_of_nondegenerate, Polynomial.dvd_derivative_iff, Polynomial.coeff_mul_monomial_zero, LinearMap.coe_domRestrict, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, Submodule.localized'_eq_span, Module.End.isNilpotent_restrict_maxGenEigenspace_sub_algebraMap, AdicCompletion.of_surjective, PiTensorProduct.dualDistrib_apply, DFinsupp.lsum_single, CliffordAlgebraQuaternion.ofQuaternion_mk, Algebra.Generators.Cotangent.exact, Matrix.toLinOfInv_symm_apply, LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv', ModuleCat.hom_sum, LinearMap.toMatrix_smulRight, ModularFormClass.qExpansion_coeff_zero, ContinuousLinearMap.range_coeFn_eq, Polynomial.resultant_taylor, LinearMap.toMatrix₂Aux_eq, Representation.averageMap_invariant, Matrix.represents_iff, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, imaginaryPart_apply_coe, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, IsModuleTopology.continuous_of_linearMap, MvPolynomial.monomial_zero', MultilinearMap.curryLeft_apply, LinearMap.restrictScalars_add, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl, MvPowerSeries.coeff_truncFun', LinearMap.lsmul_apply, Submodule.coe_subtypeₗᵢ, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, Submodule.IsCompl.projection_add_projection_eq_self, LieDerivation.toLinearMapLieHom_injective, Finsupp.counit_single, MvPolynomial.weightedHomogeneousComponent_directSum, Polynomial.natDegree_hasseDeriv, vecMulVecBilin_apply_apply, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, isAdjointPair_toLinearMap₂', Orientation.areaForm_comp_rightAngleRotation, RootPairing.Equiv.coweightMap_coweightEquiv_symm, Module.Dual.baseChange_apply_tmul, Matrix.toLin'_apply', LinearMap.rTensor_baseChange, Representation.asModuleEquiv_symm_map_rho, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, LinearMap.toMatrix₂_symm, Module.End.commute_exp_left_of_commute, AdjoinRoot.powerBasisAux'_repr_symm_apply, Polynomial.Bivariate.swap_monomial_monomial, MvPowerSeries.coeff_prod, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, Matrix.Represents.congr_fun, LinearMap.congr_fun₂, groupHomology.π_comp_H1Iso_hom_apply, TensorPower.toTensorAlgebra_gMul, TensorProduct.directSumLeft_symm_lof_tmul, Matrix.ker_toLin'_eq_bot_iff, Representation.ofModule_asModule_act, LinearMap.vecCons₂_apply, Finsupp.lsum_apply, ModuleCat.hom_nsmul, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LinearMap.eval_charpoly, LinearMap.SeparatingLeft.toMatrix₂, LinearMap.toMatrix'_toLinearMap₂', TensorProduct.lift_comp_map, TensorPower.toTensorAlgebra_gOne, Derivation.llcomp_apply, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, Algebra.adjoin_inl_union_inr_eq_prod, LinearMap.BilinForm.toLin'Flip_apply, LinearMap.reduceModIdeal_apply, Finset.weightedVSubOfPoint_smul, groupCohomology.map_id_comp_H0Iso_hom_apply, PolynomialModule.equivPolynomial_single, MvPolynomial.homogeneousComponent_apply, BilinForm.toMatrix_mul_basis_toMatrix, ModuleCat.forget_obj, LinearMap.convexOn, exteriorPower.pairingDual_apply_apply_eq_one, Polynomial.toFn_comp_ofFn_eq_id, MultilinearMap.dfinsuppFamilyₗ_apply, AffineMap.derivWithin, LieDerivation.lie_coe_lieDerivation_apply, Rep.standardComplex.d_of, Module.Flat.tensorProduct_mapIncl_injective_of_left, SemimoduleCat.id_apply, imaginaryPart_comp_subtype_selfAdjoint, Submodule.Quotient.equiv_symm_apply, AffineMap.add_linear, LinearMap.coe_snd, Polynomial.supNorm_monomial, Polynomial.derivative_comp, LinearMap.isPositive_zero, LinearMap.BilinForm.mul_toMatrix', MvPowerSeries.coeff_C_mul, MvPolynomial.divMonomial_mul_monomial, IsGroupLikeElem.antipode, Finsupp.linearCombination_unique, PresheafOfModules.toPresheaf_map_app_apply, TensorProduct.AlgebraTensorModule.map_add_right, CliffordAlgebra.reverse.commutes, LinearMap.map_mul_iff, PowerSeries.X_eq, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, Finsupp.coe_lsum, LinearMap.toSpanSingleton_homothety, CStarMatrix.mul_entry_mul_eq_inner_toCLM, MvPolynomial.weightedHomogeneousComponent_finsupp, LaurentSeries.hasseDeriv_coeff, Matrix.toLinearMap₂_symm, Polynomial.gaussNorm_monomial, ExteriorAlgebra.toTrivSqZeroExt_ι, AddMonoidHom.coe_toRatLinearMap, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, Module.Flat.iff_lTensor_injectiveₛ, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, Finsupp.linearCombination_mapDomain, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, Span.finsupp_linearCombination_repr, SymmetricAlgebra.equivMvPolynomial_symm_X, LinearMap.sumOfConjugates_apply, ModuleCat.HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, Polynomial.taylor_taylor, MeasureTheory.OuterMeasure.le_comap_map, RootPairing.Equiv.bijective_coweightMap, LinearMap.toMatrixAlgEquiv_symm, DirectSum.component.lof_self, LinearMap.toMatrixRight'_id, leibniz_cross, Orientation.inner_rightAngleRotation_left, lp.lsingle_apply, Polynomial.expand_monomial, HVertexOperator.coeff_inj, MvPolynomial.prod_X_pow_eq_monomial, AffineMap.isOpenMap_linear_iff, Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants, Submodule.coe_torsionBySet, fwdDiff_aux.fwdDiffₗ_apply, LinearMap.minpoly_toMatrix, LinearMap.lTensor_zero, LinearMap.det_dualMap, PiToModule.fromEnd_apply_single_one, MvPowerSeries.weightedHomogeneousComponent_mul_of_le_weightedOrder, Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one, Rep.indToCoindAux_mul_snd, ModuleCat.FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, CharacterModule.homEquiv_symm_apply_apply_apply, CoalgHom.coe_linearMap_injective, ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier, LinearMap.BilinForm.IsRefl.neg, MvPolynomial.constantCoeff_monomial, RootPairing.coroot_root_two, CliffordAlgebra.reverse_mem_evenOdd_iff, PiTensorProduct.piTensorHomMapFun₂_smul, LinearMap.adjoint_lTensor, LieModule.Cohomology.add_apply_apply, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, SemimoduleCat.hom_zero, Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, LinearMap.slope_comp, MultilinearMap.map_add_eq_map_add_linearDeriv_add, multilinearCurryLeftEquiv_apply, CliffordAlgebra.evenToNeg_ι, ModuleCat.ExtendScalars.map_tmul, LinearMap.toMatrixOrthonormal_apply, TensorProduct.AlgebraTensorModule.map_one, Representation.asAlgebraHom_of, LinearMap.BilinMap.toQuadraticMap_list_sum, LinearMap.IsPositive.smul_of_nonneg, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, diffToIdealOfQuotientCompEq_apply, LinearMap.lTensor_comp_mk, Module.Basis.toDual_injective, ModuleCat.FilteredColimits.forget_reflectsFilteredColimits, IsAdjoinRootMonic.coeff_apply_lt, Seminorm.comp_apply, LieModule.traceForm_eq_zero_if_mem_lcs_of_mem_ucs, LinearMap.map_mul_algebraMap, LinearMap.detAux_comp, AlternatingMap.compLinearMap_zero, MvPolynomial.divMonomial_monomial, LinearMap.surjective_of_comp_eq_id, realPart_surjective, StrongDual.toLpₗ_apply, Orientation.kahler_apply_self, Module.Invertible.rTensorInv_leftInverse, RootPairing.Hom.weight_coweight_transpose_apply, Polynomial.derivative_sq, LinearMap.prodMapAlgHom_apply_apply, LinearMap.BilinForm.IsSymm.add, Module.End.eigenspace_def, IntermediateField.AdjoinSimple.trace_gen_eq_zero, ModuleCat.free_μ_freeMk_tmul_freeMk, ModuleCat.forget₂_obj_moduleCat_of, MvPowerSeries.coeff_zero_one, TensorProduct.forall_vanishesTrivially_iff_forall_rTensor_injective, QuadraticForm.toDualProd_apply, tendsto_iff_forall_eval_tendsto_topDualPairing, CategoryTheory.Iso.toLinearEquiv_apply, IsLocalFrameOn.coeff_apply_zero_at, LinearMap.IsNonneg.nonneg, SymmetricAlgebra.lift_comp_ι, Orientation.inner_mul_areaForm_sub', Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, RootPairing.CoPolarization_apply, LinearMap.det_id, LinearMap.compLeft_apply, AdicCompletion.sum_of, Submodule.equivSubtypeMap_apply, AlternatingMap.curryLeftLinearMap_apply, SymmetricAlgebra.lift_ι, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, IsLocalRing.split_injective_iff_lTensor_residueField_injective, Algebra.Extension.Hom.mapKer_apply_coe, Algebra.toMatrix_lmul', Submodule.isIdempotentElemEquiv_symm_apply_coe, LinearMap.continuous_of_nonzero_on_open, Polynomial.hasseDeriv_monomial, PowerSeries.trunc_trunc_pow, PolynomialLaw.isCompat, PowerSeries.coeff_mul, Profinite.NobelingProof.πs_apply_apply, Module.Invertible.leftInverse_iff_rightInverse, AffineMap.homothety_linear, LinearMap.apply_single, Algebra.Extension.contangentEquiv_tmul, LinearMap.BilinForm.isAlt_neg, Representation.IntertwiningMap.toLinearMap_apply, SheafOfModules.pushforwardComp_hom_app_val_app, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_ne, Polynomial.derivativeFinsupp_map, Ideal.quotOfMul_surjective, Submodule.map₂_span_span, CochainComplex.HomComplex.δ_hom_apply, Pretrivialization.linearMapAt_symmₗ, LinearMap.isNilpotent_mulRight_iff, Submodule.det_reflection, LinearMap.BilinForm.ext_iff, Finsupp.llift_symm_apply, IsLocalizedModule.map_id, Orientation.kahler_rotation_left', Representation.linHom.invariantsEquivRepHom_symm_apply_coe, AffineMap.toConstProdLinearMap_apply, LinearMap.quotKerEquivRange_apply_mk, Matrix.ker_diagonal_toLin', Polynomial.monomial_add, Algebra.Generators.cMulXSubOneCotangent_eq, LinearMap.restrictScalars_neg, CliffordAlgebraComplex.toComplex_ι, Rep.linearization_obj_ρ, AdicCompletion.AdicCauchySequence.map_apply_coe, Rep.toCoinvariantsMkQ_hom, RootPairing.RootPositiveForm.two_mul_apply_root_root, MvPolynomial.isHomogeneous_monomial, Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd, Ideal.toCotangent_apply, Polynomial.hasDerivWithinAt_aeval, groupHomology.isoCycles₁_hom_comp_i_apply, LinearMap.coe_rTensorHom, LinearMap.isLinearMap_of_compatibleSMul, HahnSeries.coeff_toPowerSeries, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, LinearMap.baseChange_sub, Module.Basis.det_comp, DirectSum.single_eq_lof, Coalgebra.lift_lsmul_comp_counit_comp_comul, LinearMap.convOne_def, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_mem, Algebra.TensorProduct.opAlgEquiv_symm_apply, PowerSeries.coeff_smul, Polynomial.coeff_monomial_same, PiLp.projₗ_apply, SheafOfModules.Presentation.map_relations_I, TensorProduct.map_mul, ModuleCat.instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, Bialgebra.counit_mul, Orientation.abs_areaForm_le, LieModule.traceForm_eq_sum_finrank_nsmul, LinearEquiv.symmEquiv_apply_apply, Matrix.toBilin'_apply, Pretrivialization.symmₗ_apply, LinearMap.det_restrictScalars, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, Submodule.linearMap_eq_iff_of_eq_span, CliffordAlgebra.changeForm_ι, Polynomial.hasStrictDerivAt_aeval, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, LinearMap.flip_injective_iff₂, MvPowerSeries.coeff_add_mul_monomial, Matrix.adjugate_def, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, LinearMap.compQuadraticMap_apply, LinearMap.toMatrix_prodMap, Matrix.toLin_apply, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero, groupCohomology.H1π_eq_zero_iff, Matrix.toLin'_one, groupHomology.H1AddEquivOfIsTrivial_symm_apply, Polynomial.iterate_derivative_eq_zero_of_degree_lt, AdicCompletion.mk_surjective, MvPowerSeries.monomial_pow, RootPairing.reflection_dualMap_eq_coreflection, Orientation.normSq_kahler, Ideal.toCotangent_eq_zero, Module.Basis.constr_apply_fintype, DFinsupp.coprodMap_apply_single, LinearMap.IsSymmetric.invariant_orthogonalComplement_eigenspace, TensorProduct.LieModule.lift_apply, Matrix.cramer_submatrix_equiv, MvPolynomial.decomposition.decompose'_apply, MultilinearMap.ofSubsingletonₗ_apply, Profinite.NobelingProof.GoodProducts.square_commutes, CliffordAlgebra.ι_mul_ι_add_swap_of_isOrtho, groupHomology.d₃₂_single_one_fst, inhomogeneousCochains.d_hom_apply, Algebra.Generators.toKaehler_tmul_D, DFinsupp.lsum_symm_apply, LinearMap.finsupp_sum_apply, Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity, PowerSeries.coeff_monomial_same, Submodule.mulRightMap_apply, LinearEquiv.conjAlgEquiv_apply_apply, MultilinearMap.piFamilyₗ_apply, TrivSqZeroExt.liftEquivOfComm_apply, TensorProduct.isBaseChange, Rep.coind'_ext_iff, Polynomial.iterate_derivative_prod_X_sub_C, Module.isTorsionBy_iff_mem_ker_lsmul, MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous, mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, Module.injOn_dualMap_subtype_span_range_range, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, LinearMap.concaveOn, Submodule.map₂_le, LinearMap.eventually_isCompl_ker_pow_range_pow, LaurentPolynomial.comul_C, LaurentSeries.hasseDeriv_single_add, LinearMap.IsSymmetric.smul, Submodule.isOpenMap_mkQ, MeasureTheory.Measure.mapₗ_apply_of_measurable, Derivation.coeFn_coe, PiTensorProduct.mul_def, RootPairing.rootForm_self_sum_of_squares, finsuppLEquivDirectSum_single, LinearMap.map_zero₂, Polynomial.opRingEquiv_symm_monomial, Polynomial.toAddCircle_monomial_eq_smul_fourier, Matrix.toLin_conjTranspose, mulRightLinearMap_apply, imaginaryPart_surjective, Orthonormal.inner_finsupp_eq_sum_left, MvPolynomial.map_monomial, PresheafOfModules.Elements.fromFreeYoneda_app_apply, Finsupp.comul_single, HopfAlgebra.mul_antipode_rTensor_comul_apply, MvPolynomial.monomial_mem_restrictSupport, DirectedSystem.lTensor, LinearMap.BilinForm.isRefl_neg, IsBaseChange.iff_lift_unique, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, ModuleCat.HasColimit.coconePointSMul_apply, Algebra.Extension.Cotangent.map_toInfinitesimal_bijective, QuadraticMap.canLift', groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, LinearIndependent.finsuppLinearCombination_injective, Ideal.cotangentEquivIdeal_apply, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, LinearMap.det_eq_sign_charpoly_coeff, Module.End.eventually_disjoint_ker_pow_range_pow, Derivation.map_one_eq_zero', Finsupp.lapply_apply, ModuleCat.smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, MvPowerSeries.coeff_zero_X_mul, AdicCompletion.congr_symm_apply, ModuleCat.hom_add, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, TensorProduct.AlgebraTensorModule.lTensor_comp, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, LinearMap.map_span, homTensorHomEquiv_toLinearMap, Subspace.dualLift_of_mem, ExteriorAlgebra.