Quotient 📖 | CompOp | 1430 mathmath: MulAction.Quotient.coe_smul_out, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, QuotientAddGroup.kerLift_mk, Ideal.quotientEquivAlgOfEq_coe_eq_factorₐ, Ideal.toCotangent_to_quotient_square, Ideal.Quotient.nontrivial_of_liesOver_of_isPrime, Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Ideal.Quotient.isScalarTower, AddCircle.not_isOfFinAddOrder_iff_forall_rat_ne_div, Ideal.Quotient.exists_algHom_fixedPoint_quotient_under, LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff, lTensor.inverse_comp_lTensor, QuotientGroup.homQuotientZPowOfHom_id, IsLocalization.surjective_quotientMap_of_maximal_of_localization, Subgroup.card_eq_card_quotient_mul_card_subgroup, AdicCompletion.val_sub_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, Algebra.PreSubmersivePresentation.jacobiMatrix_naive, AddSubgroup.quotientEquivProdOfLE_symm_apply, Submodule.QuotientBot.infinite, Algebra.FiniteType.quotient, QuotientAddGroup.exists_norm_mk_lt, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim, QuotientGroup.mk_one, QuotientGroup.isQuotientMap_mk, IsSemisimpleModule.exists_submodule_linearEquiv_quotient, QuotientAddGroup.instT3Space, Module.support_quotient, Module.Presentation.cokernelSolution_var, Subgroup.quotientEquivOfEq_mk, Ideal.Quotient.map_ker_stabilizer_subtype, AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply_mk, QuotientGroup.norm_mk, Valuation.supp_quot_supp, QuotientGroup.image_coe_inj, groupHomology.map₁_quotientGroupMk'_epi, QuotientGroup.kerLift_mk, MeasureTheory.IsFundamentalDomain.absolutelyContinuous_map, QuotientGroup.lift_mk, groupHomology.coinfNatTrans_app, Int.quotientSpanEquivZMod_comp_Quotient_mk, Polynomial.Monic.free_quotient, StandardEtalePair.inv_aeval_X_g, AddCircle.coe_eq_zero_iff, Algebra.Presentation.naive_toGenerators, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, RingTheory.Sequence.isWeaklyRegular_cons_iff', QuotientGroup.coe_mk', QuotientAddGroup.completeSpace_right', MonoidHom.restrictHomKerEquiv_apply_coe, Module.End.IsNilpotent.mapQ, Submodule.annihilator_quotient, AdicCompletion.map_val_apply, NumberField.Units.fun_eq_repr, covBy_iff_quot_is_simple, LieSubmodule.Quotient.mk_eq_zero, Ideal.quotientEquiv_symm_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, ModuleCat.epi_as_hom''_mkQ, Ideal.rank_prime_pow_ramificationIdx, QuotientGroup.discreteTopology, Ideal.algebraMap_quotient_injective, Subgroup.transferTransversal_apply, QuotientGroup.instSecondCountableTopology, Module.isTorsionBySet_quotient_set_smul, finrank_quotient_span_eq_natDegree_norm, DiscreteTiling.PlacedTile.ext_iff_of_preimage, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, AddSubgroup.norm_normedMk_le, QuotientGroup.borelSpace, Ring.coe_jacobson_quotient, QuotientGroup.finite, QuotientGroup.norm_mk_eq_zero, Polynomial.fiberEquivQuotient_tmul, nilpotencyClass_quotient_center, AddSubgroup.index_eq_zero_iff_infinite, QuotientGroup.nhds_eq, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, Ideal.quotientMap_comp_mk, AddCircle.coe_real_preimage_closedBall_eq_iUnion, Submodule.mapQ_apply, Submodule.dualQuotEquivDualAnnihilator_apply, AddSubgroup.IsComplement.quotientAddGroupMk_leftQuotientEquiv, RingHom.quotientKerEquivOfSurjective_symm_apply, Ideal.Quotient.factor_comp_mk, Submodule.Quotient.mk_add, Ideal.comap_cotangentIdeal, Submodule.factor_mk, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, Module.isTorsionBySet_quotient_ideal_smul, QuotientGroup.preimage_image_mk, QuotSMulTop.equivTensorQuot_naturality, DoubleQuot.coe_quotQuotMkₐ, Ideal.Quotient.factorₐ_comp_mk, Submodule.t3_quotient_of_isClosed, QuotientAddGroup.univ_eq_iUnion_vadd, Submodule.Quotient.instIsBoundedSMul, Int.quotientSpanNatEquivZMod_comp_Quotient_mk, IsLocalRing.finrank_quotient_map, StandardEtalePresentation.toPresentation_algebra_smul, Module.supportDim_eq_ringKrullDim_quotient_annihilator, Submodule.quotDualCoannihilatorToDual_apply, QuotientGroup.rangeKerLift_injective, Ideal.quotient_map_C_eq_zero, InfiniteGalois.normalAutEquivQuotient_apply, Submodule.dualPairing_apply, AddCircle.coe_neg, Submodule.unique_quotient_iff_eq_top, lTensor.inverse_of_rightInverse_comp_lTensor, AdicCompletion.val_smul, QuotientAddGroup.le_norm_iff, Polynomial.IsDistinguishedAt.map_eq_X_pow, QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure, AlgHom.IsArithFrobAt.mk_apply, Ideal.map_mk_comap_factor, WittVector.factorPowSucc_comp_fontaineThetaModPPow, PowerBasis.quotientEquivQuotientMinpolyMap_apply, DoubleQuot.coe_quotLeftToQuotSupₐ, AdicCompletion.incl_apply, Ideal.quotientInfToPiQuotient_inj, QuotientAddGroup.equivQuotientZSMulOfEquiv_symm, QuotientGroup.completeSpace_left, AdicCompletion.val_smul_eq_evalₐ_smul, QuotientGroup.card_quotient_rightRel, Submodule.quotientPi_aux.map_smul, Ideal.inertiaDeg_algebraMap, MulAction.quotient_out_smul_fixedPoints, Ideal.torsionMapQuot_apply, QuotientAddGroup.mk'_eq_mk', Submodule.Quotient.instDiscreteMeasurableSpaceQuotient, Ideal.Quotient.algEquivOfEqMap_apply, Ideal.range_cotangentToQuotientSquare, Ideal.Quotient.factor_mk, Module.supportDim_add_length_eq_supportDim_of_isRegular, Algebra.QuasiFinite.instQuotientIdeal, Ideal.algebraMap_quotient_residueField_mk, groupHomology.H1CoresCoinf_X₃, instIsSeparableQuotientIdealOfResidueField, instFiniteQuotientRingOfIntegersIdealOfNumberFieldOfIsMaximal, Submodule.finrank_quotient_add_finrank, finrank_quotient_span_eq_natDegree', Ideal.Quotient.instFaithfulSMul, Ideal.quotientInfToPiQuotient_surj, NormedAddGroupHom.lift_mk, Module.exists_smul_eq_zero_and_mk_eq, TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensor, QuotientAddGroup.mk_surjective, QuotientMapQuotient.isNoetherian, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, QuotientAddGroup.isOpenQuotientMap_mk, ModularForm.norm_eq_zero_iff, TensorProduct.quotientTensorQuotientEquiv_symm_apply_mk_tmul, QuotientAddGroup.ker_map, Submodule.Quotient.instSubsingletonQuotient, QuotientAddGroup.subsingleton_quotient_top, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, QuotientAddGroup.coe_mk', QuotientAddGroup.completeSpace_left, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, isArtinian_iff_submodule_quotient, QuotientAddGroup.equivIocMod_zero, Module.Grassmannian.rankAtStalk_eq, Ideal.height_eq_height_add_of_liesOver_of_hasGoingDown, Ideal.Quotient.tower_quotient_map_quotient, QuotientGroup.kerLift_mk', QuotientAddGroup.instSecondCountableTopology