addCommMonoid 📖 | CompOp | 1823 mathmath: Pi.comul_eq_adjoint, det_toContinuousLinearMap, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, lTensor_ker_subtype_tensorKerEquiv_symm, isSymm_zero, RootPairing.InvariantForm.apply_reflection_reflection, CliffordAlgebra.contractRight_algebraMap_mul, restrictScalars_toMatrix, Orientation.kahler_map_complex, RootPairing.rootForm_self_smul_coroot, LieDerivation.IsKilling.ad_mem_ker_killingForm_ad_range_of_mem_orthogonal, apply_symm_toPerfPair_self, SeparatingRight.toMatrix₂', RootPairing.RootPositiveForm.algebraMap_rootLength, SemimoduleCat.Hom.hom₂_apply, charpoly_def, LinearEquiv.congrRight₂_refl, iSupIndep.dfinsupp_lsum_injective, BilinForm.dualSubmoduleParing_spec, PiTensorProduct.lift_reindex, BilinForm.zero_right, dot_self_cross, CliffordAlgebra.contractRight_algebraMap, DFinsupp.lsum_lsingle, Matrix.toLin_kronecker, Matrix.toLin'_symm, Matrix.SeparatingLeft.toBilin', detAux_def'', RootPairing.posRootForm_posForm_apply_apply, QuadraticMap.smul_toBilin, BilinForm.dualSubmoduleToDual_apply_apply, PiTensorProduct.lift.tprod, CliffordAlgebra.contractRight_eq, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, BilinForm.toMatrix_toBilin, Module.Basis.end_repr_apply, adjoint_adjoint, Matrix.SeparatingRight.toLinearMap₂, IsReflective.regular, BilinForm.symmCompOfNondegenerate_left_apply, PolyEquivTensor.toFunBilinear_apply_eq_sum, BilinForm.dualSubmoduleToDual_injective, Rep.MonoidalClosed.linearHomEquiv_symm_hom, instIsTorsionFree, Subspace.dualAnnihilator_dualAnnihilator_eq_map, LinearEquiv.flip_apply, PiTensorProduct.liftAlgHom_apply, BilinForm.toMatrix_symm, SimpleGraph.lapMatrix_toLinearMap₂', RootPairing.coroot_eq_polarizationEquiv_apply_root, Nondegenerate.congr, dotProductEquiv_symm_apply, addMonoidHomLequivNat_symm_apply, isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, Matrix.separatingRight_toLinearMap₂'_iff, Complex.kahler, CliffordAlgebra.changeForm_comp_changeForm, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, Complex.areaForm, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, CStarModule.innerₛₗ_apply, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, QuadraticMap.canLift, Polynomial.toMatrix_sylvesterMap', Matrix.toLinearMapRight'_mul, ContinuousLinearMap.toLinearMap₁₂_injective, isPositive_adjoint_comp_self, BilinForm.IsAlt.neg_eq, BilinMap.polar_toQuadraticMap, isAdjointPair_iff_comp_eq_compl₂, IsPerfPair.bijective_left, Submodule.map_dualCoannihilator_le, Matrix.separatingRight_toLinearMap₂_iff, LinearEquiv.coe_toLinearMap_flip, CommRing.Pic.mk_dual, Matrix.spectrum_toEuclideanLin, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, addMonoidHomLequivInt_apply, Module.Basis.toDual_linearCombination_left, Module.Basis.constr_comp, LinearEquiv.congrRight_symm, Module.Basis.constr_symm_apply, mapMatrixLinear_apply, BilinForm.toMatrixAux_eq, LieModule.trace_toEnd_eq_zero_of_mem_lcs, Matrix.toLinearMap₂'_comp, PiTensorProduct.lift_reindex_symm, RootPairing.root_coroot_two, Representation.finsupp_apply, toMatrix_apply', llcomp_apply, toMatrix₂_mul, BilinForm.smul_left_of_tower, Orientation.kahler_comp_rightAngleRotation', LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, Module.Basis.dualBasis_coord_toDualEquiv_apply, Matrix.repr_toLin, LieModule.traceForm_eq_sum_genWeightSpaceOf, LocalizedModule.restrictScalars_map_eq, polar_eq_iInter, tensorKer_tmul, TensorProduct.sum_tmul_basis_right_injective, Subspace.dualLift_of_subtype, RootPairing.EmbeddedG2.shortAddLongRoot_shortRoot, compRight_apply, Matrix.liftLinear_single, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Subspace.dualRestrict_comp_dualLift, Orientation.areaForm_le, BilinForm.congr_apply, LinearEquiv.conj_trans, LieModule.traceForm_eq_sum_finrank_nsmul', mul_apply_apply, BilinForm.toMatrix_compRight, RootPairing.rootSpan_dualAnnihilator_le_ker_rootForm, adjoint_innerₛₗ_apply, BilinMap.toQuadraticMap_add, Submodule.dualQuotEquivDualAnnihilator_apply, LinearEquiv.domMulActCongrRight_symm_apply, ContinuousLinearMap.toBilinForm_apply, LinearEquiv.conj_apply_apply, adjoint_eq_toCLM_adjoint, BilinForm.IsNonneg.nonneg, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, IsPosSemidef.add, Matrix.toLinearMap₂_toMatrix₂, toMatrix_one, IsReflective.smul_coroot, QuotSMulTop.equivTensorQuot_naturality, compl₂_apply, IsReflective.apply_self_mul_coroot_apply, Module.Flat.ker_lTensor_eq, isSelfAdjoint_toContinuousLinearMap_iff, cross_cross, Matrix.separatingRight_toBilin_iff, Matrix.spectrum_toLpLin, RootPairing.InvariantForm.pairing_mul_eq_pairing_mul_swap, Submodule.quotDualCoannihilatorToDual_apply, Module.Dual.eval_comp_comp_evalEquiv_eq, CategoryTheory.Linear.comp_apply, BilinForm.toMatrix'_symm, LinearEquiv.map_mem_invtSubmodule_conj_iff, QuadraticMap.polarBilin_prod, mem_isPairSelfAdjointSubmodule, Submodule.dualPairing_apply, NonUnitalAlgHom.coe_lmul_eq_mul, Matrix.toLin_mul_apply, tensorEqLocusEquiv_apply, toMatrix_distrib_mul_action_toLinearMap, domRestrict'_apply, Module.dualMap_dualMap_eq_iff, ModuleCat.Iso.homCongr_eq_arrowCongr, AlgEquiv.linearEquivConj_mulLeft, PiToModule.fromEnd_apply, TensorPower.gMul_eq_coe_linearMap, BilinForm.IsRefl.groupSMul, BilinForm.toMatrix'_apply, Module.Basis.dual_rank_eq, BilinMap.toQuadraticMapAddMonoidHom_apply, BilinForm.SeparatingRight.toMatrix, nondegenerate_toLinearMap₂'_of_det_ne_zero', LinearEquiv.congrRight₂_apply, cross_self, CliffordAlgebra.contractRight_mul_ι, Matrix.Nondegenerate.toLinearMap₂, rTensor_injective_iff_lcomp_surjective, TensorProduct.gradedMul_assoc, contractLeft_assoc_coevaluation, Module.Basis.flag_le_ker_dual, LieModule.lowerCentralSeries_one_inf_center_le_ker_traceForm, Matrix.intrinsicStar_toLin', coe_toContinuousLinearMap', BilinMap.toQuadraticMap_zero, SemimoduleCat.Iso.homCongr_eq_arrowCongr, LinearEquiv.dualMap_trans, Module.Basis.coe_dualBasis, QuadraticMap.toBilinHom_apply, ExteriorAlgebra.liftAlternating_ι_mul, tensorKer_coe, Real.vector_fourierIntegral_eq_integral_exp_smul, RootPairing.coPolarization_apply_eq_zero_iff, Fintype.linearIndependent_iff', QuadraticMap.associated_eq_self_apply, QuadraticMap.toMatrix'_comp, trace_mul_cycle, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, ker_localizedMap_eq_localized'_ker, exteriorPower.alternatingMapLinearEquiv_ιMulti, star_dotProduct_toMatrix₂_mulVec, RootPairing.root_coroot_eq_pairing, IsBaseChange.linearMapLeftRightHom_comp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange, Subspace.dualAnnihilator_dualAnnihilator_eq, TensorProduct.AlgebraTensorModule.lTensor_id, zero_prodMap_dualTensorHom, sum_repr_mul_repr_mulₛₗ, SemimoduleCat.hom_zsmul, TensorProduct.AlgebraTensorModule.rTensor_one, innerₛₗ_apply_apply, ringLmapEquivSelf_symm_apply, RootPairing.self_comp_coPolarization_eq_corootForm, QuadraticMap.associated_rightInverse, Matrix.toBilin_symm, spectrum_toMatrix', LieModule.trace_toEnd_genWeightSpace, Real.smul_map_diagonal_volume_pi, Algebra.traceMatrix_apply, SemimoduleCat.hom_nsmul, RootPairing.span_coroot'_eq_top, toMatrix_rotation, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, BilinForm.sum_right, separatingRight_congr_iff, Module.eval_apply_injective, AlgHom.mulLeftRightMatrix.inv_comp, Submodule.dualAnnihilator_map_dualMap_le, LieAlgebra.IsKilling.ker_traceForm_eq_bot_of_isCartanSubalgebra, le_comap_range_lTensor, Submodule.dualCopairing_eq, polar_singleton, LieModule.shiftedGenWeightSpace.toEnd_eq, TensorProduct.liftAux_tmul, RootPairing.RootPositiveForm.zero_lt_posForm_iff, QuotSMulTop.equivTensorQuot_naturality_mk, RootPairing.toLinearMap_apply_CoPolarization, BilinForm.ext_iff_of_isSymm, dot_cross_self, LieModule.Cohomology.twoCochain_alt, Module.endTensorEndAlgHom_apply, Matrix.toLpLin_mul_same, mem_skewAdjointSubmodule, Submodule.quotDualCoannihilatorToDual_nondegenerate, RootPairing.Hom.weight_coweight_transpose, Module.DualBases.coe_dualBasis, CliffordAlgebra.changeForm_self_apply, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom, Submodule.mem_dualAnnihilator, PiTensorProduct.mul_assoc, toMatrix_baseChange, RootPairing.toPerfPair_comp_root, Submodule.dualAnnihilator_eq_top_iff, TensorProduct.adjoint_map, IsContPerfPair.bijective_left, LinearEquiv.conj_comp, LinearEquiv.domMulActCongrRight_apply, TensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse, CliffordAlgebra.contractRight_comm, trace_eq_matrix_trace_of_finset, adjoint_toContinuousLinearMap, Matrix.SeparatingLeft.toLinearMap₂', rTensor_comp_flip_mk, TensorProduct.dualDistrib_apply_comm, BilinForm.IsAlt.eq_of_add_add_eq_zero, Submodule.coe_dualCoannihilator_span, Finsupp.llift_apply, ExteriorAlgebra.liftAlternating_comp, LinearEquiv.conj_refl, CharacterModule.curry_apply_apply, map_sub₂, finrank_algHom, Module.Basis.toDualEquiv_apply, CliffordAlgebra.changeFormAux_changeFormAux, Fintype.bilinearCombination_apply_single, BilinForm.nondegenerate_toMatrix_iff, toMatrixₛₗ₂'_symm, Ideal.range_mul', dotProductEquiv_apply_apply, rank_diagonal, ker_localizedMap_eq_localized₀_ker, QuotSMulTop.map_comp_mkQ, RootPairing.injOn_dualMap_subtype_span_root_coroot, RootPairing.disjoint_corootSpan_ker_corootForm, TensorProduct.flip_mk_surjective, separatingRight_toMatrix₂'_iff, Matrix.toEuclideanLin_apply, Submodule.biSup_eq_range_dfinsupp_lsum, CliffordAlgebra.changeForm.add_proof, ContinuousLinearMap.toLinearMap₁₂_apply, Algebra.toMatrix_lmul_eq, LieModule.traceForm_eq_zero_of_isNilpotent, isAdjointPair_toLinearMap₂, LinearEquiv.congrLeft_symm_apply, LieModule.Cohomology.d₂₃_apply, BilinForm.sub_left, exteriorPower.alternatingMapLinearEquiv_symm_map, LieIdeal.coe_killingCompl_top, ModN.basis_apply_eq_mkQ, Matrix.liftLinear_singleLinearMap, LieModule.Cohomology.d₁₂_apply_apply, FiniteDimensional.mem_span_of_iInf_ker_le_ker, Matrix.liftLinear_comp_singleLinearMap, ofIsComplProd_apply, mul_apply', toMatrix_symm, Matrix.toBilin_apply, toMatrix₂'_compl₁₂, RootPairing.flip_comp_polarization_eq_rootForm, prodEquiv_apply, Module.Basis.toLin_toMatrix, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, flip_injective_iff₁, Matrix.toLinearEquivRight'OfInv_symm_apply, Pi.counit_eq_adjoint, BilinForm.coeFnAddMonoidHom_apply, IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite, LocalizedModule.map_surjective, IsLocalizedModule.map_linearMap_of_isLocalization, Matrix.toLin'_mul_apply, Orientation.areaForm_to_volumeForm, Matrix.toLinearMapₛₗ₂'_single, LieAlgebra.bracket_ofTwoCocycle, Matrix.nondegenerate_toBilin'_iff, TensorProduct.AlgebraTensorModule.restrictScalars_curry, trace_eq_contract_of_basis', BilinForm.congr_comp, Algebra.traceForm_apply, BilinForm.apply_dualBasis_left, QuadraticMap.add_toBilin, Basis.linearEquiv_dual_iff_finiteDimensional, Orientation.areaForm_neg_orientation, toMatrix'_toLin', MultilinearMap.curryRight_apply, Module.mapEvalEquiv_apply, CliffordAlgebra.changeForm.zero_proof, RootPairing.ker_copolarization_eq_ker_corootForm, TensorProduct.toMatrix_assoc, Subspace.finrank_dualCoannihilator_eq, applyₗ'_apply_apply, Matrix.toLinearMap₂'_apply', RootPairing.exists_ge_zero_eq_rootForm, PiToModule.fromEnd_injective, coe_lTensorHom, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, toMatrix_id, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, Orientation.kahler_eq_zero_iff, eq_adjoint_iff_basis_left, BilinForm.isNonneg_def, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, ProperCone.mem_dual, Subspace.finiteDimensional_quot_dualCoannihilator_iff, QuadraticMap.associated_prod, SemimoduleCat.ofHom₂_hom_apply_hom, toMatrix_transpose, toMatrix₂_toLinearMapₛₗ₂, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, LieIdeal.mem_killingCompl, Orientation.areaForm_swap, ContinuousLinearMap.holderₗ_apply_apply, isSymm_dualProd, trace_smulRight, IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, Orientation.kahler_swap, Matrix.toLinearMap₂'Aux_single, Matrix.vecMulBilin_apply, mk₂'ₛₗ_apply, cross_anticomm, dualMap_surjective_of_injective, Rep.ihom_ev_app_hom, IsBaseChange.endHom_toMatrix, Ideal.range_mul, ModuleCat.homLinearEquiv_symm_apply, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, Submodule.dualAnnihilator_anti, BilinForm.sum_left, GradedTensorProduct.mul_def, QuadraticForm.polarBilin_tmul, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, LocalizedModule.map_injective, QuadraticMap.Ring.polarBilin_pi, RootPairing.toLinearMap_apply_apply_Polarization, BilinForm.Nondegenerate.congr, SemimoduleCat.homLinearEquiv_apply, TensorProduct.equivFinsuppOfBasisLeft_symm, IsProj.eq_conj_prodMap, flip_surjective_iff₁, tensorEqLocus_coe, dfinsuppSum_apply, toAddMonoidHom'_apply, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, TensorProduct.curry_injective, Matrix.toLinearMap₂'_apply, lTensorHomEquivHomLTensor_apply, BilinForm.separatingLeft_toMatrix'_iff, extendScalarsOfIsLocalizationEquiv_apply, rank_lt_rank_dual', QuotSMulTop.map_surjective, Module.dual_finite, trace_mul_comm, trace_eq_contract, Orientation.kahler_comp_rightAngleRotation, toKerLocalized_isLocalizedModule, CliffordAlgebra.changeFormAux_apply_apply, LinearEquiv.arrowCongr_symm_apply, lcomp_injective_of_surjective, trace_eq_sum_inner, BilinForm.not_nondegenerate_zero, Module.FinitePresentation.linearEquivMap_symm_apply, restrictScalarsₗ_apply, Subspace.dualPairing_nondegenerate, Matrix.isNilpotent_toLin'_iff, trace_one, homTensorHomEquiv_apply, QuadraticMap.associated_apply, IsModuleTopology.continuous_bilinear_of_pi_fintype, TensorProduct.mk_apply, Matrix.toLinearEquiv'_symm_apply, BilinForm.IsSymm.eq, BilinForm.mul_toMatrix'_mul, Matrix.toLin_symm, SeparatingDual.dualMap_surjective_iff, InnerProductGeometry.norm_toLp_symm_crossProduct, dualTensorHom_apply, BilinForm.mul_toMatrix_mul, isNoetherian_linearMap_pi, Module.Invertible.rTensorEquiv_apply_apply, localized'_range_eq_range_localizedMap, lTensorHomEquivHomLTensor_toLinearMap, trace_comp_eq_mul_of_commute_of_isNilpotent, Module.Basis.linearMap_apply, Submodule.dualCoannihilator_iSup_eq, Module.comap_eval_surjective, Matrix.toLinearMap₂_compl₁₂, dualMap_id, ExteriorAlgebra.liftAlternating_ιMulti, linearIndependent_algHom_toLinearMap', CliffordAlgebra.changeForm_ι_mul, LieModule.traceForm_lieSubalgebra_mk_right, lsum_apply, Matrix.toLinearMapₛₗ₂'_symm, localized'_ker_eq_ker_localizedMap, mk₂_apply, polyCharpoly_baseChange, CliffordAlgebra.changeForm_self, isAlt_iff_eq_neg_flip, RootPairing.RootPositiveForm.exists_eq, RootPairing.corootSpan_map_flip_toPerfPair, toLinearMap_toContPerfPair, TensorProduct.AlgebraTensorModule.rTensor_comp, coevaluation_apply_one, MatrixEquivTensor.toFunBilinear_apply, isSymmetric_adjoint_mul_self, Submodule.dualRestrict_ker_eq_dualAnnihilator, IsBaseChange.transvection, toBilin'Aux_toMatrixAux, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, IsLocalRing.map_tensorProduct_mk_eq_top, Module.Dual.eval_apply, toMatrix₂_compl₂, DFinsupp.sum_mapRange_index.linearMap, InnerProductSpace.trace_rankOne, rTensorHomEquivHomRTensor_apply, trace_eq_contract_apply, ExteriorAlgebra.liftAlternatingEquiv_apply, dualTensorHomEquivOfBasis_symm_cancel_right, Matrix.toLpLin_symm_pow, IsLocalization.tensorProduct_isLocalizedModule, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', RootPairing.rootForm_root_self, IsBaseChange.det_endHom, polyCharpolyAux_map_eval, Matrix.toLinearMapₛₗ₂'_aux_eq, IsLocalizedModule.mapExtendScalars_apply_apply, CommRing.Pic.inv_eq_dual, BilinForm.isRefl_zero, IsPerfectCompl.isCompl_right, KaehlerDifferential.linearMapEquivDerivation_apply_apply, BilinForm.tensorDistribEquiv_toLinearMap, Module.preReflection_preReflection, Matrix.linfty_opNNNorm_toMatrix, Module.Basis.end_apply_apply, Module.Basis.coe_constrL, QuadraticMap.toQuadraticMap_associated, Module.Invertible.bijective_curry, Algebra.traceForm_toMatrix, trace_eq_zero_of_mapsTo_ne, Module.Basis.coe_sumCoords_of_fintype, cross_anticomm', Matrix.toLin_scalar, Module.rank_linearMap, adjoint_rTensor, toBilin'Aux_toMatrixAux, adjoint_inner_right, BilinForm.dotProduct_toMatrix_mulVec, BilinForm.tensorDistrib_tmul, TensorProduct.AlgebraTensorModule.mk_apply, trace_transpose', IntrinsicStar.starLinearEquiv_eq_arrowCongr, IsTensorProduct.equiv_symm_apply, Projectivization.cross_mk_of_cross_ne_zero, Matrix.toLpLin_one, RootPairing.InvariantForm.exists_apply_eq_or, Module.Dual.transpose_apply, Module.Invertible.instDual, isPosSemidef_iff_posSemidef_toMatrix, RootPairing.zero_le_rootForm, TensorProduct.AlgebraTensorModule.rTensor_tmul, Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, IsLocalizedModule.map_comp', QuadraticMap.toBilin_apply, Submodule.comap_dualAnnihilator, linearIndependent_algHom_toLinearMap, KaehlerDifferential.linearMapEquivDerivation_symm_apply, BilinForm.smul_right_of_tower, BilinForm.tensorDistribEquiv_apply, linearIndependent_toLinearMap, Matrix.piLp_ofLp_toEuclideanLin, BilinForm.toMatrix_apply, LieAlgebra.killingForm_apply_eq_zero_of_mem_rootSpace_of_add_ne_zero, RootPairing.reflectionPerm_coroot, TensorProduct.map₂_apply_tmul, LieSubmodule.traceForm_eq_zero_of_isTrivial, PowerBasis.constr_pow_algebraMap, dualProd_apply_apply, lieEquivMatrix'_apply, TensorProduct.dualDistribEquivOfBasis_symm_apply, BilinForm.toMatrix_toBilin, Module.dual_free, isSymm_def, Matrix.toPerfectPairing_apply_apply, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, BilinForm.IsRefl.smul, intrinsicStar_zero, BilinForm.IsNonneg.add, compr₂_apply, minpoly_toMatrix', BilinForm.IsPosSemidef.smul, trace_prodMap, Submodule.iSup_dualAnnihilator_le_iInf, liftBaseChangeEquiv_symm_apply, QuadraticForm.dualProd_apply, Fintype.bilinearCombination_apply, toMatrix₂_comp, lsmul_flip_apply, Matrix.SeparatingRight.toLinearMap₂', Module.Basis.toDual_ker, killingForm_eq_zero_of_mem_zeroRoot_mem_posFitting, Module.Basis.dualBasis_apply_self, TensorProduct.lift.tmul', PointedCone.mem_dual, Submodule.mem_iSup_iff_exists_dfinsupp, Submodule.map₂_map_left, prodEquiv_symm_apply, BilinForm.add_left, tensorProductEnd_apply, lift_rank_lt_rank_dual', Matrix.toLpLin_pow, trace_eq_contract', RootPairing.toLinearMap_apply_PolarizationIn, Module.finrank_linearMap, LinearEquiv.symm_flip, InnerProductSpace.AlgebraOfCoalgebra.mul_def, BilinForm.separatingRight_toMatrix'_iff, Matrix.isUnit_toLin'_iff, Module.piEquiv_apply_apply, RootPairing.EmbeddedG2.long_eq_three_mul_short, BilinForm.smul_left, range_dualMap_eq_dualAnnihilator_ker, Submodule.dualCoannihilator_map_linearEquiv_flip, RootPairing.rootSpan_map_toPerfPair, innerₗ_apply, RootPairing.GeckConstruction.trace_toEnd_eq_zero, Matrix.toLin'_mul, Submodule.iSup_eq_range_dfinsupp_lsum, isNilpotent_toMatrix_iff, BilinForm.lieInvariant_iff, LieModule.Cohomology.twoCochain_skew, BilinForm.dotProduct_toMatrix_mulVec, Module.End.rTensorAlgHom_apply_apply, det_eq_det_toMatrix_of_finset, LieModule.traceForm_comm, LieSubmodule.trace_eq_trace_restrict_of_le_idealizer, toMatrix_reindexRange, ExteriorAlgebra.liftAlternating_apply_ιMulti, Matrix.ofLp_toLpLin, Module.range_piEquiv, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, Matrix.toBilin'_symm, Module.Basis.dualBasis_equivFun, PiTensorProduct.piTensorHomMap_tprod_tprod, RootPairing.corootSpan_dualAnnihilator_map_eq, isSymmetric_sum, toMatrix_smulBasis_left, VertexOperator.ncoeff_apply, Module.Dual.transpose_comp, BilinForm.isSymm_iff_flip, RootPairing.corootForm_apply_apply, flip_bijective_iff₁, flip_bijective_iff₂, BilinForm.mem_dualSubmodule, range_dualMap_dual_eq_span_singleton, det_toLin', Matrix.kroneckerMapBilinear_apply_apply, SeparatingRight.congr, Ideal.pi_tensorProductMk_quotient_surjective, Matrix.rank_eq_finrank_range_toLin, Matrix.toLinearMapRight'_mul_apply, BilinForm.toMatrix_comp, CliffordAlgebra.EvenHom.contract, Module.Basis.linearCombination_dualBasis, PiTensorProduct.norm_eval_le_injectiveSeminorm, transpose_dualTensorHom, Matrix.toLin_mul, Rep.indResAdjunction_counit_app_hom_hom, Matrix.toLin_pow, LieSubmodule.mem_baseChange_iff, QuadraticMap.associated_tmul, Module.Free.linearMap, Matrix.toLin_self, Module.Finite.linearMap, Submodule.dualCoannihilator_bot, Finsupp.lsum_single, BilinForm.neg_left, BilinForm.sum_repr_mul_repr_mul, Orientation.kahler_neg_orientation, QuadraticForm.dualProdIsometry_invFun, separatingLeft_toMatrix₂'_iff, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, CliffordAlgebra.contractLeft_contractLeft, TensorProduct.algebraMap_gradedMul, Submodule.dualCoannihilator_top, hasEigenvector_toLin'_diagonal, lcomp_apply, separatingRight_iff_flip_ker_eq_bot, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, Module.Dual.instIsReflecive, BilinForm.inf_orthogonal_self_le_ker_restrict, BilinForm.IsAlt.self_eq_zero, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, Matrix.toLinearMapₛₗ₂'_toMatrix', continuous_of_isContPerfPair, toMatrix'_algebraMap, isNoetherian_linearMap, PiTensorProduct.liftEquiv_symm_apply, PiToModule.fromMatrix_apply_single_one, LocalizedModule.coe_map_eq, Representation.linHom_apply, QuadraticMap.associated_toQuadraticMap, dualMap_injective_of_surjective, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, dualMap_injective_iff, LinearEquiv.instIsPerfPair, Module.Basis.eval_range, BilinearForm.toMatrixAux_eq, CliffordAlgebra.contractLeft_ι_mul, QuadraticMap.two_nsmul_associated, RootPairing.rootForm_reflection_reflection_apply, dualPairing_nondegenerate, RootPairing.posRootForm_posForm_pos_of_ne_zero, Matrix.SeparatingLeft.toBilin, Matrix.charpoly_toLin, FGModuleCat.FGModuleCatCoevaluation_apply_one, toMatrixOrthonormal_symm_apply, LinearEquiv.congrLeft_apply, IsLocalizedModule.map_linearCombination, BilinMap.baseChange_tmul, Module.Flat.eqLocus_lTensor_eq, Subspace.dualRestrict_leftInverse, StrongDual.dualPairing_apply, BilinForm.IsPosSemidef.add, LinearEquiv.piRing_symm_apply, CliffordAlgebra.even.lift_ι, toMatrix_mulVec_repr, BilinForm.zero_left, toMatrix_innerₛₗ_apply, QuadraticMap.associated_left_inverse', LieModule.Cohomology.mem_twoCochain_iff, TensorProduct.lift.tmul, Matrix.toLin_apply_eq_zero_iff, TensorProduct.lTensorHomToHomLTensor_apply, IsLocalizedModule.mapEquiv_apply, Matrix.nondegenerate_toBilin_iff, range_toContinuousLinearMap, Matrix.toLin'_reindex, BilinForm.toDual_def, CliffordAlgebra.contractRight_mul_algebraMap, Matrix