ιMulti_apply, RootPairing.algebraMap_posRootForm_posForm, CliffordAlgebra.EquivEven.v_sq_scalar, IsAdjoinRootMonic.coeff_injective, CharacterModule.dual_bijective_iff_bijective, DomMulAct.mk_smul_linearMap_apply, endVecAlgEquivMatrixEnd_apply_apply, AffineMap.sub_linear, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Submodule.coe_torsionBy, MvPolynomial.homogeneousComponent_eq_zero, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Polynomial.coe_basisMonomials, MvPowerSeries.map_monomial, PowerSeries.trunc_apply, Ideal.quotientToQuotientRangePowQuotSucc_injective, Seminorm.cont_withSeminorms_normedSpace, groupCohomology.cocyclesMk₁_eq, AffineMap.toConstProdLinearMap_symm_apply, LinearMap.baseChange_neg, SemimoduleCat.hom_injective, instInvertibleReprₛ, AlgCat.forget₂_module_obj, sectionOfRetractionKerToTensor_algebraMap, LinearMap.BilinForm.nondegenerate_congr_iff, NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subset, LinearMap.aeval_self_charpoly, exteriorPower.alternatingMapLinearEquiv_comp, Matrix.trace_toLin'_eq, signedDist_linear_apply, Finset.weightedVSub_filter_of_ne, TensorProduct.gradedComm_of_zero_tmul, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, Matrix.toLin'OfInv_symm_apply, Orientation.rotation_eq_matrix_toLin, ModuleCat.instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, LinearMap.BilinForm.flip_apply, RootPairing.orthogonal_corootSpan_eq, SheafOfModules.relationsOfIsCokernelFree_I, PiTensorProduct.map_tprod, AlternatingMap.curryLeft_smul, Representation.isTrivial_def, Derivation.coe_sub_linearMap, MonomialOrder.sPolynomial_monomial_mul, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, IsGroupLikeElem.antipode_mul_cancel, Finsupp.coe_lmapDomain, Module.Basis.sumCoords_self_apply, Algebra.trace_localization, Finset.weightedVSub_vadd, ModuleCat.MonoidalCategory.tensorμ_apply, RootPairing.ker_rootForm_eq_dualAnnihilator, Finsupp.lapply_comp_lsingle_of_ne, LinearMap.BilinForm.compRight_apply, SymmetricAlgebra.equivMvPolynomial_ι_apply, AddCommGroup.DirectLimit.directedSystem, Module.FinitePresentation.linearEquivMapExtendScalars_apply, Polynomial.isNilpotent_monomial_iff, IsLocalizedModule.iso_symm_apply_aux, Polynomial.as_sum_range', ContinuousLinearMap.sub_apply', Submodule.inf_comap_le_comap_add, IsBaseChange.endHom_apply, LinearMap.isSkewAdjoint_iff_neg_self_adjoint, LinearIndependent.fintypeLinearCombination_injective, AffineMap.vsub_linear, LinearMap.mulRight_zero_eq_zero, AdicCompletion.AdicCauchySequence.map_comp_apply, StrongDual.norm_toLpₗ_le, MvPolynomial.homogeneousComponent_zero, PowerSeries.coeff_monomial, Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem, LinearMap.mul''_apply, Polynomial.natDegree_monomial, selfAdjoint.realPart_coe, Module.Invertible.rTensorInv_injective, TensorProduct.AlgebraTensorModule.lTensor_mul, Rep.quotientToInvariantsFunctor_obj_V, LinearEquiv.toLinearMap_smul, LinearMap.bijective_or_eq_zero, Polynomial.factorial_mul_shiftedLegendre_eq, MvPolynomial.monomial_left_injective, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T, Algebra.TensorProduct.one_mul, Ideal.constr_basisSpanSingleton, IsAdjoinRootMonic.map_modByMonicHom, MeasureTheory.Measure.map_toOuterMeasure, Function.Exact.iff_linearMap_rangeRestrict, Module.Flat.iff_rTensor_exact, LinearMap.mem_polar_singleton, MvPolynomial.monomial_sum_index, LinearMap.baseChange_zero, LinearEquiv.isUnit_det, LinearMap.IsSymm.eq, SemimoduleCat.MonoidalCategory.associator_inv_apply, Polynomial.separable_def, CliffordAlgebra.contractLeft_ι, LinearMap.polyCharpolyAux_map_aeval, MvPolynomial.monic_monomial_eq, MvPowerSeries.coeff_zero_iff, KaehlerDifferential.map_surjective, Trivialization.coe_symmₗ, Pi.counit_coe_finsupp, Polynomial.iterate_derivative_smul, Finset.weightedVSubOfPoint_apply_const, WithLp.sndₗ_apply, PowerSeries.coeff_X, KaehlerDifferential.map_compDer, MvPolynomial.pderiv_monomial_single, Algebra.TensorProduct.piRightHom_one, Algebra.trace_eq_matrix_trace, LinearMap.prodMap_zero, LinearMap.liftBaseChange_tmul, Polynomial.sumIDeriv_X, Algebra.traceMatrix_of_basis, groupHomology.d₂₁_apply_mem_cycles₁, AlgEquiv.one_toLinearMap, Algebra.trace_algebraMap_of_basis, AdicCompletion.of_ofLinearEquiv_symm, AdicCompletion.kerProj_of, LieModule.traceForm_lieSubalgebra_mk_left, LinearMap.instStarModuleId, LieDerivation.commutator_coe_linear_map, LieModule.Cohomology.smul_apply_apply, Polynomial.contentIdeal_monomial, groupCohomology.coboundariesToCocycles₂_apply, linearIndependent_iff_injective_fintypeLinearCombination, HahnSeries.coeff_toPowerSeries_symm, CliffordAlgebra.changeForm.neg_proof, Polynomial.injective_ofFn, Matrix.spectrum_toLin, TensorAlgebra.ι_leftInverse, ModuleCat.ihom_map_apply, Submodule.quotDualCoannihilatorToDual_injective, Module.Basis.eval_injective, PowerSeries.IsWeierstrassDivisorAt.coeff_div, PolyEquivTensor.toFunBilinear_apply_apply, LinearMap.BilinForm.IsSymm.neg, LinearMap.toMatrix'_comp, Matrix.toLinearEquiv'_apply, LinearMap.isUnit_toMatrix'_iff, Submodule.quotientPi_symm_apply, LinearMap.BilinForm.add_right, Matrix.toBilin_toMatrix, IsBaseChange.toDual_apply, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, Real.map_linearMap_volume_pi_eq_smul_volume_pi, PolyEquivTensor.toFunLinear_tmul_apply, SemimoduleCat.MonoidalCategory.whiskerLeft_apply, Finsupp.bilinearCombination_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.H2π_eq_zero_iff, MvPolynomial.DirectSum.coeLinearMap_eq_finsum, Matrix.nondegenerate_toLinearMap₂_iff, UniversalEnvelopingAlgebra.ι_apply, Polynomial.coeff_iterate_derivative, LinearMap.fst_apply, LieHom.coe_toLinearMap, LaurentSeries.hasseDeriv_comp, Finsupp.apply_linearCombination, StrongDual.toLpₗ_of_not_memLp, LinearMap.zero_smulRight, PiTensorProduct.mapL_apply, Submodule.liftQ_apply, LinearMap.BilinForm.comp_congr, Module.Relations.Solution.IsPresentation.surjective_π, LinearMap.disjoint_ker_iff_injOn, Matrix.cramer_subsingleton_apply, Matrix.toBilin'_comp, Matrix.isHermitian_iff_isSymmetric, MvPolynomial.support_monomial_subset, LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain, Subspace.dualRestrict_surjective, MvPolynomial.monomial_mul, Module.compHom.toLinearMap_apply, RootPairing.InvariantForm.apply_eq_or_aux, KaehlerDifferential.kerTotal_mkQ_single_mul, MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrder, IsBaseChange.endHom_one, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, SemimoduleCat.hom_bijective, DirectedSystem.rTensor, AdicCompletion.evalOneₐ_of, Algebra.Generators.H1Cotangent.exact_map_δ', WeakBilin.coeFn_continuous, Lagrange.degree_interpolate_le, Polynomial.bernoulli_def, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Submodule.map₂_span_singleton_eq_map, Polynomial.derivative_eval₂_C, MvPowerSeries.weightedOrder_eq_nat, Representation.averageMap_id, groupCohomology.H1π_comp_map_apply, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, LinearMap.intrinsicStar_id, Module.FaithfullyFlat.zero_iff_lTensor_zero, LocalizedModule.lift_mk, PowerSeries.as_tsum, CliffordAlgebra.invOf_ι, LinearMap.lTensor_bij_iff_rTensor_bij, Orientation.kahler_rightAngleRotation_left, Rep.leftRegularHom_hom_single, isCompactOperator_iff_isCompact_closure_image_closedBall, LinearMap.separatingLeft_congr_iff, Module.Basis.end_repr_symm_apply, MvPowerSeries.expand_monomial, TensorAlgebra.GradedAlgebra.ι_apply, LinearMap.GeneralLinearGroup.coe_ofLinearEquiv, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, LinearMap.continuous_of_finiteDimensional, Module.evalEquiv_apply, DistribMulActionHom.coe_toLinearMap, LinearMap.IsReflective.dvd_two_mul, CliffordAlgebra.contractRight_contractRight, InnerProductSpace.toMatrix_rankOne, TensorProduct.AlgebraTensorModule.map_mul, LinearMap.equivariantProjection_apply, LieAlgebra.InvariantForm.mem_orthogonal, Coalgebra.Repr.convMul_apply, MvPolynomial.rTensor_symm_apply_single, PowerSeries.derivative_coe, LinearMap.BilinMap.toQuadraticMap_multiset_sum, LieModule.toEnd_apply_apply, MeasureTheory.ComplexMeasure.im_apply, LinearMap.IsPerfPair.bijective_right, PowerSeries.coeff_zero_eq_constantCoeff_apply, CliffordAlgebra.star_ι, Polynomial.X_pow_mul_monomial, Seminorm.continuous_from_bounded, Representation.free_single_single, Submodule.isQuotientEquivQuotientPrime_iff, LinearMap.mul_toMatrix₂_mul, Submodule.map_smul', Polynomial.aeval_derivative_of_splits, span_eq_top_of_isLocalizedModule, MeasureTheory.OuterMeasure.isometryEquiv_map_mkMetric, MvPolynomial.pderiv_monomial, Algebra.trace_quotient_mk, CoalgCat.forget₂_obj, IsLocalization.bijective_linearMap_mul', LinearMap.lTensor_comp_apply, Representation.IntertwiningMap.isIntertwining', Module.Flat.iff_forall_exists_factorization, skewAdjointPart_apply_coe, CliffordAlgebra.involute_ι, LinearMap.image_convexHull, Orientation.abs_areaForm_of_orthogonal, Module.Basis.mk_coord_apply, continuous_selfAdjointPart, Polynomial.lsum_apply, LinearMap.exact_zero_iff_injective, CoalgHom.coe_toLinearMap, LinearMap.isSymmetricProjection_iff, LinearMap.BilinForm.tensorDistribEquiv_tmul, innerₗ_apply_apply, Algebra.trace_surjective, HahnSeries.ofPowerSeriesAlg_apply_coeff, Module.Dual.lie_apply, LinearMap.coe_inl, LinearMap.trace_tensorProduct', Algebra.Generators.toComp_toAlgHom_monomial, Module.Relations.Solution.π_comp_map, MonoidAlgebra.GroupSMul.linearMap_apply, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, Module.Finite.exists_comp_eq_id_of_projective, LinearMap.IsReflective.coroot_apply_self, Representation.Coinvariants.mk_eq_zero, KaehlerDifferential.D_tensorProductTo, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Polynomial.derivative_pow, Trivialization.symmₗ_linearMapAt, DFinsupp.coeFnLinearMap_apply, Algebra.Extension.toKaehler_surjective, LinearMap.det_eq_one_of_finrank_eq_zero, hfdifferential_apply, LinearMap.congr_fun, TensorAlgebra.range_lift, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, PiTensorProduct.one_mul, Submodule.IsCompl.projection_apply_eq_zero_iff, QuotSMulTop.equivQuotTensor_naturality_mk, Finset.weightedVSubOfPoint_eq_of_weights_eq, MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree, Module.Flat.iff_lTensor_preserves_injective_linearMapₛ, Submodule.linearMap_eq_zero_iff_of_span_eq_top, CompactlySupportedContinuousMap.toNNRealLinear_apply, Polynomial.derivative_prod, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, LinearMap.rank_zero, LinearMap.toMatrix'_id, setBasisOfTopLeSpanOfCardEqFinrank_repr_apply, LinearMap.polyCharpolyAux_coeff_eval, AffineMap.linear_eq_zero_iff_exists_const, Module.Invertible.lTensor_injective_iff, LinearMap.range_smul', weightedVSub_mem_vectorSpan, LinearMap.coe_comp, LocalizedModule.mul_by_divBy, EuclideanGeometry.inner_weightedVSub, Orientation.kahler_rotation_left, Representation.le_comap_invariants, LinearMap.exact_map_mkQ_range, LindemannWeierstrass.integral_exp_mul_eval, LinearEquiv.symmEquiv_symm_apply_apply, Derivation.tensorProductTo_mul, ModularFormClass.hasSum_qExpansion_of_abs_lt, Matrix.toLinearMapₛₗ₂_symm, PowerSeries.coeff_map, contractLeft_apply, Algebra.Extension.Cotangent.mk_surjective, Polynomial.valuation_monomial_eq_valuation_X_pow, LinearMap.BilinMap.tensorDistrib_tmul, Projectivization.cross_mk, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, LinearMap.BilinForm.mul_toMatrix_mul, Polynomial.eval_sumIDeriv_of_pos, LinearMap.trace_transpose, MvPolynomial.dvd_monomial_mul_iff_exists, Trivialization.coe_linearMapAt_of_mem, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Polynomial.mkDerivation_X, LineDeriv.tensorLineDerivTwo_eq_lineDerivOp_lineDerivOp, Representation.invariants_eq_inter, IsBaseChange.endHom_comp_apply, LinearMap.BilinForm.toMatrix_mul_basis_toMatrix, inner_map_self_eq_zero, LinearMap.coe_single, LinearAlgebra.FreeProduct.rel_id, Matrix.toLinAlgEquiv_apply, AffineMap.linearHom_apply, LinearMap.nondegenerate_toMatrix₂'_iff, Orientation.inner_sq_add_areaForm_sq, TensorProduct.range_map_eq_span_tmul, LinearMap.BilinForm.toMatrix'_comp, LinearMap.mapMatrix_apply, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, MonomialOrder.div_set, RCLike.reLm_coe, LinearMap.smul_compAlternatingMap, MvPowerSeries.coeff_rescale, Submodule.exists_injOn_mkQ_image_span_eq_of_span_eq_map_mkQ_of_le_jacobson_bot, DFinsupp.lmk_apply, CharacterModule.dual_rTensor_conj_homEquiv, SchwartzMap.convolution_continuous_left, Submodule.IsCompl.projection_apply, TensorProduct.equivFinsuppOfBasisRight_apply, mulLinearMap_apply_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff, LinearMap.intrinsicStar_mulLeft, CliffordAlgebra.changeForm_contractLeft, GroupLike.val_inv, LinearMap.instIsScalarTower, IsLocalization.map_eq_toLinearMap_mapₐ, MvPowerSeries.WithPiTopology.hasSum_of_monomials_self, Submodule.map_zero, triple_product_eq_det, AdicCompletion.factor_eval_liftRingHom, QuadraticMap.coe_associatedHom