, Submodule.dualCopairing_eq, LieSubmodule.Quotient.mk'_ker, DoubleQuot.quotQuotEquivComm_symmₐ, ringKrullDim_quotient, Ideal.Quotient.subsingleton_iff, QuotientAddGroup.measurableVAdd, WittVector.factorPowSucc_fontaineThetaModPPow_eq, Ideal.Quotient.coe_factorₐ, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, Subgroup.quotientEquivProdOfLE_apply, Ideal.Quotient.factor_comp_apply, QuotSMulTop.equivTensorQuot_naturality_mk, IsLocalRing.map_mkQ_eq, Submodule.quotDualCoannihilatorToDual_nondegenerate, Submodule.quotEquivOfEqBot_symm_apply, QuotientGroup.instDiscreteMeasurableSpace, AddAction.Quotient.vadd_coe, SlashInvariantForm.quotientFunc_smul, Module.Presentation.cokernel_relation, MeasureTheory.AddQuotientMeasureEqMeasurePreimage.addInvariantMeasure_quotient, AddAction.injective_ofQuotientStabilizer, QuotientAddGroup.liftEquiv_coe, LieHom.quotKerEquivRange_toFun, Ideal.quotientEquivAlg_mk, AddCircle.coe_zsmul, AddSubgroup.quotient_finite_of_isOpen', Module.equiv_directSum_of_isTorsion, Ring.jacobson_quotient_of_le, AddAction.Quotient.coe_vadd_out, QuotSMulTop.map_comp_mkQ, AddSubgroup.card_eq_card_quotient_mul_card_addSubgroup, LieSubmodule.Quotient.toEnd_comp_mk', TensorProduct.tensorQuotEquivQuotSMul_comp_mkQ_lTensor, QuotientAddGroup.ker_mk', Ideal.quotientEquivAlgOfEq_coe_eq_factor, RingHom.quotientKerEquivOfSurjective_symm_comp, CuspForm.coe_trace, Ideal.rootsOfUnityMapQuot_injective, Subgroup.instDiscreteTopologyQuotientOfContinuousMul, Ideal.Quotient.factorₐ_apply_mk, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div, Ideal.Quotient.instIsPrimeQuotientMapRingHomAlgebraMapMkOfLiesOver, AddCircle.isAddQuotientCoveringMap_coe, AddCircle.isLocalHomeomorph_coe, QuotientGroup.norm_mk_eq_zero_iff_mem_closure, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, algebra_finiteType_of_liesOver, IsLocalRing.basisQuotient_repr, AdjoinRoot.evalEval_apply, QuotientAddGroup.instContinuousVAdd, LinearMap.range_mkQ_comp, finite_iff_subgroup_quotient, Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero, Subgroup.Normal.quotient_commutative_iff_commutator_le, rTensor.inverse_of_rightInverse_apply, AlgEquiv.quotientBot_mk, AdicCompletion.pi_apply_coe, QuotientGroup.isClosedMap_coe, MulAction.Quotient.smul_mk, LinearMap.exact_subtype_mkQ, Ideal.Quotient.stabilizerHom_surjective, RingEquiv.quotientBot_symm_mk, Module.Presentation.cokernel_R, RingTheory.Sequence.isWeaklyRegular_iff_Fin, Ideal.quotEquivOfEq_mk, AdicCompletion.val_add_apply, Ideal.Quotient.algebraMap_eq, Ideal.injective_quotient_le_comap_map, Subgroup.quotientCentralizerEmbedding_apply, Ideal.Quotient.algebraMap_quotient_map_quotient, AddSubgroup.norm_trivial_quotient_mk, AdicCompletion.smul_eval, PreTilt.mk_comp_untilt_eq_coeff_zero, AddCircle.norm_div_natCast, DoubleQuot.quotQuotEquivComm_comp_quotQuotMk, QuotientGroup.liftEquiv_coe, IsPGroup.to_quotient, Submodule.rank_quotient_add_rank, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', Algebra.Presentation.quotientEquiv_symm, DoubleQuot.quotQuotEquivComm_quotQuotMk, Subspace.finiteDimensional_quot_dualCoannihilator_iff, MeasureTheory.QuotientMeasureEqMeasurePreimage.mulInvariantMeasure_quotient, ZSpan.quotientEquiv_apply_mk, Polynomial.Monic.quotient_isIntegral, Ideal.Quotient.exists_inv, QuotientGroup.preimage_image_mk_eq_mul, Module.Presentation.cokernelSolution.isPresentation, WittVector.mk_pow_fontaineTheta, Ideal.ker_Pi_Quotient_mk, DoubleCoset.left_bot_eq_left_quot, AdicCompletion.factor_eval_eq_evalₐ, Submodule.goursat, Algebra.Generators.naive_val, Ideal.Quotient.factorₐ_apply, Submodule.quotientQuotientEquivQuotientAux_mk, QuotientAddGroup.isOpenMap_coe, AddSubgroup.instFiniteQuotientOfContinuousAddOfCompactSpace, QuotientGroup.completeSpace_right, Ideal.powQuotSuccInclusion_apply_coe, FiniteDimensional.finiteDimensional_quotient, QuotientGroup.quotientKerEquivOfRightInverse_apply, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Module.IsTorsionBySet.mk_smul, lTensor.inverse_of_rightInverse_apply, Submodule.mapQ_pow, Subgroup.smul_leftQuotientEquiv, Submodule.range_mkQ, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, QuotientAddGroup.equivQuotientZSMulOfEquiv_trans, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, Subgroup.quotientSubgroupOfEmbeddingOfLE_apply_mk, Submodule.isOpenQuotientMap_mkQ, Ideal.Quotient.lift_surjective_of_surjective, AddValuation.self_le_supp_comap, Submodule.factor_eq_factor, MeasureTheory.QuotientMeasureEqMeasurePreimage.haarMeasure_quotient, PrimeSpectrum.comap_quotientMk_bijective_of_le_nilradical, Subspace.dualPairing_nondegenerate, Subgroup.discreteTopology, Ideal.Quotient.factorₐ_refl, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, AlgebraicGeometry.Scheme.Hom.liftQuotient_comp, Algebra.Presentation.naive_relation, Submodule.Quotient.completeSpace, NormedAddGroupHom.lift_normNoninc, Subgroup.finite_quotient_of_finiteIndex, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot, QuotientAddGroup.completeSpace_right, Submodule.linearMap_qext_iff, Ideal.kerLiftAlg_injective, NumberField.Units.logEmbeddingQuot_apply, QuotientAddGroup.norm_lt_iff, Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero, AddValuation.onQuot_comap_eq, AdicCompletion.mkₐ_apply_coe, QuotientGroup.completeSpace_right', DiscreteTiling.PlacedTile.ext_iff, Algebra.FormallyUnramified.isField_quotient_map_maximalIdeal, TensorProduct.quotientTensorEquiv_symm_apply_mk_tmul, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, Subgroup.leftCoset_cover_const_iff_surjOn, Ideal.map_mk_comap_factorPow, AddCircle.add_projection_respects_measure, QuotientGroup.liftEquiv_mk, Ideal.Quotient.span_singleton_one, normalizedFactorsEquivOfQuotEquiv_symm, Submodule.strictMono_comap_prod_map, Submodule.Quotient.equiv_symm, PowerSeries.IsWeierstrassDivisionAt.degree_lt, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, CategoryTheory.ShortComplex.abLeftHomologyData_π, Ideal.map_mk_eq_bot_of_le, QuotientAddGroup.preimage_image_mk, QuotientAddGroup.norm_eq_infDist, QuotientAddGroup.liftEquiv_mk, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, QuotientGroup.eq_class_eq_leftCoset, LinearMap.surjective_range_liftQ, IsLocalRing.residue_def, AdicCompletion.val_sum, Polynomial.Monic.quotient_isIntegralElem, QuotientGroup.congr_refl, PowerSeries.IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, groupCohomology.infNatTrans_app, Ideal.pi_mkQ_surjective, QuotientAddGroup.finite, Algebra.FormallySmooth.comp_lift, QuotientAddGroup.nontrivial_iff, QuotientGroup.nontrivial_iff, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, isNoetherian_iff_submodule_quotient, QuotientGroup.nhds_one_hasBasis, RingQuot.idealQuotientToRingQuot_apply, AddCircle.norm_coe_mul, Ideal.height_le_height_add_of_liesOver, Submodule.Quotient.mk_sub, IsDedekindDomain.selmerGroup.monotone, QuotientGroup.congr_symm, lTensor.inverse_apply, AddCircle.norm_half_period_eq, LinearMap.comap_leq_ker_subToSupQuotient, QuotientGroup.instIsMulTorsionFree, Ideal.height_le_height_add_one_of_mem, Submodule.map_mkQ_eq_top, Ideal.Quotient.mkₐ_toRingHom, RingEquiv.quotientBot_mk, KaehlerDifferential.End_equiv_aux, finrank_quotient_span_eq_natDegree, AddGroup.exponent_quotient_dvd, finite_iff_addSubgroup_quotient, QuotientAddGroup.norm_mk, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, MvPolynomial.quotient_map_C_eq_zero, Representation.ofQuotient_coe_apply, AddSubgroup.isAddQuotientCoveringMap_of_comm, QuotientGroup.univ_eq_iUnion_smul, isArtinian_of_quotient_of_artinian, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, LinearMap.quotientInfEquivSupQuotient_apply_mk, KaehlerDifferential.kerTotal_mkQ_single_add, AddCircle.addOrderOf_div_of_gcd_eq_one, AdicCompletion.range_eval, ringKrullDim_quotient_le, Ideal.Quotient.smul_top, MonoidHom.restrictHomKerEquiv_symm_coe_apply, Submodule.finiteQuotient_iff, Ideal.comp_quotientMap_eq_of_comp_eq, Ideal.Quotient.eq_zero_iff_dvd, Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, QuotientGroup.quotientQuotientEquivQuotientAux_mk, AdicCompletion.val_neg_apply, Function.Exact.exact_mapQ_iff, QuotientGroup.lift_comp_mk', Module.Quotient.mk_smul_mk, Algebra.FormallySmooth.exists_mkₐ_comp_eq_of_isAdicComplete, liftOfDerivationToSquareZero_mk_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, AddSubgroup.card_add_eq_card_addSubgroup_add_card_quotient, QuotientAddGroup.strictMono_comap_prod_image, Ideal.Quotient.isDomain_iff_prime, Ideal.Factors.isScalarTower, Ideal.quotientEquiv_symm_mk, Ideal.Quotient.index_eq_zero, AddCircle.coe_sub, isStronglyTranscendental_mk_radical_conductor, QuotientAddGroup.discreteTopology_iff, Ideal.Quotient.nontrivial_iff, NumberField.Units.fundSystem_mk, AddSubgroup.goursat_surjective, Ideal.Quotient.normal, Ideal.Quotient.mk_singleton_self, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, Submodule.mapQ_zero, Algebra.Presentation.naive_relation_apply, LieSubmodule.Quotient.range_mk', Module.Finite.quotient, AdicCompletion.transitionMap_comp_eval, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, QuotientGroup.instT2Space, groupHomology.H1CoresCoinf_g, AddAction.Quotient.mk_vadd_out, Ideal.quotientToQuotientRangePowQuotSucc_mk, Ideal.absNorm_ne_zero_iff, AlgHom.IsArithFrobAt.apply_of_pow_eq_one, AdjoinRoot.quotEquivQuotMap_apply, AddSubgroup.quotientiInfEmbedding_apply_mk, QuotientAddGroup.lift_mk', Ideal.finrank_prime_pow_ramificationIdx, Ideal.Quotient.stabilizerHom_surjective_of_profinite, Submodule.subsingleton_quotient_iff_eq_top, AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply, Submodule.coe_quotEquivOfEqBot_symm, Ideal.quotientKerAlgEquivOfRightInverse_symm_apply, Subgroup.smul_apply_eq_smul_apply_inv_smul, NumberField.Units.rank_modTorsion, Ideal.pi_tensorProductMk_quotient_surjective, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, QuotientAddGroup.subsingleton_iff, CharacterModule.intSpanEquivQuotAddOrderOf_apply, QuotientAddGroup.map_comp_map, AddCircle.coe_eq_zero_iff_of_mem_Ico, Valuation.comap_onQuot_eq, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, QuotientAddGroup.t1Space_iff, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, Action.FintypeCat.toEndHom_apply, QuotientGroup.mk'_apply, Submodule.annihilator_map_mkQ_eq_colon, IsGalois.normalAutEquivQuotient_apply, Ideal.Quotient.mk_bijective_iff_eq_bot, QuotientGroup.rangeKerLift_surjective, QuotientAddGroup.instIsTopologicalAddGroup, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, QuotientAddGroup.instT2Space, AddSubgroup.isComplement_range_left, Algebra.FormallySmooth.mk_lift, RingHom.lift_injective_of_ker_le_ideal, AdicCompletion.coe_eval, QuotientAddGroup.measurable_from_quotient, IsPrimitiveRoot.finite_quotient_span_sub_one', Ideal.mem_quotient_iff_mem, Subgroup.index_eq_zero_iff_infinite, QuotientRing.isOpenMap_coe, QuotientAddGroup.fg, QuotientGroup.quotientKerEquivOfRightInverse_symm_apply, AdicCompletion.factorₐ_evalₐ_one, Submodule.ker_liftQ_eq_bot', TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, QuotientRing.isQuotientMap_coe_coe, Ideal.quotientKerAlgEquivOfRightInverse_apply, Subgroup.quotientEquivProdOfLE_symm_apply, quotient_norm_add_le, QuotientAddGroup.ker_le_range_iff, IsPrimitiveRoot.finite_quotient_span_sub_one, AdicCompletion.val_mul, Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisors, QuotientGroup.map_id, Ideal.Quotient.mk_span_range, Submodule.Quotient.mk_smul, Algebra.PreSubmersivePresentation.naive_toPresentation, MulAction.coe_quotient_smul_fixedPoints, Polynomial.quotientSpanXSubCAlgEquiv_mk, isFiniteLength_quotient_span_singleton, QuotientAddGroup.mk'_comp_subtype, Submodule.mkQ_apply, instIsAlgebraicQuotientIdealResidueField, DoubleQuot.ker_quotQuotMk, AddSubgroup.discreteTopology, ringKrullDim_le_ringKrullDim_quotient_add_card, AdicCompletion.mk_ofAlgEquiv_symm, Ideal.exact_mulQuot_quotOfMul, AdicCompletion.mk_smul_mk, AddCircle.coe_nsmul, AlgHom.IsArithFrobAt.restrict_injective, Submodule.card_quotient_mul_card_quotient, DoubleQuot.coe_quotQuotEquivQuotSupₐ, Submodule.factor_comp, Ideal.quotientMulEquivQuotientProd_snd, QuotientAddGroup.strictMono_comap_prod_map, QuotientAddGroup.mk_add, Ideal.height_le_ringKrullDim_quotient_add_one, Subspace.flip_quotDualCoannihilatorToDual_bijective, rank_quotient_add_rank_of_isDomain, Ideal.isPrime_map_quotientMk_of_isPrime, AddSubgroup.Characteristic.comap_quotient_mk, AddSubgroup.isComplement_addSubgroup_right_iff_bijective, algebraMap_mk, Ideal.Quotient.stabilizerHom_apply, Ideal.fst_comp_quotientMulEquivQuotientProd, Submodule.quotEquivOfEqBot_apply_mk, QuotientGroup.dense_preimage_mk, AddSubgroup.isComplement_addSubgroup_right_iff_existsUnique_quotientAddGroupMk, IsSemisimpleModule.exists_quotient_linearEquiv_submodule, LinearMap.quotientInfEquivSupQuotient_injective, QuotientGroup.mk'_comp_subtype, QuotientAddGroup.equivIcoMod_symm_apply, RingTheory.Sequence.IsWeaklyRegular.regular_mod_prev, QuotientGroup.mk'_eq_mk', QuotientGroup.map_mk', AlgebraicGeometry.IsClosedImmersion.spec_of_quotient_mk, QuotientAddGroup.image_coe_inj, Ideal.Quotient.torsionBy_eq_span_singleton, QuotientAddGroup.comap_map_mk', RingHom.pi_bijective_of_isIdempotentElem, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, QuotSMulTop.equivQuotTensor_naturality, QuotientAddGroup.instCompactSpaceQuotientAddSubgroup, QuotientAddGroup.sound, MulAction.isPretransitive_quotient, KaehlerDifferential.derivationQuotKerTotal_apply, ModP.preVal_mk, Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le, AdicCompletion.transitionMap_comp_reduceModIdeal, Ideal.Quotient.nontrivial, AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule, isNoetherian_of_liesOver, Ideal.map_quotient_self, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, QuotientGroup.map_mk, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, Submodule.dualCopairing_apply, QuotientGroup.measurableSMul, QuotientGroup.quotientMapSubgroupOfOfLe_mk, Submodule.le_comap_mkQ, finite_iff_ideal_quotient, Ideal.Quotient.exists_algEquiv_fixedPoint_quotient_under, QuotientAddGroup.homQuotientZSMulOfHom_comp_of_rightInverse, LinearMap.exact_smul_id_smul_top_mkQ, Ideal.mk_mem_cotangentIdeal, Int.quotientSpanEquivZMod_comp_castRingHom, coe_lowerCentralSeries_ideal_quot_eq, IsPGroup.cyclic_center_quotient_of_card_eq_prime_sq, associatedPrimes.eq_singleton_of_isPrimary, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, AddCircle.coe_image_Icc_eq, Submodule.Quotient.restrictScalarsEquiv_symm_mk, QuotientAddGroup.preimage_image_mk_eq_add, QuotientGroup.ker_map, Submodule.finite_quotient_smul, Ideal.Quotient.alg_map_eq, MeasureTheory.QuotientMeasureEqMeasurePreimage.smulInvariantMeasure_quotient, Submodule.natAbs_det_equiv, Rep.quotientToInvariantsFunctor_map_hom, module_finite_of_liesOver, Ideal.quotientMap_mk, AdicCompletion.smul_mk, Submodule.mapQ_eq_factor, exists_integral_inj_algHom_of_quotient, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, Rep.quotientToCoinvariantsFunctor_map_hom, quotAdjoinEquivQuotMap_apply_mk, AddSubgroup.index_ne_zero_iff_finite, MixedCharZero.charP_quotient, QuotientGroup.lift_mk', LinearMap.injective_range_liftQ_of_exact, QuotientAddGroup.nhds_zero_hasBasis, Module.Grassmannian.finite_quotient, Module.Presentation.cokernel_var, AddCircle.coe_real_preimage_closedBall_inter_eq, AddSubgroup.vadd_leftQuotientEquiv, IsLocalizedModule.toLocalizedQuotient', IsPrimitiveRoot.finite_quotient_toInteger_sub_one, Ideal.Quotient.lift_mk, Ideal.quotientToQuotientRangePowQuotSucc_surjective, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, WittVector.ker_map_le_ker_mk_comp_ghostComponent, IsLocalization.Away.quotient_of_isIdempotentElem, Algebra.FormallyUnramified.comp_injective, WittVector.fontaineThetaModPPow_teichmuller, Submodule.quotientPi_apply, QuotientGroup.discreteTopology_iff, rTensor.inverse_of_rightInverse_comp_rTensor, AddCircle.coe_image_Ioc_eq, Ideal.Quotient.factor_surjective, Subspace.quotAnnihilatorEquiv_apply, Subgroup.quotientiInfSubgroupOfEmbedding_apply_mk, Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy, QuotientGroup.kerLift_injective, QuotientAddGroup.quotientAddEquivOfEq_mk, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, RingTheory.Sequence.isWeaklyRegular_append_iff', Valuation.supp_quot, QuotientAddGroup.ker_lift, Ideal.kerLiftAlg_toRingHom, instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient, isNoetherian_quotient, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, OrthogonalIdempotents.surjective_pi, Ideal.ker_tensorProductMk_quotient, instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient, Ideal.Quotient.eq_zero_iff_mem, ringKrullDim_add_length_eq_ringKrullDim_of_isRegular, TensorProduct.quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, tensorKaehlerQuotKerSqEquiv_tmul_D, QuotientGroup.instT3Space, Subgroup.quotientEquivSigmaZMod_apply, TensorProduct.tensorQuotientEquiv_apply_mk_tmul, isSMulRegular_quotient_iff_mem_of_smul_mem, Ideal.finrank_quotient_map, derivationToSquareZeroEquivLift_symm_apply_apply_coe, WittVector.ghostComponentModPPow_teichmuller_coeff, rTensor.inverse_comp_rTensor, Ideal.Quotient.algEquivOfEqComap_apply, QuotientAddGroup.lift_comp_mk', surjective_cosetToCuspOrbit, Ideal.quotEquivOfEq_eq_factor, AddSubgroup.isAddQuotientCoveringMap, Ideal.quotientKerAlgEquivOfSurjective_apply, DoubleQuot.quotQuotMkₐ_toRingHom, Action.FintypeCat.quotientToEndHom_mk, LinearMap.liftQ₂_mk, Submodule.quotientEquivOfIsCompl_apply_mk_coe, Ideal.ker_quotient_lift, QuotientGroup.quotientQuotientEquivQuotientAux_mk_mk, Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing, QuotientGroup.congr_apply, Submodule.comapMkQOrderEmbedding_eq, QuotientAddGroup.lift_mk, Ideal.height_le_ringKrullDim_quotient_add_encard, Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx, RingHom.prod_bijective_of_isIdempotentElem, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ, QuotientGroup.preimage_image_mk_eq_iUnion_image, groupHomology.π_comp_H1Iso_hom_apply, QuotientAddGroup.mk_sub, RingHom.quotientKerEquivOfRightInverse.Symm.apply, LinearMap.quotKerEquivRange_symm_apply_image, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, AdicCompletion.Ideal.mk_eq_mk, rTensor_mkQ, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, LinearMap.reduceModIdeal_apply, RingTheory.Sequence.isWeaklyRegular_append_iff, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_nonZeroDivisors, AdjoinRoot.quotEquivQuotMap_apply_mk, LieModule.isNilpotent_quotient_iff, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Submodule.Quotient.equiv_symm_apply, Submodule.pi_liftQ_eq_liftQ_pi, QuotientAddGroup.quotientKerEquivOfRightInverse_symm_apply, QuotientGroup.mk_pow, Ideal.comap_map_quotientMk, Algebra.FormallySmooth.exists_lift, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, Subgroup.instFiniteQuotientSubtypeMemOpenSubgroupOfIsTopologicalGroupOfCompactSpace, HasRankNullity.rank_quotient_add_rank, QuotientGroup.continuous_mk, quotient_norm_mk_eq, Ideal.minimalPrimes_eq_comap, Submodule.unitsQuotEquivRelPic_symm_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, Submodule.torsionBy.mk_ideal_smul, QuotientGroup.range_mk', Ideal.Quotient.mkₐ_ker, QuotientGroup.range_mk, IsModuleTopology.instQuot, AddSubgroup.quotientiInfEmbedding_apply, Submodule.comap_map_mkQ, AddCircle.norm_coe_eq_abs_iff, AddSubgroup.leftCoset_cover_const_iff_surjOn, Ideal.Quotient.mk_surjective, QuotientAddGroup.measurable_coe, Ideal.Quotient.eq, Ideal.quotientEquivAlgOfEq_mk, QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk, Submodule.ker_liftQ_eq_bot, RingHom.quotientKerEquivOfSurjective_apply_mk, QuotientAddGroup.btw_coe_iff, QuotientGroup.strictMono_comap_prod_image, Module.IsTorsionBySet.quotient, LieSubmodule.Quotient.map_mk'_eq_bot_le, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, Polynomial.Monic.finite_quotient, QuotientGroup.homQuotientZPowOfHom_comp_of_rightInverse, Submodule.Quotient.instSmallQuotient, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson, CharP.quotient', MulAction.stabilizer_quotient, idealFactorsEquivOfQuotEquiv_symm, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, Ideal.injective_lift_iff, QuotientAddGroup.dense_image_mk, QuotientGroup.ker_lift, comap_upperCentralSeries_quotient_center, Submodule.Quotient.nontrivial_of_ne_top, Ideal.quotOfMul_surjective, Ideal.Quotient.factor_ker, LinearMap.quotKerEquivRange_apply_mk, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, Ideal.snd_comp_quotientMulEquivQuotientProd, Ideal.Quotient.isScalarTower_of_liesOver, DoubleQuot.ker_quotLeftToQuotSup, MulAction.Quotient.mk_smul_out, Algebra.FormallySmooth.comp_surjective, QuotientAddGroup.mk_nat_mul, AddCircle.denseRange_zsmul_coe_iff, isSimpleModule_iff_quot_maximal, Ideal.annihilator_quotient, Algebra.FormallyEtale.iff_comp_bijective, QuotientGroup.fg, Ideal.quotientEquiv_apply, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, Ideal.quotientInfEquivQuotientProd_snd, LieSubmodule.Quotient.isCentralScalar, QuotientAddGroup.norm_lift_apply_le, QuotientAddGroup.instDiscreteMeasurableSpace, LieHom.quotKerEquivRange_invFun, Subgroup.index_ne_zero_iff_finite, Submodule.isOpenMap_mkQ, MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, Subgroup.transferTransversal_apply', Submodule.quotientEquivOfIsCompl_symm_apply, Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot, Ring.DirectLimit.quotientMk_of, IsSemiprimaryRing.isSemisimpleRing, Ideal.cotangentEquivIdeal_apply, QuotientGroup.map_normal, Ideal.comap_map_mk, AddCircle.coe_eq_zero_of_pos_iff, QuotientGroup.instContinuousSMul, MulAction.orbitEquivQuotientStabilizer_symm_apply, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, Ideal.quotientToQuotientRangePowQuotSucc_injective, AddSubgroup.finite_quotient_of_finiteIndex, AddSubgroup.instDiscreteTopologyQuotientOfContinuousAdd, QuotientAddGroup.mk_zero, Submodule.finiteQuotientOfFreeOfRankEq, LieSubmodule.Quotient.surjective_mk', EqualCharZero.nonempty_algebraRat_iff, MulActionHom.toQuotient_apply, QuotientGroup.homQuotientZPowOfHom_comp, QuotientAddGroup.instLocallyCompactSpace, groupCohomology.H1InfRes_X₁, QuotientGroup.subsingleton_quotient_top, Rep.quotientToInvariantsFunctor_obj_V, Ideal.Quotient.ringHom_ext_iff, Subgroup.quotientiInfEmbedding_apply_mk, QuotientAddGroup.norm_mk_eq_zero, QuotientGroup.exists_norm_mk_lt, TensorProduct.quotTensorEquivQuotSMul_symm_mk, Subgroup.finiteIndex_iff_finite_quotient, Submodule.quotDualCoannihilatorToDual_injective, Submodule.quotientPi_symm_apply, AlgebraicGeometry.IsClosedImmersion.Spec_iff, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, QuotientGroup.completeSpace_left', Subgroup.quotientiInfEmbedding_apply, ringKrullDim_le_ringKrullDim_add_card, Module.jacobson_quotient_of_le, RingHom.kerLift_injective, SlashInvariantForm.coe_trace, Ideal.Quotient.isDomain, Submodule.liftQ_apply, QuotientGroup.lift_surjective_of_surjective, MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse, KaehlerDifferential.kerTotal_mkQ_single_mul, AdicCompletion.evalOneₐ_of, Subgroup.isComplement_range_left, Algebra.FormallySmooth.iff_split_surjection, AddCircle.norm_neg_period, QuotientAddGroup.quotientBot_apply, Ideal.Quotient.mk_out, instIsArtinianRingQuotientIdeal, ClassGroup.equivPic_symm_apply, QuotientAddGroup.equivIocMod_symm_apply, Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot, Subgroup.card_quotient_dvd_card, Submodule.Quotient.isCentralScalar, AdicCompletion.val_add, LieSubmodule.Quotient.lieModuleHom_ext_iff, Submodule.isQuotientEquivQuotientPrime_iff, Algebra.trace_quotient_mk, Finset.le_card_quotient_mul_sq_inter_subgroup, QuotientAddGroup.quotientKerEquivOfRightInverse_apply, UnitAddCircle.norm_eq, Submodule.quotientPi_aux.map_add, Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk, Module.Presentation.cokernel_G, QuotientGroup.congr_mk', Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Finset.le_card_quotient_add_sq_inter_addSubgroup, QuotientGroup.mk_inv, MvPolynomial.quotient_mk_comp_C_injective, QuotSMulTop.equivQuotTensor_naturality_mk, Module.exists_isPrincipal_quotient_of_finite, QuotientAddGroup.preimage_image_coe, AddAction.orbitEquivQuotientStabilizer_symm_apply, AddSubgroup.surjective_normedMk, AlgebraicClosure.Monics.map_eq_prod, LinearMap.exact_map_mkQ_range, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, AdicCompletion.val_one, QuotientAddGroup.mk_zsmul, Ideal.quotientMap_injective', Submodule.mkQ_map_self, MulAction.zpowersQuotientStabilizerEquiv_symm_apply, QuotientAddGroup.mk_nsmul, Subgroup.quotient_finite_of_isOpen', Module.equiv_free_prod_directSum, Ideal.quotientEquivAlg_symm, AlgHom.IsArithFrobAt.card_pos, rank_quotient_add_rank_le, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, MulAction.injective_ofQuotientStabilizer, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, RingHom.IsIntegral.quotient, QuotientAddGroup.btw_coe_iff', Submodule.toLocalizedQuotient'_mk, QuotientAddGroup.image_coe, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, QuotientAddGroup.instFirstCountableTopology, IsDedekindDomain.selmerGroup.fromUnit_ker, Ideal.Factors.finrank_pow_ramificationIdx, AddCircle.continuous_mk', DividedPowers.Quotient.isDPMorphism, Ideal.quotientMulEquivQuotientProd_fst, Submodule.Quotient.mk_surjective, AddCircle.coe_real_preimage_closedBall_period_zero, MulAction.stabilizer_image_coe_quotient, KaehlerDifferential.kerTotal_mkQ_single_smul, QuotientAddGroup.dense_preimage_mk, Submodule.topologicalAddGroup_quotient, Subgroup.goursat_surjective, IsPrimitiveRoot.card_quotient_toInteger_sub_one, QuotientGroup.isOpenMap_coe, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, Algebra.weaklyQuasiFiniteAt_iff, Ideal.rank_pow_quot_aux, QuotientAddGroup.comap_comap_center, Ideal.Quotient.mkₐ_eq_mk, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Ideal.rootsOfUnityMapQuot_apply, StandardEtalePresentation.toPresentation_σ', TensorProduct.quotientTensorEquiv_apply_tmul_mk, Submodule.QuotientTorsion.instIsTorsionFree, Submodule.Quotient.isScalarTower, solvable_quotient_of_solvable, QuotientAddGroup.instContinuousConstVAdd, Module.IsTorsionBySet.isScalarTower, AddSubgroup.ker_normedMk, QuotientAddGroup.isQuotientMap_mk, Module.isTorsionBySet_quotient_iff, AdicCompletion.surjective_evalₐ, ZSpan.quotientEquiv.symm_apply, QuotientGroup.exists_norm_mul_lt, WittVector.quotientPEquiv_mk, instIsIntegralQuotientIdeal, QuotientAddGroup.mk_sum, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, AdicCompletion.transitionMap_map_pow, QuotientGroup.equivQuotientZPowOfEquiv_trans, isAssociatedPrime_iff_exists_injective_linearMap, rank_quotient_le, Ideal.Quotient.ker_stabilizerHom, Ideal.rank_pow_quot, EqualCharZero.iff_not_mixedCharZero, QuotientAddGroup.map_mk', AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, Ideal.map_height_le_one_of_mem_minimalPrimes, Submodule.mk_quotientEquivOfIsCompl_apply, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, QuotientGroup.comap_map_mk', Subspace.dualCopairing_nondegenerate, Submodule.map_liftQ, Submodule.piQuotientLift_single, LieSubmodule.Quotient.mk_eq_zero', QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, CategoryTheory.PreGaloisCategory.has_decomp_quotients, LieSubalgebra.normalizer_eq_self_iff, Submodule.liftQSpanSingleton_apply, Module.IsTorsionBySet.isSemisimpleModule_iff, Submodule.Quotient.mk_neg, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, Subgroup.index_eq_card, Ideal.pi_mkQ_rTensor, KaehlerDifferential.quotKerTotalEquiv_symm_apply, NormedAddGroupHom.lift_norm_le, Ideal.quotientKerAlgEquivOfSurjective_symm_apply, IsDedekindDomain.selmerGroup.fromUnitLift_injective, LinearMap.quotKerEquivOfSurjective_symm_apply, Submodule.mapQ_mkQ, LieSubmodule.Quotient.mk_bracket, NumberField.Units.logEmbeddingQuot_injective, Ideal.quotientKerAlgEquivOfSurjective_mk, Ideal.Quotient.nontrivial_of_liesOver_of_ne_top, Ideal.mem_quotient_iff_mem_sup, QuotientGroup.map_id_apply, rTensor.inverse_apply, AdicCompletion.val_sub, Module.Basis.sumQuot_inr, IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure, DoubleQuot.quotQuotEquivCommₐ_toRingEquiv, DoubleQuot.coe_quotQuotToQuotSupₐ, Ideal.Quotient.norm_mk_lt, Submodule.quotientPi_aux.left_inv, Valuation.onQuot_comap_eq, AlgEquiv.quotientBot_symm_mk, IsLocalRing.basisQuotient_apply, Ideal.torsionMapQuot_injective, Action.FintypeCat.quotientToQuotientOfLE_hom_mk, RingTheory.Sequence.IsRegular.quot_ofList_smul_nontrivial, Ideal.injective_algebraMap_quotient_residueField, Subgroup.quotientCenterEmbedding_apply, trace_quotient_eq_trace_localization_quotient, Ideal.Quotient.mk_eq_mk_iff_sub_mem, Ideal.quotientEquiv_mk, Ideal.quotientMap_surjective, AdicCompletion.val_neg, Ideal.ker_quotientMap_mk, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, Ideal.Quotient.algebra_isIntegral_of_liesOver, Ideal.powQuotSuccInclusion_injective, Module.isTorsionBy_quotient_iff, Submodule.factor_comp_apply, Submodule.quotEquivOfEq_mk, QuotientGroup.measurable_coe, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, Algebra.trace_quotient_eq_of_isDedekindDomain, Ideal.quotient_map_comp_mkₐ, Subgroup.isQuotientCoveringMap_of_comm, StandardEtalePair.aeval_X_g_mul_mk_X, AdicCompletion.transitionMap_ideal_mk, idealFactorsFunOfQuotHom_id, Finset.card_pow_quotient_mul_pow_inter_subgroup_le, ModularForm.coe_norm, QuotientAddGroup.quotientBot_symm_apply, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply, Ideal.Quotient.smulCommClass', Ideal.finite_quotient_pow, instIsScalarTowerQuotientIdealResidueField, Ideal.card_stabilizer_eq_card_inertia_mul_finrank, AdicCompletion.transitionMap_map_mul, QuotientAddGroup.addMonoidHom_ext_iff, Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, QuotientAddGroup.isClosedMap_coe, NormedAddGroupHom.norm_lift_le, Ideal.quotientInfToPiQuotient_mk', AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, Ideal.Quotient.mk_eq_mk, nilpotencyClass_quotient_le, Sylow.card_quotient_normalizer_modEq_card_quotient, Function.Exact.linearEquivOfSurjective_apply, QuotientAddGroup.range_mk', Subgroup.normalCore_eq_ker, Ideal.quotEquivOfEq_symm, groupHomology.H1CoresCoinfOfTrivial_g, Subgroup.quotientiInfSubgroupOfEmbedding_apply, LinearMap.coe_quotientInfToSupQuotient, Submodule.range_dualMap_mkQ_eq, QuotientAddGroup.map_mk, Ideal.Quotient.instRingHomSurjectiveQuotientMk, QuotientGroup.map_comp_map, groupCohomology.π_comp_H2Iso_hom_apply, QuotientAddGroup.lift_surjective_of_surjective, QuotientGroup.automorphize_smul_left, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, CharP.quotient, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, AddAction.Quotient.vadd_mk, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Algebra.FormallyUnramified.quotient, isLocalHom_of_le_jacobson_bot, QuotientAddGroup.equivQuotientZSMulOfEquiv_refl, QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff, LieSubmodule.Quotient.lieQuotientLieModule, QuotientAddGroup.norm_eq_addGroupSeminorm, Ideal.quotientInfToPiQuotient_mk, derivationToSquareZeroEquivLift_apply_coe_apply, QuotientGroup.norm_eq_infDist, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, QuotientGroup.le_norm_iff, QuotientAddGroup.continuous_mk, AlgHom.ker_kerSquareLift, height_le_ringKrullDim_quotient_add_spanFinrank, liftOfDerivationToSquareZero_mk_apply', Ideal.quotientInfEquivQuotientProd_fst, Ideal.univ_eq_iUnion_image_add, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, QuotientGroup.mk_zpow, QuotientAddGroup.map_normal, AddCircle.coe_period, Submodule.finite_dualAnnihilator_iff, QuotientAddGroup.map_id, Algebra.FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eq, Representation.quotient_apply, groupCohomology.π_comp_H1Iso_hom_apply, Ideal.quotientMap_algebraMap, DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv, Algebra.FormallyUnramified.iff_comp_injective, WittVector.quotEquivOfEq_ghostComponentModPPow, AdicCompletion.evalₐ_of, CosetSpace.borelSpace, QuotientGroup.measurable_from_quotient, Ideal.Quotient.isNoetherianRing, AdjoinRoot.quotEquivQuotMap_symm_apply, CompleteOrthogonalIdempotents.bijective_pi', PowerSeries.isWeierstrassDivisionAt_iff, StandardEtalePresentation.toPresentation_val, Ideal.isDomain_map_C_quotient, Ideal.height_le_height_add_encard_of_subset, QuotientGroup.instContinuousConstSMul, QuotientAddGroup.map_map, linearIndepOn_union_iff_quotient, Subgroup.transferFunction_apply, QuotientAddGroup.lift_quot_mk, QuotientGroup.card_preimage_mk, DividedPowers.Quotient.dpow_apply, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, QuotientAddGroup.nhds_eq, NormedAddGroupHom.isQuotientQuotient, Ideal.Quotient.mk_eq_one_iff_sub_mem, Algebra.instEssFiniteTypeQuotientIdeal, Submodule.ker_mkQ, QuotientAddGroup.norm_mk_le_norm, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, groupHomology.