.PosSemidef.toLinearMap₂'_zero_iff, BilinForm.toMatrix'_compLeft, Matrix.toLinearMapₛₗ₂_apply, BilinForm.dualBasis_repr_apply, PiTensorProduct.liftEquiv_apply, lsmul_injective, Module.IsReflexive.bijective_dual_eval', AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, ExteriorAlgebra.liftAlternating_one, Subspace.flip_quotDualCoannihilatorToDual_bijective, isSelfAdjoint_iff', Subspace.dual_finrank_eq, Submodule.apply_mem_map₂, Orientation.areaForm'_apply, Module.Basis.end_apply, Submodule.set_smul_eq_map, Matrix.Nondegenerate.toBilin, BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, toMatrix'_apply, mem_span_iff_continuous_of_finite, Matrix.toLpLin_toLp, apply_eq_dotProduct_toMatrix₂_mulVec, coe_toContinuousLinearMap, IsLocalizedModule.map_injective, BilinForm.separatingRight_toMatrix_iff, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, flip_apply, BilinForm.SeparatingLeft.toMatrix', TensorProduct.mapBilinear_apply, LinearEquiv.conj_apply, Module.Basis.toDual_range, PiTensorProduct.dualDistribInvOfBasis_apply, Submodule.map₂_eq_span_image2, Rep.ihom_obj_ρ_apply, Matrix.ker_toLin_eq_bot, TensorProduct.AlgebraTensorModule.dualDistrib_apply, ContinuousLinearMap.toLinearMap_innerSL_apply, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, Submodule.dualAnnihilator_sup_eq, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, GradedTensorProduct.auxEquiv_mul, Fintype.linearIndependent_iff'ₛ, IsSymmetric.adjoint_eq, isPositive_sum, Module.FinitePresentation.linearEquivMap_apply, BilinMap.isSymm_iff_eq_flip, llcomp_apply', Submodule.dualCoannihilator_sup_eq, BilinForm.zero_apply, QuotSMulTop.equivQuotTensor_naturality, smulRightₗ_apply, IsNonneg.smul, IsLocalizedModule.mapEquiv_symm_apply, toMatrix'_symm, Module.symm_dualMap_evalEquiv, RootPairing.algebraMap_rootFormIn, InnerProductGeometry.norm_ofLp_crossProduct, TensorProduct.AlgebraTensorModule.uncurry_apply, coe_sum, polyCharpolyAux_map_eq_charpoly, toContinuousLinearMap_eq_iff_eq_toLinearMap, Submodule.baseChange_eq_span, linearMap_toMatrix_mul_basis_toMatrix, Submodule.dualCopairing_apply, Module.dualPairing_apply, polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, TensorProduct.AlgebraTensorModule.coe_lTensor, BilinForm.isNonneg_zero, RootPairing.toPerfPair_flip_comp_coroot, Coalgebra.rTensor_counit_comp_comul, toMatrix_transpose_apply, toMatrix_dualTensorHom, LinearEquiv.arrowCongr_apply, BilinForm.nondegenerate_iff_ker_eq_bot, ContinuousLinearMap.coeLM_apply, exteriorPower.alternatingMapLinearEquiv_apply_ιMulti, RootPairing.isCompl_rootSpan_ker_rootForm, CliffordAlgebra.changeForm_ι_mul_ι, TensorProduct.AlgebraTensorModule.homTensorHomMap_apply, RootPairing.reflectionPerm_root, isPositive_toContinuousLinearMap_iff, Matrix.range_toLin', prodMapLinear_apply, Submodule.map₂_span_singleton_eq_map_flip, RootPairing.rootForm_self_eq_zero_iff, PiTensorProduct.piTensorHomMap_tprod_eq_map, dualMap_apply', mul_toMatrix', Matrix.liftLinear_apply, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, PiTensorProduct.lift_comp_reindex, ext_iff₂, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, dualMap_bijective_iff, TensorPower.multilinearMapToDual_apply_tprod, HVertexOperator.of_coeff_coeff, PiTensorProduct.map₂_tprod_tprod, star_eq_adjoint, Module.Basis.sum_dual_apply_smul_coord, toMatrix_smulBasis_right, Matrix.toLpLin_symm_id, Module.Basis.toDual_eq_repr, Matrix.range_toLin_eq_top, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm, Module.Basis.baseChange_end, Matrix.toLin_finTwoProd_apply, HVertexOperator.coeff_inj_iff, BilinForm.dualBasis_eq_iff, Matrix.isPositive_toEuclideanLin_iff, addMonoidEndRingEquivInt_apply, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, Matrix.toBilin'Aux_single, LieModule.lie_traceForm_eq_zero, IsLocalizedModule.map_mk', exteriorPower.pairingDual_ιMulti_ιMulti, mul_toMatrix₂, PointwiseConvergenceCLM.coeLMₛₗ_apply, QuadraticMap.discr_comp, Module.Basis.linearMap_repr_apply, exteriorPower.alternatingMapLinearEquiv_comp_ιMulti, coe_dfinsuppSum, lsmul_eq_DistribMulAction_toLinearMap, Module.eval_apply_eq_zero_iff, coeFn_sum, IsModuleTopology.continuous_bilinear_of_finite_left, lsum_single, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, LieModule.trace_comp_toEnd_genWeightSpace_eq, nondegenerate_congr_iff, TensorProduct.gradedMul_one, CliffordAlgebra.contractLeft_comm, Orientation.areaForm_comp_linearIsometryEquiv, FractionalIdeal.mem_dual, toMatrix'_mul, IsBaseChange.end, adjoint_toSpanSingleton, lcomp_apply', mul_basis_toMatrix, Module.Basis.toDual_toDual, Module.dualProdDualEquivDual_apply_apply, RootPairing.zero_le_posForm, BilinForm.sub_apply, IsLocalizedModule.rTensor, LinearEquiv.conj_symm_conj, killingForm_apply_apply, trace_id, toMatrix_algebraMap, spectrum_toMatrix, PowerBasis.constr_pow_gen, BilinForm.congr_refl, SeparatingRight.toMatrix₂, Module.Finite.of_isComplemented_domain, Matrix.isUnit_toLin_iff, RootPairing.InvariantForm.apply_weylGroup_smul, Subspace.quotAnnihilatorEquiv_apply, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, Matrix.diagonal_toLin', re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, Module.isTorsionBySet_iff_subseteq_ker_lsmul, TensorProduct.AlgebraTensorModule.curry_apply, isPositive_self_comp_adjoint, Algebra.TensorProduct.mul_one, Matrix.charpoly_toLin', BilinForm.toMatrix_symm, BilinMap.toQuadraticMap_smul, Matrix.toLinearMap₂'_toMatrix', rank_dual_eq_card_dual_of_aleph0_le_rank', Matrix.toLinearMapₛₗ₂'_apply, IsLocalizedModule.map_apply, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, Matrix.toLin'_pow, LieModule.Cohomology.mem_twoCocycle_iff, Ideal.ker_tensorProductMk_quotient, rank_dual_eq_card_dual_of_aleph0_le_rank, BilinForm.SeparatingLeft.toMatrix, TensorProduct.AlgebraTensorModule.mapBilinear_apply, BilinMap.toQuadraticMapLinearMap_apply, Matrix.l2_opNNNorm_def, RootPairing.rootForm_apply_apply, LieModule.traceForm_eq_zero_of_isTrivial, Module.Basis.dualBasis_apply, apply_toPerfPair_flip, apply_eq_star_dotProduct_toMatrix₂_mulVec, toMatrix_mul, toMatrix₂_compl₁₂, BilinForm.IsSymm.smul, Matrix.minpoly_toLin', RootPairing.iInf_ker_root'_eq, lift_rank_lt_rank_dual, eq_adjoint_iff, GradedTensorProduct.mulHom_apply, BilinForm.toMatrix_compRight, BilinForm.nondegenerate_toMatrix'_iff, instIsStablyFiniteRingEnd, Polynomial.wronskianBilin_apply, toMatrix₂_toLinearMap₂, detAux_def', toMatrix_transpose_apply', toMatrix'_intrinsicStar, BilinForm.congr_congr, isPosSemidef_zero, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, cross_apply, LinearEquiv.lieConj_apply, IsBaseChange.toDual_comp_apply, IsBaseChange.linearMapLeftRightHom_toMatrix, BilinForm.isAlt_zero, BilinForm.toMatrixAux_apply, PiTensorProduct.mapMultilinear_apply, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, LinearEquiv.dualMap_symm, PiTensorProduct.dualDistrib_apply, DFinsupp.lsum_single, Matrix.toLinOfInv_symm_apply, ModuleCat.hom_sum, toMatrix_smulRight, toMatrix₂Aux_eq, lsmul_apply, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, vecMulVecBilin_apply_apply, isAdjointPair_toLinearMap₂', Orientation.areaForm_comp_rightAngleRotation, Module.Dual.baseChange_apply_tmul, Matrix.toLin'_apply', QuotSMulTop.map_exact, isPairSelfAdjoint_equiv, toMatrix₂_symm, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, congr_fun₂, Matrix.ker_toLin'_eq_bot_iff, vecCons₂_apply, Finsupp.lsum_apply, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, SeparatingLeft.toMatrix₂, toMatrix'_toLinearMap₂', TensorProduct.lift_comp_map, Derivation.llcomp_apply, BilinForm.toLin'Flip_apply, BilinForm.toMatrix_mul_basis_toMatrix, exteriorPower.pairingDual_apply_apply_eq_one, QuadraticForm.dualProdIsometry_toFun, BilinForm.mul_toMatrix', map_mul_iff, Finsupp.coe_lsum, Matrix.toLinearMap₂_symm, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, toMatrixRight'_id, leibniz_cross, Orientation.inner_rightAngleRotation_left, HVertexOperator.coeff_inj, minpoly_toMatrix, PiToModule.fromEnd_apply_single_one, CharacterModule.homEquiv_symm_apply_apply_apply, RootPairing.coroot_root_two, PiTensorProduct.piTensorHomMapFun₂_smul, adjoint_lTensor, LieModule.Cohomology.add_apply_apply, Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, multilinearCurryLeftEquiv_apply, CliffordAlgebra.evenToNeg_ι, toMatrixOrthonormal_apply, BilinMap.toQuadraticMap_list_sum, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, lTensor_comp_mk, Module.Basis.toDual_injective, LieModule.traceForm_eq_zero_if_mem_lcs_of_mem_ucs, RootPairing.iInf_ker_coroot'_eq, Module.dualProdDualEquivDual_apply, Orientation.kahler_apply_self, Module.Invertible.rTensorInv_leftInverse, RootPairing.Hom.weight_coweight_transpose_apply, BilinForm.IsSymm.add, QuadraticForm.toDualProd_apply, tendsto_iff_forall_eval_tendsto_topDualPairing, IsNonneg.nonneg, Orientation.inner_mul_areaForm_sub', AlternatingMap.curryLeftLinearMap_apply, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, Algebra.toMatrix_lmul', Submodule.map₂_span_span, BilinForm.ext_iff, Finsupp.llift_symm_apply, IsLocalizedModule.map_id, Orientation.kahler_rotation_left', Representation.linHom.invariantsEquivRepHom_symm_apply_coe, AffineMap.toConstProdLinearMap_apply, Matrix.ker_diagonal_toLin', RootPairing.RootPositiveForm.two_mul_apply_root_root, polyCharpolyAux_baseChange, coe_rTensorHom, range_dualMap_eq_dualAnnihilator_ker_of_surjective, Coalgebra.lift_lsmul_comp_counit_comp_comul, FGModuleCat.Iso.conj_eq_conj, Orientation.abs_areaForm_le, LieModule.traceForm_eq_sum_finrank_nsmul, Matrix.toBilin'_apply, LieAlgebra.conj_ad_apply, flip_injective_iff₂, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, toMatrix_prodMap, Matrix.toLin_apply, Matrix.toLin'_one, RootPairing.reflection_dualMap_eq_coreflection, Orientation.normSq_kahler, AlgEquiv.linearEquivConj_mulLeftRight, Module.Basis.constr_apply_fintype, LinearEquiv.symm_conj_apply, TensorProduct.LieModule.lift_apply, MultilinearMap.ofSubsingletonₗ_apply, DFinsupp.lsum_symm_apply, finsupp_sum_apply, TensorProduct.isBaseChange, Module.isTorsionBy_iff_mem_ker_lsmul, Module.injOn_dualMap_subtype_span_range_range, Submodule.map₂_le, PiTensorProduct.mul_def, RootPairing.rootForm_self_sum_of_squares, map_zero₂, Matrix.toLin_conjTranspose, LinearEquiv.conj_conj_symm, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, QuadraticMap.canLift', TensorProduct.AlgebraTensorModule.lTensor_comp, homTensorHomEquiv_toLinearMap, Subspace.dualLift_of_mem, RootPairing.algebraMap_posRootForm_posForm, Submodule.dualAnnihilator_gc, AffineMap.toConstProdLinearMap_symm_apply, RootPairing.span_root'_eq_top, BilinForm.nondegenerate_congr_iff, exteriorPower.alternatingMapLinearEquiv_comp, Matrix.trace_toLin'_eq, Matrix.toLin'OfInv_symm_apply, Orientation.rotation_eq_matrix_toLin, BilinForm.flip_apply, RootPairing.orthogonal_corootSpan_eq, Module.eval_ker, isNilpotent_trace_of_isNilpotent, RootPairing.ker_rootForm_eq_dualAnnihilator, BilinForm.compRight_apply, Submodule.sup_dualAnnihilator_le_inf, Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsBaseChange.endHom_apply, isSkewAdjoint_iff_neg_self_adjoint, Module.Invertible.rTensorInv_injective, TensorProduct.AlgebraTensorModule.lTensor_mul, IsSemisimpleModule.exists_end_ringEquiv, Algebra.TensorProduct.one_mul, Ideal.constr_basisSpanSingleton, mem_polar_singleton, LinearEquiv.isUnit_det, IsSymm.eq, CliffordAlgebra.contractLeft_ι, polyCharpolyAux_map_aeval, Subspace.dualAnnihilator_iInf_eq, Algebra.traceMatrix_of_basis, LieModule.traceForm_lieSubalgebra_mk_left, LieModule.Cohomology.smul_apply_apply, Matrix.spectrum_toLin, Submodule.quotDualCoannihilatorToDual_injective, Module.Basis.eval_injective, PolyEquivTensor.toFunBilinear_apply_apply, toMatrix'_comp, Matrix.toLinearEquiv'_apply, isUnit_toMatrix'_iff, BilinForm.add_right, Matrix.toBilin_toMatrix, IsBaseChange.toDual_apply, PolyEquivTensor.toFunLinear_tmul_apply, Finsupp.bilinearCombination_apply, Matrix.nondegenerate_toLinearMap₂_iff, BilinForm.comp_congr, Matrix.toBilin'_comp, Matrix.isHermitian_iff_isSymmetric, LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain, Subspace.dualRestrict_surjective, RootPairing.InvariantForm.apply_eq_or_aux, IsBaseChange.endHom_one, toMatrix_directSum_collectedBasis_eq_blockDiagonal', WeakBilin.coeFn_continuous, Submodule.map₂_span_singleton_eq_map, lift_lsmul_mul_eq_lsmul_lift_lsmul, Orientation.kahler_rightAngleRotation_left, separatingLeft_congr_iff, Module.Basis.end_repr_symm_apply, Module.evalEquiv_apply, Orientation.kahler_comp_linearIsometryEquiv, IsReflective.dvd_two_mul, CliffordAlgebra.contractRight_contractRight, InnerProductSpace.toMatrix_rankOne, LieAlgebra.InvariantForm.mem_orthogonal, BilinMap.toQuadraticMap_multiset_sum, IsPerfPair.bijective_right, mul_toMatrix₂_mul, Orientation.abs_areaForm_of_orthogonal, exteriorPower.alternatingMapToDual_apply_ιMulti, BilinForm.tensorDistribEquiv_tmul, innerₗ_apply_apply, trace_tensorProduct', polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, eq_adjoint_iff_basis, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, PiTensorProduct.one_mul, QuotSMulTop.equivQuotTensor_naturality_mk, Module.dual_rank_eq, toMatrix'_id, polyCharpolyAux_coeff_eval, Orientation.kahler_rotation_left, Matrix.toLinearMapₛₗ₂_symm, contractLeft_apply, SemimoduleCat.Iso.conj_eq_conj, BilinMap.tensorDistrib_tmul, Projectivization.cross_mk, BilinForm.mul_toMatrix_mul, trace_transpose, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, IsBaseChange.endHom_comp_apply, BilinForm.toMatrix_mul_basis_toMatrix, nondegenerate_toMatrix₂'_iff, Orientation.inner_sq_add_areaForm_sq, BilinForm.toMatrix'_comp, ker_dualMap_eq_dualCoannihilator_range, CharacterModule.dual_rTensor_conj_homEquiv, mulLinearMap_apply_apply, CliffordAlgebra.changeForm_contractLeft, IsLocalization.map_eq_toLinearMap_mapₐ, triple_product_eq_det, LinearEquiv.dualMap_apply, QuadraticMap.coe_associatedHom, LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplitting, mem_selfAdjointSubmodule, IsNonneg.add, finrank_range_dualMap_eq_finrank_range, LocalizedModule.map_exact, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, Module.bijective_dual_eval, Matrix.toLinearMapRight'_apply, BilinForm.toMatrix_mul, Module.FaithfullyFlat.tensorProduct_mk_injective, Matrix.ofLp_toEuclideanLin_apply, Matrix.toLinearMap₂_apply, CliffordAlgebra.forall_mul_self_eq_iff, RootPairing.coroot_root_eq_pairing, compl₁₂_apply, rTensorHomEquivHomRTensor_toLinearMap, mem_span_of_iInf_ker_le_ker, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, MultilinearMap.uncurryRight_apply, nondegenerate_toLinearMap₂'_iff_det_ne_zero, PiTensorProduct.piTensorHomMapFun₂_add, Matrix.mulVecBilin_apply, Module.Basis.dualBasis_repr, PiTensorProduct.mul_one, CategoryTheory.Abelian.Ext.bilinearCompOfLinear_apply_apply, lieEquivMatrix'_symm_apply, Matrix.proj_diagonal, Module.Dual.baseChange_baseChange, separatingDual_iff_injective, TensorProduct.dualDistribInvOfBasis_apply, trace_eq_sum_trace_restrict, map_smul₂, disjoint_ker_of_nondegenerate_restrict, intrinsicStarModule, dualTensorHom_prodMap_zero, IsContPerfPair.bijective_right, isUnit_toMatrix_iff, Subspace.dualEquivDual_def, LocalizedModule.map_id, TensorProduct.AlgebraTensorModule.rTensor_mul, MultilinearMap.curryMidLinearEquiv_apply, BilinForm.toMatrix_compLeft, trace_eq_matrix_trace, RootPairing.polarizationEquiv_symm_apply_coroot, BilinForm.toMatrix_apply, Matrix.linfty_opNorm_toMatrix, Matrix.toBilin'_apply', Module.Basis.linearCombination_coord, BilinForm.IsSymm.polarization, Matrix.toLinearMap₂'_single, ExteriorAlgebra.liftAlternating_comp_ιMulti, separatingRight_toLinearMap₂'_of_det_ne_zero', Algebra.TensorProduct.mul_assoc, adjoint_inner_left, TensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse, Module.Basis.toDual_apply, BilinForm.mul_toMatrix, Subspace.dualLift_rightInverse, coprodEquiv_apply, QuadraticMap.associated_linMulLin, Rep.ihom_map_hom, dualTensorHomEquivOfBasis_toLinearMap, QuadraticForm.associated_isSymm, IsBaseChange.dual, Module.apply_evalEquiv_symm_apply, Submodule.coe_dualAnnihilator_span, Orientation.kahler_mul, trace_conj', Matrix.SpecialLinearGroup.toLin'_to_linearMap, mul_toMatrix₂'_mul, toMatrix₂'_mul, IsTensorProduct.lift_eq, BilinForm.flip_flip, Algebra.toMatrix_lsmul, toMatrix_innerSL_apply, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, Matrix.separatingLeft_toLinearMap₂'_iff, QuadraticMap.exists_companion', triple_product_permutation, separatingLeft_toLinearMap₂'_of_det_ne_zero', PiTensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse, Module.End.baseChangeHom_apply_apply, PiTensorProduct.mul_tprod_tprod, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, BilinForm.toMatrix_mul, Subspace.dualCopairing_nondegenerate, Module.finite_dual_iff, toMatrix_comp, Module.dual_projective, Module.Basis.coe_toDual_self, RootPairing.RootPositiveForm.exists_pos_eq, Matrix.separatingLeft_toBilin'_iff, Submodule.dualAnnihilator_top, Matrix.trace_toLin_eq, toMatrix₂_mul_basis_toMatrix, TensorProduct.AlgebraTensorModule.lift_apply, Module.Basis.toMatrix_eq_toMatrix_constr, lcompₛₗ_apply, polyCharpoly_map_eq_charpoly, Ideal.pi_mkQ_rTensor, BilinMap.toQuadraticMap_sum, Orientation.kahler_map, CliffordAlgebra.contractRight_one, PolyEquivTensor.toFunBilinear_apply_eq_smul, isOrthoᵢ_def, BilinForm.isSymm_def, PiTensorProduct.lift_tprod, Matrix.toLinOfInv_apply, TensorProduct.lcurry_apply, TensorProduct.curry_apply, dualTensorHomEquivOfBasis_symm_cancel_left, IsPerfPair.id, Module.Invertible.rTensorEquiv_symm_apply_apply, Module.Flat.iff_lift_lsmul_comp_subtype_injective, PiTensorProduct.liftIsometry_apply_apply, ContinuousLinearMap.coeLMₛₗ_apply, CliffordAlgebra.foldr'Aux_apply_apply, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, LinearEquiv.conj_id, IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite, Matrix.toBilin'Aux_eq, TensorProduct.lift.equiv_symm_apply, addMonoidHomLequivNat_apply, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, IntrinsicStar.isSelfAdjoint_iff_toMatrix', Matrix.toLin_finTwoProd_toContinuousLinearMap, IsBaseChange.linearMapLeftRight, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, map_add₂, Submodule.mem_traceDual, domRestrict₂_apply, RootPairing.flip_toFun_apply, Orientation.areaForm_map, Matrix.toPerfectPairing, PiTensorProduct.norm_eval_le_projectiveSeminorm, IsProj.trace, map_neg₂, LinearEquiv.congrRight₂_trans, Subspace.map_le_dualAnnihilator_dualAnnihilator, BilinForm.isSymm_zero, TensorProduct.AlgebraTensorModule.rTensor_id, Matrix.kroneckerTMulBilinear_apply, BilinForm.orthogonal_top_eq_ker, InnerProductSpace.toLinearMap_rankOne, RootPairing.rootSpan_dualAnnihilator_map_eq_iInf_ker_root', Submodule.image2_subset_map₂, Algebra.norm_eq_zero_iff', Module.Basis.linearMap_apply_apply, addMonoidHomLequivInt_symm_apply, trace_tensorProduct, comp_dualTensorHom, QuadraticForm.dualProdProdIsometry_toFun, Matrix.toLinearEquivRight'OfInv_apply, hasEigenvalue_toLin'_diagonal_iff, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, LinearEquiv.smul_id_of_finrank_eq_one_apply, BilinForm.coe_injective, toMatrix'_toLinearMapₛₗ₂', BilinForm.smul_right, isStarProjection_toContinuousLinearMap_iff, Matrix.toLpLin_mul, Matrix.toLin'_submatrix, TensorProduct.gradedMul_algebraMap, Matrix.separatingLeft_toLinearMap₂_iff, ModuleCat.localizedModuleMap_hom_apply, Orientation.inner_rightAngleRotationAux₁_right, ringLmapEquivSelf_apply, Matrix.toLin_toMatrix, LieModule.traceForm_genWeightSpace_eq, PiTensorProduct.lift_comp_map, TensorProduct.homTensorHomMap_apply, tensorEqLocus_tmul, LieModule.traceForm_apply_apply, cross_dot_cross, toMatrix₂_apply, ModuleCat.Hom.hom₂_apply, RootPairing.rootFormIn_self_smul_coroot, IsSymmetric.trace_eq_sum_eigenvalues, adjoint_comp, RootPairing.corootForm_self_smul_root, PiToModule.fromMatrix_apply, RootPairing.exists_form_eq_form_and_form_ne_zero, toContPerfPair_apply, LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, Matrix.toEuclideanLin_apply_piLp_toLp, dualMap_apply, LieModule.Cohomology.twoCochain_val_apply, dualMap_surjective_iff, multilinearCurryLeftEquiv_symm_apply, MultilinearMap.piLinearMap_apply_apply_apply, TensorProduct.toLinearMap_symm_lid, QuadraticMap.associated_sq, dualMap_def, iSupIndep_iff_dfinsupp_lsum_injective, RootPairing.toPerfPair_conj_reflection, QuadraticMap.associated_comp, TensorProduct.tmul_of_gradedMul_of_tmul, IsLocalizedModule.map_exact, QuadraticMap.associated_isOrtho, CliffordAlgebra.contractLeft_mul_algebraMap, map_dualTensorHom, Submodule.range_dualMap_mkQ_eq, Subspace.dualLift_injective, MultilinearMap.curryMidLinearEquiv_symm_apply, Polynomial.toMatrix_sylvesterMap, smulRightₗ_apply_apply, Finsupp.lsum_comp_lsingle, IsRefl.eq_iff, TensorProduct.AlgebraTensorModule.lTensor_one, Module.finrank_linearMap_self, Matrix.separatingRight_toBilin'_iff, vecEmpty₂_apply, Orientation.areaForm_map_complex, RootPairing.InvariantForm.apply_root_root_zero_iff, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, Matrix.toLin_finTwoProd, BilinForm.apply_toDual_symm_apply, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, CliffordAlgebra.even.lift.aux_apply, Module.Basis.linearMap_repr_symm_apply, CliffordAlgebra.even.lift.aux_ι, BilinForm.neg_apply, RootPairing.rootForm_pos_of_ne_zero, Module.Basis.constr_basis, LinearEquiv.charpoly_conj, tensorProduct_apply, BilinForm.isPosSemidef_zero, exteriorPower.pairingDual_apply_apply_eq_one_zero, ModuleCat.homLinearEquiv_apply, Rep.coinvariantsTensorMk_apply, Orientation.inner_rightAngleRotation_right, WeakBilin.eval_continuous, QuotSMulTop.map_comp, LieModule.traceForm_apply_lie_apply, Projectivization.cross_mk_of_ne, not_separatingLeft_zero, CharacterModule.uncurry_apply, Rep.homEquiv_symm_apply_hom, QuadraticMap.Ring.associated_pi, nondegenerate_toMatrix₂_iff, Matrix.trace_kroneckerMapBilinear, AlgEquiv.linearEquivConj_mulRight, ModuleCat.Iso.conj_eq_conj, innerₛₗ_apply, Matrix.toLin_one, CliffordAlgebra.contractLeft_algebraMap_mul, BilinForm.compLeft_apply, contractRight_apply, trace_eq_contract_of_basis, range_dualMap_le_dualAnnihilator_ker, Matrix.toLin_transpose, Complex.toMatrix_conjAe, Submodule.finite_dualAnnihilator_iff, Representation.leftRegular_norm_apply, BilinForm.mul_