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, LinearMap.IsNonneg.add, LinearIndependent.inl_union_inr, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, LinearMap.BilinForm.IsAlt.neg, LinearMap.extendScalarsOfSurjective_apply, ModuleCat.mkOfSMul_smul, Module.Basis.det_basis, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, TensorProduct.directSum_symm_lof_tmul, Module.bijective_dual_eval, LinearMap.isLinear, PowerSeries.coeff_one, Representation.norm_self_apply, HopfAlgebra.counit_antipode, Submodule.toLocalizedQuotient'_mk, Submodule.image_span_subset, PowerSeries.eq_shift_mul_X_add_const, Algebra.Extension.Hom.subToKer_apply_coe, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Matrix.toLinearMapRight'_apply, LinearMap.BilinForm.toMatrix_mul, AlgebraicGeometry.StructureSheaf.comapₗ_const, PowerSeries.coeff_prod, Module.FaithfullyFlat.tensorProduct_mk_injective, Polynomial.span_minpoly_eq_annihilator, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, AffineMap.zero_linear, Finset.weightedVSub_congr, hahnEmbedding_isOrderedModule_rat, LinearMap.ker_zero, Polynomial.iterate_derivative_C_mul, LinearMap.nonUnitalAlgHom_comp_convMul_distrib, Module.End.genEigenrange_nat, Continuous.matrix_cramer, MonoidAlgebra.comul_single, PowerSeries.coeff_mul_X_pow', LinearMap.GeneralLinearGroup.coe_toLinearEquiv, SchwartzMap.pairing_continuous_left, PolyEquivTensor.invFun_monomial, LieAlgebra.SpecialLinear.val_single, LinearMap.eventually_iInf_range_pow_eq, Matrix.ofLp_toEuclideanLin_apply, Matrix.toLinearMap₂_apply, AdicCompletion.of_inj, ExteriorAlgebra.map_surjective_iff, MvPolynomial.weightedHomogeneousComponent_eq_zero_of_notMem, Polynomial.mkDerivation_one_eq_derivative, LinearMap.vecEmpty_apply, SpecialLinearGroup.toGeneralLinearGroup_injective, MeasureTheory.OuterMeasure.restrict_biInf, CliffordAlgebra.forall_mul_self_eq_iff, LinearMap.mem_range, LinearMap.IsSymmetric.apply_eigenvectorBasis, groupHomology.cyclesMk₂_eq, AffineMap.decomp, RootPairing.coroot_root_eq_pairing, LinearMap.compl₁₂_apply, LinearMap.leftInverse_apply_of_inj, Representation.smul_tprod_one_asModule, rTensorHomEquivHomRTensor_toLinearMap, mem_span_of_iInf_ker_le_ker, AdicCompletion.ofTensorProduct_tmul, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, KaehlerDifferential.kerTotal_mkQ_single_smul, LinearMap.intrinsicStar_lTensor, MultilinearMap.uncurryRight_apply, LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension, MvPolynomial.rTensor_apply_monomial_tmul, CliffordAlgebraRing.ι_eq_zero, Polynomial.iterate_derivative_mul_X_pow, PiTensorProduct.piTensorHomMapFun₂_add, Matrix.mulVecBilin_apply, PowerSeries.coeff_zero_C, Algebra.Generators.repr_CotangentSpaceMap, DirectSum.toModule_lof, groupHomology.H1π_eq_zero_iff, Algebra.normalizedTrace_minpoly, IsAdjoinRootMonic.modByMonicHom_root_pow, PiTensorProduct.mul_one, CategoryTheory.Abelian.Ext.bilinearCompOfLinear_apply_apply, AlternatingMap.uncurryFin_smul, lieEquivMatrix'_symm_apply, MvPowerSeries.eq_zero_iff_forall_coeff_zero, LinearMap.compQuadraticMap'_apply, Matrix.proj_diagonal, imaginaryPart_ofReal, Module.Dual.baseChange_baseChange, separatingDual_iff_injective, LightCondMod.hom_naturality_apply, Module.Relations.Solution.IsPresentation.bijective, TensorProduct.dualDistribInvOfBasis_apply, Pi.comul_coe_finsupp, Polynomial.taylor_coeff_one, LinearMap.map_smul₂, groupHomology.d₂₁_single_one_fst, PowerSeries.forall_coeff_eq_zero, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, LinearMap.disjoint_ker_of_nondegenerate_restrict, Polynomial.sup_ker_aeval_le_ker_aeval_mul, Polynomial.fderivWithin_aeval, LinearMap.intrinsicStarModule, NNRealRMK.le_rieszMeasure_of_tsupport_subset, dualTensorHom_prodMap_zero, MvPowerSeries.coeff_truncFun, PolyEquivTensor.toFunLinear_one_tmul_one, LinearMap.comp_smul, Polynomial.fderivWithin, LinearMap.IsContPerfPair.bijective_right, PowerSeries.coeff_C, IsLocalFrameOn.eq_iff_coeff, HahnSeries.coeff_toMvPowerSeries_symm, Polynomial.monomial_neg, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, LinearMap.isUnit_toMatrix_iff, LinearMap.det_smul, Polynomial.hasDerivAt, Module.Basis.linearCombination_repr, MvPolynomial.mkDerivationₗ_C, LinearMap.IsSymmetric.zero, LocalizedModule.map_id, ContinuousMultilinearMap.ofSubsingleton_apply_toMultilinearMap, MvPowerSeries.isWeightedHomogeneous_weightedHomogeneousComponent, Seminorm.ball_comp, TensorProduct.AlgebraTensorModule.rTensor_mul, MultilinearMap.curryMidLinearEquiv_apply, LinearMap.BilinForm.toMatrix_compLeft, Polynomial.monomial_zero_right, LinearMap.trace_eq_matrix_trace, RootPairing.polarizationEquiv_symm_apply_coroot, BilinForm.toMatrix_apply, PolynomialModule.lsingle_apply, Algebra.SubmersivePresentation.cotangentComplexAux_surjective, LinearMap.continuous_on_pi, Matrix.linfty_opNorm_toMatrix, Representation.self_inv_apply, RingHom.toSemilinearMap_apply, LinearEquiv.transvection.coe_apply, Polynomial.iterate_derivative_sub, Matrix.toBilin'_apply', Module.Basis.linearCombination_coord, LinearMap.BilinForm.IsSymm.polarization, Polynomial.signVariations_monomial, LinearMap.surjective_comp_linearProjOfIsCompl, LinearMap.exact_subtype_ker_map, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, Derivation.map_aeval, IsSelfAdjoint.coe_selfAdjointPart_apply, Matrix.toLinearMap₂'_single, ExteriorAlgebra.liftAlternating_comp_ιMulti, CliffordAlgebra.toEven_ι, Algebra.Extension.H1Cotangent.map_apply_coe, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero', Algebra.TensorProduct.mul_assoc, LinearMap.adjoint_inner_left, TensorProduct.map_zero_left, LocallyConstant.mapₗ_apply_apply, Submodule.mulMap'_surjective, Polynomial.monomial_mul_X_pow, Module.Basis.toDual_apply, ContinuousAffineMap.coe_contLinear, PowerSeries.coeff_inv, LinearMap.BilinForm.mul_toMatrix, MvPowerSeries.coeff_expand_of_not_dvd, aeval_derivative_mem_differentIdeal, MeasureTheory.Measure.addHaar_preimage_linearMap, Algebra.trace_eq_zero_of_not_isSeparable, Algebra.Generators.toKaehler_cotangentSpaceBasis, Polynomial.iterate_derivative_X_pow_eq_C_mul, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, IsAdjoinRootMonic.coeff_algebraMap, Subspace.dualLift_rightInverse, Representation.Coinvariants.mk_eq_iff, MvPowerSeries.coeff_zero_C, LinearMap.coprodEquiv_apply, QuadraticMap.associated_linMulLin, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, Polynomial.derivative_X_pow, Representation.isTrivial_apply, AffineMap.linear_bijective_iff, Rep.ihom_map_hom, LinearMap.rTensor_map, Ideal.natAbs_det_equiv, dualTensorHomEquivOfBasis_toLinearMap, LinearMap.map_coe_ker, QuadraticForm.associated_isSymm, Polynomial.sumIDeriv_derivative, MvPowerSeries.coeff_monomial, LinearMap.coe_addHom_mk, Submodule.coe_dualAnnihilator_span, MvPowerSeries.X_dvd_iff, TensorAlgebra.tprod_apply, Polynomial.X_mul_monomial, Orientation.kahler_mul, MvPowerSeries.coeff_C, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, Lagrange.interpolate_eq_add_interpolate_erase, LinearMap.trace_conj', Module.Invertible.rTensor_surjective_iff, ModuleCat.piIsoPi_hom_ker_subtype_apply, StandardEtalePair.HasMap.isUnit_derivative_f, Matrix.SpecialLinearGroup.toLin'_to_linearMap, TwoSidedIdeal.coe_subtype, ModularFormClass.qExpansion_coeff_eq_circleIntegral, ModuleCat.reflectsColimitsOfShape, Representation.IsIntertwiningMap.isIntertwining, groupHomology.H1AddEquivOfIsTrivial_apply, ModuleCat.MonoidalCategory.whiskerRight_apply, LinearMap.mul_toMatrix₂'_mul, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Module.Relations.toQuotient_map_apply, LinearMap.toMatrix₂'_mul, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, LinearMap.snd_prodOfFinsuppNat, CliffordAlgebra.reverseEquiv_symm_apply, LinearMap.ofIsCompl_add, Polynomial.aeval_sumIDeriv_eq_eval, Submodule.apply_mem_span_image_of_mem_span, AdicCompletion.transitionMap_map_pow, PowerSeries.coeff_expand_of_not_dvd, ModuleCat.free_δ_freeMk, Submodule.FG.directedSystem, IsCoprime.wronskian_eq_zero_iff, IsTensorProduct.lift_eq, LinearIndependent.of_isLocalizedModule, ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize, LinearMap.BilinForm.flip_flip, LinearMap.rTensor_zero, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Algebra.trace_complex_apply, MvPowerSeries.homogeneousComponent_mul_of_le_order, Algebra.toMatrix_lsmul, AlgEquiv.moduleEndSelf_apply_apply, exteriorPower.map_injective, LinearMap.mulRight_apply, toMatrix_innerSL_apply, Finset.weightedVSub_eq_linear_combination, LinearMap.intrinsicStar_single, isAssociatedPrime_iff_exists_injective_linearMap, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, Finsupp.linearCombination_fin_zero, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, MvPolynomial.support_sum_monomial_coeff, LinearMap.mulRight_eq_zero_iff, Matrix.separatingLeft_toLinearMap₂'_iff, Module.Relations.Solution.π_relation, TensorProduct.AlgebraTensorModule.map_smul_right, QuadraticMap.exists_companion', PolynomialModule.eval_apply, triple_product_permutation, LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero', Polynomial.leval_apply, CoalgCat.forget₂_map, AlternatingMap.ofSubsingleton_symm_apply_apply, LinearMap.intrinsicStar_smulRight, exists_derivative_mul_eq_and_isIntegral_coeff, Module.End.baseChangeHom_apply_apply, groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂, PiTensorProduct.mul_tprod_tprod, Polynomial.ofFn_degree_lt, Polynomial.taylor_monomial, MvPolynomial.weightedDecomposition.decompose'_eq, LinearMap.restrictScalars_zero, LinearMap.isProj_range_iff_isIdempotentElem, Rep.unit_iso_comm, Finsupp.linearCombination_equivMapDomain, BilinForm.toMatrix_mul, LinearMap.map_smul, Rep.leftRegularHomEquiv_symm_single, Lagrange.interpolate_apply, MultilinearMap.ofSubsingleton_symm_apply_apply, exists_lt_rieszContentAux_add_pos, LinearMap.toMatrix_comp, Polynomial.valuation_aeval_monomial_eq_valuation_pow, Algebra.normalizedTrace_algebraMap_apply, Submodule.piQuotientLift_single, LinearMap.add_compAlternatingMap, LinearMap.charpoly_one, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, CategoryTheory.NatTrans.appLinearMap_apply, ModularGroup.tendsto_lcRow0, PowerSeries.coeff_zero_eq_constantCoeff, Polynomial.factorial_smul_hasseDeriv, Matrix.toLinAlgEquiv_self, DirectSum.sigmaLuncurry_apply, Module.Basis.coe_toDual_self, RootPairing.RootPositiveForm.exists_pos_eq, FiniteField.minpoly_frobeniusAlgHom, Matrix.separatingLeft_toBilin'_iff, Matrix.trace_toLin_eq, Module.AEval'_def, LinearMap.inr_eq_prod, LinearMap.toMatrix₂_mul_basis_toMatrix, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T, TensorProduct.AlgebraTensorModule.lift_apply, groupCohomology.cocyclesMk₂_eq, Module.Basis.toMatrix_eq_toMatrix_constr, Finset.weightedVSub_vadd_affineCombination, TensorProduct.comul_tmul, LinearMap.lcompₛₗ_apply, Polynomial.hasDerivAt_aeval, DirectSum.lof_apply, LinearMap.polyCharpoly_map_eq_charpoly, Ideal.pi_mkQ_rTensor, MvPolynomial.coeffsIn_eq_span_monomial, Submodule.range_map_nonempty, IsBaseChange.basis_apply, Polynomial.aeval_root_derivative_of_splits, LinearMap.BilinMap.toQuadraticMap_sum, Orthonormal.inner_finsupp_eq_zero, LinearMap.zero_compAlternatingMap, Algebra.Generators.ofComp_toAlgHom_monomial_sumElim, Submodule.mulLeftMap_apply_single, KaehlerDifferential.quotKerTotalEquiv_symm_apply, LinearEquiv.toFGModuleCatIso_hom, LaurentSeries.coeff_zero_of_lt_intValuation, Polynomial.iterate_derivative_neg, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Orientation.kahler_map, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, Matrix.mulVec_cramer, AdicCompletion.of_injective, DirectSum.apply_eq_component, CliffordAlgebra.contractRight_one, PolyEquivTensor.toFunBilinear_apply_eq_smul, LinearMap.det_comp, LinearMap.isOrthoᵢ_def, CliffordAlgebraDualNumber.equiv_ι, MvPowerSeries.WithPiTopology.summable_iff_summable_coeff, MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, Polynomial.sum_taylor_eq, LinearMap.BilinForm.isSymm_def, PiTensorProduct.lift_tprod, Matrix.toLinOfInv_apply, Polynomial.taylor_eval_sub, TensorProduct.lcurry_apply, TrivSqZeroExt.snd_map, TensorProduct.curry_apply, Polynomial.derivative_prod_finset, LinearMap.GeneralLinearGroup.congrLinearEquiv_symm, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, dualTensorHomEquivOfBasis_symm_cancel_left, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, MvPolynomial.monomial_eq, TensorProduct.map_tmul, TensorProduct.mapIsometry_apply, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, signedDist_apply_linear_apply, LinearMap.transvection.det, Module.Invertible.rTensorEquiv_symm_apply_apply, CliffordAlgebra.changeForm_algebraMap, LaurentPolynomial.counit_C_mul_T, Module.Flat.iff_lift_lsmul_comp_subtype_injective, PiTensorProduct.liftIsometry_apply_apply, image_parallelepiped, Differential.deriv_aeval_eq, ContinuousLinearMap.coeLMₛₗ_apply, LinearMap.IsSymmetric.sub, CliffordAlgebra.foldr'Aux_apply_apply, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, Polynomial.hasseDeriv_C, Finsupp.sum_smul_index_semilinearMap', selfAdjointPart_apply_coe, CliffordAlgebra.reverse.map_one, Polynomial.coeff_list_sum, groupHomology.cyclesMk₁_eq, Module.End.isNilpotent_restrict_sub_algebraMap, minpoly_algEquiv_toLinearMap, Finset.weightedVSub_apply, Polynomial.smeval_monomial, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, Submodule.FG.lTensor.directLimit_apply, PowerSeries.X_pow_eq, PowerBasis.trace_gen_eq_sum_roots, Matrix.toBilin'Aux_eq, TensorProduct.lift.equiv_symm_apply, MvPowerSeries.coeff_invOfUnit, SemimoduleCat.inv_hom_apply, LinearEquiv.det_mul_det_symm, addMonoidHomLequivNat_apply, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, MvPolynomial.esymm_eq_sum_monomial, Polynomial.homogenize_monomial_of_lt, MeasureTheory.OuterMeasure.comap_boundedBy, Finset.weightedVSubOfPoint_eq_of_sum_eq_zero, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', Matrix.toLin_finTwoProd_toContinuousLinearMap, LightCondensed.ihom_map_val_app, IsBaseChange.linearMapLeftRight, MvPowerSeries.coeff_map, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, LieDerivation.leibniz', LinearMap.coe_withLpMap, LinearMap.map_add₂, PowerSeries.monomial_eq_C_mul_X_pow, trace_quotient_eq_trace_localization_quotient, StandardEtalePair.cond, LinearMap.toContinuousLinearMap₁_apply, AlternatingMap.curryLeft_compAlternatingMap, LinearMap.congr_arg, Submodule.mem_traceDual, Seminorm.coe_comp, LinearMap.map_smulₛₗ, LinearMap.domRestrict₂_apply, LinearMap.toMatrixAlgEquiv'_symm, LinearMap.map_lTensor, MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc', RootPairing.flip_toFun_apply, Algebra.normalizedTrace_trans_apply, LinearMap.comp_sub, TensorProduct.enorm_map, LinearMap.coe_toAddHom, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, Orientation.areaForm_map, IsGroupLikeElem.counit_eq_one, Polynomial.derivative_sub, ModuleCat.FreeMonoidal.μIso_inv_freeMk, LinearMap.derivWithin, Bialgebra.counit_algebraMap, TensorProduct.mapOfCompatibleSMul_tmul, Rep.Action_ρ_eq_ρ, LinearMap.coe_prodMap, PiTensorProduct.norm_eval_le_projectiveSeminorm, isCompactOperator_iff_image_ball_subset_compact, Algebra.FormallySmooth.kerCotangentToTensor_injective_iff, MeasureTheory.OuterMeasure.map_id, Polynomial.hasStrictDerivAt, DistribSMul.toLinearMap_apply, Ideal.powQuotSuccInclusion_injective, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, MvPolynomial.weightedHomogeneousComponent_eq_zero, LinearMap.map_neg₂, LinearMap.update_apply, ContinuousLinearMap.coe_neg, LinearEquiv.congrRight₂_trans, CliffordAlgebra.reverseOp_ι, LinearMap.surjective, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, LinearEquiv.conjRingEquiv_symm_apply_apply, LinearMap.BilinForm.isSymm_zero, Submodule.factor_comp_apply, NumberField.mixedEmbedding.commMap_apply_of_isReal, Algebra.norm_one_add_smul, TensorProduct.AlgebraTensorModule.rTensor_id, AffineMap.hasStrictDerivAt, Matrix.kroneckerTMulBilinear_apply, groupCohomology.mapCocycles₁_comp_i_apply, LinearMap.BilinForm.orthogonal_top_eq_ker, TensorProduct.map_map_assoc, QuadraticMap.apply_linearCombination', InnerProductSpace.toLinearMap_rankOne, KaehlerDifferential.tensorProductTo_surjective, ModuleCat.hom_zsmul, MvPolynomial.totalDegree_monomial_le, SemimoduleCat.forget_map, PowerSeries.coeff_divXPowOrder, groupHomology.mapCycles₂_id_comp_apply, Algebra.norm_apply, Submodule.image2_subset_map₂, Polynomial.aroots_monomial, Coalgebra.rTensor_counit_comul, MeasureTheory.OuterMeasure.isometry_map_mkMetric, Algebra.norm_eq_zero_iff', Module.Basis.linearMap_apply_apply, Rep.trivial_def, addMonoidHomLequivInt_symm_apply, PowerSeries.trunc_one, CliffordAlgebra.ι_mul_ι_comm_of_isOrtho, LinearMap.prodMap_smul, LinearMap.trace_tensorProduct, Polynomial.derivative_monomial_succ, comp_dualTensorHom, Polynomial.resultant_deriv, LocalizedModule.lift_mk_one, Algebra.trace_quotient_eq_of_isDedekindDomain, Algebra.Extension.h1Cotangentι_apply, Finsupp.linearCombination_linearCombination, Matrix.toLinearEquivRight'OfInv_apply, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, Submodule.coe_subtype, hasEigenvalue_toLin'_diagonal_iff, ContDiffMapSupportedIn.structureMapLM_zero_injective, LinearMap.surjective_or_eq_zero, ContinuousLinearMapWOT.continuous_inducingFn, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, PowerSeries.ext_iff, LinearEquiv.smul_id_of_finrank_eq_one_apply, LinearMap.BilinForm.coe_injective, Algebra.Extension.cotangentComplex_injective_iff, LinearMap.toMatrix'_toLinearMapₛₗ₂', AdicCompletion.transitionMap_ideal_mk, LinearMap.BilinForm.smul_right, AffineMap.continuous_linear_iff, LinearMap.isStarProjection_toContinuousLinearMap_iff, DirectSum.coeFnLinearMap_apply, PowerSeries.coeff_X_pow_self, Rep.MonoidalClosed.linearHomEquiv_hom, PowerSeries.trunc_succ, Matrix.toLpLin_mul, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, TensorProduct.map_convMul_map, LinearMap.rTensor_exact_iff_lTensor_exact, MvPowerSeries.coeff_smul, MvPolynomial.weightedHomogeneousComponent_C_mul, realPart_imaginaryPart, Matrix.toLin'_submatrix, TensorProduct.gradedMul_algebraMap, QuaternionAlgebra.imJₗ_apply, IsAdjoinRootMonic.coeff_one, Polynomial.monomial_one_right_eq_X_pow, LinearMap.det_conj, Derivation.compAEval_eq, ContDiffMapSupportedIn.seminorm_postcompLM_le, AlgEquiv.toLinearMap_apply, Matrix.separatingLeft_toLinearMap₂_iff, stdSimplex.image_linearMap, ModuleCat.localizedModuleMap_hom_apply, Derivation.tensorProductTo_tmul, Rep.hom_comm_apply, Polynomial.hasseDeriv_apply_one, Finsupp.lift_symm_apply, AdicCompletion.transitionMap_map_mul, SheafOfModules.pushforwardNatTrans_app_val_app, Polynomial.aeval_endomorphism, Module.End.genEigenspace_div, MvPowerSeries.coeff_zero_X, Orientation.inner_rightAngleRotationAux₁_right, LinearMap.ringLmapEquivSelf_apply, Module.Flat.iff_rTensor_preserves_injective_linearMapₛ, groupHomology.H2π_comp_map_apply, Matrix.toLin_toMatrix, LieModule.traceForm_genWeightSpace_eq, PiTensorProduct.lift_comp_map, TensorProduct.homTensorHomMap_apply, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, LinearMap.toSpanSingleton_convMul_toSpanSingleton, LinearMap.tensorEqLocus_tmul, exteriorPower.map_comp_ιMulti_family, ModularFormClass.qExpansion_isBigO, LaurentPolynomial.antipode_C, LieModule.traceForm_apply_apply, cross_dot_cross, MvPolynomial.mul_monomial_mem_coeffsIn, LinearMap.toMatrix₂_apply, ModuleCat.Hom.hom₂_apply, AdicCompletion.sumEquivOfFintype_apply, sectionOfRetractionKerToTensorAux_algebraMap, LinearMap.iterateRange_coe, RootPairing.rootFormIn_self_smul_coroot, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, ModuleCat.HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, LocallyConvexSpace.induced, Submodule.tensorToSpan_apply_tmul, LinearMap.adjoint_comp, ModuleCat.forget₂_addCommGrp_additive, LinearMap.intrinsicStar_apply, RootPairing.Equiv.weightEquiv_symm_weightMap, PolynomialModule.comp_eval, LinearMap.ofIsCompl_left_apply, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, RootPairing.corootForm_self_smul_root, PiToModule.fromMatrix_apply, RootPairing.exists_form_eq_form_and_form_ne_zero, Polynomial.surjective_toFn, LinearPMap.smul_graph, LinearMap.toContPerfPair_apply, MonomialOrder.sPolynomial_monomial_mul', LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, LinearMap.IsPositive.inner_nonneg_right, Matrix.toEuclideanLin_apply_piLp_toLp, HahnSeries.coeff_toMvPowerSeries, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, LinearMap.dualMap_apply, LinearMap.ker_le_iff, LieModule.Cohomology.twoCochain_val_apply, Lagrange.interpolate_empty, LinearIsometry.norm_map', LinearMap.isSelfAdjoint_iff_map_star, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, TensorAlgebra.ι_inj, bernsteinPolynomial.derivative_succ, LinearMap.dualMap_surjective_iff, multilinearCurryLeftEquiv_symm_apply, Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd, Algebra.SubmersivePresentation.aevalDifferentialEquiv_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, ContinuousLinearMap.coe_sub, skewAdjointPart_eq_I_smul_imaginaryPart, MultilinearMap.piLinearMap_apply_apply_apply, HahnSeries.coeff.linearMap_apply, TensorProduct.toLinearMap_symm_lid, TensorAlgebra.ι_eq_zero_iff, LinearMap.rTensor_comp_apply, MvPolynomial.C_mul_X_pow_eq_monomial, Finsupp.linearCombination_option, SMulMemClass.subtype_injective, LinearMap.mulLeftRight_apply, Polynomial.iterate_derivative_X_sub_pow_self, QuadraticMap.associated_sq, Polynomial.derivativeFinsupp_one, LinearMap.dualMap_def, iSupIndep_iff_dfinsupp_lsum_injective, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, MvPowerSeries.order_monomial, ExteriorAlgebra.map_apply_ιMulti, QuadraticMap.associated_comp, LinearMap.isSymmetric_iff_isSelfAdjoint, MvPolynomial.weightedHomogeneousComponent_mem, TensorProduct.tmul_of_gradedMul_of_tmul, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, SchwartzMap.convolution_flip, QuadraticMap.associated_isOrtho, Lagrange.eq_interpolate_of_eval_eq, Submodule.lTensorOne'_one_tmul, LinearMap.mem_graph_iff, Matrix.cramer_one, CliffordAlgebra.contractLeft_mul_algebraMap, LinearMap.coe_quotientInfToSupQuotient, map_dualTensorHom, LinearMap.isSymmetric_iff_sesqForm, Polynomial.taylor_zero, Subspace.dualLift_injective, Algebra.Generators.cotangentRestrict_mk, IsLocalizedModule.lift_apply, MultilinearMap.curryMidLinearEquiv_symm_apply, Polynomial.toMatrix_sylvesterMap, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc, GradedAlgebra.proj_apply, LinearMap.smulRightₗ_apply_apply, Representation.toCoinvariants_mk, MvPolynomial.optionEquivLeft_monomial, IsAdjoinRootMonic.modByMonicHom_root, GroupLike.val_inv_toUnits_apply, Bialgebra.comul_pow, Finsupp.lsum_comp_lsingle, Submodule.IsCompl.projection_eq_self_sub_projection, LinearMap.IsRefl.eq_iff, AlternatingMap.uncurryFin_add, Algebra.Generators.cotangentRestrict_bijective_of_basis_kaehlerDifferential, TensorProduct.AlgebraTensorModule.lTensor_one, LinearMap.eqLocus_eq_ker_sub, CliffordAlgebra.toProd_one_tmul_ι, Module.finrank_linearMap_self, Matrix.separatingRight_toBilin'_iff, Derivation.coe_add_linearMap, LinearMap.vecEmpty₂_apply, MvPowerSeries.substAlgHom_monomial, Polynomial.derivative_neg, Representation.IsTrivial.out, groupCohomology.π_comp_H2Iso_hom_apply, Orientation.areaForm_map_complex, RootPairing.InvariantForm.apply_root_root_zero_iff, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, Matrix.toLin_finTwoProd, ModuleCat.HasLimit.lift_hom_apply, Polynomial.deriv, Coalgebra.counitCoalgHom_apply, LinearMap.BilinForm.apply_toDual_symm_apply, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_invariant, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, qExpansion_mul_coeff_zero, CliffordAlgebra.even.lift.aux_apply, CliffordAlgebra.toBaseChange_involute, LinearMap.IsProj.bot, Module.Basis.linearMap_repr_symm_apply, Derivation.coe_smul_linearMap, Matrix.toLinAlgEquiv'_toMatrixAlgEquiv', MeasureTheory.Measure.mapₗ_eq_zero_iff, LinearMap.funLeft_apply, CliffordAlgebra.even.lift.aux_ι, Hausdorffification.lift_of, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, LinearMap.BilinForm.neg_apply, RootPairing.rootForm_pos_of_ne_zero, Module.Basis.constr_basis, IsBaseChange.equiv_tmul, PowerSeries.trunc_coe_eq_self, instCharPLinearMapSubtypeMemSubringCenterId, Bialgebra.comul_one, LinearMap.tensorProduct_apply, LinearMap.BilinForm.isPosSemidef_zero, LinearMap.map_sub, exteriorPower.pairingDual_apply_apply_eq_one_zero, ModuleCat.homLinearEquiv_apply, Polynomial.hasseDeriv_natDegree_eq_C, Rep.coinvariantsTensorMk_apply, Polynomial.hasFDerivWithinAt_aeval, Orientation.inner_rightAngleRotation_right, SpecialLinearGroup.toGeneralLinearGroup_toLinearEquiv_apply, WeakBilin.eval_continuous, QuotSMulTop.map_comp, LieModule.traceForm_apply_lie_apply, LinearMap.snd_surjective, Projectivization.cross_mk_of_ne, LinearMap.not_separatingLeft_zero, LinearMap.single_apply, Module.End.genEigenspace_nat, LinearMap.continuous_of_isClosed_ker, Rep.indMap_hom, PowerSeries.coeff_derivative, endVecAlgEquivMatrixEnd_symm_apply_apply, LinearMap.det_zero'', Representation.coind_apply, CharacterModule.uncurry_apply, Polynomial.derivative_C_mul_X_pow, AdicCompletion.of_bijective, LinearMap.IsSymmetric.im_inner_apply_self, Polynomial.derivative_C, Rep.homEquiv_symm_apply_hom, QuadraticMap.Ring.associated_pi, LinearMap.nondegenerate_toMatrix₂_iff, Matrix.trace_kroneckerMapBilinear, Polynomial.derivative_bernoulli_add_one, LinearMap.frobenius_def, span_range_eq_top_iff_surjective_finsuppLinearCombination, FunOnFinite.linearMap_piSingle, LinearMap.inl_apply, LinearMap.map_span_le, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, ModuleCat.extendScalarsComp_hom_app_one_tmul, Polynomial.hasseDeriv_apply, Polynomial.addSubmonoid_closure_setOf_eq_monomial, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Module.Invertible.lTensor_surjective_iff, innerₛₗ_apply, LinearMap.mapMatrix_add, Matrix.toLinAlgEquiv'_one, Polynomial.eval₂_derivative_of_splits, LinearPMap.vadd_apply, trace_eq_sum_embeddings, Matrix.toLin_one, CliffordAlgebra.contractLeft_algebraMap_mul, PowerSeries.coeff_subst_finite, LinearMap.BilinForm.compLeft_apply, DFinsupp.lapply_comp_lsingle_of_ne, contractRight_apply, LinearMap.trace_eq_contract_of_basis, CliffordAlgebra.reverseEquiv_apply, PowerSeries.coeff_X_pow, Matrix.toLin_transpose, Complex.toMatrix_conjAe, MvPowerSeries.isHomogeneous_homogeneousComponent, LaurentPolynomial.counit_T, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, Representation.leftRegular_norm_apply, BilinForm.mul_toMatrix, inner_map_polarization, ModularFormClass.hasSum_qExpansion_of_norm_lt, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, groupCohomology.