toMatrix, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, TensorProduct.mk_surjective, Matrix.toLpLin_symm_comp, Module.Basis.toDual_linearCombination_right, Matrix.toLinearMapₛₗ₂_apply_basis, VertexOperator.ncoeff_of_coeff, RootPairing.restrictScalars_toLinearMap_apply_apply, ExteriorAlgebra.liftAlternating_algebraMap, Orientation.kahler_apply_apply, Orientation.inner_rightAngleRotationAux₁_left, toMatrix_toSpanSingleton, RootPairing.toPerfPair_flip_conj_coreflection, VertexOperator.ncoeff_eq_zero_of_lt_order, toMatrix₂_symm', Module.Invertible.bijective, Orientation.areaForm_apply_self, Nondegenerate.toMatrix₂', TensorProduct.equivFinsuppOfBasisRight_symm, HVertexOperator.compHahnSeries_coeff, Subspace.dualAnnihilator_le_dualAnnihilator_iff, RootPairing.InvariantForm.apply_eq_or, Matrix.Nondegenerate.toBilin', FDRep.Iso.conj_ρ, IsAlt.eq_of_add_add_eq_zero, VectorFourier.fourierIntegral_comp_add_right, BilinForm.congr_trans, toMatrix_singleton, isNonneg_def, BilinForm.toMatrix'_mul, dotProductBilin_apply_apply, trace_restrict_eq_of_forall_mem, exteriorPower.alternatingMapLinearEquiv_symm_apply, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, instIsStablyFiniteRingEndForallOfFinite, sum_apply, toMatrix₂'_compl₂, restrictScalars₁₂_injective, map_sum₂, VectorFourier.fourierIntegral_probChar, IsSymm.add, Submodule.le_dualAnnihilator_iff_le_dualCoannihilator, LieAlgebra.IsKilling.traceForm_coroot, TensorProduct.AlgebraTensorModule.curry_injective, Orientation.kahler_rotation_right, Submodule.span_eq_top_of_ne_zero, ContinuousLinearMap.coe_sum, BilinForm.comp_apply, Module.Basis.traceDual_repr_apply, PiTensorProduct.lift.unique', Matrix.nondegenerate_toLinearMap₂'_iff, separatingRight_toMatrix₂_iff, LieModule.traceForm_eq_sum_finrank_nsmul_mul, Coalgebra.lTensor_counit_comp_comul, CliffordAlgebra.changeForm.associated_neg_proof, BilinForm.neg_right, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, CliffordAlgebra.ofEven_ι, BilinForm.IsNonneg.smul, QuotSMulTop.map_apply_mk, Submodule.dualAnnihilator_bot, Representation.linHom.mem_invariants_iff_comm, BilinForm.linMulLin_apply, RootPairing.corootSpan_dualAnnihilator_le_ker_rootForm, mk₂'_apply, IsLocalizedModule.map_comp, Module.Dual.eval_naturality, BilinForm.comp_symmCompOfNondegenerate_apply, HVertexOperator.coeff_comp, ModuleCat.ofHom₂_hom_apply_hom, LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, trace_conj, isSMulRegular_on_quot_iff_lsmul_comap_eq, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, BilinForm.congr_fun, jacobi_cross, separatingLeft_toMatrix₂_iff, Module.map_eval_injective, HVertexOperator.coeff_apply_apply, basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix, Module.Basis.toDualFlip_apply, RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot, mem_span_iff_bound, Set.Finite.convexHull_eq_image, TensorProduct.dualDistrib_apply, BilinForm.toLin_restrict_ker_eq_inf_orthogonal, groupHomology.mkH1OfIsTrivial_apply, BilinForm.toMatrix'_toBilin', neg_cross, LocalizedModule.map_mk, PowerBasis.liftEquiv'_symm_apply_apply, PiTensorProduct.lift_comp_reindex_symm, QuadraticMap.separatingLeft_of_anisotropic, PowerBasis.constr_pow_mul, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, det_toMatrix', Matrix.separatingLeft_toBilin_iff, eq_adjoint_iff_basis_right, LinearEquiv.arrowCongr_trans, LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebra, Nondegenerate.toMatrix₂, evalAddMonoidHom_apply, Matrix.toLin'OfInv_apply, IsModuleTopology.continuous_bilinear_of_finite_right, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, BilinForm.isOrtho_def, innerₛₗ_apply_coe, BilinMap.toQuadraticMap_apply, RootPairing.rootSpan_dualAnnihilator_map_eq, BilinForm.Nondegenerate.toMatrix', isSymm_iff_basis, Module.Basis.constr_self, toMatrix_basis_equiv, restrictScalars₁₂_apply_apply, Module.evalEquiv_toLinearMap, MultilinearMap.compLinearMapMultilinear_apply, LieModule.traceForm_apply_eq_zero_of_mem_lcs_of_mem_center, topDualPairing_apply, trace_prodMap', toSeminormFamily_apply, TensorProduct.AlgebraTensorModule.lift_tmul, dualMap_comp_dualMap, separatingLeft_iff_ker_eq_bot, Matrix.SeparatingRight.toBilin', lflip_symm, ltoFun_apply, Orientation.areaForm_rightAngleRotation_right, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, compBilinForm_apply_apply, lid_comp_rTensor, coe_toContinuousLinearMap_symm, Matrix.range_diagonal, BilinForm.Nondegenerate.ker_eq_bot, IsSymmetric.re_trace_eq_sum_eigenvalues, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, extendScalarsOfIsLocalizationEquiv_symm_apply, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Module.Basis.constr_def, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, cardinalMk_algHom, trace_comp_comm, addMonoidEndRingEquivInt_symm_apply, trace_eq_sum_trace_restrict', BilinForm.toMatrix_compLeft, IsPositive.adjoint_eq, Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace, Algebra.coe_lmul_eq_mul, Module.Basis.toDual_apply_left, nilRank_le_natTrailingDegree_charpoly, toPerfPair_apply, toMatrix₂'_comp, Matrix.toLinearMap₂_apply_basis, LinearPMap.mem_adjoint_domain_iff, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, TensorProduct.Algebra.moduleAux_apply, toMatrix_pow, RootPairing.disjoint_rootSpan_ker_rootForm, Module.FinitePresentation.isLocalizedModule_mapExtendScalars, BilinMap.polarBilin_toQuadraticMap, IsBaseChange.linearMapLeftRightHom_apply, Algebra.trace_apply, coprodEquiv_symm_apply, BilinForm.toMatrix_comp, LinearEquiv.map_mem_invtSubmodule_iff, Matrix.SpecialLinearGroup.toLin'_symm_apply, coe_innerₛₗ_apply, trace_comp_cycle, Algebra.FormallyUnramified.comp_sec, Module.Basis.toDual_apply_right, trace_comp_cycle', Submodule.dualAnnihilator_map_linearEquiv_flip_symm, toMatrix'_one, Representation.dual_apply, Submodule.baseChange_span, BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal, Module.surjective_piEquiv_apply_iff, Submodule.dualAnnihilator_iSup_eq, Module.Dual.eq_of_preReflection_mapsTo', Submodule.dualAnnihilator_eq_bot_iff, TensorProduct.quotTensorEquivQuotSMul_comp_mk, Orientation.kahler_rightAngleRotation_right, PointedCone.mem_maxTensorProduct, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, LinearEquiv.dualMap_refl, QuadraticMap.exists_companion, BilinForm.IsAlt.add, cross_cross_eq_smul_sub_smul', rank_lt_rank_dual, TensorProduct.rTensorHomToHomRTensor_apply, Module.Dual.congr_apply_apply, LieAlgebra.IsKilling.span_weight_eq_top, tensorKerEquiv_apply, basis_toMatrix_mul_linearMap_toMatrix, IsAlt.self_eq_zero, toMatrixₛₗ₂'_apply, Representation.dualTensorHom_comm, exact_lcomp_of_exact_of_surjective, transvection.baseChange, polar_mem_iff, Submodule.mem_biSup_iff_exists_dfinsupp, IsContPerfPair.continuous_uncurry, Matrix.toLinearMapRight'_one, isSMulRegular_iff_ker_lsmul_eq_bot, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, IsLocalizedModule.map_surjective, QuadraticForm.associated_tmul, ModN.instModuleFinite, RootPairing.toLinearMap_apply_apply_mem_range_algebraMap, Orientation.norm_kahler, Submodule.dualRestrict_apply, TensorProduct.one_gradedMul, IsLocalizedModule.map_iso_commute, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, LieModule.traceForm_apply_lie_apply', Module.Basis.SmithNormalForm.toMatrix_restrict_eq_toMatrix, flip_surjective_iff₂, RootPairing.RootPositiveForm.algebraMap_posForm, lsum_piSingle, IsBaseChange.linearMapRight, Submodule.dualAnnihilator_eq_bot_iff', Module.Basis.constr_range, ker_lsmul, PiTensorProduct.mul_comm, Matrix.toLpLin_apply, Matrix.toLin'_apply, CliffordAlgebra.contractRight_ι, QuotSMulTop.map_id, LinearEquiv.arrowCongr_comp, isSMulRegular_on_quot_iff_lsmul_comap_le, Submodule.map_dualCoannihilator_linearEquiv_flip, Module.Basis.constr_apply, DFinsupp.lsum_apply_apply, BilinForm.SeparatingRight.toMatrix', TensorProduct.toLinearMap_symm_rid, toMatrix_adjoint, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, TensorProduct.AlgebraTensorModule.coe_rTensor, diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne, Subspace.map_dualCoannihilator, LieAlgebra.Extension.twoCocycleOf_coe_coe, separatingLeft_toLinearMap₂'_iff_det_ne_zero, CharacterModule.homEquiv_apply_apply, map_smulₛₗ₂, BilinForm.Nondegenerate.toMatrix, RootPairing.isCompl_corootSpan_ker_corootForm, dualCoannihilator_range_eq_ker_flip, im_inner_adjoint_mul_self_eq_zero, QuadraticMap.associated_flip, BilinForm.congr_symm, compr₂ₛₗ_apply, Matrix.l2_opNorm_def, signedDist_apply_linear, Matrix.toEuclideanLin_toLp, BilinForm.baseChange_tmul, toLinearMap_toPerfPair, LieAlgebra.IsKilling.ker_killingForm_eq_bot, RootPairing.corootSpan_dualAnnihilator_map_eq_iInf_ker_coroot', BilinForm.isSymm_iff_basis, PowerBasis.constr_pow_aeval, RootPairing.invtSubmodule_reflection_of_invtSubmodule_coreflection, CliffordAlgebra.EvenHom.contract_mid, det_toMatrix, Algebra.traceForm_toMatrix_powerBasis, Matrix.minpoly_toLin, basis_toMatrix_mul, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, SemimoduleCat.homLinearEquiv_symm_apply, Matrix.toLin'_toMatrix', AlternatingMap.alternatizeUncurryFinLM_apply, det_toLin, posSemidef_toMatrix_iff, Representation.linHom.invariantsEquivRepHom_apply_hom, instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation, trace_mul_cycle', BilinForm.nondegenerate_toBilin'_of_det_ne_zero', BilinForm.sum_apply, RootPairing.InvariantForm.apply_eq_or_of_apply_ne, QuadraticMap.associated_isSymm, FGModuleCat.Iso.conj_hom_eq_conj, RootPairing.InvariantForm.two_mul_apply_root_root, Module.Basis.toDual_eq_equivFun, SeparatingLeft.toMatrix₂', isNonneg_zero, TensorProduct.toMatrix_comm, dualTensorHomEquivOfBasis_apply, polar_mem, toMatrix₂'_apply, isAdjointPair_inner, ModuleCat.monoidalClosed_pre_app, IsPositive.adjoint_conj, LieModule.Cohomology.d₂₃_comp_d₁₂, Subspace.quotDualCoannihilatorToDual_bijective, ker_tensorProductMk, orthogonal_span_singleton_eq_to_lin_ker, ker_dualMap_eq_dualAnnihilator_range, PiTensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, LinearEquiv.trans_dualMap_symm_flip, BilinForm.separatingLeft_toMatrix_iff, trace_comp_comm', TensorProduct.sum_tmul_basis_left_injective, PiTensorProduct.lift.unique, QuadraticForm.associated_baseChange, Real.volume_preserving_transvectionStruct, Matrix.toBilin'_toMatrix', trace_baseChange, CliffordAlgebra.contractLeftAux_apply_apply, Matrix.toLinearMapₛₗ₂_toMatrix₂, BilinForm.IsAlt.smul, CliffordAlgebra.contractLeft_one, le_comap_range_rTensor, toMatrix'_mulVec, RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot, trace_eq_sum_trace_restrict_of_eq_biSup, RootPairing.ker_corootForm_eq_dualAnnihilator, Subspace.dualAnnihilator_inf_eq, VertexOperator.coeff_eq_ncoeff, lsum_symm_apply, IsBaseChange.toDualBaseChange_tmul, IsLocalizedModule.map_LocalizedModules, Matrix.SeparatingLeft.toLinearMap₂, hasEigenvector_toLin_diagonal, separatingRight_toLinearMap₂'_iff_det_ne_zero, Module.rank_linearMap_self, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, domRestrict₁₂_apply, SemimoduleCat.hom_sum, dotProduct_toMatrix₂_mulVec, LieModule.range_traceForm_le_span_weight, TensorProduct.gradedComm_gradedMul, Matrix.diagonal_comp_single, rank_finset_sum_le, IsPerfectCompl.isCompl_left, Submodule.map_dualAnnihilator_linearEquiv_flip_symm, IsBaseChange.endHom_comp, traceAux_def, mem_span_iff_continuous, Algebra.leftMulMatrix_apply, InnerProductSpace.symm_toEuclideanLin_rankOne, Subspace.isCompl_dualAnnihilator, BilinForm.toMatrix'_compRight, VertexOperator.coeff_eq_zero_of_lt_order, IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_end, Module.Basis.eval_ker, ExteriorAlgebra.liftAlternating_ι, TensorProduct.AlgebraTensorModule.lcurry_apply, Matrix.SeparatingRight.toBilin, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, CliffordAlgebra.contractLeftAux_contractLeftAux, coe_finsupp_sum, Subspace.comap_dualAnnihilator_dualAnnihilator, toMatrix_apply, RootPairing.ker_polarization_eq_ker_rootForm, Module.erange_coe, TensorProduct.toMatrix_map, Matrix.rank_vecMulVec, continuous_uncurry_of_isContPerfPair, Submodule.mem_traceDual_iff_isIntegral, RootPairing.polarization_apply_eq_zero_iff, Submodule.le_dualCoannihilator_dualAnnihilator, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_longRoot, PositiveLinearMap.toLinearMap_nsmul, Orientation.areaForm_rightAngleRotation_left, BilinForm.restrict_apply, toMatrix_id_eq_basis_toMatrix, contractLeft_assoc_coevaluation', TensorProduct.dualDistribEquivOfBasis_apply_apply, baseChangeHom_apply, toMatrixRight'_comp, isOrtho_def, Module.dualProdDualEquivDual_symm_apply, trace_map, Module.Basis.constr_eq, Module.FinitePresentation.isLocalizedModule_map, HVertexOperator.coeff_of_coeff, lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, applyₗ_apply_apply, dualProd.toQuadraticForm, IsAlt.neg, Subspace.finrank_add_finrank_dualAnnihilator_eq, Matrix.toBilin_comp, CliffordAlgebra.changeForm_changeForm, polyCharpoly_coeff_eval, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, BilinForm.apply_smul_sub_smul_sub_eq, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, lsum_comp_mapRange_toSpanSingleton, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', RootPairing.orthogonal_rootSpan_eq, MultilinearMap.ofSubsingletonₗ_symm_apply, det_toMatrix_eq_det_toMatrix, Algebra.TensorProduct.mul_apply, Matrix.SpecialLinearGroup.toLin'_apply, Module.Finite.of_isComplemented_codomain, Submodule.piQuotientLift_mk, QuadraticMap.polarBilin_apply_apply, toKerIsLocalized_apply_coe, ModuleCat.ihom_ev_app, adjoint_id, BilinForm.add_apply, Submodule.flip_quotDualCoannihilatorToDual_injective, lflip_apply, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule, TensorProduct.lift.equiv_apply, IsBaseChange.linearMapLeftRightHom_comp, Rep.indResHomEquiv_symm_apply_hom, Subspace.dualPairing_eq, QuadraticForm.dualProdProdIsometry_invFun, SeparatingLeft.congr, Matrix.Nondegenerate.toLinearMap₂', AlgHom.mulLeftRightMatrix.comp_inv, Orientation.inner_mul_areaForm_sub, IsLocalizedModule.map_lTensor, Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂, Module.Basis.coord_toDualEquiv_symm_apply, Finsupp.lsum_symm_apply, Module.Basis.baseChange_linearMap, BilinForm.sub_right, IsRefl.ker_flip, toMatrix₂Aux_apply, Module.mapEvalEquiv_symm_apply, Subspace.dualEquivDual_apply, BilinForm.iIsOrtho_def, TensorProduct.uncurry_apply, BilinForm.apply_dualBasis_right, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, Module.Dual.congr_symm_apply_apply, PointedCone.dual_singleton, TensorPower.pairingDual_tprod_tprod, sum_repr_mul_repr_mul, IsPositive.conj_adjoint, ker_toContinuousLinearMap, TensorProduct.AlgebraTensorModule.lTensor_tmul, charpoly_toMatrix, toLinearMap₂'Aux_toMatrix₂Aux, isSymm_iff_isHermitian_toMatrix, trace_lie, lsmul_eq_distribSMultoLinearMap, Matrix.toBilin'_single, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, separatingLeft_dualProd, toMatrix_toLin, range_localizedMap_eq_localized₀_range, Module.Basis.traceDual_eq_iff, IsTensorProduct.map_eq, DirectSum.gMulLHom_apply_apply, polyCharpolyAux_map_eq_toMatrix_charpoly, Matrix.toLinearEquiv_apply, LinearEquiv.piRing_apply, hasEigenvalue_toLin_diagonal_iff, PiTensorProduct.lift_symm, CliffordAlgebra.contractLeft_algebraMap, Matrix.spectrum_toLin', dualAnnihilator_ker_eq_range_flip, LieAlgebra.killingForm_of_equiv_apply
|
instFunLike 📖 | CompOp | 4658 mathmath: AdicCompletion.of_surjective_iff, ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, Polynomial.fderiv, CliffordAlgebra.unop_reverseOp, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂, DFinsupp.coprodMap_apply, MvPolynomial.pUnitAlgEquiv_symm_monomial, MvPowerSeries.coeff_zero_eq_constantCoeff_apply, 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, lTensor_ker_subtype_tensorKerEquiv_symm, comp_toSpanSingleton, KaehlerDifferential.kerCotangentToTensor_toCotangent, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, Finset.weightedVSub_sdiff, RootPairing.InvariantForm.apply_reflection_reflection, MvPolynomial.dvd_monomial_one_iff_exists, CliffordAlgebra.contractRight_algebraMap_mul, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr, Submodule.starProjection_apply_eq_isComplProjection, Lagrange.interpolate_one, StarModule.decomposeProdAdjointL_symm_apply, Orientation.kahler_map_complex, Algebra.normalizedTrace_map, RootPairing.rootForm_self_smul_coroot, CliffordAlgebra.toBaseChange_reverse, StarModule.selfAdjointPart_add_skewAdjointPart, ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, Polynomial.taylor_eval, AlgHom.coe_toLinearMap, Bialgebra.comulAlgHom_apply, TensorProduct.forall_vanishesTrivially_iff_forall_fg_rTensor_injective, apply_symm_toPerfPair_self, PowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, ModuleCat.forget_preservesLimits, Bialgebra.comul_natCast, Finsupp.linearCombination_apply_of_mem_supported, 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, baseChange_eq_ltensor, Module.Flat.iff_lTensor_exact', Module.Basis.det_comp_basis, Lagrange.eval_iterate_derivative_eq_sum, MonomialOrder.sPolynomial_leadingTerm_mul', iSupIndep.dfinsupp_lsum_injective, 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, MvPowerSeries.coeff_zero_eq_constantCoeff, BilinForm.zero_right, dot_self_cross, Finset.affineCombination_vsub, CliffordAlgebra.contractRight_algebraMap, Submodule.coe_continuous_linearProjOfClosedCompl', Lagrange.interpolate_eq_of_values_eq_on, Orthonormal.inner_left_finsupp, ModuleCat.restrictScalars.map_apply, MvPolynomial.totalDegree_monomial, AlgEquiv.moduleEndSelfOp_apply_apply, Polynomial.derivative_X_sq, RootPairing.posRootForm_posForm_apply_apply, ModuleCat.forget₂_reflectsLimitsOfSize, TensorProduct.LieModule.liftLie_apply, PowerSeries.coeff_mul_one_sub_of_lt_order, BilinForm.dualSubmoduleToDual_apply_apply, IsLocalizedModule.liftOfLE_apply, Polynomial.smeval_monomial_mul, PiTensorProduct.lift.tprod, toAddMonoidHom_coe, Coalgebra.lTensor_counit_comul, CliffordAlgebra.contractRight_eq, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, Module.Relations.Solution.ofπ'_var, 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, coe_toSeminorm, MvPowerSeries.weightedOrder_monomial, Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker, AdicCompletion.mk_zero_of, MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum, LinearIsometry.coe_toLinearMap, PowerSeries.coeff_mul_of_lt_order, IsReflective.regular, RootPairing.linearIndepOn_root_baseOf', taylorWithin_succ, BilinForm.symmCompOfNondegenerate_left_apply, PolyEquivTensor.toFunBilinear_apply_eq_sum, BilinForm.dualSubmoduleToDual_injective, Rep.MonoidalClosed.linearHomEquiv_symm_hom, groupCohomology.isoCocycles₁_hom_comp_i_apply, DFinsupp.lsingle_apply, Seminorm.continuous_of_continuous_comp, Module.Presentation.cokernelSolution_var, coe_mk, Polynomial.monomial_eq_monomial_iff, inr_apply, RootPairing.Polarization_apply, PolynomialModule.comp_single, LinearEquiv.flip_apply, PolynomialModule.map_lsingle, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_same, Polynomial.coeff_derivative, funLeft_id, LinearIsometryEquiv.coe_ofLinearIsometry_symm, PowerSeries.coeff_of_lt_order_toNat, PiTensorProduct.liftAlgHom_apply, groupCohomology.mem_cocycles₂_def, RootPairing.root'In_corootSpanMem_eq_pairingIn, PowerSeries.constantCoeff_subst, ExteriorAlgebra.ι_eq_algebraMap_iff, PowerSeries.WithPiTopology.continuous_coeff, SimpleGraph.lapMatrix_toLinearMap₂', coe_compAlternatingMap, 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, compAlternatingMap_apply, ModuleCat.forget_preservesLimitsOfSize, groupCohomology.d₂₃_hom_apply, Algebra.PreSubmersivePresentation.cotangentComplexAux_apply, MvPolynomial.degrees_monomial, CliffordAlgebraQuaternion.j_quaternionBasis, ExteriorAlgebra.ι_inj, dotProductEquiv_symm_apply, groupHomology.d₁₀_single_one, DirectSum.component.of, Polynomial.hasseDeriv_zero', isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, realPart_idem, MvPolynomial.one_def, Algebra.Generators.H1Cotangent.δAux_mul, Complex.kahler, CliffordAlgebra.mul_ι_mul_ι_of_isOrtho, MvPowerSeries.coeff_mul_monomial, 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, map_add, zero_apply, Ideal.toCotangent_eq, CStarModule.innerₛₗ_apply, Module.Flat.toAlgebra_injective, Submodule.mulMap_tmul, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, Polynomial.derivWithin_aeval, Module.End.smul_def, Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd, Finset.weightedVSubOfPoint_apply, PowerSeries.coeff_rescale, Profinite.NobelingProof.injective_πs', MvPolynomial.scalarRTensor_apply_monomial_tmul, AffineMap.hasDerivAtFilter, MvPolynomial.homogeneousComponent_eq_zero', QuadraticMap.canLift, Polynomial.derivative_intCast_mul, injective_iff_surjective_of_finrank_eq_finrank, LieModule.toEnd_pow_apply_map, LaurentPolynomial.comul_T, DirectSum.coe_toModule_eq_coe_toAddMonoid, eval_minpolyDiv_self, Algebra.normalizedTrace_surjective, IsPositive.ne_zero_iff, Submodule.exists_fg_le_eq_rTensor_inclusion, SkewPolynomial.monomial_add, BilinForm.IsAlt.neg_eq, Rep.diagonalSuccIsoFree_inv_hom_single, BilinMap.polar_toQuadraticMap, PolynomialModule.smul_def, isAdjointPair_iff_comp_eq_compl₂, IsPerfPair.bijective_left, MonomialOrder.degree_monomial, CategoryTheory.Functor.coe_mapLinearMap, exact_zero_iff_surjective, Matrix.cramer_transpose_row_self, AdicCompletion.map_val_apply, PowerSeries.coeff_expand_mul, Module.End.HasUnifEigenvector.pow_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, Representation.repOfTprodIso_apply, coe_semilinearMap, Polynomial.derivative_C_mul, ModuleCat.freeHomEquiv_apply, AffineSubspace.map_pointwise_vadd, eval₂_minpolyDiv_self, rTensor_comm, Derivation.coe_to_linearMap_comp, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, RootPairing.Hom.root_weightMap, 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, 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, Module.Basis.constr_comp, Polynomial.card_rootSet_le_derivative, PowerSeries.coeff_X_mul_largeSchroderSeries, realPart_ofReal, Module.Basis.constr_symm_apply, mapMatrixLinear_apply, LightCondensed.forget_obj_val_map, 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, 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, Rep.coindToInd_of_support_subset_orbit, PiTensorProduct.map_reindex_symm, RootPairing.root_coroot_two, ModuleCat.extendScalarsId_hom_app_one_tmul, MvPolynomial.X_pow_eq_monomial, toMatrix_apply', Polynomial.opRingEquiv_op_monomial, Polynomial.natDegree_monomial_le, Module.Flat.iff_rTensor_preserves_injective_linearMap, Module.Presentation.directSum_var, llcomp_apply, BilinForm.smul_left_of_tower, groupHomology.mapCycles₁_comp_apply, Orientation.kahler_comp_rightAngleRotation', groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, AddMonoidAlgebra.comul_single, Module.Basis.dualBasis_coord_toDualEquiv_apply, PowerSeries.trunc_X_pow_self_mul, Matrix.repr_toLin, AdicCompletion.of_ofAlgEquiv_symm, Lagrange.derivative_nodal, CliffordAlgebra.even.lift.aux_mul, LocalizedModule.restrictScalars_map_eq, Representation.Coinvariants.mk_inv_tmul, polar_eq_iInter, PolynomialModule.map_smul, Submodule.linearProjOfIsCompl_apply_right, MvPowerSeries.coeff_pow, Module.forall_dual_apply_eq_zero_iff, Polynomial.monomial_mem_lifts, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, 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, tensorKer_tmul, IsSymmetric.diagonalization_apply_self_apply, TensorProduct.sum_tmul_basis_right_injective, ModuleCat.restrictScalarsComp'App_hom_apply, Subspace.dualLift_of_subtype, 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, compRight_apply, LightCondensed.ihomPoints_symm_comp, Trivialization.linearMapAt_symmₗ, Polynomial.C_mul_X_eq_monomial, Matrix.liftLinear_single, IsSymmetric.im_inner_self_apply, imaginaryPart_I_smul, LinearEquiv.coe_mk, Pi.counit_coe_dFinsupp, RootPairing.Equiv.coweightEquiv_symm_coweightMap, 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, PowerSeries.coeff_of_lt_order, MvPowerSeries.constantCoeff_subst, Orientation.areaForm_le, BilinForm.congr_apply, Rep.indToCoindAux_self, id'_coe, TensorAlgebra.toTrivSqZeroExt_ι, DomMulAct.smul_linearMap_apply, mul_apply_apply, eval₂_minpolyDiv_of_eval₂_eq_zero, MvPolynomial.divMonomial_add_modMonomial, ModuleCat.AlternatingMap.postcomp_apply, ext_ring_op_iff, Submodule.mapQ_apply, adjoint_innerₛₗ_apply, continuousLinearMapClassOfFiniteDimensional, Polynomial.hasseDeriv_one', Polynomial.derivative_comp_one_sub_X, SemimoduleCat.instReflectsIsomorphismsAddCommMonCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, Submodule.dualQuotEquivDualAnnihilator_apply, PolynomialModule.comp_smul, ContinuousLinearMap.toBilinForm_apply, WittVector.IsocrystalHom.frob_equivariant, MvPolynomial.eval₂Hom_monomial, LinearEquiv.conj_apply_apply, Coalgebra.sum_map_tmul_counit_eq, Polynomial.derivative_pow_eq_zero, BilinForm.IsNonneg.nonneg, MvPolynomial.homogeneousComponent_of_mem, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, PowerSeries.coeff_succ_mul_X, Module.exists_dual_forall_apply_eq_one, LinearIndependent.linearCombination_repr, ModuleCat.linearIndependent_shortExact, PolynomialModule.aeval_equivPolynomial, Profinite.NobelingProof.coe_πs, 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, LinearEquiv.conjAlgEquiv_symm_apply_apply, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, ModuleCat.monoidalClosed_uncurry, QuaternionAlgebra.imIₗ_apply, IsReflective.smul_coroot, QuotSMulTop.equivTensorQuot_naturality, Module.Basis.mk_repr, Polynomial.roots_monomial, MvPowerSeries.coeff_X_pow, submoduleComap_apply_coe, compl₂_apply, MvPolynomial.support_monomial, CliffordAlgebraDualNumber.equiv_symm_eps, 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, SpecialLinearGroup.mem_center_iff_spec, Rep.diagonalHomEquiv_symm_apply, Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span, cross_cross, Polynomial.derivative_expand, Polynomial.derivative_sum, Polynomial.isCoveringMapOn_eval, IsBaseChange.of_fintype_basis_eq, MvPolynomial.mul_def, ExteriorAlgebra.ι_eq_zero_iff, Complex.reLm_coe, Polynomial.derivative_pow_succ, LieModuleHom.coe_mk, CondensedMod.isDiscrete_tfae, RootPairing.InvariantForm.pairing_mul_eq_pairing_mul_swap, sum_smul_minpolyDiv_eq_X_pow, Polynomial.derivative_ofNat, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, Submodule.quotDualCoannihilatorToDual_apply, LinearIndependent.of_isLocalizedModule_of_isRegular, Submodule.injective_inclusionSpan, Polynomial.monomial_one_one_eq_X, toAddMonoidHom_mulLeft, CategoryTheory.Linear.comp_apply, Coalgebra.coassoc_symm_apply, Matrix.cramer_row_self, Span.repr_def, mem_isPairSelfAdjointSubmodule, 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, prodMap_apply, Polynomial.derivative_smul, tensorEqLocusEquiv_apply, groupCohomology.coe_mapCocycles₁, domRestrict'_apply, PowerSeries.gaussNorm_monomial, groupHomology.mem_cycles₂_iff, MvPowerSeries.X_pow_eq, Polynomial.Splits.monomial, 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, lTensor_id_apply, BilinForm.toMatrix'_apply, ContinuousLinearMap.coe_restrictScalarsₗ, Polynomial.iterate_derivative_X_add_pow, Finsupp.sum_smul_index_linearMap', linearIndependent_iff_injective_finsuppLinearCombination, groupCohomology.d₁₂_hom_apply, Module.FaithfullyFlat.lTensor_exact_iff_exact, AdicCompletion.incl_apply, AdicCompletion.map_ext'_iff, AdicCompletion.ofTensorProduct_surjective_of_finite, MeasureTheory.Measure.comapₗ_eq_comap, RootPairing.Hom.root_weightMap_apply, PresheafOfModules.pushforward_map_app_apply, cross_self, eval_minpolyDiv_of_aeval_eq_zero, Module.Basis.mk_coord_apply_eq, Polynomial.derivative_X, Rep.to_Module_monoidAlgebra_map_aux, CliffordAlgebra.contractRight_mul_ι, groupCohomology.coboundariesToCocycles₁_apply, Polynomial.sumIDeriv_map, Module.FaithfullyFlat.lTensor_bijective_iff_bijective, rTensor_injective_iff_lcomp_surjective, MvPolynomial.smul_monomial, Algebra.Extension.h1Cotangentι_injective, TensorProduct.gradedMul_assoc, CliffordAlgebra.op_reverse, inl_injective, Lagrange.eval_interpolate_not_at_node, Polynomial.mirror_monomial, Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff, AnalyticOnNhd.eval_linearMap', FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, CliffordAlgebra.reverse_involute_commute, compPMap_apply, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same, 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, coe_toContinuousLinearMap', KaehlerDifferential.polynomialEquiv_D, Polynomial.ofFn_eq_sum_monomial, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, Module.Basis.coe_mkFinConsOfLE, Matrix.coe_mulVecLin, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Matrix.mulVecLin_apply, PowerSeries.coeff_ne_zero_C, IsLocalizedModule.iso_symm_apply, QuadraticMap.toBilinHom_apply, ExteriorAlgebra.liftAlternating_ι_mul, 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, Polynomial.abc, HahnSeries.embDomainLinearMap_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, Algebra.TensorProduct.piRightHom_mul, Module.le_rank_iff_exists_linearMap, HVertexOperator.coeff_isPWOsupport, Finsupp.linearCombination_zero_apply, QuadraticMap.associated_eq_self_apply, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, trace_mul_cycle, Submodule.map_span_le, BoundedContinuousFunction.toContinuousMapLinearMap_apply, Module.exists_smul_eq_zero_and_mk_eq, Submodule.val_mulMap'_tmul, Finset.weightedVSub_apply_const, fst_surjective, ContinuousAlternatingMap.toAlternatingMapLinear_apply, TestFunction.continuous_iff_continuous_comp, RootPairing.coroot'In_rootSpanMem_eq_pairingIn, ker_localizedMap_eq_localized'_ker, Polynomial.Splits.eval_root_derivative, ModuleCat.forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, TensorProduct.directSum_lof_tmul_lof, IsLocalizedModule.iso_apply_mk, KaehlerDifferential.kerToTensor_apply, RatFunc.laurent_div, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, Submodule.coe_subtypeL', Finsupp.mem_span_iff_linearCombination, star_dotProduct_toMatrix₂_mulVec, isStablyFiniteRing_iff_injective_of_surjective, 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, setBasisOfLinearIndependentOfCardEqFinrank_repr_apply, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, MvPowerSeries.monomial_mem_nonzeroDivisors, LocallyConstant.toContinuousMapLinearMap_apply, Algebra.Presentation.differentials.hom₁_single, Module.End.intCast_apply, Profinite.NobelingProof.Products.max_eq_eval, LocalizedModule.divBy_apply, TensorProduct.AlgebraTensorModule.lTensor_id, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, Algebra.Generators.exists_presentation_of_basis_cotangent, Bialgebra.counitBialgHom_apply, zero_prodMap_dualTensorHom, sum_repr_mul_repr_mulₛₗ, Polynomial.derivative_monomial, TensorProduct.AlgebraTensorModule.rTensor_one, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerₛₗ_apply_apply, groupCohomology.cocycles₂.d₂₃_apply, lTensor_surj_iff_rTensor_surj, liftBaseChange_one_tmul, groupCohomology.d₀₁_hom_apply, QuadraticMap.associated_rightInverse, Polynomial.aeval_sumIDeriv, Representation.ofMulAction_apply, DirectSum.lmap_apply, Rep.linearization_single, 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, MvPowerSeries.coeff_mul_right_one_sub_of_lt_weightedOrder, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, Polynomial.coeff_taylor_natDegree, groupHomology.d₃₂_single_one_thd, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, BilinForm.sum_right, rTensor_id_apply, Module.eval_apply_injective, IsSelfAdjoint.selfAdjointPart_apply, le_comap_range_lTensor, Matrix.diagLinearMap_apply, polar_singleton, Matrix.diagonalLinearMap_apply, 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, 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, groupCohomology.H0IsoOfIsTrivial_inv_apply, Polynomial.toFinsupp_monomial, mem_skewAdjointSubmodule, 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, Representation.apply_sub_id_partialSum_eq, Rep.finsuppToCoinvariantsTensorFree_single, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, Submodule.mem_dualAnnihilator, PolyEquivTensor.toFunAlgHom_apply_tmul, groupCohomology.eq_d₂₃_comp_inv_apply, PiTensorProduct.mul_assoc, PolynomialLaw.exists_lift', HahnSeries.SummableFamily.lsum_apply, groupCohomology.eq_d₁₂_comp_inv_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, Coalgebra.sum_counit_tmul_eq, Finset.weightedVSub_map, PresheafOfModules.restrictScalarsObj_map, PolynomialLaw.toFun_eq_rTensor_φ_toFun', QuadraticMap.linMulLin_apply, groupHomology.chains₁ToCoinvariantsKer_surjective, MeasureTheory.OuterMeasure.comap_iInf, IsContPerfPair.bijective_left, Algebra.trace_eq_of_algEquiv, Rep.coinvariantsTensorFreeLEquiv_symm_apply, CliffordAlgebra.contractRight_comm, submoduleMap_coe_apply, TrivSqZeroExt.map_inr, Matrix.coe_vecMulLinear, Module.End.mem_invtSubmodule_iff_mapsTo, CliffordAlgebra.EquivEven.reverse_e0, CStarMatrix.toCLM_injective, MvPolynomial.monomial_zero, Polynomial.monomial_mul_C, trace_eq_matrix_trace_of_finset, Polynomial.X_pow_eq_monomial, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, rTensor_comp_flip_mk, TensorProduct.dualDistrib_apply_comm, 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, map_sub₂, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, Matrix.sum_cramer, ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape, signedDist_linear_apply_apply, mem_vectorSpan_iff_eq_weightedVSub, Module.Basis.toDualEquiv_apply, Module.End.mapsTo_genEigenspace_of_comm, CliffordAlgebra.changeFormAux_changeFormAux, ModuleCat.forget_reflectsLimitsOfSize, Function.Exact.iff_of_ladder_linearEquiv, Fintype.bilinearCombination_apply_single, Matrix.derivative_det_one_add_X_smul, coe_inr, IsGroupLikeElem.antipode_antipode, coe_smul, Ideal.range_mul', PositiveLinearMap.coe_toLinearMap, CliffordAlgebra.ι_mul_ι_comm, PowerSeries.binomialSeries_coeff, RootPairing.root'_coroot_eq_pairing, dotProductEquiv_apply_apply, LinearPMap.adjointAux_unique, 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, SemimoduleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, TensorProduct.directLimitRight_tmul_of, sub_mem_ker_iff, Ideal.finsuppTotal_apply, ContinuousAlternatingMap.toAlternatingMap_curryLeft, TensorProduct.flip_mk_surjective, smul_apply, rTensor_tmul, Matrix.toEuclideanLin_apply, Polynomial.taylor_injective, ContinuousLinearMap.toLinearMap₁₂_apply, groupCohomology.mem_cocycles₁_def, Polynomial.iterate_derivative_mul_X, isAdjointPair_toLinearMap₂, HahnSeries.single.linearMap_apply, MvPowerSeries.monomial_mem_nonzeroDivisorsLeft, CliffordAlgebra.ι_sq_scalar, LieModule.Cohomology.d₂₃_apply, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, id_apply, BilinForm.sub_left, Algebra.intTrace_eq_of_isLocalization, PowerSeries.coeff_subst, Polynomial.sumIDeriv_eq_self_add, Submodule.span_range_inclusion_restrictScalars_eq_top, SemimoduleCat.forget_obj, restrictScalars_apply, Algebra.trace_algebraMap, Polynomial.self_sub_monomial_natDegree_leadingCoeff, AffineMap.map_vadd', QuadraticForm.tmul_tensorMap_apply, HahnEmbedding.Partial.truncLT_mem_range_extendFun, Polynomial.iterate_derivative_X, ModN.basis_apply_eq_mkQ, Module.Flat.out, ExteriorAlgebra.ιMulti_succ_apply, LieModule.Cohomology.d₁₂_apply_apply, Polynomial.eval₂_monomial, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, smulRight_apply, Module.AEval'.X_smul_of, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotent, PowerSeries.coeff_coe, LieModule.mem_posFittingCompOf, ofIsComplProd_apply, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, 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, Representation.Coinvariants.lift_mk, Matrix.toBilin_apply, ModuleCat.forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, Module.Relations.surjective_toQuotient, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MvPolynomial.monomial_eq_monomial_iff, Polynomial.derivative'_apply, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, Module.End.ringHomEndFinsupp_apply_apply, Profinite.NobelingProof.Products.eval_πs', Polynomial.mem_support_derivative, MvPowerSeries.coeff_X, ker_eq_bot, PowerSeries.eq_shift_mul_X_pow_add_trunc, Polynomial.monomial_pow, Representation.ofMulAction_single, 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, 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, ConvexCone.coe_map, Module.FaithfullyFlat.lTensor_surjective_iff_surjective, Rep.norm_comm_apply, BilinForm.coeFnAddMonoidHom_apply, CategoryTheory.Linear.leftComp_apply, toMatrixOrthonormal_apply_apply, IsLocalizedModule.map_linearMap_of_isLocalization, 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, exact_subtype_mkQ, Representation.ofDistribMulAction_apply_apply, Algebra.Extension.Cotangent.val_mk, Representation.coinvariantsFinsuppLEquiv_apply, ModuleCat.HasColimit.colimitCocone_ι_app, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, id_coe, Submodule.linearDisjoint_iff, toMatrixAlgEquiv_apply, 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, BilinForm.apply_dualBasis_left, ContinuousLinearMapWOT.inducingFn_apply, DFinsupp.injective_pi_lapply, CStarMatrix.inner_toCLM_conjTranspose_left, Module.exists_finite_presentation, 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, add_apply, range_toAddSubmonoid, QuadraticModuleCat.forget₂_map, applyₗ'_apply_apply, Submodule.mem_map, Matrix.toLinearMap₂'_apply', PresheafOfModules.Derivation.postcomp_d_apply, RootPairing.exists_ge_zero_eq_rootForm, exteriorPower.ιMultiDual_apply_diag, Module.DualBases.eval_of_ne, MvPolynomial.expand_monomial, ModuleCat.forget₂_addCommGroup_full, sumOfConjugatesEquivariant_apply, Polynomial.X_pow_smul_rTensor_monomial, Finset.weightedVSubOfPoint_vadd, PiToModule.fromEnd_injective, isCompactOperator_iff_isCompact_closure_image_ball, 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, Polynomial.smul_monomial, NNRealRMK.lintegral_rieszMeasure, groupHomology.d₁₀_comp_coinvariantsMk_apply, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, Orientation.kahler_eq_zero_iff, eq_adjoint_iff_basis_left, BilinForm.isNonneg_def, MvPowerSeries.hasSum_aeval, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, 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, QuadraticMap.associated_prod, Pretrivialization.coe_linearMapAt, 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, toMatrix_transpose, Representation.leftRegular_norm_eq_zero_iff, MeasureTheory.VectorMeasure.restrictₗ_apply, ModuleCat.biprodIsoProd_inv_comp_snd_apply, 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, extendTo𝕜'_apply, LieIdeal.mem_killingCompl, Orientation.areaForm_swap, ContinuousLinearMap.holderₗ_apply_apply, HopfAlgebra.sum_mul_antipode_eq_smul, Algebra.Extension.subsingleton_h1Cotangent, ext_inner_map, trace_smulRight, convOne_apply, AdicCompletion.factor_eval_eq_evalₐ, Module.Relations.Solution.fromQuotient_toQuotient, AddMonoidAlgebra.counit_single, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, isIdempotentElem_map_one_iff, Algebra.Generators.exists_presentation_of_free_cotangent, MvPolynomial.X_mul_pderiv_monomial, QuadraticAlgebra.imₗ_apply, HahnEmbedding.Seed.strictMono_coeff, 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, Lagrange.interpolate_eq_sum, Algebra.Extension.CotangentSpace.map_tmul, Submodule.quotientQuotientEquivQuotientAux_mk, Orientation.kahler_swap, Matrix.toLinearMap₂'Aux_single, groupCohomology.H2π_comp_map_apply, Matrix.vecMulBilin_apply, MvPowerSeries.LinearTopology.mem_basis_iff, Coalgebra.comm_comul, Module.Relations.Solution.IsPresentation.linearEquiv_apply, MvPowerSeries.subst_monomial, IsSymmetric.inner_map_self_eq_zero, mk₂'ₛₗ_apply, cross_anticomm, OrthonormalBasis.prod_apply, RingEquiv.moduleEndSelf_symm_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, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, IsAdicComplete.of_liftRingHom, Algebra.discr_powerBasis_eq_norm, BilinForm.sum_left, 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, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, Finset.weightedVSubOfPoint_filter_of_ne, orzechProperty_iff, ModuleCat.uliftFunctorForgetIso_hom_app, MvPowerSeries.coeff_of_lt_order, RootPairing.toLinearMap_apply_apply_Polarization, Polynomial.map_monomial, rieszContentAux_image_nonempty, isGroupLikeElem_iff, PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sq, ModuleCat.smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, TensorProduct.equivFinsuppOfBasisLeft_symm, isClosedEmbedding_of_injective, flip_surjective_iff₁, tensorEqLocus_coe, TensorAlgebra.toExterior_ι, AlternatingMap.alternatizeUncurryFin_apply, span_preimage_le, Submodule.mem_comap, dfinsuppSum_apply, IsPositive.inner_nonneg_left, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, Matrix.toLinearMap₂'_apply, Profinite.NobelingProof.GoodProducts.smaller_factorization, matPolyEquiv_coeff_apply_aux_1, funLeft_surjective_of_injective, mem_submoduleImage_of_le, Submodule.mulLeftMap_apply, lTensorHomEquivHomLTensor_apply, TensorProduct.finsuppScalarRight_apply, Algebra.FormallySmooth.iff_injective_lTensor_residueField, AdicCompletion.sumInv_apply, Polynomial.derivative_X_sub_C_sq, MvPolynomial.homogeneousComponent_isHomogeneous, Module.Relations.Solution.ofQuotient_var, trace_mul_comm, Orientation.kahler_comp_rightAngleRotation, toKerLocalized_isLocalizedModule, FiniteField.algebraMap_trace_eq_sum_pow, ModuleCat.CoextendScalars.smul_apply, CliffordAlgebra.changeFormAux_apply_apply, Submodule.isOpenQuotientMap_mkQ, Submodule.factor_eq_factor, DirectSum.coeLinearMap_of, AdicCompletion.sum_lof, LinearEquiv.arrowCongr_symm_apply, Representation.single_smul, Polynomial.smeval.linearMap_apply, trace_eq_sum_inner, Polynomial.eval_derivative_of_splits, MvPolynomial.sum_homogeneousComponent, DirectSum.coeLinearMap_eq_dfinsuppSum, Module.FinitePresentation.linearEquivMap_symm_apply, exists_basis_of_pairing_ne_zero, RootPairing.polarizationIn_Injective, Algebra.IsEpi.injective_lift_mul, restrictScalarsₗ_apply, exists_antilipschitzWith, divRadical_dvd_derivative, ModuleCat.exteriorPower.desc_mk, MvPolynomial.coe_monomial, trace_one, PresheafOfModules.unit_map_one, 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, LieModule.mem_genWeightSpace, 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, 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, Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero, IsLocalFrameOn.coeff_congr, Profinite.NobelingProof.πs'_apply_apply, MeasureTheory.OuterMeasure.map_comap_le, Polynomial.ofFinsupp_single, MvPowerSeries.ext_iff, BilinForm.IsSymm.eq, AffineMap.linear_injective_iff, hasStrictDerivAt, AddMonoidAlgebra.lsingle_apply, CategoryTheory.preadditiveYoneda_obj, SemimoduleCat.forget₂_obj_moduleCat_of, TensorProduct.mapOfCompatibleSMul_surjective, Polynomial.le_trailingDegree_monomial, Polynomial.iterate_derivative_derivative_mul_X_sq, MvPolynomial.single_eq_monomial, 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, CompactlySupportedContinuousMap.coe_toRealLinearMap, SeparatingDual.dualMap_surjective_iff, InnerProductGeometry.norm_toLp_symm_crossProduct, dualTensorHom_apply, FunOnFinite.continuous_linearMap, IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Module.Invertible.rTensorEquiv_apply_apply, Rep.coindVEquiv_symm_apply_coe, localized'_range_eq_range_localizedMap, exists_extension_of_le_sublinear, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, MeasureTheory.OuterMeasure.map_le_restrict_range, trace_comp_eq_mul_of_commute_of_isNilpotent, PowerSeries.trunc_trunc_mul_trunc, PowerSeries.coeff_invOfUnit, LinearAlgebra.FreeProduct.