π_comp_H1Iso_hom_apply, Representation.coinvariantsToFinsupp_mk_single, LinearMap.continuous_iff_isClosed_ker, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, Polynomial.sum_modByMonic_coeff, Algebra.Generators.CotangentSpace.map_toComp_injective, TensorProduct.mk_surjective, AdicCompletion.evalₐ_of, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Module.End.lTensorAlgHom_apply_apply, PowerSeries.expand_monomial, Matrix.toLpLin_symm_comp, Polynomial.aeval_monomial, MvPowerSeries.aeval_eq_sum, Representation.ind_mk, IntrinsicStar.StarHomClass.isSelfAdjoint, Module.Basis.toDual_linearCombination_right, Matrix.toLinearMapₛₗ₂_apply_basis, IsLocalRing.CotangentSpace.span_image_eq_top_iff, LaurentPolynomial.counit_C, qExpansion_coeff_unique, Polynomial.Chebyshev.iterate_derivative_T_eval_one, VertexOperator.ncoeff_of_coeff, LinearMap.toSeminorm_ball_zero, CliffordAlgebraRing.reverse_apply, Lagrange.eval_interpolate_at_node, RootPairing.restrictScalars_toLinearMap_apply_apply, MvPolynomial.divMonomial_monomial_mul, DFinsupp.counit_single, LocallyConstant.constₗ_apply_apply, ExteriorAlgebra.liftAlternating_algebraMap, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, LinearMap.ofIsCompl_right_apply, Orientation.kahler_apply_apply, LinearMap.det_zero', groupHomology.d₂₁_single_one_snd, LinearMap.convMul_comp_coalgHom_distrib, imaginaryPart_imaginaryPart, PowerSeries.coeff_subst', Orientation.inner_rightAngleRotationAux₁_left, LinearMap.GeneralLinearGroup.congrLinearEquiv_trans', LinearMap.sub_apply, TensorProduct.AlgebraTensorModule.map_tmul, Polynomial.sylvesterMap_apply_coe, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, LinearMap.toMatrix_toSpanSingleton, LinearEquiv.coe_inv_det, VertexOperator.ncoeff_eq_zero_of_lt_order, PolynomialLaw.isCompat_apply', LinearMap.comp_add, LinearMap.toMatrix₂_symm', MvPolynomial.sum_monomial_eq, Module.Invertible.bijective, Module.Invertible.lTensor_bijective_iff, LinearMap.toSeminorm_apply, IsLocalizedModule.fromLocalizedModule'_mk, riesz_extension, linearIndepOn_union_iff_quotient, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, Pi.comul_single, TrivSqZeroExt.sndHom_apply, MvPolynomial.degrees_monomial_eq, LinearMap.mulRight_toAddMonoidHom, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Coalgebra.coassoc_apply, TwoSidedIdeal.subtypeMop_apply, mulLeftLinearMap_zero_eq_zero, groupHomology.π_map_apply, LinearMap.continuous_of_isClosed_graph, pinGroup.involute_act_ι_mem_range_ι, LinearMap.GeneralLinearGroup.toLinearEquiv_mul, Module.End.mem_genEigenspace_nat, Submodule.inclusion_injective, LinearEquiv.coe_toLinearMap, ProbabilityTheory.variance_linearMap_gaussianReal, HopfAlgebra.mul_antipode_lTensor_comul_apply, Representation.coinvariantsFinsuppLEquiv_symm_apply, LeftInvariantDerivation.evalAt_mul, LinearMap.Nondegenerate.toMatrix₂', MvPolynomial.pUnitAlgEquiv_monomial, conductor_mul_differentIdeal, Polynomial.support_derivativeFinsupp_subset_range, MvPolynomial.coeff_monomial, TensorProduct.equivFinsuppOfBasisRight_symm, MvPolynomial.coeff_mul_monomial, CliffordAlgebraDualNumber.ι_mul_ι, Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_lt, Polynomial.monomial_zero_left, groupHomology.d₃₂_single_one_snd, MvPolynomial.mem_ideal_span_monomial_image_iff_dvd, HVertexOperator.compHahnSeries_coeff, HahnSeries.map_smul, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, IsSMulRegular.subsingleton_linearMap_iff, Bialgebra.counit_one, IsRegular.monomial, groupHomology.π_comp_H2Iso_hom_apply, LinearMap.instSMulCommClassDomMulAct, Profinite.NobelingProof.CC_comp_zero, RootPairing.InvariantForm.apply_eq_or, SheafOfModules.relationsOfIsCokernelFree_s, Submodule.quotientPiLift_mk, Matrix.Nondegenerate.toBilin', ModuleCat.forget₂_reflectsLimits, CliffordAlgebra.isUnit_ι_of_isUnit, FDRep.Iso.conj_ρ, LinearMap.isPositive_iff, TensorProduct.directLimitLeft_tmul_of, Lagrange.interpolate_poly_eq_self, LinearMap.IsAlt.eq_of_add_add_eq_zero, VectorFourier.fourierIntegral_comp_add_right, LinearMap.isIntegral, ContDiffMapSupportedIn.postcompLM_apply, LinearMap.BilinForm.congr_trans, Polynomial.taylor_coeff, LinearMap.toMatrix_singleton, LinearMap.isNonneg_def, FDRep.of_ρ, LinearMap.BilinForm.toMatrix'_mul, LinearMap.injOn_of_disjoint_ker, Algebra.trace_prod_apply, Module.Flat.iff_rTensor_injectiveₛ, dotProductBilin_apply_apply, MvPolynomial.monomial_pow, LaurentSeries.derivative_iterate, Algebra.trace_trace_of_basis, ModuleCat.forget₂PreservesColimitsOfShape, Submodule.mkQ_surjective, Polynomial.taylor_inj, Polynomial.derivative_zero, Algebra.traceMatrix_of_basis_mulVec, IsBaseChange.basis_repr_comp, MvPowerSeries.monomial_zero_one, MvPowerSeries.monomial_one_eq, Algebra.Extension.Hom.sub_tmul, PowerSeries.IsRestricted.monomial, exteriorPower.alternatingMapLinearEquiv_symm_apply, MvPolynomial.eval₂_monomial, det_rotation, SkewPolynomial.monomial_mul_monomial, PowerSeries.coeff_expand, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, IsAdicComplete.mk_lift, Rep.ihom_coev_app_hom, Algebra.map_intTraceAux, LinearMap.sum_apply, ModuleCat.biproductIsoPi_inv_comp_π_apply, QuadraticMap.apply_linearCombination, LinearMap.toMatrix₂'_compl₂, LinearMap.restrictScalars₁₂_injective, LaurentPolynomial.comul_C_mul_T, PiTensorProduct.map_reindex, AdicCompletion.factor_evalₐ_eq_eval, Profinite.NobelingProof.eval_eq_πJ, PositiveLinearMap.toLinearMap_zero, Matrix.toLinAlgEquiv'_symm, Rep.leftRegularHomEquiv_apply, imaginaryPart_smul, LinearMap.map_sum₂, VectorFourier.fourierIntegral_probChar, Submodule.mem_map_of_mem, LinearMap.IsSymm.add, PresheafOfModules.pushforward_obj_map_apply', MeasureTheory.OuterMeasure.map_top_of_surjective, RootPairing.Hom.coroot_coweightMap_apply, Matrix.entryLinearMap_apply, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, LieAlgebra.IsKilling.traceForm_coroot, Polynomial.succ_signVariations_X_sub_C_mul_monomial, IsAdjoinRootMonic.coeff_apply_coe, TensorProduct.AlgebraTensorModule.curry_injective, Polynomial.derivative_X_add_C_sq, Orientation.kahler_rotation_right, Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative, PointedCone.mem_comap, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, ContinuousLinearMap.coe_sum, LieDerivation.coe_add_linearMap, LinearMap.BilinForm.comp_apply, Polynomial.as_sum_support, AlternatingMap.coe_compLinearMap, MvPolynomial.monomial_one_dvd_monomial_one, Ideal.cotangentEquivIdeal_symm_apply, Module.flat_iff, MultilinearMap.compLinearMap_apply, MeasureTheory.OuterMeasure.restrict_apply, LinearMap.smulRight_zero, Module.Basis.traceDual_repr_apply, MvPolynomial.mul_monomial_modMonomial, MeasureTheory.ComplexMeasure.re_apply, PiTensorProduct.lift.unique', Matrix.nondegenerate_toLinearMap₂'_iff, LinearMap.separatingRight_toMatrix₂_iff, FGModuleCat.FGModuleCatEvaluation_apply', Polynomial.natTrailingDegree_monomial_le, ModuleCat.forget₂AddCommGroup_reflectsLimit, LieModule.traceForm_eq_sum_finrank_nsmul_mul, Submodule.exists_fg_le_eq_rTensor_subtype, TensorProduct.piScalarRight_apply, CliffordAlgebra.lift_comp_ι, groupHomology.coe_mapCycles₁, Coalgebra.lTensor_counit_comp_comul, PowerSeries.eval₂_trunc_eq_sum_range, SpecialLinearGroup.coe_toGeneralLinearGroup_apply, AlternatingMap.curryLeft_compLinearMap, LinearMap.comp_neg, LinearMap.fst_eq_coprod, LinearMap.det_ring, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis, SMulMemClass.subtype_apply, CliffordAlgebra.changeForm.associated_neg_proof, LinearMap.coe_det, PowerSeries.trunc_one_X, Module.Relations.toQuotient_relation, Polynomial.leval_coe_eq_smeval, LinearMap.BilinForm.neg_right, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, CliffordAlgebra.ofEven_ι, exteriorPower.map_apply_ιMulti, MvPolynomial.mkDerivationₗ_X, LinearMap.BilinForm.IsNonneg.smul, Algebra.H1Cotangent.exact_map_δ, QuadraticMap.Isometry.toLinearMap_injective, LocallyConstant.coeFnₗ_apply, groupCohomology.d₀₁_comp_d₁₂_apply, MvPowerSeries.monomial_eq, Algebra.Generators.Hom.toAlgHom_monomial, Finset.sum_smul_vsub_const_eq_weightedVSub, Algebra.normalizedTrace_algebraMap_of_lifts, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, realPart_apply_coe, QuotSMulTop.map_apply_mk, LinearMap.IsSymmetric.conj_inner_sym, ModuleCat.free_map_apply, Matrix.cramer_smul, MeasureTheory.Measure.restrictₗ_apply, Module.projective_def, TensorProduct.gradedCommAux_lof_tmul, Representation.linHom.mem_invariants_iff_comm, LinearMap.algHom_comp_convMul_distrib, Module.End.ringEquivEndFinsupp_apply_apply_support, CompletelyPositiveMap.map_cstarMatrix_nonneg', IsLocalFrameOn.coeff_eq_of_eq, LinearMap.BilinForm.linMulLin_apply, DFinsupp.lapply_apply, LinearMap.eventually_codisjoint_ker_pow_range_pow, TensorProduct.directLimitLeft_symm_of_tmul, Representation.IntertwiningMap.isIntertwining, LinearMap.coe_smulRight, groupHomology.mapCycles₂_comp_i_apply, TensorProduct.norm_map, RootPairing.Equiv.id_weightMap_apply, PolynomialModule.monomial_smul_apply, ContinuousLinearMap.coe_le_coe_iff, PiTensorProduct.mapMonoidHom_apply, AdicCompletion.eval_of, RootPairing.corootSpan_dualAnnihilator_le_ker_rootForm, PowerSeries.coeff_succ_X_mul, LinearMap.pi_zero, Module.End.isNilpotent_restrict_genEigenspace_top, LinearMap.toMvPolynomial_eval_eq_apply, LinearMap.mk₂'_apply, IsLocalizedModule.map_comp, LinearMap.BilinForm.comp_symmCompOfNondegenerate_apply, HVertexOperator.coeff_comp, MvPowerSeries.coeff_monomial_ne, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ModuleCat.ofHom₂_hom_apply_hom, AdicCompletion.map_zero, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, groupHomology.boundariesToCycles₂_apply, LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot, Polynomial.logMahlerMeasure_monomial, Function.ExtendByZero.linearMap_apply, PowerSeries.trunc_trunc, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, LinearEquiv.arrowCongrAddEquiv_apply, AdicCompletion.component_sumInv, LinearMap.trace_conj, QuadraticMap.Isometry.tmul_apply, LinearMap.det_eq_det_mul_det, isSMulRegular_on_quot_iff_lsmul_comap_eq, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, Rep.freeLift_hom, Polynomial.rootSet_monomial, Ideal.coe_torsionOf, LinearMap.map_smul_of_tower, Polynomial.monomial_left_inj, RatFunc.taylor_mem_nonZeroDivisors, LinearMap.toSpanSingleton_zero, LinearMap.injective_domRestrict_iff, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, LinearMap.BilinForm.congr_fun, jacobi_cross, CliffordAlgebra.toBaseChange_ι, Polynomial.newtonMap_apply, LinearMap.separatingLeft_toMatrix₂_iff, HVertexOperator.coeff_apply_apply, basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix, AdicCompletion.evalₐ_mk, Module.Basis.toDualFlip_apply, LinearMap.toSpanSingleton_one, RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot, LinearMap.mem_span_iff_bound, Set.Finite.convexHull_eq_image, AdicCompletion.piEquivOfFintype_apply, MvPolynomial.monomial_sum_one, Algebra.algebraMap_intTrace, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, TensorProduct.dualDistrib_apply, AlternatingMap.uncurryFin_apply, LinearMap.lTensor_pow, LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal, LinearEquiv.det_coe_symm, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.π_map_apply, Rep.indToCoindAux_snd_mul_inv, CliffordAlgebra.ι_mem_evenOdd_one, Representation.ofMulDistribMulAction_apply_apply, LinearMap.BilinForm.IsAlt.sub, ModuleCat.hom_sub, DirectSum.linearEquivFunOnFintype_symm_single, Submodule.map_span, LinearPMap.vadd_domain, LinearMap.BilinForm.toMatrix'_toBilin', Fintype.linearCombination_apply_single, SimplexCategory.coe_toTopMap, isSimpleModule_iff_toSpanSingleton_surjective, LinearMap.rTensor_neg, SchwartzMap.fourier_convolution_apply, AlternatingMap.compLinearMap_apply, Fintype.linearCombination_apply, LinearMap.GeneralLinearGroup.congrLinearEquiv_trans, neg_cross, Projectivization.generalLinearGroup_smul_def, Rep.res_obj_ρ, LinearAlgebra.FreeProduct.lift_apply, LinearMap.surjective_rangeRestrict, LocalizedModule.map_mk, PowerBasis.liftEquiv'_symm_apply_apply, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, PiTensorProduct.lift_comp_reindex_symm, PiTensorProduct.map_update_smul, Polynomial.natDegree_iterate_derivative, Module.exists_surjective_quotient_of_finite, QuadraticMap.separatingLeft_of_anisotropic, IsAdicComplete.StrictMono.of_lift, Pi.comul_coe_dFinsupp, MultilinearMap.linearDeriv_apply, PowerBasis.constr_pow_mul, PolynomialLaw.isCompat_apply, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, TensorProduct.map_smul_left, HahnEmbedding.Partial.eval_eq_truncLT, AddMonoidHom.coe_toIntLinearMap, Submodule.span_preimage_le, LinearMap.det_toMatrix', LinearMap.GeneralLinearGroup.ofLinearEquiv_mul, Matrix.separatingLeft_toBilin_iff, PresheafOfModules.freeYonedaEquiv_comp, ModuleCat.forget₂AddCommGroup_preservesLimit, SMulMemClass.coe_subtype, LinearMap.eq_adjoint_iff_basis_right, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, LinearEquiv.arrowCongr_trans, Polynomial.eval_add_of_sq_eq_zero, Polynomial.derivative_X_add_C_pow, Module.Finite.exists_fin', LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebra, LinearMap.Nondegenerate.toMatrix₂, MeasureTheory.OuterMeasure.map_top, LinearMap.toMatrixAlgEquiv_apply', IsLocalizedModule.eq_iff_exists, LinearMap.lTensor_map, trace_eq_sum_automorphisms, LinearMap.evalAddMonoidHom_apply, Matrix.toLin'OfInv_apply, MvPowerSeries.coeff_subst_finite, MonomialOrder.div, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Profinite.NobelingProof.injective_πs, MultilinearMap.toLinearMap_apply, IsModuleTopology.continuous_bilinear_of_finite_right, mulLeftLinearMap_eq_zero_iff, Finsupp.linearCombination_surjective, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, LinearMap.existsUnique_eq_smul_id_of_finrank_eq_one, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, LinearMap.BilinForm.isOrtho_def, MvPolynomial.scalarRTensor_symm_apply_single, DFinsupp.mapRange.linearMap_apply, LinearMap.rank_add_le, Representation.smul_one_tprod_asModule, Polynomial.natDegree_monomial_eq, LinearMap.isStarProjection_iff_isSymmetricProjection, ModuleCat.FreeMonoidal.