ι_apply, Finsupp.lcoeFun_apply, Module.Finite.exists_nat_not_surjective, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, 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, AdicCompletion.map_comp_apply, CondensedMod.isDiscrete_iff_isDiscrete_forget, PowerSeries.trunc_mul_C, CliffordAlgebra.changeForm_ι_mul, PresheafOfModules.map_smul, LieModule.traceForm_lieSubalgebra_mk_right, Matrix.cramer_apply, FGModuleCat.FGModuleCatEvaluation_apply, ModuleCat.epi_iff_surjective, Module.Basis.forall_coord_eq_zero_iff, localized'_ker_eq_ker_localizedMap, Module.Relations.Solution.postcomp_var, mk₂_apply, iterateFrobenius_def, RootPairing.PolarizationIn_eq, RootPairing.RootPositiveForm.exists_eq, toLinearMap_toContPerfPair, TensorProduct.AlgebraTensorModule.rTensor_comp, PresheafOfModules.Monoidal.tensorObj_map_tmul, 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, Representation.isProj_averageMap, ModuleCat.exteriorPower.map_mk, AffineMap.decomp', IsBaseChange.transvection, MvPowerSeries.le_lexOrder_iff, 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, Module.End.isUnit_inv_apply_apply_of_isUnit, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, SameRay.map, Finset.weightedVSubOfPoint_sdiff, DFinsupp.sum_mapRange_index.linearMap, InnerProductSpace.trace_rankOne, MonomialOrder.span_leadingTerm_eq_span_monomial, Ideal.pi_mkQ_surjective, rTensorHomEquivHomRTensor_apply, trace_eq_contract_apply, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, ExteriorAlgebra.liftAlternatingEquiv_apply, RCLike.imLm_coe, dualTensorHomEquivOfBasis_symm_cancel_right, toPMap_apply, MonomialOrder.span_leadingTerm_eq_span_monomial₀, groupCohomology.d₁₂_apply_mem_cocycles₂, IsModuleTopology.continuous_of_linearMapₛₗ, Module.Invertible.embAlgebra_injective, ModuleCat.hom_inv_apply, Polynomial.mkDerivation_one_eq_derivative', spinGroup.units_involute_act_eq_conjAct, IsAdicComplete.of_lift, Polynomial.derivative_X_add_C, IsLocalization.tensorProduct_isLocalizedModule, Submodule.coe_linearProjOfIsCompl_apply, Submodule.inclusion_apply, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, RootPairing.rootForm_root_self, MvPowerSeries.monomial_mem_nonzeroDivisorsRight, ModuleCat.monoidalClosed_curry, Polynomial.hermite_succ, groupCohomology.d₀₁_apply_mem_cocycles₁, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, proj_apply, IsBaseChange.det_endHom, polyCharpolyAux_map_eval, AlternatingMap.curryLeft_apply_apply, IsLocalizedModule.mapExtendScalars_apply_apply, stdSimplex.map_coe, MvPolynomial.C_mul_X_eq_monomial, Module.End.algebraMap_isUnit_inv_apply_eq_iff', ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, PowerSeries.coeff_derivativeFun, KaehlerDifferential.linearMapEquivDerivation_apply_apply, Submodule.surjective_tensorToSpan, PolyEquivTensor.toFunLinear_mul_tmul_mul, Representation.Coinvariants.mk_self_apply, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, Polynomial.hermite_eq_iterate, AffineMap.continuous_iff, Rep.indToCoindAux_fst_mul_inv, MvPowerSeries.coeff_index_single_self_X, QuadraticMap.comp_apply, MvPowerSeries.WithPiTopology.as_tsum, MeasureTheory.OuterMeasure.isometry_comap_mkMetric, inCoordinates_apply_eq₂, Module.Basis.end_apply_apply, KaehlerDifferential.tensorKaehlerEquivBase_tmul, 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, ModuleCat.restrictScalarsId'App_hom_apply, groupCohomology.subtype_comp_d₀₁_apply, Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNil, MvPolynomial.monomialOneHom_apply, Module.Basis.coe_sumCoords_of_fintype, coprod_apply, realPart.norm_le, SheafOfModules.pushforwardComp_inv_app_val_app, Submodule.span_range_inclusion_eq_top, cross_anticomm', spinGroup.conjAct_smul_ι_mem_range_ι, TensorProduct.instDirectedSystemCoeLinearMapIdRTensor, Submodule.image_span_subset_span, LeftInvariantDerivation.evalAt_coe, ModuleCat.FilteredColimits.forget_preservesFilteredColimits, Polynomial.iterate_derivative_natCast_mul, groupCohomology.H2π_eq_iff, DirectSum.sigmaLcurry_apply, toBilin'Aux_toMatrixAux, IsSimpleModule.toSpanSingleton_surjective, MvPolynomial.coeff_homogeneousComponent, adjoint_inner_right, TensorAlgebra.equivFreeAlgebra_ι_apply, BilinForm.dotProduct_toMatrix_mulVec, BilinForm.tensorDistrib_tmul, AdjoinRoot.mk_leftInverse, CliffordAlgebra.coe_toEven_reverse_involute, Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, TensorProduct.AlgebraTensorModule.mk_apply, trace_transpose', Polynomial.natTrailingDegree_monomial, MvPowerSeries.WithPiTopology.uniformContinuous_coeff, ContinuousAffineMap.coe_linear_eq_coe_contLinear, comp_apply, IsTensorProduct.equiv_symm_apply, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, Projectivization.cross_mk_of_cross_ne_zero, 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, Module.End.HasEigenvector.apply_eq_smul, inner_map_polarization', mul'_apply, map_neg, RootPairing.InvariantForm.exists_apply_eq_or, Rep.coinvariantsTensorFreeLEquiv_apply, SchwartzMap.pairing_apply, MvPolynomial.monomial_left_inj, Finsupp.leftInverse_lcomapDomain_mapDomain, Module.Dual.transpose_apply, Polynomial.map_taylor, 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, 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, Module.End.isNilpotent_iff_of_finite, TensorAlgebra.lift_ι_apply, Matrix.singleLinearMap_apply, MeasureTheory.OuterMeasure.restrict_univ, Module.Basis.repr_eq_iff, PowerSeries.eval₂_eq_tsum, MvPolynomial.C_mul_monomial, neg_apply, Algebra.normalizedTrace_intermediateField, BilinForm.smul_right_of_tower, BilinForm.tensorDistribEquiv_apply, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Representation.ofQuotient_coe_apply, Algebra.Generators.H1Cotangent.exact_map_δ, Matrix.piLp_ofLp_toEuclideanLin, Algebra.Generators.H1Cotangent.δAux_monomial, coe_fst, BilinForm.toMatrix_apply, 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, dualProd_apply_apply, AnalyticOnNhd.eval_linearMap, PresheafOfModules.mono_iff_surjective, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, PowerSeries.trunc_X_of, map_zero, TensorProduct.dualDistribEquivOfBasis_symm_apply, AlgHom.toLinearMap_apply, SemimoduleCat.MonoidalCategory.tensorLift_tmul, toFun_eq_coe, IsLocalizedModule.linearEquiv_apply, Polynomial.derivative_X_pow_succ, isSymm_def, Matrix.toPerfectPairing_apply_apply, CliffordAlgebra.EquivEven.neg_e0_mul_v, Representation.mem_invariants, quotientInfEquivSupQuotient_apply_mk, KaehlerDifferential.kerTotal_mkQ_single_add, FunOnFinite.linearMap_apply_apply, ProbabilityTheory.gaussianReal_map_linearMap, realPart_add_I_smul_imaginaryPart, Rep.indToCoindAux_comm, MeasureTheory.Measure.map_def, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, Module.DirectLimit.congr_symm_apply_of, LieDerivation.exp_map_apply, subset_tangentConeAt_prod_left, LinearEquiv.funCongrLeft_apply, Submodule.localized'_span, compr₂_apply, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, LieSubalgebra.coe_ad_pow, MvPolynomial.bind₂_monomial_one, Derivation.leibniz', Polynomial.degree_monomial_le, Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd, liftBaseChangeEquiv_symm_apply, QuadraticForm.dualProd_apply, Fintype.bilinearCombination_apply, Polynomial.coeff_monomial_of_ne, Algebra.TensorProduct.equivFinsuppOfBasis_apply, CompactlySupportedContinuousMap.toRealLinearMap_apply, compQuadraticMap_polar, Polynomial.derivative_X_sub_C_pow, exteriorPower.map_apply_ιMulti_family, Lagrange.degree_interpolate_erase_lt, LinearEquiv.conj_exact_iff_exact, Algebra.isNilpotent_trace_of_isNilpotent, lsmul_flip_apply, groupHomology.cyclesIso₀_comp_H0π_apply, Algebra.TensorProduct.opAlgEquiv_apply, ContinuousAffineMap.coe_mk_const_linear_eq_linear, Bialgebra.counit_surjective, isLocalizedModule_iff, deriv, 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, Module.Basis.dualBasis_apply_self, Submodule.apply_coe_mem_map, PowerSeries.order_monomial, Coalgebra.sum_counit_smul, isClosed_range_coe, TensorProduct.lift.tmul', Module.DirectLimit.of_f, PointedCone.mem_dual, Submodule.mem_iSup_iff_exists_dfinsupp, 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, BilinForm.add_left, toSpanSingleton_apply_one, PointwiseConvergenceCLM.isInducing_inducingFn, KaehlerDifferential.tensorKaehlerEquiv_tmul, DomMulAct.coe_smul_linearMap, TensorProduct.inner_mapIncl_mapIncl, RootPairing.toLinearMap_apply_PolarizationIn, Algebra.Generators.H1Cotangent.δAux_toAlgHom, 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, extendTo𝕜_apply, 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, BilinForm.smul_left, Finsupp.lift_apply, Module.End.pow_apply, LinearIndependent.linearCombinationEquiv_apply_coe, Polynomial.exists_iterate_derivative_eq_factorial_smul, innerₗ_apply, Finset.weightedVSub_smul, TensorAlgebra.toClifford_ι, RootPairing.GeckConstruction.trace_toEnd_eq_zero, Polynomial.monomial_injective, Polynomial.taylor_eq_zero, MonoidAlgebra.lsingle_apply, TensorProduct.gradedComm_tmul_of_zero, LieModule.Cohomology.twoCochain_skew, Module.Relations.Solution.directSum_var, LocallyConstant.evalₗ_apply, BilinForm.dotProduct_toMatrix_mulVec, Lagrange.degree_interpolate_lt, ModuleCat.inv_hom_apply, Module.End.rTensorAlgHom_apply_apply, LieModule.traceForm_comm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, Algebra.linearMap_apply, ModuleCat.forget₂AddCommGroup_preservesLimits, ExteriorAlgebra.liftAlternating_apply_ιMulti, ContinuousLinearMap.coe_smulRightₗ, Module.Flat.iff_lTensor_exact, PolynomialLaw.exists_lift, MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict, QuadraticAlgebra.reₗ_apply, LaurentSeries.derivative_apply, groupHomology.mapCycles₁_id_comp_apply, ker_toAddSubmonoid, vecCons_apply, RatFunc.laurentAux_div, Matrix.ofLp_toLpLin, traceForm_dualSubmodule_adjoin, DirectSum.lof_eq_of, polyEquivTensor_symm_apply_tmul, RootPairing.coroot'_apply_apply_mem_of_mem_span, IsSymmetric.continuous, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, Ideal.quotientToQuotientRangePowQuotSucc_mk, MvPowerSeries.weightedHomogeneousComponent_of_lt_weightedOrder_eq_zero, StarModule.decomposeProdAdjoint_symm_apply, Module.Basis.dualBasis_equivFun, PresheafOfModules.presheaf_map_apply_coe, charpoly_eq_X_pow_iff, 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, MeasureTheory.OuterMeasure.comap_top, IsAdjoinRootMonic.modByMonicHom_map, RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs, VertexOperator.ncoeff_apply, Module.Dual.transpose_comp, Polynomial.derivativeFinsupp_apply_apply, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, Module.Basis.prod_apply, RootPairing.corootForm_apply_apply, flip_bijective_iff₁, Polynomial.taylor_apply, Submodule.comap_coe, flip_bijective_iff₂, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, Algebra.Extension.Cotangent.mk_eq_zero_iff, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, BilinForm.mem_dualSubmodule, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Polynomial.iterate_derivative_comp_one_sub_X, mapMatrixModule_apply, Algebra.Presentation.differentials.surjective_hom₁, DirectSum.lmap_eq_map, LinearPMap.apply_comp_inclusion, DFinsupp.filterLinearMap_apply, DirectSum.coe_congr_linearEquiv, LieSubmodule.toEnd_comp_subtype_mem, Representation.norm_ofMulDistribMulAction_eq, Matrix.kroneckerMapBilinear_apply_apply, LaurentSeries.powerSeriesPart_coeff, PowerBasis.trace_gen_eq_nextCoeff_minpoly, Ideal.pi_tensorProductMk_quotient_surjective, 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, TensorProduct.nnnorm_map, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_ne, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, CliffordAlgebra.EvenHom.contract, Polynomial.derivative_natCast_mul, AlgHom.mulLeftRight_apply, 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, coe_proj, CliffordAlgebra.map_apply_ι, LieSubmodule.mem_baseChange_iff, Module.End.aeval_apply_of_hasEigenvector, QuadraticMap.associated_tmul, Submodule.FG.lTensor.directLimit_apply', TensorProduct.directSumLeft_tmul_lof, Algebra.Generators.H1Cotangent.exact_δ_map, PowerSeries.coeff_invUnitsSub, SemimoduleCat.hom_inv_apply, SkewPolynomial.monomial_zero_one, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Derivation.liftKaehlerDifferential_comp, Matrix.toLin_self, Rep.coindToInd_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, 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, fwdDiff_aux.shiftₗ_pow_apply, Finsupp.lsum_single, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, MvPolynomial.dvd_monomial_iff_exists, AlgCat.forget₂Module_preservesLimitsOfSize, BilinForm.neg_left, ModuleCat.comp_apply, AlgHom.toKerIsLocalization_apply, BilinForm.sum_repr_mul_repr_mul, Orientation.kahler_neg_orientation, PowerSeries.prod_monomial, ModuleCat.restrictScalarsCongr_hom_app, AdicCompletion.coe_eval, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, KaehlerDifferential.mapBaseChange_surjective, PowerSeries.coeff_succ_C, Polynomial.sum_monomial_eq, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, TannakaDuality.FiniteGroup.leftRegular_apply, ContinuousMap.coeFnLinearMap_apply, LeftInvariantDerivation.left_invariant'', groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CliffordAlgebra.contractLeft_contractLeft, pi_apply, TensorProduct.algebraMap_gradedMul, trace_eq_finrank_mul_minpoly_nextCoeff, PowerSeries.trunc_trunc_mul, lcomp_apply, Matrix.GeneralLinearGroup.toLin'_apply, mapMatrixModule_id_apply, Representation.apply_bijective, CategoryTheory.whiskering_linearYoneda, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, MvPolynomial.mkDerivationₗ_monomial, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, toMatrixAlgEquiv'_apply, LieAlgebra.ad_pow_lie, Submodule.FG.rTensor.directLimit_apply, IntrinsicStar.isSelfAdjoint_iff_map_star, TensorProduct.directLimitLeft_rTensor_of, IsSymmetric.toSelfAdjoint_apply, MeasureTheory.Lp.constₗ_apply, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, BilinForm.IsAlt.self_eq_zero, Polynomial.degree_derivative_eq, Polynomial.C_mul_monomial, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, 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, continuous_of_isContPerfPair, ConvexCone.mem_map, Bialgebra.comul_algebraMap, ext_iff, Matrix.cramer_reindex, Submodule.inclusionSpan_apply_coe, Module.End.coe_pow, groupHomology.coe_mapCycles₂, TensorProduct.counit_tmul, PiToModule.fromMatrix_apply_single_one, LocalizedModule.coe_map_eq, Representation.linHom_apply, MvPolynomial.sum_weightedHomogeneousComponent, QuadraticMap.associated_toQuadraticMap, MvPowerSeries.HasSubst.coeff_zero, dualMap_injective_iff, CategoryTheory.whiskering_linearCoyoneda₂, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, MeasureTheory.OuterMeasure.map_map, AlternatingMap.curryLeft_apply_toMultilinearMap, Polynomial.as_sum_range, SkewPolynomial.monomial_zero_right, MeasureTheory.SignedMeasure.re_toComplexMeasure, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, 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, isAdjointPair_one, CliffordAlgebra.comp_ι_sq_scalar, RootPairing.posRootForm_posForm_pos_of_ne_zero, inr_injective, FGModuleCat.FGModuleCatCoevaluation_apply_one, Module.Basis.coe_sumCoords_eq_finsum, map_dfinsuppSumAddHom, Derivation.compAlgebraMapL_apply_apply, IsLocalizedModule.map_linearCombination, BilinMap.baseChange_tmul, Module.Flat.eqLocus_lTensor_eq, Subspace.dualRestrict_leftInverse, StrongDual.dualPairing_apply, semilinearMapClass, HopfAlgebra.sum_antipode_mul_eq_smul, LinearEquiv.piRing_symm_apply, Module.DirectLimit.congr_apply_of, MeasureTheory.OuterMeasure.restrict_empty, trace_eq_trace_adjoin, CliffordAlgebra.even.lift_ι, toMatrix_mulVec_repr, BilinForm.zero_left, Submodule.IsCompl.projection_eq_self_iff, 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, 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, extendTo𝕜'_apply_re, IsLocalizedModule.mapEquiv_apply, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, Coalgebra.sum_counit_tmul_map_eq, Ideal.exact_mulQuot_quotOfMul, MvPolynomial.decompose'_apply, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable, transvection.apply, PowerSeries.IsRestricted.isRestricted_iff, BilinForm.toDual_def, CliffordAlgebra.contractRight_mul_algebraMap, MeasureTheory.OuterMeasure.map_ofFunction, Matrix.PosSemidef.toLinearMap₂'_zero_iff, groupHomology.π_comp_H0Iso_hom_apply, 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, BilinForm.dualBasis_repr_apply, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, MultilinearMap.map_add_sub_map_add_sub_linearDeriv, MvPowerSeries.coeff_one, smul_lTensor, Polynomial.iterate_derivative_X_pow_eq_natCast_mul, lsmul_injective, ModuleCat.MonoidalCategory.tensorLift_tmul, Profinite.NobelingProof.Products.eval_πs_image', Module.IsReflexive.bijective_dual_eval', AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, Polynomial.natDegree_taylor, Unitization.sndHom_apply, Polynomial.degree_taylor, 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, 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, Rep.freeLiftLEquiv_apply, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors, Module.End.ringEquivEndFinsupp_apply_apply_apply, TensorProduct.rTensor_injective_of_forall_vanishesTrivially, PowerSeries.coeff_mk, MvPolynomial.coe_basisMonomials, Polynomial.hasFDerivAt, MultilinearMap.curryMid_apply_apply, PresheafOfModules.surjective_of_epi, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, Polynomial.aeval_apply_smul_mem_of_le_comap, RingHom.toKerIsLocalization_apply, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, PowerSeries.sub_const_eq_X_mul_shift, coe_range, SemimoduleCat.MonoidalCategory.tensorμ_apply, Derivation.coe_comp, ModuleCat.adj_homEquiv, toMatrix'_apply, 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, Rep.indToCoindAux_mul_fst, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, flip_apply, mulLeft_apply, TensorProduct.finsuppLeft_apply, ext_ring_iff, MvPolynomial.irreducible_sumSMulX, 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, PiTensorProduct.dualDistribInvOfBasis_apply, kerComplementEquivRange_apply_coe, CStarAlgebra.linear_combination_nonneg, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, 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, 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, Module.End.isUnit_iff, LinearMapClass.ker_eq_bot, CondensedMod.hom_naturality_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, star_mul_self_add_self_mul_star, GradedTensorProduct.auxEquiv_mul, Fintype.linearIndependent_iff'ₛ, HahnSeries.ofPowerSeries_apply_coeff, MvPowerSeries.eval₂_eq_tsum, Submodule.lTensorOne'_tmul, RootPairing.CoPolarizationIn_eq, Module.FinitePresentation.linearEquivMap_apply, 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, BilinMap.isSymm_iff_eq_flip, Submodule.rTensorOne'_tmul_one, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, llcomp_apply', imaginaryPart.norm_le, AffineBasis.det_smul_coords_eq_cramer_coords, LinearIndependent.map', ModuleCat.Derivation.desc_d, BilinForm.zero_apply, Prod.comul_apply, reesAlgebra.monomial_mem, 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, linearIndependent_iff, QuotSMulTop.equivQuotTensor_naturality, AddMonoidHom.coe_toNatLinearMap, smulRightₗ_apply, Submodule.rTensorOne'_tmul, PowerSeries.derivativeFun_coe, JacobsonNoether.exist_pow_eq_zero_of_le, CliffordAlgebra.reverse.map_mul, IsLocalizedModule.mapEquiv_symm_apply, MvPowerSeries.le_weightedOrder_subst, ModuleCat.free_ε_one, Polynomial.coeff_monomial, Module.Invertible.rTensor_injective_iff, injective_of_comp_eq_id, AdicCompletion.of_bijective_iff, groupCohomology.norm_ofAlgebraAutOnUnits_eq, Algebra.lsmul_injective, MvPowerSeries.monomial_zero_eq_C_apply, RootPairing.algebraMap_rootFormIn, KaehlerDifferential.derivationQuotKerTotal_apply, InnerProductGeometry.norm_ofLp_crossProduct, TensorProduct.AlgebraTensorModule.uncurry_apply, TensorProduct.map_comm, Module.DirectLimit.exists_of, coe_sum, Pretrivialization.linearMapAt_apply, 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, polyCharpolyAux_map_eq_charpoly, Submodule.LinearDisjoint.injective, DirectSum.lmap_surjective, Submodule.baseChange_eq_span, CliffordAlgebra.isUnit_ι_iff, mem_submoduleImage, Submodule.dualCopairing_apply, Module.dualPairing_apply, Polynomial.mul_eq_sum_sum, PowerSeries.monomial_pow, Polynomial.mkDerivationEquiv_apply, Derivation.liftKaehlerDifferential_comp_D, polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, CStarMatrix.toCLM_apply_eq_sum, TensorProduct.AlgebraTensorModule.coe_lTensor, exact_smul_id_smul_top_mkQ, Coalgebra.rTensor_counit_comp_comul, toMatrix_transpose_apply, 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, PowerSeries.trunc_trunc_of_le, PolynomialModule.comp_apply, LinearEquiv.arrowCongr_apply, 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, 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, prodMapLinear_apply, LinearIndependent.span_repr_eq, MeasureTheory.OuterMeasure.map_iSup, Submodule.map₂_span_singleton_eq_map_flip, pi_apply_eq_sum_univ, RootPairing.rootForm_self_eq_zero_iff, linearIndependent_iff_of_disjoint, ModularFormClass.qExpansion_coeff, Submodule.prodEquivOfIsCompl_symm_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, PiTensorProduct.piTensorHomMap_tprod_eq_map, Module.End.coe_mul, Rep.ofDistribMulAction_ρ_apply_apply, LinearEquiv.skewProd_symm_apply, Submodule.injective_tensorToSpan, MvPolynomial.as_sum, dualMap_apply', Matrix.liftLinear_apply, Rep.linearization_η_hom_apply, 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, ext_iff₂, CliffordAlgebra.EquivEven.neg_v_mul_e0, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, coe_prod, dualMap_bijective_iff, TensorPower.multilinearMapToDual_apply_tprod, HVertexOperator.of_coeff_coeff, PiTensorProduct.map₂_tprod_tprod, skewAdjoint.negISMul_apply_coe, Polynomial.toFn_zero, IsLocalizedModule.mk'_one, Module.Basis.sum_dual_apply_smul_coord, compMultilinearMapₗ_apply, Polynomial.ofFn_zero', Matrix.mul_adjugate_apply, Polynomial.derivative_C_mul_X, IsLocalFrameOn.eventually_eq_sum_coeff_smul, LinearEquiv.conjRingEquiv_apply_apply, 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, Trivialization.coe_linearMapAt, coe_toAffineMap, Unitization.inrHom_apply, LinearAlgebra.FreeProduct.identify_one, Matrix.toLin_finTwoProd_apply, Submodule.mapQ_eq_factor, ModuleCat.forget_reflectsLimits, CliffordAlgebra.reverse_prod_map_ι, MeasureTheory.OuterMeasure.restrict_iSup, ModuleCat.uliftFunctorForgetIso_inv_app, PowerSeries.coeff_exp, HVertexOperator.coeff_inj_iff, BilinForm.dualBasis_eq_iff, Finsupp.linearCombination_apply, PointedCone.mem_map, FreeAlgebra.toTensor_ι, Polynomial.iterate_derivative_eq_zero, FourierTransform.fourierₗ_apply, AffineMap.map_vadd, uncurryMid_apply, RootPairing.polarizationEquiv_apply, Polynomial.hasseDeriv_coeff, Matrix.toBilin'Aux_single, IsLocalizedModule.map_mk', exteriorPower.pairingDual_ιMulti_ιMulti, Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors, Polynomial.monomial_zero_one, Polynomial.hasseDeriv_mul, ExteriorAlgebra.map_apply_ι, PointwiseConvergenceCLM.coeLMₛₗ_apply, 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, mem_range_self, MvPolynomial.monomial_eq_zero, coe_dfinsuppSum, AlgEquiv.toLinearMapHom_apply_apply, lsmul_eq_DistribMulAction_toLinearMap, groupHomology.H1AddEquivOfIsTrivial_single, Module.eval_apply_eq_zero_iff, MvPolynomial.eval_monomial, LaurentSeries.hasseDeriv_comp_coeff, MvPolynomial.coeff_coe, coeFn_sum, AdicCompletion.map_mk, groupCohomology.mem_cocycles₁_iff, imaginaryPart_realPart, Ideal.quotientToQuotientRangePowQuotSucc_surjective, IsModuleTopology.continuous_bilinear_of_finite_left, MvPolynomial.coeff_monomial_mul', Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, PresheafOfModules.unitHomEquiv_apply_coe, Algebra.Generators.cotangentCompAwaySec_apply, LieModule.trace_comp_toEnd_genWeightSpace_eq, MvPolynomial.monomial_mem_coeffsIn, IsProj.top, 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, 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, Orientation.areaForm_comp_linearIsometryEquiv, Matrix.traceLinearMap_apply, FractionalIdeal.mem_dual, Finset.weightedVSub_const_smul, MvPowerSeries.coeff_zero_mul_X, groupHomology.isoCycles₂_hom_comp_i_apply, coe_compMultilinearMap, Algebra.trace_self_apply, adjoint_toSpanSingleton, Module.End.lie_apply, lcomp_apply', CliffordAlgebra.ofBaseChange_tmul_ι, Representation.Coinvariants.map_mk, 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, injective_iff_surjective, Submodule.quotientPi_apply, CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero, Polynomial.linearIndependent_powers_iff_aeval, Polynomial.Chebyshev.derivative_U_eval_one, BilinForm.sub_apply, IsLocalizedModule.rTensor, toSpanSingleton_apply, SheafOfModules.pushforwardCongr_inv_app_val_app, killingForm_apply_apply, imaginaryPart_eq_neg_I_smul_skewAdjointPart, trace_id, Algebra.trace_trace, AdicCompletion.ofAlgEquiv_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, PowerBasis.constr_pow_gen, Polynomial.monomial_one_eq_iff, LaurentPolynomial.leval_apply, StandardEtalePresentation.toSubmersivePresentation_jacobian, LieSubalgebra.mem_engel_iff, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, IsBaseChange.equiv_symm_apply, Function.Exact.inr_fst, MvPowerSeries.coeff_weightedHomogeneousComponent, RootPairing.InvariantForm.apply_weylGroup_smul, Convex.linear_image, Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic, Subspace.quotAnnihilatorEquiv_apply, conjugate_apply, PowerSeries.HasSubst.monomial', Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, CStarMatrix.toCLM_apply, Polynomial.coeff_monomial_zero_mul, Submodule.coe_mulMap_comp_eq, Bialgebra.counit_natCast, TensorProduct.AlgebraTensorModule.curry_apply, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, Algebra.TensorProduct.mul_one, IsAdjoinRootMonic.ext_elem_iff, Lagrange.iterate_derivative_interpolate, Polynomial.taylorAlgHom_apply, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, Polynomial.pow_sub_dvd_iterate_derivative_pow, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, Matrix.toLinearMapₛₗ₂'_apply, Polynomial.hasFDerivAt_aeval, PolynomialModule.eval_lsingle, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply, IsLocalizedModule.map_apply, sectionOfRetractionKerToTensorAux_prop, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, ModuleCat.free_η_freeMk, Module.Flat.iff_lTensor_injective, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, pi_ext_iff, range_eq_top, IsSymmetricAlgebra.equiv_symm_apply, LieModule.Cohomology.mem_twoCocycle_iff, CliffordAlgebra.ofBaseChangeAux_ι, Ideal.ker_tensorProductMk_quotient, MvPowerSeries.coeff_apply, Finset.affineCombination_apply, IsSymmetric.eigenvectorBasis_apply_self_apply, Bialgebra.comul_mul, Derivation.liftKaehlerDifferential_unique_iff, PowerSeries.constantCoeff_divXPowOrder, AffineMap.linear_surjective_iff, LocallyConstant.comapₗ_apply_apply, TensorProduct.AlgebraTensorModule.mapBilinear_apply, BilinMap.toQuadraticMapLinearMap_apply, SemimoduleCat.MonoidalCategory.braiding_hom_apply, Matrix.toLinAlgEquiv'_apply, groupHomology.inhomogeneousChains.d_single, PowerSeries.monomial_eq_mk, Polynomial.natDegree_derivative_le, TensorProduct.piRightHom_tmul, lTensor_comm, RootPairing.rootForm_apply_apply, Module.Basis.dualBasis_apply, 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, BialgHom.coe_toLinearMap, Subrepresentation.apply_mem_toSubmodule, Finsupp.linearCombination_single, realPart_I_smul, Module.Presentation.CokernelData.π_lift, TwoSidedIdeal.subtype_injective, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, RootPairing.Equiv.bijective_weightMap, hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, SemimoduleCat.MonoidalCategory.braiding_inv_apply, QuadraticForm.tensorDistrib_tmul, selfAdjoint.realPart_unitarySelfAddISMul, IsLocalizedModule.linearEquiv_symm_apply, ExteriorAlgebra.ι_add_mul_swap, equivProdOfSurjectiveOfIsCompl_apply, MvPolynomial.rename_monomial, Representation.coind'_apply_apply, eq_adjoint_iff, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, GradedTensorProduct.mulHom_apply, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, Polynomial.wronskianBilin_apply, Module.DirectLimit.linearEquiv_symm_mk, Orthonormal.inner_right_finsupp, MultilinearMap.fromDirectSumEquiv_lof, TensorProduct.directSumRight_tmul_lof, 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, norm_extendTo𝕜'_apply_sq, WithSeminorms.equicontinuous_TFAE, Module.Invertible.rTensor_bijective_iff, eqOn_span_iff, MultilinearMap.domCoprod'_apply, Submodule.linearMap_eq_iff_of_span_eq_top, TrivSqZeroExt.inrHom_apply, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, map_rTensor, PowerSeries.trunc_C, Algebra.PreSubmersivePresentation.aevalDifferential_single, cross_apply, MvPolynomial.isWeightedHomogeneous_monomial, isPositive_iff_complex, IsBaseChange.toDual_comp_apply, IsBaseChange.linearMapLeftRightHom_toMatrix, Polynomial.sumIDeriv_apply, RootPairing.PolarizationIn_apply, Submodule.injective_subtype, BilinForm.toMatrixAux_apply, Polynomial.sylvesterDeriv_updateRow, Submodule.linearProjOfIsCompl_isCompl_projection, MeasureTheory.OuterMeasure.comap_mono, mem_ker, Module.Flat.iff_rTensor_exact', MeasureTheory.Measure.addHaar_image_linearMap, liftQ₂_mk, IsLocalFrameOn.coeff_apply_of_notMem, BilinForm.isAdjointPair_iff_eq_of_nondegenerate, Polynomial.dvd_derivative_iff, Polynomial.coeff_mul_monomial_zero, coe_domRestrict, Submodule.localized'_eq_span, AdicCompletion.of_surjective, PiTensorProduct.dualDistrib_apply, DFinsupp.lsum_single, CliffordAlgebraQuaternion.ofQuaternion_mk, Algebra.Generators.Cotangent.exact, Matrix.toLinOfInv_symm_apply, toMatrix_smulRight, ModularFormClass.qExpansion_coeff_zero, ContinuousLinearMap.range_coeFn_eq, Polynomial.resultant_taylor, 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, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl, MvPowerSeries.coeff_truncFun', lsmul_apply, Submodule.coe_subtypeₗᵢ, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, Submodule.IsCompl.projection_add_projection_eq_self, 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, rTensor_baseChange, Representation.asModuleEquiv_symm_map_rho, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, isPairSelfAdjoint_equiv, 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, congr_fun₂, groupHomology.π_comp_H1Iso_hom_apply, TensorPower.toTensorAlgebra_gMul, TensorProduct.directSumLeft_symm_lof_tmul, isIdempotentElem_apply_one_iff, Representation.ofModule_asModule_act, vecCons₂_apply, Finsupp.lsum_apply, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, 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, BilinForm.toLin'Flip_apply, reduceModIdeal_apply, Finset.weightedVSubOfPoint_smul, charpoly_constantCoeff_eq_zero_iff, groupCohomology.map_id_comp_H0Iso_hom_apply, PolynomialModule.equivPolynomial_single, MvPolynomial.homogeneousComponent_apply, ModuleCat.forget_obj, convexOn, Polynomial.toFn_comp_ofFn_eq_id, MultilinearMap.dfinsuppFamilyₗ_apply, AffineMap.derivWithin, Rep.standardComplex.d_of, Module.Flat.tensorProduct_mapIncl_injective_of_left, SemimoduleCat.id_apply, Submodule.Quotient.equiv_symm_apply, QuadraticMap.half_moduleEnd_apply_eq_half_smul, coe_snd, Polynomial.supNorm_monomial, Polynomial.derivative_comp, MvPowerSeries.coeff_C_mul, MvPolynomial.divMonomial_mul_monomial, IsGroupLikeElem.antipode, LieModule.toEnd_lie, Finsupp.linearCombination_unique, PresheafOfModules.toPresheaf_map_app_apply, CliffordAlgebra.reverse.commutes, map_mul_iff, PowerSeries.X_eq, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, Finsupp.coe_lsum, toSpanSingleton_homothety, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, CStarMatrix.mul_entry_mul_eq_inner_toCLM, MvPolynomial.weightedHomogeneousComponent_finsupp, LaurentSeries.hasseDeriv_coeff, Polynomial.gaussNorm_monomial, ExteriorAlgebra.toTrivSqZeroExt_ι, AddMonoidHom.coe_toRatLinearMap, 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, sumOfConjugates_apply, ModuleCat.HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, Polynomial.taylor_taylor, MeasureTheory.OuterMeasure.le_comap_map, RootPairing.Equiv.bijective_coweightMap, DirectSum.component.lof_self, 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, Submodule.coe_torsionBySet, Submodule.mem_dualCoannihilator, fwdDiff_aux.fwdDiffₗ_apply, 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, ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier, MvPolynomial.constantCoeff_monomial, RootPairing.coroot_root_two, CliffordAlgebra.reverse_mem_evenOdd_iff, LieModule.Cohomology.add_apply_apply, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, slope_comp, MultilinearMap.map_add_eq_map_add_linearDeriv_add, CliffordAlgebra.evenToNeg_ι, ModuleCat.ExtendScalars.map_tmul, fwdDiff_aux.shiftₗ_apply, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, diffToIdealOfQuotientCompEq_apply, 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, map_mul_algebraMap, MvPolynomial.divMonomial_monomial, 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, prodMapAlgHom_apply_apply, IntermediateField.AdjoinSimple.trace_gen_eq_zero, ModuleCat.free_μ_freeMk_tmul_freeMk, ModuleCat.forget₂_obj_moduleCat_of, Module.DualBases.eval_same, 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, IsNonneg.nonneg, Orientation.inner_mul_areaForm_sub', Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, RootPairing.CoPolarization_apply, Module.End.one_apply, compLeft_apply, AdicCompletion.sum_of, Submodule.equivSubtypeMap_apply, AlternatingMap.curryLeftLinearMap_apply, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, IsLocalRing.split_injective_iff_lTensor_residueField_injective, Algebra.Extension.Hom.mapKer_apply_coe, Module.preReflection_apply, continuous_of_nonzero_on_open, LieAlgebra.ad_apply, Polynomial.hasseDeriv_monomial, LieAlgebra.toEnd_pow_apply_mem, PowerSeries.trunc_trunc_pow, PolynomialLaw.isCompat, PowerSeries.coeff_mul, Profinite.NobelingProof.πs_apply_apply, Module.Invertible.leftInverse_iff_rightInverse, Module.DualBases.dual_lc, apply_single, Algebra.Extension.contangentEquiv_tmul, 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, BilinForm.ext_iff, Finsupp.llift_symm_apply, IsLocalizedModule.map_id, Orientation.kahler_rotation_left', quotKerEquivRange_apply_mk, Polynomial.monomial_add, Algebra.Generators.cMulXSubOneCotangent_eq, CliffordAlgebraComplex.toComplex_ι, AdicCompletion.AdicCauchySequence.map_apply_coe, RootPairing.RootPositiveForm.two_mul_apply_root_root, MvPolynomial.isHomogeneous_monomial, Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd, Ideal.toCotangent_apply, Module.End.mem_iInf_maxGenEigenspace_iff, Polynomial.hasDerivWithinAt_aeval, groupHomology.isoCycles₁_hom_comp_i_apply, coe_rTensorHom, isLinearMap_of_compatibleSMul, HahnSeries.coeff_toPowerSeries, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, Module.Basis.det_comp, DirectSum.single_eq_lof, 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, ModuleCat.instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, Bialgebra.counit_mul, Orientation.abs_areaForm_le, LinearEquiv.symmEquiv_apply_apply, Matrix.toBilin'_apply, Pretrivialization.symmₗ_apply, 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, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, flip_injective_iff₂, MvPowerSeries.coeff_add_mul_monomial, Matrix.adjugate_def, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, RestrictScalars.lsmul_apply_apply, compQuadraticMap_apply, Matrix.toLin_apply, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero, groupCohomology.H1π_eq_zero_iff, groupHomology.H1AddEquivOfIsTrivial_symm_apply, Polynomial.iterate_derivative_eq_zero_of_degree_lt, AdicCompletion.mk_surjective, MvPowerSeries.monomial_pow, Orientation.normSq_kahler, Ideal.toCotangent_eq_zero, Module.Basis.constr_apply_fintype, DFinsupp.coprodMap_apply_single, IsSymmetric.invariant_orthogonalComplement_eigenspace, TensorProduct.LieModule.lift_apply, Matrix.cramer_submatrix_equiv, MvPolynomial.decomposition.decompose'_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, finsupp_sum_apply, Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity, PowerSeries.coeff_monomial_same, Submodule.mulRightMap_apply, LinearEquiv.conjAlgEquiv_apply_apply, MultilinearMap.piFamilyₗ_apply, TensorProduct.isBaseChange, Rep.coind'_ext_iff, Polynomial.iterate_derivative_prod_X_sub_C, MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous, mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, concaveOn, Submodule.map₂_le, LaurentPolynomial.comul_C, LaurentSeries.hasseDeriv_single_add, Submodule.isOpenMap_mkQ, MeasureTheory.Measure.mapₗ_apply_of_measurable, Derivation.coeFn_coe, PiTensorProduct.mul_def, RootPairing.rootForm_self_sum_of_squares, finsuppLEquivDirectSum_single, map_zero₂, Polynomial.opRingEquiv_symm_monomial, Polynomial.toAddCircle_monomial_eq_smul_fourier, 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, 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, Derivation.map_one_eq_zero', Finsupp.lapply_apply, SheafOfModules.Presentation.mapRelations_mapGenerators, MvPowerSeries.coeff_zero_X_mul, AdicCompletion.congr_symm_apply, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, TensorProduct.AlgebraTensorModule.lTensor_comp, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, map_span, 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, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Submodule.coe_torsionBy, MvPolynomial.homogeneousComponent_eq_zero, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, Polynomial.coe_basisMonomials, MvPowerSeries.map_monomial, PowerSeries.trunc_apply, Ideal.quotientToQuotientRangePowQuotSucc_injective, Seminorm.cont_withSeminorms_normedSpace, groupCohomology.cocyclesMk₁_eq, instInvertibleReprₛ, AlgCat.forget₂_module_obj, sectionOfRetractionKerToTensor_algebraMap, NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subset, 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, ModuleCat.instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, BilinForm.flip_apply, SheafOfModules.relationsOfIsCokernelFree_I, PiTensorProduct.map_tprod, MonomialOrder.sPolynomial_monomial_mul, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, IsGroupLikeElem.antipode_mul_cancel, Finsupp.coe_lmapDomain, Module.Basis.sumCoords_self_apply, VertexOperator.ext_iff, Algebra.trace_localization, Finset.weightedVSub_vadd, ModuleCat.MonoidalCategory.tensorμ_apply, isNilpotent_trace_of_isNilpotent, BilinForm.compRight_apply, SymmetricAlgebra.equivMvPolynomial_ι_apply, Module.algebraMap_end_apply, AddCommGroup.DirectLimit.directedSystem, Module.FinitePresentation.linearEquivMapExtendScalars_apply, Polynomial.isNilpotent_monomial_iff, IsLocalizedModule.iso_symm_apply_aux, Polynomial.as_sum_range', ContinuousLinearMap.sub_apply', IsBaseChange.endHom_apply, LinearIndependent.fintypeLinearCombination_injective, AdicCompletion.AdicCauchySequence.map_comp_apply, StrongDual.norm_toLpₗ_le, MvPolynomial.homogeneousComponent_zero, PowerSeries.coeff_monomial, Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem, mul''_apply, Polynomial.natDegree_monomial, selfAdjoint.realPart_coe, Module.Invertible.rTensorInv_injective, TensorProduct.AlgebraTensorModule.lTensor_mul, 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, Module.End.mem_eigenspace_iff, Algebra.TensorProduct.one_mul, IsAdjoinRootMonic.map_modByMonicHom, MeasureTheory.Measure.map_toOuterMeasure, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, Function.Exact.iff_linearMap_rangeRestrict, Module.Flat.iff_rTensor_exact, mem_polar_singleton, MvPolynomial.monomial_sum_index, IsSymm.eq, SemimoduleCat.MonoidalCategory.associator_inv_apply, Polynomial.separable_def, CliffordAlgebra.contractLeft_ι, 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, HVertexOperator.ext_iff, 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, liftBaseChange_tmul, Polynomial.sumIDeriv_X, groupHomology.d₂₁_apply_mem_cycles₁, Algebra.trace_algebraMap_of_basis, AdicCompletion.of_ofLinearEquiv_symm, AdicCompletion.kerProj_of, LieModule.traceForm_lieSubalgebra_mk_left, LieModule.Cohomology.smul_apply_apply, Polynomial.contentIdeal_monomial, groupCohomology.coboundariesToCocycles₂_apply, linearIndependent_iff_injective_fintypeLinearCombination, HahnSeries.coeff_toPowerSeries_symm, Polynomial.injective_ofFn, TensorAlgebra.ι_leftInverse, ModuleCat.ihom_map_apply, Submodule.quotDualCoannihilatorToDual_injective, Module.Basis.eval_injective, PowerSeries.IsWeierstrassDivisorAt.coeff_div, PolyEquivTensor.toFunBilinear_apply_apply, Submodule.quotientPi_symm_apply, BilinForm.add_right, 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, UniversalEnvelopingAlgebra.ι_apply, Polynomial.coeff_iterate_derivative, fst_apply, LieHom.coe_toLinearMap, LaurentSeries.hasseDeriv_comp, Finsupp.apply_linearCombination, StrongDual.toLpₗ_of_not_memLp, PiTensorProduct.mapL_apply, Submodule.liftQ_apply, Module.Relations.Solution.IsPresentation.surjective_π, disjoint_ker_iff_injOn, Matrix.cramer_subsingleton_apply, MvPolynomial.support_monomial_subset, Subspace.dualRestrict_surjective, MvPolynomial.monomial_mul, LieModule.toEnd_pow_lie, 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, DirectedSystem.rTensor, AdicCompletion.evalOneₐ_of, Representation.norm_ofDistribMulAction_eq, Module.End.HasUnifEigenvector.apply_eq_smul, 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, lift_lsmul_mul_eq_lsmul_lift_lsmul, LocalizedModule.lift_mk, PowerSeries.as_tsum, CliffordAlgebra.invOf_ι, lTensor_bij_iff_rTensor_bij, Orientation.kahler_rightAngleRotation_left, Rep.leftRegularHom_hom_single, isCompactOperator_iff_isCompact_closure_image_closedBall, Module.Basis.end_repr_symm_apply, MvPowerSeries.expand_monomial, TensorAlgebra.GradedAlgebra.ι_apply, GeneralLinearGroup.coe_ofLinearEquiv, LieSubmodule.coe_toEnd, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, continuous_of_finiteDimensional, Module.evalEquiv_apply, Orientation.kahler_comp_linearIsometryEquiv, DistribMulActionHom.coe_toLinearMap, IsReflective.dvd_two_mul, CliffordAlgebra.contractRight_contractRight, equivariantProjection_apply, LieAlgebra.InvariantForm.mem_orthogonal, Coalgebra.Repr.convMul_apply, MvPolynomial.rTensor_symm_apply_single, PowerSeries.derivative_coe, LieModule.toEnd_apply_apply, MeasureTheory.ComplexMeasure.im_apply, 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, 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', lTensor_comp_apply, Representation.IntertwiningMap.isIntertwining', Module.Flat.iff_forall_exists_factorization, skewAdjointPart_apply_coe, CliffordAlgebra.involute_ι, image_convexHull, Orientation.abs_areaForm_of_orthogonal, exteriorPower.alternatingMapToDual_apply_ιMulti, Module.Basis.mk_coord_apply, continuous_selfAdjointPart, Polynomial.lsum_apply, exact_of_comp_eq_zero_of_ker_le_range, exact_zero_iff_injective, CoalgHom.coe_toLinearMap, BilinForm.tensorDistribEquiv_tmul, innerₗ_apply_apply, Algebra.trace_surjective, HahnSeries.ofPowerSeriesAlg_apply_coeff, Module.Dual.lie_apply, coe_inl, trace_tensorProduct', Algebra.Generators.toComp_toAlgHom_monomial, MonoidAlgebra.GroupSMul.linearMap_apply, polar_eq_biInter_preimage, eq_adjoint_iff_basis, Module.Finite.exists_comp_eq_id_of_projective, 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, hfdifferential_apply, 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, setBasisOfTopLeSpanOfCardEqFinrank_repr_apply, polyCharpolyAux_coeff_eval, Module.Invertible.lTensor_injective_iff, weightedVSub_mem_vectorSpan, coe_comp, LocalizedModule.mul_by_divBy, EuclideanGeometry.inner_weightedVSub, Orientation.kahler_rotation_left, exact_map_mkQ_range, LindemannWeierstrass.integral_exp_mul_eval, LinearEquiv.symmEquiv_symm_apply_apply, Derivation.tensorProductTo_mul, ModularFormClass.hasSum_qExpansion_of_abs_lt, PowerSeries.coeff_map, contractLeft_apply, Algebra.Extension.Cotangent.mk_surjective, Polynomial.valuation_monomial_eq_valuation_X_pow, BilinMap.tensorDistrib_tmul, Projectivization.cross_mk, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, Polynomial.eval_sumIDeriv_of_pos, 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, inner_map_self_eq_zero, coe_single, LinearAlgebra.FreeProduct.rel_id, Matrix.toLinAlgEquiv_apply, Orientation.inner_sq_add_areaForm_sq, TensorProduct.range_map_eq_span_tmul, mapMatrix_apply, LieModule.exists_nontrivial_weightSpace_of_isSolvable, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, MonomialOrder.div_set, RCLike.reLm_coe, MvPowerSeries.coeff_rescale, Submodule.exists_injOn_mkQ_image_span_eq_of_span_eq_map_mkQ_of_le_jacobson_bot, DFinsupp.lmk_apply, SchwartzMap.convolution_continuous_left, Submodule.IsCompl.projection_apply, TensorProduct.equivFinsuppOfBasisRight_apply, mulLinearMap_apply_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff, CliffordAlgebra.changeForm_contractLeft, GroupLike.val_inv, IsLocalization.map_eq_toLinearMap_mapₐ, MvPowerSeries.WithPiTopology.hasSum_of_monomials_self, triple_product_eq_det, LinearEquiv.dualMap_apply, AdicCompletion.factor_eval_liftRingHom, QuadraticMap.coe_associatedHom, mem_selfAdjointSubmodule, groupHomology.isoCycles₂_inv_comp_iCycles_apply, LinearIndependent.inl_union_inr, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, extendScalarsOfSurjective_apply, ModuleCat.mkOfSMul_smul, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, TensorProduct.directSum_symm_lof_tmul, Module.bijective_dual_eval, 