εIso_hom_one, LinearIndepOn.image, innerₛₗ_apply_coe, TensorProduct.equivFinsuppOfBasisLeft_apply, CharacterModule.dual_surjective_iff_injective, instExpCharLinearMapSubtypeMemSubringCenterId, Polynomial.iterate_derivative_mul, LinearMap.BilinMap.toQuadraticMap_apply, Polynomial.aeval_iterate_derivative_of_lt, Rep.freeLift_hom_single_single, Trivialization.linearMapAt_def_of_notMem, LinearMap.BilinForm.Nondegenerate.toMatrix', Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, LinearMap.isSymm_iff_basis, MvPolynomial.weightedHomogeneousComponent_of_mem, Module.Basis.constr_self, Polynomial.derivative_map, LinearMap.toMatrix_basis_equiv, Matrix.UnitaryGroup.toGL_one, LinearMap.restrictScalars₁₂_apply_apply, Finsupp.mem_span_image_iff_linearCombination, Derivation.coe_zero_linearMap, MvPowerSeries.order_eq_nat, LinearMap.CompatibleSMul.map_smul, LinearMap.charpoly_zero, MultilinearMap.compLinearMapMultilinear_apply, MvPolynomial.irreducible_sumSMulXSMulY, LieModule.traceForm_apply_eq_zero_of_mem_lcs_of_mem_center, Submodule.map_toAddSubgroup, groupHomology.π_comp_H1Iso_inv_apply, topDualPairing_apply, LinearMap.trace_prodMap', AddMonoidHom.coe_toZModLinearMap, MvPowerSeries.IsWeightedHomogeneous.coeff_eq_zero, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, PowerSeries.coeff_C_mul, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, TensorProduct.AlgebraTensorModule.lift_tmul, PowerSeries.X_pow_dvd_iff, MvPolynomial.mem_ideal_span_monomial_image, Polynomial.iterate_derivative_intCast_mul, Polynomial.taylor_mem_degreeLT, Polynomial.leadingCoeff_monomial, AddMonoidAlgebra.antipode_single, IsLocalizedModule.fromLocalizedModule.surj, Lagrange.eval_nodal_derivative_eval_node_eq, Finset.weightedVSub_subtype_eq_filter, LinearMap.separatingLeft_iff_ker_eq_bot, Matrix.SeparatingRight.toBilin', LinearMap.lflip_symm, LinearMap.bijective_of_ne_zero, IsAdjoinRootMonic.coeff_apply_le, Module.Basis.traceDual_powerBasis_eq, LinearMap.ltoFun_apply, Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range, CliffordAlgebra.EquivEven.reverse_v, Polynomial.card_support_le_one_iff_monomial, Orientation.areaForm_rightAngleRotation_right, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, LinearMap.convMul_apply, Algebra.injective_lift_lsmul, MvPowerSeries.coeff_mul_left_one_sub_of_lt_order, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, Profinite.NobelingProof.coe_πs', groupCohomology.isoCocycles₂_hom_comp_i_apply, AdicCompletion.ofLinearEquiv_apply, Polynomial.coeff_mul_monomial, Algebra.algebraMap_intTrace_fractionRing, LaurentPolynomial.trunc_C_mul_T, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, ModuleCat.hom_bijective, LinearMap.compBilinForm_apply_apply, LinearMap.lid_comp_rTensor, Rep.diagonalHomEquiv_apply, LinearMap.coe_toContinuousLinearMap_symm, Matrix.range_diagonal, LinearMap.prod_apply, AdicCompletion.mk_apply_coe, Prod.counit_apply, Submodule.span_image, Module.Relations.toQuotient_map, LinearMap.BilinForm.Nondegenerate.ker_eq_bot, Polynomial.derivative_natCast, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, TwoSidedIdeal.subtypeMop_injective, groupHomology.d₂₁_single, LinearMap.extendScalarsOfIsLocalizationEquiv_symm_apply, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, LinearMap.coe_coe, IsSelfAdjoint.coe_realPart, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, Module.Flat.tensorProduct_mapIncl_injective_of_right, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, LinearMap.proj_surjective, mulLeftLinearMap_apply, Module.Basis.constr_def, SheafOfModules.Presentation.IsFinite.finite_relations, SemimoduleCat.hom_add, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, cardinalMk_algHom, LinearMap.trace_comp_comm, KaehlerDifferential.map_D, Polynomial.hasseDeriv_X, LinearMap.ofIsCompl_subtype_zero_eq, addMonoidEndRingEquivInt_symm_apply, LinearMap.pow_mulLeft, Derivation.liftKaehlerDifferential_apply, MvPolynomial.coeff_weightedHomogeneousComponent, realPart_smul, BilinForm.toMatrix_compLeft, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, LinearMap.IsPositive.adjoint_eq, groupHomology.eq_d₂₁_comp_inv_apply, PowerSeries.order_eq, Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace, Algebra.coe_lmul_eq_mul, StarHomClass.isSelfAdjoint, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, Polynomial.derivative_bernoulli, AdicCompletion.congr_apply, PiTensorProduct.map_update_add, Module.Basis.toDual_apply_left, LinearMap.nilRank_le_natTrailingDegree_charpoly, LinearMap.toPerfPair_apply, ExteriorAlgebra.comp_ι_sq_zero, KaehlerDifferential.DLinearMap_apply, CategoryTheory.whiskering_linearYoneda₂, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, LinearMap.toMatrix₂'_comp, MvPolynomial.rTensor_apply, ContinuousLinearMap.coe_injective, Matrix.toLinearMap₂_apply_basis, Polynomial.ofFn_coeff_eq_val_of_lt, Finset.weightedVSubOfPoint_erase, IsAdjoinRootMonic.coeff_root, LinearPMap.mem_adjoint_domain_iff, MvPolynomial.disjoint_support_monomial, CliffordAlgebra.ofProd_ι_mk, MvPowerSeries.monomial_mul_monomial, LinearMap.IsSymmetricProjection.le_iff_range_le_range, Module.DualBases.lc_def, ModuleCat.MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, CliffordAlgebra.GradedAlgebra.lift_ι_eq, PolynomialModule.monomial_smul_lsingle, TensorPower.toTensorAlgebra_galgebra_toFun, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, TensorProduct.Algebra.moduleAux_apply, Rep.indToCoindAux_of_not_rel, PowerSeries.coeff_zero_X_mul, LinearMap.not_hasEigenvalue_zero_tfae, LinearMap.zero_comp, LinearMap.toMatrix_pow, TensorProduct.map_range_eq_span_tmul, MvPolynomial.aeval_monomial, LinearMap.exact_iff, groupHomology.cyclesMk₀_eq, RootPairing.disjoint_rootSpan_ker_rootForm, Module.FinitePresentation.isLocalizedModule_mapExtendScalars, CommSemiring.counit_apply, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Rep.applyAsHom_hom, NNRealRMK.integral_rieszMeasure, Module.Relations.Solution.IsPresentation.exact, ExteriorAlgebra.ι_mul_prod_list, LinearMap.BilinMap.polarBilin_toQuadraticMap, IsBaseChange.linearMapLeftRightHom_apply, Algebra.trace_apply, LinearIsometry.rTensor_apply, TensorAlgebra.toDirectSum_ι, ModuleCat.forget_map, LinearMap.coprodEquiv_symm_apply, LinearEquiv.arrowCongrAddEquiv_symm_apply, CompactlySupportedContinuousMap.monotone_of_nnreal, LinearMap.BilinForm.toMatrix_comp, ExteriorAlgebra.ιMulti_succ_curryLeft, LinearMap.mul'_comm, Matrix.SpecialLinearGroup.toLin'_symm_apply, Submodule.map_neg, DirectSum.lmap_of, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, LinearMap.map_smul_inv, Finset.weightedVSub_sdiff_sub, QuadraticAlgebra.det_toLinearMap_eq_norm, CoalgHomClass.map_comp_comul_apply, ExteriorAlgebra.leftInverse_map_iff, IsLocalizedModule.map_integerMultiple, Submodule.comap_smul', coe_innerₛₗ_apply, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange, Coalgebra.Repr.eq, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, TensorProduct.finsuppScalarLeft_apply, MonomialOrder.degree_monomial_le, LinearMap.trace_comp_cycle, LinearMap.intrinsicStar_comp, ModularGroup.lcRow0_apply, PowerSeries.WithPiTopology.tendsto_trunc_atTop, Algebra.FormallyUnramified.comp_sec, MulOpposite.coe_opLinearEquiv_symm_toLinearMap, Module.Basis.toDual_apply_right, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, LinearMap.trace_comp_cycle', IsLinearMap.mk'_apply, MvPolynomial.coeff_mul_monomial', LinearMap.toMatrix'_one, Representation.dual_apply, LieAlgebra.SpecialLinear.val_singleSubSingle, lipschitzGroup.involute_act_ι_mem_range_ι, Polynomial.monomial_natDegree_leadingCoeff_eq_self, AdicCompletion.transitionMap_comp_eval_apply, Finsupp.linearCombination_comapDomain, AdicCompletion.of_injective_iff, Submodule.map_coe, Submodule.baseChange_span, LinearMap.surjective_comp_left_of_exists_rightInverse, LinearMap.BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal, Module.Basis.det_smul_mk_coord_eq_det_update, Module.surjective_piEquiv_apply_iff, PowerSeries.coeff_C_mul_X_pow, LinearPMap.coe_vadd, Module.Dual.eq_of_preReflection_mapsTo', TensorAlgebra.lift_unique, TensorProduct.quotTensorEquivQuotSMul_comp_mk, Submodule.map_toAddSubmonoid', Orientation.kahler_rightAngleRotation_right, RingHom.coe_toSemilinearMap, bernsteinPolynomial.derivative_zero, PointedCone.mem_maxTensorProduct, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, Polynomial.iterate_derivative_map, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, Polynomial.sumIDeriv_apply_of_le, LinearEquiv.automorphismGroup.toLinearMapMonoidHom_apply, QuadraticMap.exists_companion, DirectSum.lmap_injective, LinearMap.BilinForm.IsAlt.add, cross_cross_eq_smul_sub_smul', rank_lt_rank_dual, ModuleCat.homAddEquiv_apply, Module.Basis.repr_symm_apply, Module.fgSystem.instDirectedSystemSubtypeSubmoduleFGMemValCoeLinearMapId, Finsupp.apply_linearCombination_id, Submodule.linearProjOfIsCompl_apply_eq_zero_iff, Polynomial.Bivariate.pderiv_one_equivMvPolynomial, TensorProduct.rTensorHomToHomRTensor_apply, Module.Dual.congr_apply_apply, LieAlgebra.IsKilling.span_weight_eq_top, Algebra.coe_linearMap, TensorProduct.fromDirectLimit_of_tmul, Polynomial.support_monomial', LinearMap.tensorKerEquiv_apply, basis_toMatrix_mul_linearMap_toMatrix, LinearMap.IsAlt.self_eq_zero, AlternatingMap.alternatizeUncurryFin_smul, LinearMap.toMatrixₛₗ₂'_apply, Representation.dualTensorHom_comm, AdicCompletion.eval_lift_apply, ModuleCat.span_rightExact, LinearMap.baseChange_tmul, MvPolynomial.lcoeff_apply, CommRingCat.KaehlerDifferential.ext_iff, LinearMap.transvection.baseChange, LinearMap.polar_mem_iff, Submodule.mem_biSup_iff_exists_dfinsupp, LinearMap.IsContPerfPair.continuous_uncurry, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, Matrix.toLinearMapRight'_one, Module.injective_iff, MvPolynomial.restrictSupport_eq_span, LinearEquiv.ofLinear_symm_apply, isSMulRegular_iff_ker_lsmul_eq_bot, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt, Polynomial.taylor_X, QuadraticForm.associated_tmul, groupCohomology.cocyclesMk₀_eq, Seminorm.comp_smul_apply, ModN.instModuleFinite, ModuleCat.endRingEquiv_apply, LinearMap.rTensor_add, CharacterModule.dual_zero, Pretrivialization.symmₗ_linearMapAt, bernsteinPolynomial.iterate_derivative_at_0, LinearMap.toMatrixAlgEquiv_reindexRange, PowerSeries.coeff_X_pow_mul', RootPairing.toLinearMap_apply_apply_mem_range_algebraMap, TensorProduct.star_map_apply_eq_map_intrinsicStar, Matrix.cramer_transpose_apply, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, MvPowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto, Submodule.subtype_injective, DirectSum.toModule.unique, Orientation.norm_kahler, ModuleCat.HasColimit.reflectsColimit, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, Finset.weightedVSub_indicator_subset, Module.Relations.Solution.π_comp_map_apply, PresheafOfModules.naturality_apply, Submodule.dualRestrict_apply, Polynomial.hasFDerivWithinAt, LinearMap.hasDerivAt, TrivSqZeroExt.liftEquiv_symm_apply_coe, TensorProduct.one_gradedMul, Complex.isometryOfOrthonormal_symm_apply, IsLocalizedModule.map_iso_commute, Module.End.mem_genEigenspace, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, Algebra.coe_trace_int, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, groupHomology.single_mem_cycles₂_iff, LieModule.traceForm_apply_lie_apply', MvPowerSeries.isWeightedHomogeneous_iff_eq_weightedHomogeneousComponent, MeasureTheory.OuterMeasure.restrict_mono, TensorProduct.piScalarRightHom_tmul, LinearMap.hasDerivAtFilter, AddMonoidHom.toIntLinearMap_injective, LinearMap.flip_surjective_iff₂, RootPairing.RootPositiveForm.algebraMap_posForm, lmap_finsuppLEquivDirectSum_eq, LinearMap.lsum_piSingle, Bialgebra.counit_pow, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, IsLocalFrameOn.coeff_sum_eq, IsBaseChange.linearMapRight, Algebra.SubmersivePresentation.cotangentComplex_injective, Module.Projective.out, LinearMap.rTensor_pow, Module.Basis.constr_range, LinearMap.ker_lsmul, PiTensorProduct.mul_comm, TensorProduct.piRight_apply, Matrix.toLpLin_apply, Representation.ind_apply, PolynomialModule.eval_map', Matrix.entryLinearMap_toAddHom, Polynomial.iterate_derivative_one, PowerSeries.coeff_pow, trace_eq_sum_embeddings_gen, Matrix.toLin'_apply, Representation.isIntertwiningMap_iff, CliffordAlgebra.contractRight_ι, QuotSMulTop.map_id, LinearMap.ker_le_range_iff, ModuleCat.extendScalarsId_inv_app_apply, Polynomial.natDegree_derivative_lt, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, LinearEquiv.arrowCongr_comp, isSMulRegular_on_quot_iff_lsmul_comap_le, LinearMap.proj_comp_single_ne, LinearMap.range_le_ker_iff, Submodule.map_dualCoannihilator_linearEquiv_flip, Module.Basis.constr_apply, TensorProduct.map_pow, LinearMap.ofIsCompl_zero, AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eq_poly_in_U, PowerSeries.coeff_one_pow, Trivialization.linearMapAt_apply, LieModule.Weight.toLinear_neg, Module.Flat.iff_rTensor_preserves_injective_linearMap', DFinsupp.lsum_apply_apply, RatFunc.algebraMap_monomial, LinearMap.rTensor_smul, MvPowerSeries.monomial_smul_const, PowerSeries.coeff_mul_X_pow, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, Representation.self_comp_norm, LinearMap.BilinForm.SeparatingRight.toMatrix', ModuleCat.MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, TensorProduct.toLinearMap_symm_rid, Submodule.toLocalized'_apply_coe, Rep.diagonalSuccIsoFree_hom_hom_single, IsTensorProduct.map_mul, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, IsSymmetricAlgebra.equiv_toAlgHom, Polynomial.taylor_pow, skewAdjoint.I_smul_neg_I, Derivation.linearEquiv_coe_comp, Module.Dual.instLieModule, Finsupp.linearCombination_eq_fintype_linearCombination_apply, LinearMap.toMatrix_adjoint, Polynomial.smul_X_eq_monomial, ContinuousLinearMap.coe_mk', TensorProduct.AlgebraTensorModule.coe_rTensor, SemimoduleCat.ofHom_apply, LinearMap.diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne, QuadraticMap.tensorDistrib_tmul, Polynomial.one_lt_rootMultiplicity_iff_isRoot, ModuleCat.hom_neg, Polynomial.monomial_sub, LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, Polynomial.coeff_monomial_succ, Module.Basis.dvd_coord_smul, CharacterModule.homEquiv_apply_apply, LinearMap.map_smulₛₗ₂, LinearMap.isSymmetric_iff_inner_map_self_real, ExteriorAlgebra.GradedAlgebra.ι_apply, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, PowerSeries.trunc_sub, Algebra.SubmersivePresentation.basisCotangent_apply, Rep.ihom_obj_ρ, Submodule.linearProjOfIsCompl_surjective, LinearMap.exists_extend_of_notMem, MvPowerSeries.hasSum_eval₂, LinearMap.BilinForm.Nondegenerate.toMatrix, RootPairing.isCompl_corootSpan_ker_corootForm, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, Finset.weightedVSubOfPoint_subtype_eq_filter, LinearMap.comp_ker_subtype, Submodule.IsCompl.projection_isIdempotentElem, LinearMap.dualCoannihilator_range_eq_ker_flip, LinearMap.im_inner_adjoint_mul_self_eq_zero, PowerSeries.IsWeierstrassDivisorAt.seq_one, weightedVSub_mem_vectorSpan_pair, QuadraticMap.associated_flip, Algebra.trace_eq_of_equiv_equiv, LinearMap.BilinForm.congr_symm, Nat.Partition.coeff_genFun, Polynomial.degree_monomial, LinearMap.compr₂ₛₗ_apply, strongRankCondition_iff_succ, Matrix.l2_opNorm_def, mem_finsuppAffineCoords_iff_linearCombination, Rep.free_ext_iff, Representation.inv_self_apply, LinearMap.toMatrixAlgEquiv_mul, PresheafOfModules.toSheafify_app_apply, signedDist_apply_linear, LinearMap.detAux_id, MeasureTheory.OuterMeasure.comap_iSup, Matrix.toEuclideanLin_toLp, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, Submodule.map_add_le, Algebra.Extension.Cotangent.map_mk, RootPairing.CoPolarizationIn_apply, PowerSeries.trunc_derivativeFun, LinearAlgebra.FreeProduct.lof_map_one, Seminorm.closedBall_comp, LinearMap.BilinForm.baseChange_tmul, linearDepOn_iff', LinearMap.toLinearMap_toPerfPair, AdicCompletion.eval_surjective, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Profinite.NobelingProof.GoodProducts.max_eq_eval, Polynomial.sylveserMap_comp_adjSylvester, LieAlgebra.IsKilling.ker_killingForm_eq_bot, Matrix.entryLinearMap_toAddMonoidHom, LinearMap.toSpanSingleton_injective, LinearMap.BilinForm.isSymm_iff_basis, ConvexOn.comp_linearMap, TensorProduct.gradedComm_of_tmul_of, Representation.apply_eq_of_coe_eq, PowerBasis.constr_pow_aeval, LinearMap.range_coe, ModuleCat.ofHom_apply, Module.End.ringEquivEndFinsupp_symm_apply_apply, PowerSeries.coeff_subst_finite', QuadraticMap.Isometry.coe_toLinearMap, PowerSeries.HasSubst.monomial, CliffordAlgebra.EvenHom.contract_mid, LinearMap.baseChange_mul, LieRinehartAlgebra.Hom.toLinearMap'_apply, Submodule.IsCompl.projection_apply_mem, LinearMap.det_toMatrix, exteriorPower.toTensorPower_apply_ιMulti, Algebra.traceForm_toMatrix_powerBasis, Matrix.minpoly_toLin, LieDerivation.coeFn_coe, basis_toMatrix_mul, PowerSeries.trunc_map, MeasureTheory.OuterMeasure.map_biInf_comap, AffineMap.image_vsub_image, ContDiffMapSupportedIn.structureMapLM_zero_apply, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, LinearMap.BilinForm.isAdjointPairLeftAdjointOfNondegenerate, LinearMap.injective_iff_antilipschitz, SemimoduleCat.homLinearEquiv_symm_apply, AffineMap.deriv, Matrix.toLin'_toMatrix', ContinuousLinearMap.coe_smul, AlternatingMap.alternatizeUncurryFinLM_apply, LinearMap.compMultilinearMap_apply, LinearMap.det_toLin, LinearMap.injective_or_eq_zero, LinearMap.det_eq_one_of_subsingleton, ModuleCat.restrictScalarsCongr_inv_app, LinearMap.posSemidef_toMatrix_iff, Representation.linHom.invariantsEquivRepHom_apply_hom, PowerSeries.coeff_coe_trunc_of_lt, Function.Exact.inl_snd, Algebra.Extension.exact_cotangentComplex_toKaehler, instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation, SchwartzMap.fourier_convolution, LinearMap.trace_mul_cycle', Polynomial.isMonicOfDegree_monomial_one, LinearMap.mapMatrix_neg, MonoidAlgebra.counit_single, groupCohomology.H1InfRes_f, PowerSeries.trunc_zero', Pretrivialization.coe_linearMapAt_of_mem, Module.Flat.iff_rTensor_injective', LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero', Module.Basis.coord_unitsSMul, FractionalIdeal.trace_mem_dual_one, LinearMap.BilinForm.sum_apply, LinearMap.coe_injective, ModuleCat.imageIsoRange_hom_subtype_apply, PowerSeries.coeff_mul_prod_one_sub_of_lt_order, RootPairing.InvariantForm.apply_eq_or_of_apply_ne, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, IsLocalizedModule.mk'_cancel, QuadraticMap.associated_isSymm, Polynomial.hasseDeriv_eq_zero_of_lt_natDegree, continuous_skewAdjointPart, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, Polynomial.ofFn_coeff_eq_zero_of_ge, TensorProduct.directLimitRight_symm_of_tmul, AdicCompletion.transitionMap_map_one, RootPairing.InvariantForm.two_mul_apply_root_root, Module.Basis.toDual_eq_equivFun, MeasureTheory.OuterMeasure.restrict_iInf_restrict, LinearMap.SeparatingLeft.toMatrix₂', LinearMap.isNonneg_zero, Matrix.derivative_det_one_add_X_smul_aux, MvPolynomial.coeffsIn_le, TensorProduct.toMatrix_comm, LinearMap.lTensor_add, Polynomial.trailingDegree_monomial, PiTensorProduct.map_pow, MonomialOrder.C_mul_leadingCoeff_monomial_degree, RootPairing.Equiv.coweightHom_toLinearMap, Polynomial.hasDerivWithinAt, TensorAlgebra.ι_eq_algebraMap_iff, LinearMap.BilinMap.toQuadraticMap_neg, LinearMap.map_algebraMap_mul, dualTensorHomEquivOfBasis_apply, ModuleCat.forget₂AddCommGroupIsEquivalence, LinearMap.polar_mem, LinearMap.toMatrix₂'_apply, Submodule.FG.rTensor.directLimit_apply', IsAdjoinRootMonic.liftPolyₗ_apply, LinearMap.isAdjointPair_inner, ModuleCat.monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, IsLocalizedModule.mk'_eq_zero, LinearMap.IsPositive.adjoint_conj, Module.Flat.injective_characterModule_iff_rTensor_preserves_injective_linearMap, HahnSeries.toPowerSeries_symm_apply_coeff, SemimoduleCat.hom_smul, PowerSeries.trunc_derivative, LieModule.Cohomology.d₂₃_comp_d₁₂, LinearMap.isPositive_one, Subspace.quotDualCoannihilatorToDual_bijective, Algebra.Generators.comp_σ, IsSelfAdjoint.imaginaryPart, LinearMap.prodMap_mul, groupHomology.single_mem_cycles₁_iff, LinearMap.ker_tensorProductMk, CliffordAlgebraQuaternion.toQuaternion_ι, AdicCompletion.sumEquivOfFintype_symm_apply, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, groupHomology.d₂₁_single_ρ_add_single_inv_mul, Algebra.Generators.CotangentSpace.map_ofComp_surjective, bernsteinPolynomial.derivative_succ_aux, MvPowerSeries.monomial_smul_eq, LaurentSeries.coeff_coe_powerSeries, Ideal.toCotangent_surjective, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, LinearMap.lTensor_inj_iff_rTensor_inj, LinearMap.BilinForm.separatingLeft_toMatrix_iff, LinearMap.trace_comp_comm', ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap, Polynomial.derivative_X_sub_C, CharacterModule.dual_apply, MvPolynomial.finsum_weightedHomogeneousComponent, TensorProduct.sum_tmul_basis_left_injective, MvPowerSeries.order_monomial_of_ne_zero, finsetBasisOfLinearIndependentOfCardEqFinrank_repr_apply, LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, QuadraticForm.associated_baseChange, Real.volume_preserving_transvectionStruct, ModuleCat.hom_injective, HahnEmbedding.Partial.apply_of_mem_stratum, KaehlerDifferential.map_liftBaseChange_smul, LinearMap.range_smul, ModularFormClass.hasSum_qExpansion, MeasureTheory.OuterMeasure.map_ofFunction_le, MvPowerSeries.IsHomogeneous.coeff_eq_zero, Matrix.toBilin'_toMatrix', ContinuousMultilinearMap.toMultilinearMapLinear_apply, Seminorm.continuous_iff_continuous_comp, qExpansion_coeff_isBigO_of_norm_isBigO, Rep.linearization_map_hom_single, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, AdicCompletion.eval_apply, LinearMap.trace_baseChange, CliffordAlgebra.contractLeftAux_apply_apply, LinearPMap.adjointAux_inner, IsGroupLikeElem.mul_antipode_cancel, CategoryTheory.preadditiveCoyoneda_obj, PowerSeries.coeff_one_mul, Algebra.idealMap_apply_coe, Matrix.toLinearMapₛₗ₂_toMatrix₂, LinearMap.BilinForm.IsAlt.smul, LaurentPolynomial.comul_C_mul_T_self, Module.Basis.coord_apply, CliffordAlgebra.contractLeft_one, le_comap_range_rTensor, groupHomology.eq_d₁₀_comp_inv_apply, MultilinearMap.domCoprodDep'_apply, Rep.ihom_obj_V_carrier, LinearMap.toMatrix'_mulVec, RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot, LinearMap.trace_eq_sum_trace_restrict_of_eq_biSup, LinearEquiv.toFGModuleCatIso_inv, RootPairing.ker_corootForm_eq_dualAnnihilator, MvPowerSeries.coeff_eq_zero_of_lt_lexOrder, ModuleCat.semilinearMapAddEquiv_apply, VertexOperator.coeff_eq_ncoeff, Absorbent.subset_range_iff_surjective, LinearMap.lsum_symm_apply, PowerSeries.monomial_zero_eq_C_apply, ModuleCat.CoextendScalars.map'_hom_apply_apply, IsBaseChange.toDualBaseChange_tmul, IsLocalizedModule.map_LocalizedModules, Matrix.SeparatingLeft.toLinearMap₂, Polynomial.card_roots_toFinset_le_derivative, MvPowerSeries.coeff_mul_of_add_lexOrder, Representation.mem_invtSubmodule, AffineMap.linear_eqOn_vectorSpan, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, TensorProduct.instDirectedSystemCoeLinearMapIdLTensor, hasEigenvector_toLin_diagonal, LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero, LinearMap.IsSymmetric.coe_re_inner_apply_self, Module.Basis.coord_equivFun_symm, Module.rank_linearMap_self, Polynomial.iterate_derivative_sum, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, LinearMap.domRestrict₁₂_apply, DirectSum.toLieAlgebra_apply, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, SemimoduleCat.hom_sum, CStarMatrix.mapₙₐ_apply, groupHomology.H0π_comp_H0Iso_hom_apply, Rep.barComplex.d_single, dotProduct_toMatrix₂_mulVec, ModuleCat.freeDesc_apply, Algebra.Extension.CotangentSpace.map_comp_apply, LinearMap.compAlternatingMapₗ_apply, LinearMap.associated_det_comp_equiv, LinearIndependent.map, LieModule.range_traceForm_le_span_weight, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, RatFunc.laurentAux_ofFractionRing_mk, LinearMap.graph_eq_ker_coprod, FDRep.hom_action_ρ, Rep.mono_iff_injective, MeasureTheory.OuterMeasure.map_sup, Profinite.NobelingProof.Products.eval_πs_image, LinearMap.le_rank_iff_exists_linearIndependent_finset, HVertexOperator.comp_apply, TensorProduct.gradedComm_gradedMul, Matrix.diagonal_comp_single, LinearMap.canLiftContinuousLinearMap, SemimoduleCat.comp_apply, LinearMap.inr_map_mul, FDRep.dualTensorIsoLinHom_hom_hom, LinearMap.rank_finset_sum_le, Algebra.Generators.H1Cotangent.equiv_apply, ModuleCat.ExtendScalars.hom_ext_iff, TensorPower.toTensorAlgebra_tprod, MvPolynomial.monomial_single_add, LinearMap.toMatrixAlgEquiv_transpose_apply, groupCohomology.coe_mapCocycles₂, LinearMap.toSpanSingleton_isIdempotentElem_iff, LinearMap.injective_rangeRestrict_iff, MultilinearMap.compLinearMapₗ_apply, LinearMap.quotientInfEquivSupQuotient_surjective, AdicCompletion.piEquivFin_apply, Polynomial.coeff_coe, MvPolynomial.monomial_one_mul_cancel_right_iff, Polynomial.sumIDeriv_apply_of_lt, Polynomial.erase_monomial, IsBaseChange.lift_eq, MvPowerSeries.coeff_eq_zero_of_lt_weightedOrder, LinearMap.const_apply, IsLocalizedModule.lift_iso, TensorProduct.directSumRight_symm_lof_tmul, ModuleCat.toKernelSubobject_arrow, Polynomial.homogenizeLM_apply, LinearMap.isNilpotent_mulLeft_iff, Polynomial.degree_derivative_le, Module.Basis.SmithNormalForm.coord_apply_embedding_eq_smul_coord, LinearMap.domRestrict_apply, LinearMap.surjective_comp_subtype_of_isComplemented, MvPolynomial.degreeOf_monomial_eq, Finsupp.linearCombination_zero, IsBaseChange.endHom_comp, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, Polynomial.derivative_one, Polynomial.taylorLinearEquiv_apply_coe, PowerSeries.natDegree_trunc_lt, MeasureTheory.OuterMeasure.comap_ofFunction, LinearMap.traceAux_def, LinearMap.mem_span_iff_continuous, LinearMap.surjective_of_ne_zero, Condensed.instAB4CondensedMod, CategoryTheory.Linear.rightComp_apply, Module.Flat.iff_lTensor_injective', SkewPolynomial.smul_monomial, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, Algebra.leftMulMatrix_apply, Complex.imLm_coe, Polynomial.Chebyshev.derivative_T_eval_one, Polynomial.taylor_C, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, AdicCompletion.ofLinearEquiv_symm_of, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, LinearMap.BilinForm.toMatrix'_compRight, LocalizedModule.mkLinearMap_apply, Polynomial.derivative_apply, PowerSeries.trunc_X, VertexOperator.coeff_eq_zero_of_lt_order, HopfAlgebra.antipode_one, LinearMap.toAddMonoidHom_mulRight, Algebra.normalizedTrace_self_apply, Submodule.map_toAddSubmonoid, TensorProduct.map_zero_right, ZLattice.coe_comap, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, Pi.counit_single, ContDiffMapSupportedIn.structureMapLM_apply, ExteriorAlgebra.liftAlternating_ι, TensorProduct.AlgebraTensorModule.lcurry_apply, trace_adjoinSimpleGen, Polynomial.monomial_comp, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, Matrix.SeparatingRight.toBilin, TwoSidedIdeal.subtype_apply, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, LinearPMap.adjoint_apply_of_dense, CliffordAlgebra.contractLeftAux_contractLeftAux, Module.reflection_mul_reflection_zpow, LinearMap.coe_finsupp_sum, DirectSum.lmap_eq_iff, groupHomology.H0π_comp_map_apply, MvPowerSeries.monomial_eq', Complex.det_conjLIE, LinearMap.toMatrix_apply, RootPairing.ker_polarization_eq_ker_rootForm, PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, linearDepOn_iff'ₛ, PiTensorProduct.map_range_eq_span_tprod, SemimoduleCat.forget₂_obj, LinearMap.intrinsicStar_eq_comp, LinearMap.baseChange_add, LinearPMap.toFun_eq_coe, LinearMap.IsSymmetric.intCast, Polynomial.ofFn_natDegree_lt, MvPolynomial.weightedHomogeneousComponent_apply, ModuleCat.restrictScalarsId'App_inv_apply, CliffordAlgebra.EquivEven.involute_v, TensorProduct.toMatrix_map, Matrix.toLinAlgEquiv_toMatrixAlgEquiv, Matrix.rank_vecMulVec, LinearMap.continuous_uncurry_of_isContPerfPair, Submodule.mem_traceDual_iff_isIntegral, AdicCompletion.map_of, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, LinearMap.neg_comp, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, PowerSeries.coeff_X_pow_mul, CStarMatrix.mapₗ_apply, RootPairing.polarization_apply_eq_zero_iff, IsLocalizedModule.mk'_eq_iff, Polynomial.monomial_mul_monomial, PowerSeries.coeff_zero_mul_X, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_longRoot, groupHomology.