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, AlgebraicGeometry.StructureSheaf.comapₗ_const, PowerSeries.coeff_prod, jacobson_density, Module.FaithfullyFlat.tensorProduct_mk_injective, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, Finset.weightedVSub_congr, hahnEmbedding_isOrderedModule_rat, Polynomial.iterate_derivative_C_mul, Continuous.matrix_cramer, MonoidAlgebra.comul_single, PowerSeries.coeff_mul_X_pow', GeneralLinearGroup.coe_toLinearEquiv, SchwartzMap.pairing_continuous_left, PolyEquivTensor.invFun_monomial, LieAlgebra.SpecialLinear.val_single, 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, vecEmpty_apply, MeasureTheory.OuterMeasure.restrict_biInf, CliffordAlgebra.forall_mul_self_eq_iff, mem_range, IsSymmetric.apply_eigenvectorBasis, groupHomology.cyclesMk₂_eq, AffineMap.decomp, RootPairing.coroot_root_eq_pairing, compl₁₂_apply, leftInverse_apply_of_inj, AdicCompletion.ofTensorProduct_tmul, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, KaehlerDifferential.kerTotal_mkQ_single_smul, MultilinearMap.uncurryRight_apply, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension, MvPolynomial.rTensor_apply_monomial_tmul, Polynomial.iterate_derivative_mul_X_pow, Matrix.mulVecBilin_apply, PowerSeries.coeff_zero_C, Algebra.Generators.repr_CotangentSpaceMap, DirectSum.toModule_lof, Module.Basis.dualBasis_repr, groupHomology.H1π_eq_zero_iff, Algebra.normalizedTrace_minpoly, IsAdjoinRootMonic.modByMonicHom_root_pow, PiTensorProduct.mul_one, CategoryTheory.Abelian.Ext.bilinearCompOfLinear_apply_apply, MvPowerSeries.eq_zero_iff_forall_coeff_zero, compQuadraticMap'_apply, 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, map_smul₂, groupHomology.d₂₁_single_one_fst, RootPairing.root'_apply_apply_mem_of_mem_span, PowerSeries.forall_coeff_eq_zero, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, Polynomial.fderivWithin_aeval, NNRealRMK.le_rieszMeasure_of_tsupport_subset, dualTensorHom_prodMap_zero, MvPowerSeries.coeff_truncFun, PolyEquivTensor.toFunLinear_one_tmul_one, Polynomial.fderivWithin, IsContPerfPair.bijective_right, PowerSeries.coeff_C, IsLocalFrameOn.eq_iff_coeff, HahnSeries.coeff_toMvPowerSeries_symm, Polynomial.monomial_neg, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Polynomial.hasDerivAt, Module.Basis.linearCombination_repr, MvPolynomial.mkDerivationₗ_C, LocalizedModule.map_id, MvPowerSeries.isWeightedHomogeneous_weightedHomogeneousComponent, Seminorm.ball_comp, TensorProduct.AlgebraTensorModule.rTensor_mul, Polynomial.monomial_zero_right, trace_eq_matrix_trace, RootPairing.polarizationEquiv_symm_apply_coroot, BilinForm.toMatrix_apply, PolynomialModule.lsingle_apply, Algebra.SubmersivePresentation.cotangentComplexAux_surjective, continuous_on_pi, Representation.self_inv_apply, RingHom.toSemilinearMap_apply, Polynomial.iterate_derivative_sub, Matrix.toBilin'_apply', Module.Basis.linearCombination_coord, BilinForm.IsSymm.polarization, Polynomial.signVariations_monomial, 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, Algebra.TensorProduct.mul_assoc, adjoint_inner_left, LocallyConstant.mapₗ_apply_apply, Submodule.mulMap'_surjective, Polynomial.monomial_mul_X_pow, Module.Basis.toDual_apply, ContinuousAffineMap.coe_contLinear, PowerSeries.coeff_inv, MvPowerSeries.coeff_expand_of_not_dvd, aeval_derivative_mem_differentIdeal, MeasureTheory.Measure.addHaar_preimage_linearMap, 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, QuadraticMap.associated_linMulLin, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, Polynomial.derivative_X_pow, Representation.isTrivial_apply, AffineMap.linear_bijective_iff, Rep.ihom_map_hom, rTensor_map, map_coe_ker, QuadraticForm.associated_isSymm, Polynomial.sumIDeriv_derivative, Module.apply_evalEquiv_symm_apply, MvPowerSeries.coeff_monomial, coe_addHom_mk, MvPowerSeries.X_dvd_iff, TensorAlgebra.tprod_apply, Polynomial.X_mul_monomial, Orientation.kahler_mul, MvPowerSeries.coeff_C, IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, Lagrange.interpolate_eq_add_interpolate_erase, trace_conj', Module.Invertible.rTensor_surjective_iff, ModuleCat.piIsoPi_hom_ker_subtype_apply, StandardEtalePair.HasMap.isUnit_derivative_f, TwoSidedIdeal.coe_subtype, ModularFormClass.qExpansion_coeff_eq_circleIntegral, ModuleCat.reflectsColimitsOfShape, Representation.IsIntertwiningMap.isIntertwining, groupHomology.H1AddEquivOfIsTrivial_apply, ModuleCat.MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Module.Relations.toQuotient_map_apply, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, snd_prodOfFinsuppNat, CliffordAlgebra.reverseEquiv_symm_apply, 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, Module.Projective.exists_dual_eq_one, IsCoprime.wronskian_eq_zero_iff, IsTensorProduct.lift_eq, LinearIndependent.of_isLocalizedModule, ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, Algebra.trace_complex_apply, MvPowerSeries.homogeneousComponent_mul_of_le_order, AlgEquiv.moduleEndSelf_apply_apply, exteriorPower.map_injective, mulRight_apply, toMatrix_innerSL_apply, Finset.weightedVSub_eq_linear_combination, isAssociatedPrime_iff_exists_injective_linearMap, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, MvPolynomial.support_sum_monomial_coeff, Module.Relations.Solution.π_relation, QuadraticMap.exists_companion', PolynomialModule.eval_apply, exteriorPower.basis_repr_apply, triple_product_permutation, Polynomial.leval_apply, CoalgCat.forget₂_map, AlternatingMap.ofSubsingleton_symm_apply_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, 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, isProj_range_iff_isIdempotentElem, Finsupp.linearCombination_equivMapDomain, map_smul, Rep.leftRegularHomEquiv_symm_single, Lagrange.interpolate_apply, MultilinearMap.ofSubsingleton_symm_apply_apply, exists_lt_rieszContentAux_add_pos, Polynomial.valuation_aeval_monomial_eq_valuation_pow, Algebra.normalizedTrace_algebraMap_apply, Submodule.piQuotientLift_single, 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, RootPairing.coreflection_apply, DirectSum.sigmaLuncurry_apply, Module.Basis.coe_toDual_self, RootPairing.RootPositiveForm.exists_pos_eq, Matrix.trace_toLin_eq, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T, TensorProduct.AlgebraTensorModule.lift_apply, groupCohomology.cocyclesMk₂_eq, Finset.weightedVSub_vadd_affineCombination, TensorProduct.comul_tmul, lcompₛₗ_apply, Polynomial.hasDerivAt_aeval, DirectSum.lof_apply, polyCharpoly_map_eq_charpoly, Ideal.pi_mkQ_rTensor, MvPolynomial.coeffsIn_eq_span_monomial, IsBaseChange.basis_apply, Polynomial.aeval_root_derivative_of_splits, Orthonormal.inner_finsupp_eq_zero, 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, 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, BilinForm.isSymm_def, Matrix.toLinOfInv_apply, Polynomial.taylor_eval_sub, TensorProduct.lcurry_apply, TrivSqZeroExt.snd_map, TensorProduct.curry_apply, Polynomial.derivative_prod_finset, 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, transvection.det, Module.Invertible.rTensorEquiv_symm_apply_apply, CliffordAlgebra.changeForm_algebraMap, LaurentPolynomial.counit_C_mul_T, IsIdempotentElem.isProj_range, Module.Flat.iff_lift_lsmul_comp_subtype_injective, PiTensorProduct.liftIsometry_apply_apply, image_parallelepiped, Differential.deriv_aeval_eq, ContinuousLinearMap.coeLMₛₗ_apply, CliffordAlgebra.foldr'Aux_apply_apply, 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, AlgEquiv.moduleEndSelfOp_symm_apply, Polynomial.coeff_list_sum, groupHomology.cyclesMk₁_eq, Module.End.mem_invtSubmodule_iff_forall_mem_of_mem, 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, TensorProduct.lift.equiv_symm_apply, MvPowerSeries.coeff_invOfUnit, SemimoduleCat.inv_hom_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, LightCondensed.ihom_map_val_app, MvPowerSeries.coeff_map, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, LieDerivation.leibniz', coe_withLpMap, map_add₂, PowerSeries.monomial_eq_C_mul_X_pow, trace_quotient_eq_trace_localization_quotient, StandardEtalePair.cond, toContinuousLinearMap₁_apply, AlternatingMap.curryLeft_compAlternatingMap, congr_arg, Submodule.mem_traceDual, Seminorm.coe_comp, map_smulₛₗ, domRestrict₂_apply, map_lTensor, MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc', RootPairing.flip_toFun_apply, IsIdempotentElem.mem_range_iff, Algebra.normalizedTrace_trans_apply, TensorProduct.enorm_map, coe_toAddHom, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, Orientation.areaForm_map, IsGroupLikeElem.counit_eq_one, Polynomial.derivative_sub, ModuleCat.FreeMonoidal.μIso_inv_freeMk, derivWithin, Bialgebra.counit_algebraMap, TensorProduct.mapOfCompatibleSMul_tmul, coe_prodMap, PiTensorProduct.norm_eval_le_projectiveSeminorm, isCompactOperator_iff_image_ball_subset_compact, Module.End.mem_genEigenspace_one, 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, map_neg₂, update_apply, CliffordAlgebra.reverseOp_ι, surjective, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, LinearEquiv.conjRingEquiv_symm_apply_apply, 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, TensorProduct.map_map_assoc, QuadraticMap.apply_linearCombination', InnerProductSpace.toLinearMap_rankOne, KaehlerDifferential.tensorProductTo_surjective, MvPolynomial.totalDegree_monomial_le, SemimoduleCat.forget_map, PowerSeries.coeff_divXPowOrder, Module.End.mapsTo_maxGenEigenspace_of_comm, groupHomology.mapCycles₂_id_comp_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, PowerSeries.trunc_one, CliffordAlgebra.ι_mul_ι_comm_of_isOrtho, 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, ContDiffMapSupportedIn.structureMapLM_zero_injective, surjective_or_eq_zero, ContinuousLinearMapWOT.continuous_inducingFn, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, PowerSeries.ext_iff, BilinForm.coe_injective, RootPairing.algebraMap_coroot'In_apply, Algebra.Extension.cotangentComplex_injective_iff, AdicCompletion.transitionMap_ideal_mk, BilinForm.smul_right, AffineMap.continuous_linear_iff, DirectSum.coeFnLinearMap_apply, PowerSeries.coeff_X_pow_self, Representation.ofModule_asAlgebraHom_apply_apply, PowerSeries.trunc_succ, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, rTensor_exact_iff_lTensor_exact, MvPowerSeries.coeff_smul, MvPolynomial.weightedHomogeneousComponent_C_mul, realPart_imaginaryPart, TensorProduct.gradedMul_algebraMap, QuaternionAlgebra.imJₗ_apply, IsAdjoinRootMonic.coeff_one, Polynomial.monomial_one_right_eq_X_pow, Derivation.compAEval_eq, ContDiffMapSupportedIn.seminorm_postcompLM_le, AlgEquiv.toLinearMap_apply, stdSimplex.image_linearMap, ModuleCat.localizedModuleMap_hom_apply, Derivation.tensorProductTo_tmul, Module.End.mem_maxGenEigenspace, Rep.hom_comm_apply, Polynomial.hasseDeriv_apply_one, Finsupp.lift_symm_apply, AdicCompletion.transitionMap_map_mul, SheafOfModules.pushforwardNatTrans_app_val_app, Polynomial.aeval_endomorphism, MvPowerSeries.coeff_zero_X, Orientation.inner_rightAngleRotationAux₁_right, ringLmapEquivSelf_apply, Module.Flat.iff_rTensor_preserves_injective_linearMapₛ, groupHomology.H2π_comp_map_apply, LieModule.traceForm_genWeightSpace_eq, TensorProduct.homTensorHomMap_apply, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, 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, toMatrix₂_apply, ModuleCat.Hom.hom₂_apply, AdicCompletion.sumEquivOfFintype_apply, sectionOfRetractionKerToTensorAux_algebraMap, RootPairing.rootFormIn_self_smul_coroot, IsSymmetric.trace_eq_sum_eigenvalues, ModuleCat.HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, LocallyConvexSpace.induced, Submodule.tensorToSpan_apply_tmul, ModuleCat.forget₂_addCommGrp_additive, intrinsicStar_apply, RootPairing.Equiv.weightEquiv_symm_weightMap, PolynomialModule.comp_eval, 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, RootPairing.coroot'_reflection, toContPerfPair_apply, MonomialOrder.sPolynomial_monomial_mul', LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, IsPositive.inner_nonneg_right, Matrix.toEuclideanLin_apply_piLp_toLp, HahnSeries.coeff_toMvPowerSeries, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, dualMap_apply, ker_le_iff, LieModule.Cohomology.twoCochain_val_apply, Lagrange.interpolate_empty, LinearIsometry.norm_map', isSelfAdjoint_iff_map_star, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, TensorAlgebra.ι_inj, bernsteinPolynomial.derivative_succ, dualMap_surjective_iff, Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd, Algebra.SubmersivePresentation.aevalDifferentialEquiv_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, skewAdjointPart_eq_I_smul_imaginaryPart, MultilinearMap.piLinearMap_apply_apply_apply, HahnSeries.coeff.linearMap_apply, TensorProduct.toLinearMap_symm_lid, TensorAlgebra.ι_eq_zero_iff, rTensor_comp_apply, MvPolynomial.C_mul_X_pow_eq_monomial, Finsupp.linearCombination_option, SMulMemClass.subtype_injective, mulLeftRight_apply, Polynomial.iterate_derivative_X_sub_pow_self, QuadraticMap.associated_sq, Polynomial.derivativeFinsupp_one, dualMap_def, iSupIndep_iff_dfinsupp_lsum_injective, MvPowerSeries.order_monomial, ExteriorAlgebra.map_apply_ιMulti, QuadraticMap.associated_comp, MvPolynomial.weightedHomogeneousComponent_mem, TensorProduct.tmul_of_gradedMul_of_tmul, Dual.apply_one_mul_eq, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, SchwartzMap.convolution_flip, QuadraticMap.associated_isOrtho, Lagrange.eq_interpolate_of_eval_eq, Submodule.lTensorOne'_one_tmul, mem_graph_iff, CliffordAlgebra.contractLeft_mul_algebraMap, coe_quotientInfToSupQuotient, map_dualTensorHom, isSymmetric_iff_sesqForm, Polynomial.taylor_zero, Subspace.dualLift_injective, Algebra.Generators.cotangentRestrict_mk, IsLocalizedModule.lift_apply, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc, GradedAlgebra.proj_apply, smulRightₗ_apply_apply, Representation.toCoinvariants_mk, Module.DualBases.finite, MvPolynomial.optionEquivLeft_monomial, IsAdjoinRootMonic.modByMonicHom_root, GroupLike.val_inv_toUnits_apply, Bialgebra.comul_pow, Submodule.IsCompl.projection_eq_self_sub_projection, IsRefl.eq_iff, Algebra.Generators.cotangentRestrict_bijective_of_basis_kaehlerDifferential, TensorProduct.AlgebraTensorModule.lTensor_one, eqLocus_eq_ker_sub, CliffordAlgebra.toProd_one_tmul_ι, AlgEquiv.moduleEndSelf_symm_apply, vecEmpty₂_apply, MvPowerSeries.substAlgHom_monomial, Polynomial.derivative_neg, groupCohomology.π_comp_H2Iso_hom_apply, Orientation.areaForm_map_complex, RootPairing.InvariantForm.apply_root_root_zero_iff, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, ModuleCat.HasLimit.lift_hom_apply, Polynomial.deriv, Coalgebra.counitCoalgHom_apply, BilinForm.apply_toDual_symm_apply, IsSymmetric.orthogonalComplement_iSup_eigenspaces_invariant, qExpansion_mul_coeff_zero, CliffordAlgebra.even.lift.aux_apply, CliffordAlgebra.toBaseChange_involute, IsProj.bot, Module.Basis.linearMap_repr_symm_apply, MeasureTheory.Measure.mapₗ_eq_zero_iff, funLeft_apply, CliffordAlgebra.even.lift.aux_ι, Hausdorffification.lift_of, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, BilinForm.neg_apply, RootPairing.rootForm_pos_of_ne_zero, Module.Basis.constr_basis, IsBaseChange.equiv_tmul, PowerSeries.trunc_coe_eq_self, Bialgebra.comul_one, tensorProduct_apply, map_sub, Polynomial.hasseDeriv_natDegree_eq_C, Rep.coinvariantsTensorMk_apply, Polynomial.hasFDerivWithinAt_aeval, Orientation.inner_rightAngleRotation_right, WeakBilin.eval_continuous, QuotSMulTop.map_comp, LieModule.traceForm_apply_lie_apply, snd_surjective, Projectivization.cross_mk_of_ne, single_apply, continuous_of_isClosed_ker, PowerSeries.coeff_derivative, endVecAlgEquivMatrixEnd_symm_apply_apply, CharacterModule.uncurry_apply, LinearEquiv.ofIsUnitDet_apply, Polynomial.derivative_C_mul_X_pow, AdicCompletion.of_bijective, IsSymmetric.im_inner_apply_self, Polynomial.derivative_C, Rep.homEquiv_symm_apply_hom, QuadraticMap.Ring.associated_pi, Matrix.trace_kroneckerMapBilinear, Polynomial.derivative_bernoulli_add_one, frobenius_def, span_range_eq_top_iff_surjective_finsuppLinearCombination, FunOnFinite.linearMap_piSingle, inl_apply, 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, Module.Invertible.lTensor_surjective_iff, innerₛₗ_apply, Polynomial.eval₂_derivative_of_splits, LinearPMap.vadd_apply, trace_eq_sum_embeddings, CliffordAlgebra.contractLeft_algebraMap_mul, PowerSeries.coeff_subst_finite, BilinForm.compLeft_apply, contractRight_apply, CliffordAlgebra.reverseEquiv_apply, PowerSeries.coeff_X_pow, Matrix.toLin_transpose, MvPowerSeries.isHomogeneous_homogeneousComponent, LaurentPolynomial.counit_T, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, Representation.leftRegular_norm_apply, 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, 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, Polynomial.aeval_monomial, MvPowerSeries.aeval_eq_sum, Representation.ind_mk, Module.Basis.toDual_linearCombination_right, Matrix.toLinearMapₛₗ₂_apply_basis, IsLocalRing.CotangentSpace.span_image_eq_top_iff, LaurentPolynomial.counit_C, LieAlgebra.ad_lie, qExpansion_coeff_unique, Polynomial.Chebyshev.iterate_derivative_T_eval_one, 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, ofIsCompl_right_apply, Orientation.kahler_apply_apply, groupHomology.d₂₁_single_one_snd, imaginaryPart_imaginaryPart, PowerSeries.coeff_subst', Orientation.inner_rightAngleRotationAux₁_left, sub_apply, TensorProduct.AlgebraTensorModule.map_tmul, Polynomial.sylvesterMap_apply_coe, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, PolynomialLaw.isCompat_apply', MvPolynomial.sum_monomial_eq, Module.Invertible.bijective, Module.Invertible.lTensor_bijective_iff, 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, mulRight_toAddMonoidHom, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Coalgebra.coassoc_apply, TwoSidedIdeal.subtypeMop_apply, groupHomology.π_map_apply, continuous_of_isClosed_graph, pinGroup.involute_act_ι_mem_range_ι, Submodule.inclusion_injective, LinearEquiv.coe_toLinearMap, ProbabilityTheory.variance_linearMap_gaussianReal, HopfAlgebra.mul_antipode_lTensor_comul_apply, Representation.coinvariantsFinsuppLEquiv_symm_apply, LeftInvariantDerivation.evalAt_mul, 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, Bialgebra.counit_one, IsRegular.monomial, groupHomology.π_comp_H2Iso_hom_apply, Profinite.NobelingProof.CC_comp_zero, LieSubmodule.coe_toEnd_pow, RootPairing.InvariantForm.apply_eq_or, SheafOfModules.relationsOfIsCokernelFree_s, Submodule.quotientPiLift_mk, ModuleCat.forget₂_reflectsLimits, CliffordAlgebra.isUnit_ι_of_isUnit, isPositive_iff, TensorProduct.directLimitLeft_tmul_of, Lagrange.interpolate_poly_eq_self, IsAlt.eq_of_add_add_eq_zero, VectorFourier.fourierIntegral_comp_add_right, ContDiffMapSupportedIn.postcompLM_apply, Polynomial.taylor_coeff, toMatrix_singleton, isNonneg_def, 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, MvPolynomial.eval₂_monomial, SkewPolynomial.monomial_mul_monomial, PowerSeries.coeff_expand, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, IsAdicComplete.mk_lift, LieModule.mem_genWeightSpaceOf, Algebra.map_intTraceAux, sum_apply, ModuleCat.biproductIsoPi_inv_comp_π_apply, QuadraticMap.apply_linearCombination, LaurentPolynomial.comul_C_mul_T, PiTensorProduct.map_reindex, AdicCompletion.factor_evalₐ_eq_eval, Profinite.NobelingProof.eval_eq_πJ, Rep.leftRegularHomEquiv_apply, imaginaryPart_smul, map_sum₂, VectorFourier.fourierIntegral_probChar, Submodule.mem_map_of_mem, 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, Polynomial.derivative_X_add_C_sq, Orientation.kahler_rotation_right, Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative, PointedCone.mem_comap, 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, Module.Basis.traceDual_repr_apply, MvPolynomial.mul_monomial_modMonomial, MeasureTheory.ComplexMeasure.re_apply, 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, groupHomology.coe_mapCycles₁, Coalgebra.lTensor_counit_comp_comul, PowerSeries.eval₂_trunc_eq_sum_range, AlternatingMap.curryLeft_compLinearMap, det_ring, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis, SMulMemClass.subtype_apply, CliffordAlgebra.changeForm.associated_neg_proof, PowerSeries.trunc_one_X, Module.Relations.toQuotient_relation, Polynomial.leval_coe_eq_smeval, BilinForm.neg_right, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, CliffordAlgebra.ofEven_ι, exteriorPower.map_apply_ιMulti, MvPolynomial.mkDerivationₗ_X, Algebra.H1Cotangent.exact_map_δ, Module.End.isUnit_apply_inv_apply_of_isUnit, 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, IsSymmetric.conj_inner_sym, ModuleCat.free_map_apply, Matrix.represents_iff', MeasureTheory.Measure.restrictₗ_apply, Module.projective_def, TensorProduct.gradedCommAux_lof_tmul, Representation.linHom.mem_invariants_iff_comm, Module.End.ringEquivEndFinsupp_apply_apply_support, CompletelyPositiveMap.map_cstarMatrix_nonneg', IsLocalFrameOn.coeff_eq_of_eq, BilinForm.linMulLin_apply, DFinsupp.lapply_apply, TensorProduct.directLimitLeft_symm_of_tmul, Representation.IntertwiningMap.isIntertwining, coe_smulRight, groupHomology.mapCycles₂_comp_i_apply, TensorProduct.norm_map, RootPairing.Equiv.id_weightMap_apply, PolynomialModule.monomial_smul_apply, AdicCompletion.eval_of, PowerSeries.coeff_succ_X_mul, toMvPolynomial_eval_eq_apply, mk₂'_apply, IsLocalizedModule.map_comp, 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, 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, AdicCompletion.component_sumInv, trace_conj, QuadraticMap.Isometry.tmul_apply, isSMulRegular_on_quot_iff_lsmul_comap_eq, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, Rep.freeLift_hom, Polynomial.rootSet_monomial, Ideal.coe_torsionOf, map_smul_of_tower, Polynomial.monomial_left_inj, RatFunc.taylor_mem_nonZeroDivisors, injective_domRestrict_iff, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, BilinForm.congr_fun, jacobi_cross, CliffordAlgebra.toBaseChange_ι, Polynomial.newtonMap_apply, HVertexOperator.coeff_apply_apply, AdicCompletion.evalₐ_mk, Module.Basis.toDualFlip_apply, toSpanSingleton_one, RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot, Representation.asModuleEquiv_map_smul, 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, 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, DirectSum.linearEquivFunOnFintype_symm_single, Submodule.map_span, Fintype.linearCombination_apply_single, SimplexCategory.coe_toTopMap, isSimpleModule_iff_toSpanSingleton_surjective, SchwartzMap.fourier_convolution_apply, AlternatingMap.compLinearMap_apply, Fintype.linearCombination_apply, neg_cross, surjective_rangeRestrict, LocalizedModule.map_mk, PowerBasis.liftEquiv'_symm_apply_apply, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, 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, LieAlgebra.mem_zeroRootSubalgebra, PowerBasis.constr_pow_mul, PolynomialLaw.isCompat_apply, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, HahnEmbedding.Partial.eval_eq_truncLT, AddMonoidHom.coe_toIntLinearMap, Submodule.span_preimage_le, PresheafOfModules.freeYonedaEquiv_comp, ModuleCat.forget₂AddCommGroup_preservesLimit, SMulMemClass.coe_subtype, eq_adjoint_iff_basis_right, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, Polynomial.eval_add_of_sq_eq_zero, Polynomial.derivative_X_add_C_pow, Module.Finite.exists_fin', MeasureTheory.OuterMeasure.map_top, toMatrixAlgEquiv_apply', IsLocalizedModule.eq_iff_exists, lTensor_map, trace_eq_sum_automorphisms, 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, exact_of_comp_of_mem_range, Finsupp.linearCombination_surjective, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, BilinForm.isOrtho_def, MvPolynomial.scalarRTensor_symm_apply_single, DFinsupp.mapRange.linearMap_apply, Polynomial.natDegree_monomial_eq, ModuleCat.FreeMonoidal.εIso_hom_one, LinearIndepOn.image, innerₛₗ_apply_coe, Module.End.natCast_apply, TensorProduct.equivFinsuppOfBasisLeft_apply, CharacterModule.dual_surjective_iff_injective, Polynomial.iterate_derivative_mul, BilinMap.toQuadraticMap_apply, Polynomial.aeval_iterate_derivative_of_lt, Rep.freeLift_hom_single_single, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, isSymm_iff_basis, MvPolynomial.weightedHomogeneousComponent_of_mem, Module.Basis.constr_self, Polynomial.derivative_map, restrictScalars₁₂_apply_apply, Finsupp.mem_span_image_iff_linearCombination, MvPowerSeries.order_eq_nat, CompatibleSMul.map_smul, Module.End.mul_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, trace_prodMap', AddMonoidHom.coe_toZModLinearMap, MvPowerSeries.IsWeightedHomogeneous.coeff_eq_zero, toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, PowerSeries.coeff_C_mul, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, TensorProduct.AlgebraTensorModule.lift_tmul, PowerSeries.X_pow_dvd_iff, exteriorPower.ιMultiDual_apply_nondiag, 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, bijective_of_ne_zero, IsAdjoinRootMonic.coeff_apply_le, Module.Basis.traceDual_powerBasis_eq, 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, 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, compBilinForm_apply_apply, Rep.diagonalHomEquiv_apply, prod_apply, AdicCompletion.mk_apply_coe, Prod.counit_apply, Submodule.span_image, Polynomial.derivative_natCast, LinearEquiv.ofIsUnitDet_symm_apply, Module.End.ofNat_apply, IsSymmetric.re_trace_eq_sum_eigenvalues, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, TwoSidedIdeal.subtypeMop_injective, groupHomology.d₂₁_single, LieModule.iterate_toEnd_mem_lowerCentralSeries, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, 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, proj_surjective, mulLeftLinearMap_apply, SheafOfModules.Presentation.IsFinite.finite_relations, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, KaehlerDifferential.map_D, Polynomial.hasseDeriv_X, Derivation.liftKaehlerDifferential_apply, MvPolynomial.coeff_weightedHomogeneousComponent, realPart_smul, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, PowerSeries.order_eq, Algebra.coe_lmul_eq_mul, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, Polynomial.derivative_bernoulli, AdicCompletion.congr_apply, Module.Basis.toDual_apply_left, nilRank_le_natTrailingDegree_charpoly, toPerfPair_apply, ExteriorAlgebra.comp_ι_sq_zero, equivOfIsUnitDet_apply, KaehlerDifferential.DLinearMap_apply, CategoryTheory.whiskering_linearYoneda₂, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, MvPolynomial.rTensor_apply, 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, Module.DualBases.lc_def, ModuleCat.MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, 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, TensorProduct.map_range_eq_span_tmul, MvPolynomial.aeval_monomial, exact_iff, groupHomology.cyclesMk₀_eq, CommSemiring.counit_apply, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, NNRealRMK.integral_rieszMeasure, Module.Relations.Solution.IsPresentation.exact, fwdDiff_aux.coe_fwdDiffₗ_pow, ExteriorAlgebra.ι_mul_prod_list, IsBaseChange.linearMapLeftRightHom_apply, Algebra.trace_apply, LinearIsometry.rTensor_apply, TensorAlgebra.toDirectSum_ι, ModuleCat.forget_map, CompactlySupportedContinuousMap.monotone_of_nnreal, ExteriorAlgebra.ιMulti_succ_curryLeft, mul'_comm, Matrix.SpecialLinearGroup.toLin'_symm_apply, DirectSum.lmap_of, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, map_smul_inv, Finset.weightedVSub_sdiff_sub, CoalgHomClass.map_comp_comul_apply, ExteriorAlgebra.leftInverse_map_iff, IsLocalizedModule.map_integerMultiple, coe_innerₛₗ_apply, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange, Coalgebra.Repr.eq, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, TensorProduct.finsuppScalarLeft_apply, MonomialOrder.degree_monomial_le, trace_comp_cycle, ModularGroup.lcRow0_apply, PowerSeries.WithPiTopology.tendsto_trunc_atTop, MulOpposite.coe_opLinearEquiv_symm_toLinearMap, Module.Basis.toDual_apply_right, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, trace_comp_cycle', IsLinearMap.mk'_apply, MvPolynomial.coeff_mul_monomial', 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, Module.DualBases.coeffs_apply, AdicCompletion.of_injective_iff, Submodule.map_coe, Submodule.baseChange_span, Module.surjective_piEquiv_apply_iff, PowerSeries.coeff_C_mul_X_pow, LinearPMap.coe_vadd, 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, Polynomial.sumIDeriv_apply_of_le, QuadraticMap.exists_companion, DirectSum.lmap_injective, cross_cross_eq_smul_sub_smul', 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, Algebra.coe_linearMap, TensorProduct.fromDirectLimit_of_tmul, Polynomial.support_monomial', tensorKerEquiv_apply, IsAlt.self_eq_zero, toMatrixₛₗ₂'_apply, AdicCompletion.eval_lift_apply, ModuleCat.span_rightExact, baseChange_tmul, MvPolynomial.lcoeff_apply, CommRingCat.KaehlerDifferential.ext_iff, transvection.baseChange, polar_mem_iff, Submodule.mem_biSup_iff_exists_dfinsupp, IsContPerfPair.continuous_uncurry, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, Module.injective_iff, MvPolynomial.restrictSupport_eq_span, LinearEquiv.ofLinear_symm_apply, isSMulRegular_iff_ker_lsmul_eq_bot, bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt, Polynomial.taylor_X, QuadraticForm.associated_tmul, groupCohomology.cocyclesMk₀_eq, Seminorm.comp_smul_apply, ModN.instModuleFinite, Pretrivialization.symmₗ_linearMapAt, bernsteinPolynomial.iterate_derivative_at_0, 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, hasDerivAt, TensorProduct.one_gradedMul, Complex.isometryOfOrthonormal_symm_apply, IsLocalizedModule.map_iso_commute, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, Algebra.coe_trace_int, groupHomology.single_mem_cycles₂_iff, LieModule.traceForm_apply_lie_apply', MvPowerSeries.isWeightedHomogeneous_iff_eq_weightedHomogeneousComponent, MeasureTheory.OuterMeasure.restrict_mono, TensorProduct.piScalarRightHom_tmul, hasDerivAtFilter, flip_surjective_iff₂, RootPairing.RootPositiveForm.algebraMap_posForm, lmap_finsuppLEquivDirectSum_eq, lsum_piSingle, Bialgebra.counit_pow, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, IsLocalFrameOn.coeff_sum_eq, Algebra.SubmersivePresentation.cotangentComplex_injective, Module.Projective.out, ker_lsmul, PiTensorProduct.mul_comm, RootPairing.reflection_apply, TensorProduct.piRight_apply, Matrix.toLpLin_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, ModuleCat.extendScalarsId_inv_app_apply, Polynomial.natDegree_derivative_lt, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, isSMulRegular_on_quot_iff_lsmul_comap_le, Module.Basis.constr_apply, 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, Module.Flat.iff_rTensor_preserves_injective_linearMap', DFinsupp.lsum_apply_apply, RatFunc.algebraMap_monomial, MvPowerSeries.monomial_smul_const, PowerSeries.coeff_mul_X_pow, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, 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, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, Polynomial.taylor_pow, skewAdjoint.I_smul_neg_I, Derivation.linearEquiv_coe_comp, Finsupp.linearCombination_eq_fintype_linearCombination_apply, Polynomial.smul_X_eq_monomial, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, ContinuousLinearMap.coe_mk', TensorProduct.AlgebraTensorModule.coe_rTensor, SemimoduleCat.ofHom_apply, QuadraticMap.tensorDistrib_tmul, Polynomial.one_lt_rootMultiplicity_iff_isRoot, Polynomial.monomial_sub, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, Polynomial.coeff_monomial_succ, Module.Basis.dvd_coord_smul, map_smulₛₗ₂, isSymmetric_iff_inner_map_self_real, ExteriorAlgebra.GradedAlgebra.ι_apply, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, PowerSeries.trunc_sub, Algebra.SubmersivePresentation.basisCotangent_apply, Submodule.linearProjOfIsCompl_surjective, exists_extend_of_notMem, MvPowerSeries.hasSum_eval₂, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, Finset.weightedVSubOfPoint_subtype_eq_filter, im_inner_adjoint_mul_self_eq_zero, PowerSeries.IsWeierstrassDivisorAt.seq_one, weightedVSub_mem_vectorSpan_pair, QuadraticMap.associated_flip, Algebra.trace_eq_of_equiv_equiv, Nat.Partition.coeff_genFun, Polynomial.degree_monomial, compr₂ₛₗ_apply, strongRankCondition_iff_succ, mem_finsuppAffineCoords_iff_linearCombination, Rep.free_ext_iff, Representation.inv_self_apply, PresheafOfModules.toSheafify_app_apply, signedDist_apply_linear, MeasureTheory.OuterMeasure.comap_iSup, Matrix.toEuclideanLin_toLp, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, Algebra.Extension.Cotangent.map_mk, RootPairing.CoPolarizationIn_apply, PowerSeries.trunc_derivativeFun, LinearAlgebra.FreeProduct.lof_map_one, Seminorm.closedBall_comp, BilinForm.baseChange_tmul, linearDepOn_iff', toLinearMap_toPerfPair, AdicCompletion.eval_surjective, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Profinite.NobelingProof.GoodProducts.max_eq_eval, Matrix.entryLinearMap_toAddMonoidHom, BilinForm.isSymm_iff_basis, ConvexOn.comp_linearMap, TensorProduct.gradedComm_of_tmul_of, PowerBasis.constr_pow_aeval, range_coe, ModuleCat.ofHom_apply, Module.End.ringEquivEndFinsupp_symm_apply_apply, PowerSeries.coeff_subst_finite', QuadraticMap.Isometry.coe_toLinearMap, PowerSeries.HasSubst.monomial, RootPairing.root_coroot'_eq_pairing, CliffordAlgebra.EvenHom.contract_mid, LieRinehartAlgebra.Hom.toLinearMap'_apply, Submodule.IsCompl.projection_apply_mem, exteriorPower.toTensorPower_apply_ιMulti, Algebra.traceForm_toMatrix_powerBasis, LieDerivation.coeFn_coe, PowerSeries.trunc_map, MeasureTheory.OuterMeasure.map_biInf_comap, Module.End.HasEigenvector.pow_apply, AffineMap.image_vsub_image, ContDiffMapSupportedIn.structureMapLM_zero_apply, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, BilinForm.isAdjointPairLeftAdjointOfNondegenerate, injective_iff_antilipschitz, AffineMap.deriv, AlternatingMap.alternatizeUncurryFinLM_apply, compMultilinearMap_apply, injective_or_eq_zero, ModuleCat.restrictScalarsCongr_inv_app, PowerSeries.coeff_coe_trunc_of_lt, Function.Exact.inl_snd, Algebra.Extension.exact_cotangentComplex_toKaehler, SchwartzMap.fourier_convolution, trace_mul_cycle', Polynomial.isMonicOfDegree_monomial_one, MonoidAlgebra.counit_single, PowerSeries.trunc_zero', Pretrivialization.coe_linearMapAt_of_mem, Module.Flat.iff_rTensor_injective', FractionalIdeal.trace_mem_dual_one, BilinForm.sum_apply, 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, Matrix.derivative_det_one_add_X_smul_aux, MvPolynomial.coeffsIn_le, Polynomial.trailingDegree_monomial, 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bernsteinPolynomial.derivative_succ_aux, MvPowerSeries.monomial_smul_eq, LaurentSeries.coeff_coe_powerSeries, Ideal.toCotangent_surjective, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, lTensor_inj_iff_rTensor_inj, trace_comp_comm', 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, GeneralLinearGroup.coeFn_generalLinearEquiv, QuadraticForm.associated_baseChange, Real.volume_preserving_transvectionStruct, HahnEmbedding.Partial.apply_of_mem_stratum, KaehlerDifferential.map_liftBaseChange_smul, ModularFormClass.hasSum_qExpansion, MeasureTheory.OuterMeasure.map_ofFunction_le, MvPowerSeries.IsHomogeneous.coeff_eq_zero, 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, trace_baseChange, CliffordAlgebra.contractLeftAux_apply_apply, LinearPMap.adjointAux_inner, IsGroupLikeElem.mul_antipode_cancel, CategoryTheory.preadditiveCoyoneda_obj, PowerSeries.coeff_one_mul, Algebra.idealMap_apply_coe, 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, toMatrix'_mulVec, RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot, LinearEquiv.toFGModuleCatIso_inv, MvPowerSeries.coeff_eq_zero_of_lt_lexOrder, ModuleCat.semilinearMapAddEquiv_apply, VertexOperator.coeff_eq_ncoeff, Absorbent.subset_range_iff_surjective, PowerSeries.monomial_zero_eq_C_apply, ModuleCat.CoextendScalars.map'_hom_apply_apply, IsBaseChange.toDualBaseChange_tmul, IsLocalizedModule.map_LocalizedModules, Polynomial.card_roots_toFinset_le_derivative, MvPowerSeries.coeff_mul_of_add_lexOrder, AffineMap.linear_eqOn_vectorSpan, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, TensorProduct.instDirectedSystemCoeLinearMapIdLTensor, IsSymmetric.coe_re_inner_apply_self, Module.Basis.coord_equivFun_symm, Polynomial.iterate_derivative_sum, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, domRestrict₁₂_apply, DirectSum.toLieAlgebra_apply, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, 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, compAlternatingMapₗ_apply, LinearIndependent.map, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, RatFunc.laurentAux_ofFractionRing_mk, Rep.mono_iff_injective, 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Polynomial.degree_derivative_le, domRestrict_apply, MvPolynomial.degreeOf_monomial_eq, 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, traceAux_def, mem_span_iff_continuous, 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, 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, LocalizedModule.mkLinearMap_apply, Polynomial.derivative_apply, PowerSeries.trunc_X, HopfAlgebra.antipode_one, toAddMonoidHom_mulRight, Algebra.normalizedTrace_self_apply, Submodule.map_toAddSubmonoid, 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, TwoSidedIdeal.subtype_apply, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Module.End.algebraMap_isUnit_inv_apply_eq_iff, LinearPMap.adjoint_apply_of_dense, CliffordAlgebra.contractLeftAux_contractLeftAux, coe_finsupp_sum, DirectSum.lmap_eq_iff, groupHomology.H0π_comp_map_apply, MvPowerSeries.monomial_eq', toMatrix_apply, PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, linearDepOn_iff'ₛ, PiTensorProduct.map_range_eq_span_tprod, SemimoduleCat.forget₂_obj, LinearPMap.toFun_eq_coe, Polynomial.ofFn_natDegree_lt, MvPolynomial.weightedHomogeneousComponent_apply, ModuleCat.restrictScalarsId'App_inv_apply, CliffordAlgebra.EquivEven.involute_v, continuous_uncurry_of_isContPerfPair, Submodule.mem_traceDual_iff_isIntegral, AdicCompletion.map_of, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, 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, Orientation.areaForm_rightAngleRotation_left, MvPowerSeries.coeff_mul_C, BilinForm.restrict_apply, LinearEquiv.coe_coe, Algebra.H1Cotangent.exact_δ_mapBaseChange, LaurentPolynomial.antipode_C_mul_T, map_finsupp_linearCombination, AlternatingMap.toMultilinearMapLM_apply, Module.FinitePresentation.exists_basis_localizedModule_powers, snd_apply, PolynomialModule.map_single, Algebra.SubmersivePresentation.cotangentEquiv_apply, toMatrixAlgEquiv_transpose_apply', TensorProduct.dualDistribEquivOfBasis_apply_apply, Polynomial.mkDerivation_apply, baseChangeHom_apply, Module.Relations.Solution.π_single, Finsupp.lmapDomain_apply, Polynomial.coeff_monomial_mul, linearIndepOn_iff_linearCombinationOnₛ, LinearEquiv.ofLinear_apply, Derivation.evalAt_apply, isOrtho_def, SemimoduleCat.forget₂_map, CommSemiring.comul_apply, Algebra.Generators.H1Cotangent.δ_map, ModuleCat.restrictScalarsComp'App_inv_apply, uncurryLeft_apply, trace_map, AdicCompletion.of_apply, CliffordAlgebra.reverse_ι, CliffordAlgebra.reverse_involutive, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, TensorProduct.inner_map_map, lTensor_tmul, groupHomology.mem_cycles₁_iff, lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, LaurentSeries.hasseDeriv_single, applyₗ_apply_apply, PolynomialLaw.exists_lift_of_mem_range_rTensor, IsAlt.neg, MvPolynomial.bind₁_monomial, Lagrange.interpolate_singleton, MeasureTheory.OuterMeasure.map_mono, AlternatingMap.curryLeft_same, CliffordAlgebra.changeForm_changeForm, polyCharpoly_coeff_eval, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, LieModuleHom.map_lie₂, BilinForm.apply_smul_sub_smul_sub_eq, MvPolynomial.induction_on_monomial, MeasureTheory.OuterMeasure.restrict_le_self, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', IsAdicComplete.StrictMono.mk_lift, RootPairing.algebraMap_root'In_apply, Representation.trivial_apply, groupHomology.boundariesToCycles₁_apply, groupHomology.single_mem_cycles₂_iff_inv, ModularGroup.smul_eq_lcRow0_add, groupHomology.d₁₀_single, Algebra.TensorProduct.mul_apply, UniversalEnvelopingAlgebra.lift_ι_apply', Matrix.SpecialLinearGroup.toLin'_apply, 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, extendScalarsOfIsLocalization_apply', Algebra.lsmul_coe, MvPolynomial.evalₗ_apply, toKerIsLocalized_apply_coe, Representation.self_norm_apply, CStarMatrix.norm_def, MultilinearMap.ofSubsingleton_apply_apply, submoduleMap_surjective, ModuleCat.ihom_ev_app, mapMatrixModule_comp_apply, PolynomialLaw.isCompat', Module.Relations.Solution.IsPresentation.π_desc_apply, Polynomial.derivative_C_mul_X_sq, 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, groupCohomology.cocycles₁.d₁₂_apply, TensorProduct.lift.equiv_apply, IsBaseChange.linearMapLeftRightHom_comp, MvPolynomial.monomial_modMonomial, Algebra.Extension.cotangentComplex_mk, Submodule.mulRightMap_apply_single, Polynomial.taylor_one, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, 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, retractionOfSectionOfKerSqZero_tmul_D, finsuppLEquivDirectSum_symm_lof, groupHomology.H2π_eq_zero_iff, Finset.weightedVSubOfPoint_sdiff_sub, KaehlerDifferential.linearCombination_surjective, IsLocalizedModule.map_lTensor, Finsupp.lsubtypeDomain_apply, mulLeft_toAddMonoidHom, HahnSeries.coeff_ofFinsuppLinearMap, Module.Basis.sumQuot_repr_inr, Module.Basis.coord_toDualEquiv_symm_apply, Finsupp.linearCombination_onFinset, QuaternionAlgebra.reₗ_apply, MvPowerSeries.coeff_add_monomial_mul, IsAdjoinRootMonic.coeff_root_pow, MeasureTheory.SignedMeasure.im_toComplexMeasure, CharacterModule.dual_injective_iff_surjective, BilinForm.sub_right, Module.Basis.coord_repr_symm, TensorProduct.toDirectLimit_tmul_of, id'_apply, Module.Relations.Solution.linearCombination_var_relation, Module.End.coe_one, StarModule.decomposeProdAdjoint_apply, PowerSeries.hasSum_eval₂, Polynomial.eval_multiset_prod_X_sub_C_derivative, MonomialOrder.sPolynomial_mul_monomial, toMatrix₂Aux_apply, Submodule.span_range_inclusionSpan, WithLp.fstₗ_apply, LinearEquiv.skewProd_apply, Submodule.surjOn_iff_le_map, RingEquiv.moduleEndSelfOp_symm_apply, ModuleCat.MonoidalCategory.associator_inv_apply, Subspace.dualEquivDual_apply, LieSubalgebra.coe_ad, BilinForm.iIsOrtho_def, ContMDiffMap.coeFnLinearMap_apply, MvPowerSeries.prod_monomial, Matrix.cramer_eq_adjugate_mulVec, TensorProduct.uncurry_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, 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, 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, sum_repr_mul_repr_mul, MonomialOrder.sPolynomial_leadingTerm_mul, CStarMatrix.toCLM_apply_single_apply, bernsteinPolynomial.iterate_derivative_at_1, 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, Polynomial.leadingCoeff_taylor, toLinearMap₂'Aux_toMatrix₂Aux, Polynomial.homogenize_monomial, Polynomial.derivative_add, Submodule.quotientQuotientEquivQuotientAux_mk_mk, LinearIndepOn.quotient_iff_union, trace_lie, Module.Basis.ofIsLocalizedModule_repr_apply, withSeminorms_induced, 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, separatingLeft_dualProd, hahnEmbedding_isOrderedModule, groupHomology.H1π_eq_iff, fst_prodOfFinsuppNat, IsPositive.re_inner_nonneg_left, Convex.linear_preimage, ModuleCat.biprodIsoProd_inv_comp_fst_apply, TensorProduct.includeRight_lid, Polynomial.eval_monomial, MeasureTheory.OuterMeasure.isometryEquiv_comap_mkMetric, groupHomology.d₃₂_comp_d₂₁_apply, CliffordAlgebra.even.lift.aux_algebraMap, CliffordAlgebraComplex.reverse_apply, injective_of_ne_zero, MvPowerSeries.commute_monomial, ModuleCat.CoextendScalars.map_apply, range_localizedMap_eq_localized₀_range, 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, polyCharpolyAux_map_eq_toMatrix_charpoly, Module.Relations.Solution.IsPresentation.desc_var, Algebra.Extension.H1Cotangent.map_toInfinitesimal_bijective, Matrix.toLinearEquiv_apply, LinearEquiv.piRing_apply, ModuleCat.forget₂_map, Representation.Coinvariants.mk_surjective, LeftInvariantDerivation.evalAt_apply, PowerSeries.coeff_zero_X, IsLocalizedModule.injective_iff_isRegular, CliffordAlgebra.contractLeft_algebraMap, 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
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