π_comp_H2Iso_inv_apply, TannakaDuality.FiniteGroup.rightRegular_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, PositiveLinearMap.toLinearMap_nsmul, Orientation.areaForm_rightAngleRotation_left, MvPowerSeries.coeff_mul_C, LinearMap.BilinForm.restrict_apply, LinearEquiv.coe_coe, Algebra.H1Cotangent.exact_δ_mapBaseChange, Matrix.toLinAlgEquiv_symm, LaurentPolynomial.antipode_C_mul_T, LinearMap.rTensor_mul, LinearMap.map_finsupp_linearCombination, AlternatingMap.toMultilinearMapLM_apply, Module.FinitePresentation.exists_basis_localizedModule_powers, LinearMap.snd_apply, PolynomialModule.map_single, Algebra.SubmersivePresentation.cotangentEquiv_apply, LinearMap.toMatrix_id_eq_basis_toMatrix, Seminorm.comp_add_le, LinearMap.toMatrixAlgEquiv_transpose_apply', TensorProduct.dualDistribEquivOfBasis_apply_apply, Polynomial.mkDerivation_apply, LinearMap.baseChangeHom_apply, Module.Relations.Solution.π_single, Finsupp.lmapDomain_apply, Polynomial.coeff_monomial_mul, linearIndepOn_iff_linearCombinationOnₛ, LinearMap.toMatrixRight'_comp, LinearEquiv.ofLinear_apply, Derivation.evalAt_apply, LinearMap.isOrtho_def, SemimoduleCat.forget₂_map, CommSemiring.comul_apply, Algebra.Generators.H1Cotangent.δ_map, Module.dualProdDualEquivDual_symm_apply, AlternatingMap.curryLeft_add, ModuleCat.restrictScalarsComp'App_inv_apply, LinearMap.uncurryLeft_apply, LinearMap.trace_map, AdicCompletion.of_apply, CliffordAlgebra.reverse_ι, CliffordAlgebra.reverse_involutive, LinearMap.IsSymmetric.add, FDRep.endRingEquiv_comp_ρ, Module.FinitePresentation.isLocalizedModule_map, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, TensorProduct.inner_map_map, LinearMap.lTensor_tmul, groupHomology.mem_cycles₁_iff, LinearMap.range_add_le, Module.instFinitePolynomialAEval', LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, LaurentSeries.hasseDeriv_single, LinearMap.applyₗ_apply_apply, PolynomialLaw.exists_lift_of_mem_range_rTensor, LinearMap.IsAlt.neg, MvPolynomial.bind₁_monomial, Lagrange.interpolate_singleton, MeasureTheory.OuterMeasure.map_mono, Algebra.Extension.Cotangent.map_sub_map, LinearMap.mapMatrix_sub, Matrix.toBilin_comp, AlternatingMap.curryLeft_same, CliffordAlgebra.changeForm_changeForm, LinearMap.polyCharpoly_coeff_eval, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, LieModuleHom.map_lie₂, LinearMap.BilinForm.apply_smul_sub_smul_sub_eq, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, MvPolynomial.induction_on_monomial, lsum_comp_mapRange_toSpanSingleton, MeasureTheory.OuterMeasure.restrict_le_self, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', RootPairing.orthogonal_rootSpan_eq, IsAdicComplete.StrictMono.mk_lift, Representation.trivial_apply, LinearMap.restrictScalars_injective, groupHomology.boundariesToCycles₁_apply, groupHomology.single_mem_cycles₂_iff_inv, ModularGroup.smul_eq_lcRow0_add, MultilinearMap.ofSubsingletonₗ_symm_apply, groupHomology.d₁₀_single, LinearMap.det_toMatrix_eq_det_toMatrix, Algebra.TensorProduct.mul_apply, UniversalEnvelopingAlgebra.lift_ι_apply', Matrix.SpecialLinearGroup.toLin'_apply, Module.Finite.of_isComplemented_codomain, PowerSeries.order_monomial_of_ne_zero, MatrixModCat.fromMatrixLinear_apply_coe, Matrix.GeneralLinearGroup.toLin_apply, PowerSeries.trunc_C_mul, Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U, Polynomial.coeffList_monomial, MvPowerSeries.coeff_mul, Finsupp.lsingle_apply, MvPolynomial.vars_monomial_single, Submodule.piQuotientLift_mk, QuadraticMap.polarBilin_apply_apply, LinearMap.extendScalarsOfIsLocalization_apply', MvPolynomial.evalₗ_apply, LinearMap.toKerIsLocalized_apply_coe, Representation.self_norm_apply, CStarMatrix.norm_def, MultilinearMap.ofSubsingleton_apply_apply, SemimoduleCat.hom_surjective, LinearMap.submoduleMap_surjective, ModuleCat.ihom_ev_app, LinearMap.mapMatrixModule_comp_apply, Representation.IndV.hom_ext_iff, LinearMap.adjoint_id, PolynomialLaw.isCompat', Module.Relations.Solution.IsPresentation.π_desc_apply, Polynomial.derivative_C_mul_X_sq, LinearMap.BilinForm.add_apply, PowerSeries.WithPiTopology.summable_iff_summable_coeff, Polynomial.content_monomial, Module.DirectLimit.exists_of₂, MvPowerSeries.coeff_mul_prod_one_sub_of_lt_weightedOrder, Polynomial.derivativeFinsupp_C, Submodule.flip_quotDualCoannihilatorToDual_injective, Seminorm.cont_normedSpace_to_withSeminorms, PointedCone.coe_comap, LinearMap.lflip_apply, groupCohomology.cocycles₁.d₁₂_apply, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule, TensorProduct.lift.equiv_apply, IsBaseChange.linearMapLeftRightHom_comp, MvPolynomial.monomial_modMonomial, Algebra.Extension.cotangentComplex_mk, Submodule.mulRightMap_apply_single, LinearMap.prodMapRingHom_apply, Rep.indResHomEquiv_symm_apply_hom, Polynomial.taylor_one, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, LinearMap.SeparatingLeft.congr, Matrix.Nondegenerate.toLinearMap₂', ModuleCat.FilteredColimits.colimit_add_mk_eq, Polynomial.derivativeFinsupp_X, ModuleCat.free_hom_ext_iff, Finset.sum_smul_vsub_eq_weightedVSub_sub, Orientation.inner_mul_areaForm_sub, Module.End.commute_id_left, retractionOfSectionOfKerSqZero_tmul_D, finsuppLEquivDirectSum_symm_lof, groupHomology.H2π_eq_zero_iff, Finset.weightedVSubOfPoint_sdiff_sub, KaehlerDifferential.linearCombination_surjective, IsLocalizedModule.map_lTensor, Finsupp.lsubtypeDomain_apply, LinearEquiv.coe_det, Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂, LinearMap.mulLeft_toAddMonoidHom, HahnSeries.coeff_ofFinsuppLinearMap, Module.Basis.sumQuot_repr_inr, Submodule.map_smul, Module.Basis.coord_toDualEquiv_symm_apply, Finsupp.linearCombination_onFinset, Finsupp.lsum_symm_apply, Module.Basis.baseChange_linearMap, QuaternionAlgebra.reₗ_apply, MvPowerSeries.coeff_add_monomial_mul, IsAdjoinRootMonic.coeff_root_pow, MeasureTheory.SignedMeasure.im_toComplexMeasure, CharacterModule.dual_injective_iff_surjective, LinearMap.BilinForm.sub_right, Module.Basis.coord_repr_symm, TensorProduct.toDirectLimit_tmul_of, LinearMap.id'_apply, LinearMap.BilinMap.toQuadraticMap_sub, Module.Relations.Solution.linearCombination_var_relation, LinearMap.IsRefl.ker_flip, LinearMap.toMatrixAlgEquiv'_comp, LinearMap.ker_smul, LinearMap.ofIsCompl_eq_add, QuadraticMap.linMulLin_add, StarModule.decomposeProdAdjoint_apply, PowerSeries.hasSum_eval₂, Polynomial.eval_multiset_prod_X_sub_C_derivative, MonomialOrder.sPolynomial_mul_monomial, LinearMap.toMatrix₂Aux_apply, Submodule.span_range_inclusionSpan, WithLp.fstₗ_apply, LinearEquiv.skewProd_apply, Submodule.surjOn_iff_le_map, ModuleCat.MonoidalCategory.associator_inv_apply, Subspace.dualEquivDual_apply, LinearMap.BilinForm.iIsOrtho_def, ContMDiffMap.coeFnLinearMap_apply, MvPowerSeries.prod_monomial, Matrix.cramer_eq_adjugate_mulVec, TensorProduct.uncurry_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, LinearMap.BilinForm.apply_dualBasis_right, IsLocalizedModule.eq_zero_iff, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, CategoryTheory.Functor.mapLinearMap_apply, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors', TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, CStarMatrix.inner_toCLM_conjTranspose_right, Module.Dual.congr_symm_apply_apply, Module.Basis.coe_sumCoords, IsLocalizedModule.surj', Matrix.det_smul_inv_vecMul_eq_cramer_transpose, CliffordAlgebra.even.lift.aux_one, LieModule.Weight.toLinear_apply, MvPolynomial.decomposition.decompose'_eq, PositiveLinearMap.toLinearMap_add, IsLocalizedModule.surj, DirectSum.coe_congrLinearEquiv, PointedCone.dual_singleton, RootPairing.Equiv.coweightEquiv_apply, MvPowerSeries.prod_smul_X_eq_smul_monomial_one, PowerSeries.coeff_one_X, TensorPower.pairingDual_tprod_tprod, LinearMap.sum_repr_mul_repr_mul, MonomialOrder.sPolynomial_leadingTerm_mul, CStarMatrix.toCLM_apply_single_apply, bernsteinPolynomial.iterate_derivative_at_1, LinearMap.IsPositive.conj_adjoint, LinearMap.ker_toContinuousLinearMap, TensorProduct.AlgebraTensorModule.lTensor_tmul, Lagrange.nodalWeight_eq_eval_derivative_nodal, CliffordAlgebra.ι_mul_ι_mul_of_isOrtho, Polynomial.derivative_intCast, IsLocalizedModule.iso_mk_one, rieszContentAux_le, ZLattice.comap_refl, LinearMap.charpoly_toMatrix, Polynomial.leadingCoeff_taylor, LinearMap.toLinearMap₂'Aux_toMatrix₂Aux, Polynomial.homogenize_monomial, Polynomial.derivative_add, LinearMap.IsSymmetric.pow, LinearMap.isSymm_iff_isHermitian_toMatrix, Submodule.quotientQuotientEquivQuotientAux_mk_mk, LinearIndepOn.quotient_iff_union, ContinuousLinearMap.coe_zero, LinearMap.trace_lie, Module.Basis.ofIsLocalizedModule_repr_apply, LinearMap.withSeminorms_induced, LinearMap.lsmul_eq_distribSMultoLinearMap, Submodule.factor_surjective, Module.Relations.Solution.IsPresentationCore.desc_var, Matrix.toBilin'_single, Polynomial.monomial_add_erase, Profinite.NobelingProof.GoodProducts.max_eq_eval_unapply, Submodule.Quotient.equiv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, LinearMap.separatingLeft_dualProd, hahnEmbedding_isOrderedModule, groupHomology.H1π_eq_iff, LinearMap.fst_prodOfFinsuppNat, LinearMap.toMatrix_toLin, LinearMap.IsPositive.re_inner_nonneg_left, Convex.linear_preimage, ModuleCat.biprodIsoProd_inv_comp_fst_apply, TensorProduct.includeRight_lid, SemimoduleCat.homAddEquiv_symm_apply_hom, Polynomial.eval_monomial, MeasureTheory.OuterMeasure.isometryEquiv_comap_mkMetric, groupHomology.d₃₂_comp_d₂₁_apply, CliffordAlgebra.even.lift.aux_algebraMap, CliffordAlgebraComplex.reverse_apply, LinearMap.injective_of_ne_zero, MvPowerSeries.commute_monomial, LinearMap.toSpanSingleton_add, ModuleCat.CoextendScalars.map_apply, LinearMap.range_localizedMap_eq_localized₀_range, LinearMap.isProj_iff_isIdempotentElem, Module.Basis.traceDual_eq_iff, CategoryTheory.Functor.mapExtLinearMap_apply, SemimoduleCat.MonoidalCategory.associator_hom_apply, MvPolynomial.monomial_dvd_monomial, ContinuousLinearMap.coeFn_ofIsClosedGraph, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd', SheafOfModules.unitHomEquiv_apply_coe, PowerSeries.order_eq_nat, IsTensorProduct.map_eq, PolynomialModule.eval_single, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, Polynomial.aeval_sumIDeriv_of_pos, MvPolynomial.monomial_mul_modMonomial, DirectSum.gMulLHom_apply_apply, LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly, Representation.ofMulAction_def, Module.Relations.Solution.IsPresentation.desc_var, Algebra.Extension.H1Cotangent.map_toInfinitesimal_bijective, Matrix.toLinearEquiv_apply, LinearEquiv.piRing_apply, ModuleCat.forget₂_map, hasEigenvalue_toLin_diagonal_iff, Representation.Coinvariants.mk_surjective, PiTensorProduct.lift_symm, Submodule.le_comap_pow_of_le_comap, LeftInvariantDerivation.evalAt_apply, PowerSeries.coeff_zero_X, IsLocalizedModule.injective_iff_isRegular, CliffordAlgebra.contractLeft_algebraMap, Matrix.spectrum_toLin', LinearMap.dualAnnihilator_ker_eq_range_flip, AdicCompletion.ofAlgEquiv_symm_of, Derivation.apply_aeval_eq, PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_mem, PowerSeries.trunc_derivative', Ideal.mulQuot_injective, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, ConvexCone.mem_comap, LieAlgebra.killingForm_of_equiv_apply
strongDualPairing 📖	CompOp	—
topDualPairing 📖	CompOp	5 math math: StrongDual.dualPairing_apply, StrongDual.dualPairing_separatingLeft, tendsto_iff_forall_eval_tendsto_topDualPairing, topDualPairing_apply, Real.zero_at_infty_vector_fourierIntegral
«term_→L[_]_» 📖	CompOp	—
«term_→SL[_]_» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
topDualPairing_apply 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule LinearMap.instFunLike ContinuousLinearMap ContinuousLinearMap.addCommMonoid LinearMap.addCommMonoid ContinuousLinearMap.module Algebra.to_smulCommClass Algebra.id LinearMap.module topDualPairing ContinuousLinearMap.funLike	—	Algebra.to_smulCommClass

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