π_comp_H2Iso_hom_apply, QuotientGroup.preimage_image_coe, Submodule.quotientPiLift_mk, Submodule.continuousSMul_quotient, AddCircle.addOrderOf_period_div, measurePreserving_quotientAddGroup_mk_of_AddQuotientMeasureEqMeasurePreimage, Subgroup.IsComplement'.QuotientMulEquiv_symm_apply, Submodule.mkQ_surjective, Subgroup.instFiniteQuotientOfContinuousMulOfCompactSpace, topologicalRing_quotient, Ideal.quotientMap_injective, AdicCompletion.evalOneₐ_surjective, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul, AdicCompletion.factor_evalₐ_eq_eval, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, AddAction.stabilizer_image_coe_quotient, isStronglyTranscendental_mk_of_mem_minimalPrimes, QuotientAddGroup.preimage_image_mk_eq_iUnion_image, Function.Exact.linearEquivOfSurjective_symm_apply, Ideal.Factors.finiteDimensional_quotient_pow, QuotientAddGroup.kerLift_mk', Module.length_quotient, AddSubgroup.index_eq_card, Ideal.cotangentEquivIdeal_symm_apply, Ideal.Quotient.smulCommClass, QuotientAddGroup.equivIcoMod_zero, QuotientGroup.instT1Space, AddCircle.norm_eq, RingHom.quotientKerEquivOfRightInverse.apply, fourier_coe_apply', NumberField.Units.logEmbeddingEquiv_apply, Ideal.Quotient.liftₐ_apply, QuotientAddGroup.automorphize_smul_left, isJacobsonRing_quotient, MvPolynomial.eval₂_C_mk_eq_zero, isSimpleModule_iff_isCoatom, QuotientGroup.monoidHom_ext_iff, Ideal.Quotient.instNonemptyQuotient, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, QuotientAddGroup.equivIcoMod_coe, QuotientAddGroup.quotientQuotientEquivQuotientAux_mk, QuotientGroup.mk_surjective, Module.supportDim_quotient_eq_ringKrullDim, AdicCompletion.eval_of, rank_quotient_add_rank_of_divisionRing, QuotientGroup.quotientBot_apply, QuotientGroup.isOpenQuotientMap_mk, QuotientAddGroup.eq_zero_iff, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, ringKrullDim_le_ringKrullDim_add_spanFinrank, Submodule.quotientPi_aux.right_inv, AddCircle.addOrderOf_div_of_gcd_eq_one', QuotientAddGroup.mk_int_mul, LinearMap.det_eq_det_mul_det, isSMulRegular_on_quot_iff_lsmul_comap_eq, Ideal.Quotient.finite_of_isInvariant, AddCircle.coe_image_Ico_eq, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, AdicCompletion.evalₐ_mk, QuotientAddGroup.mk'_surjective, DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, Ideal.KerLift.map_smul, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, QuotientGroup.congr_mk, Subgroup.transferTransversal_apply'', Algebra.IsIntegral.quotient, QuotientGroup.preimage_mk_one, DoubleQuot.quotQuotEquivComm_mk_mk, AddSubgroup.quotientEquivProdOfLE_apply, Module.exists_surjective_quotient_of_finite, AlgHom.IsArithFrobAt.restrict_mk, AdicCompletion.evalₐ_mkₐ, Ideal.ncard_primesOver_mul_card_inertia_mul_finrank, Algebra.Presentation.quotientEquiv_mk, Submodule.Quotient.subsingleton_iff, CharacterModule.intSpanEquivQuotAddOrderOf_apply_self, QuotientAddGroup.discreteTopology, QuotientGroup.instFirstCountableTopology, Submodule.Quotient.smulCommClass, EqualCharZero.of_algebraRat, isSemiprimaryRing_iff, QuotientAddGroup.kerLift_injective, QuotientAddGroup.eq_class_eq_leftCoset, QuotientAddGroup.mk_neg, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, upperCentralSeriesStep_eq_comap_center, nilpotencyClass_eq_quotient_center_plus_one, QuotientAddGroup.map_mk'_self, QuotientGroup.map_mk'_self, AddSubgroup.finiteIndex_iff_finite_quotient, AddSubgroup.norm_normedMk, ClassGroup.equiv_mk0, Ideal.Quotient.quotient_ring_saturate, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, Module.Grassmannian.projective_quotient, Subgroup.isComplement_subgroup_right_iff_existsUnique_quotientGroupMk, Subgroup.card_mul_eq_card_subgroup_mul_card_quotient, Ideal.Quotient.factorₐ_comp, AdicCompletion.val_zero, Valuation.self_le_supp_comap, groupHomology.π_comp_H1Iso_inv_apply, Ideal.mk_ker, LinearMap.quotientInfEquivSupQuotient_symm_apply_left, QuotientAddGroup.exists_norm_add_lt, Sylow.prime_dvd_card_quotient_normalizer, Ideal.height_le_height_add_spanFinrank_of_le, AddCircle.intCast_div_mul_eq_zsmul, groupHomology.H1CoresCoinfOfTrivial_X₃, AdicCompletion.mk_apply_coe, Submodule.torsionBySet.mk_smul, Subgroup.quotientEquivSigmaZMod_symm_apply, QuotientGroup.ker_le_range_iff, Submodule.Quotient.norm_mk_le, QuotientGroup.mk'_surjective, NumberField.Units.instFiniteIntAdditiveQuotientUnitsRingOfIntegersSubgroupTorsion, Ideal.Quotient.factor_comp, QuotientGroup.equivQuotientZPowOfEquiv_refl, QuotientGroup.mk_mul, IsLocalRing.map_mkQ_eq_top, CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroup, Ideal.Quotient.mk_comp_algebraMap, QuotientGroup.image_coe, DoubleQuot.coe_quotQuotEquivCommₐ, QuotientGroup.norm_eq_groupSeminorm, RingTheory.Sequence.map_first_exact_on_four_term_right_exact_of_isSMulRegular_last, AddCircle.addOrderOf_coe_rat, RingTheory.Sequence.isWeaklyRegular_iff, Subgroup.IsComplement'.QuotientMulEquiv_apply, StandardEtalePresentation.toPresentation_relation, Submodule.mapQ_comp, Ideal.fst_comp_quotientInfEquivQuotientProd, Sylow.instFiniteQuotientSubgroupNormalizerOfFactPrime, CharP.quotient_iff_le_ker_natCast, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk, Submodule.goursat_surjective, measurePreserving_quotientGroup_mk_of_QuotientMeasureEqMeasurePreimage, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, IsDedekindDomain.exists_representative_mod_finset, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι_ι, QuotientGroup.norm_lt_iff, AddSubgroup.quotient_finite_of_isOpen, AdicCompletion.transitionMap_comp_eval_apply, QuotientAddGroup.borelSpace, MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, Ideal.quotient_mk_maps_eq, QuotientGroup.equivQuotientZPowOfEquiv_symm, QuotientGroup.mk_prod, TensorProduct.quotTensorEquivQuotSMul_comp_mk, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_smul, AddCircle.norm_eq', QuotientGroup.comap_comap_center, Subgroup.IsComplement.leftQuotientEquiv_apply, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, QuotientGroup.instLocallyCompactSpace, isIntegral_quotientMap_iff, Submodule.finrank_quotient_le, AddValuation.comap_onQuot_eq, MeasureTheory.AddQuotientMeasureEqMeasurePreimage.addHaarMeasure_quotient, AlgebraicGeometry.Scheme.Hom.toImage_app, Ideal.Quotient.lift_comp_mk, Algebra.isSeparable_residueField_iff, QuotientGroup.map_map, ClassGroup.equivPic_apply, AdicCompletion.val_zero_apply, QuotientAddGroup.instT1Space, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, rank_quotient_eq_of_le_torsion, QuotientGroup.instIsTopologicalGroup, QuotientGroup.ker_mk', Module.Finite.exists_fin_quot_equiv, Submodule.finrank_quotient, Sylow.card_eq_card_quotient_normalizer, Submodule.liftQ_mkQ, ModularForm.coe_trace, PreTilt.mk_untilt_eq_coeff_zero, LieSubmodule.Quotient.isNoetherian, Submodule.dualAnnihilator_eq_bot_iff', AddSubgroup.quotientAddSubgroupOfEmbeddingOfLE_apply_mk, AlgHom.kerSquareLift_mk, Ideal.Quotient.factor_eq, AddSubgroup.goursat, LinearMap.ker_le_range_iff, Ideal.bijective_algebraMap_quotient_residueField, isSMulRegular_on_quot_iff_lsmul_comap_le, WittVector.mk_fontaineTheta, Submodule.Quotient.norm_mk_lt, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, IsNilpotent.isUnit_quotient_mk_iff, AddCircle.coe_add, QuotientGroup.dense_image_mk, Ideal.Quotient.norm_mk_le, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, Ideal.snd_comp_quotientInfEquivQuotientProd, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, MeasureTheory.IsAddFundamentalDomain.absolutelyContinuous_map, Submodule.ker_liftQ, Submodule.QuotientTorsion.torsion_eq_bot, QuotientGroup.eq_one_iff, AddSubgroup.normedMk.apply, PowerSeries.IsWeierstrassDivisorAt.seq_one, TensorProduct.tensorQuotientEquiv_symm_apply_tmul_mk, LieSubmodule.Quotient.mk'_apply, DoubleQuot.quotLeftToQuotSupₐ_toRingHom, LinearMap.ker_eq_bot_range_liftQ_iff, Ideal.bot_quotient_isMaximal_iff, AdicCompletion.eval_surjective, QuotientGroup.lift_quot_mk, Subgroup.commProb_quotient_le, MixedCharZero.reduce_to_maximal_ideal, AddCircle.isCoveringMap_coe, Ideal.Factors.piQuotientEquiv_mk, Ideal.quotient_map_mkₐ, RingHom.kerLift_mk, Rep.mkQ_hom, CategoryTheory.ShortComplex.abLeftHomologyData_H_coe, QuotientGroup.strictMono_comap_prod_map, groupCohomology.H1InfRes_f, Submodule.Quotient.nontrivial_iff, IsLocalRing.finite_quotient_iff, QuotientRing.isOpenQuotientMap_mk, Ideal.quotientEquivAlgOfEq_symm, AdicCompletion.transitionMap_map_one, Module.jacobson_quotient_jacobson, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, Ideal.Quotient.isScalarTower_right, QuotientGroup.quotientBot_symm_apply, QuotientGroup.mk_div, Subspace.quotDualCoannihilatorToDual_bijective, LinearMap.ker_tensorProductMk, Ideal.ringChar_quot, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, lTensor_mkQ, QuotientAddGroup.card_quotient_rightRel, Ideal.cotangentIdeal_square, QuotientGroup.le_comap_mk', CharP.quotient_iff, Subgroup.quotient_finite_of_isOpen, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, LinearMap.quotientInfEquivSupQuotient_symm_apply_right, Ideal.eval₂_C_mk_eq_zero, Module.torsion_by_prime_power_decomposition, QuotientAddGroup.rangeKerLift_injective, AddValuation.supp_quot_supp, Ideal.Quotient.liftₐ_comp, Ideal.Quotient.mk_smul_mk_quotient_map_quotient, AdicCompletion.eval_apply, IsSemisimpleModule.quotient, AddValuation.supp_quot, AddSubgroup.card_quotient_dvd_card, Submodule.Quotient.equiv_trans, MeasureTheory.AddQuotientMeasureEqMeasurePreimage.vaddInvariantMeasure_quotient, IsLocalRing.isOpen_iff_finite_quotient, Subgroup.isComplement_subgroup_right_iff_bijective, Ideal.Quotient.mkₐ_surjective, KaehlerDifferential.quotKerTotalEquiv_apply, nilpotent_quotient_of_nilpotent, IsDedekindDomain.quotientEquivPiFactors_mk, AddAction.ofQuotientStabilizer_vadd, MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, quotient_prod_linearEquiv, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, Ring.jacobson_quotient_jacobson, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, Algebra.FinitePresentation.quotient, QuotientAddGroup.instIsAddTorsionFree, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, AddCircle.norm_eq_of_zero, Sylow.mem_fixedPoints_mul_left_cosets_iff_mem_normalizer, Module.IsTorsionBy.mk_smul, instCompactSpaceQuotientIdeal, MulAction.ofQuotientStabilizer_smul, RingTheory.Sequence.isRegular_cons_iff', Submodule.Quotient.restrictScalarsEquiv_mk, Subgroup.Characteristic.comap_quotient_mk, LinearMap.quotientInfEquivSupQuotient_surjective, ClassGroup.mk_def, QuotientGroup.subsingleton_iff, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, QuotientGroup.sound, Ideal.Quotient.zero_eq_one_iff, Module.finrank_quotient_add_finrank_le, Ideal.finiteQuotientOfFreeOfNeBot, AlgebraicGeometry.Scheme.Hom.liftQuotient_comp_assoc, DoubleQuot.coe_liftSupQuotQuotMkₐ, AdicCompletion.val_sum_apply, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, QuotientAddGroup.range_mk, SlashInvariantForm.coe_norm, groupHomology.mapCycles₁_quotientGroupMk'_epi, Submodule.Quotient.mk_eq_zero, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk, LinearMap.quotKerEquivOfSurjective_apply_mk, Submodule.Quotient.nontrivial_of_lt_top, Ideal.Quotient.maximal_ideal_iff_isField_quotient, Algebra.FormallyEtale.comp_bijective, QuotientAddGroup.rangeKerLift_surjective, MulAction.Quotient.smul_coe, Int.quotientSpanNatEquivZMod_comp_castRingHom, QuotientAddGroup.quotientQuotientEquivQuotientAux_mk_mk, Submodule.torsionBy.mk_smul, Submodule.comap_liftQ, groupHomology.π_comp_H2Iso_inv_apply, IsZGroup.instQuotientSubgroupOfFinite, Subgroup.goursat, QuotientGroup.instCompactSpaceQuotientSubgroup, instFiniteQuotientIdealOfIsMaximal, Submodule.Quotient.mk_zero, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, QuotientAddGroup.mk'_apply, AdicCompletion.of_apply, WittVector.ghostComponentModPPow_map_mk, QuotientGroup.norm_mk_le_norm, Algebra.FormallySmooth.iff_comp_surjective, Polynomial.IsDistinguishedAt.coe_natDegree_eq_order_map, AddCosetSpace.borelSpace, AddSubgroup.instFiniteQuotientSubtypeMemOpenAddSubgroupOfIsTopologicalAddGroupOfCompactSpace, Subgroup.IsComplement.quotientGroupMk_leftQuotientEquiv, ClassGroup.equiv_mk, EqualCharZero.of_not_mixedCharZero, AddSubgroup.IsComplement.leftQuotientEquiv_apply, Module.isTorsionBy_quotient_element_smul, QuotientAddGroup.preimage_mk_zero, Ideal.kerLiftAlg_mk, QuotientAddGroup.homQuotientZSMulOfHom_comp, Algebra.Presentation.mem_ker_naive, Module.IsTorsionBy.quotient, Ideal.isRadical_iff_quotient_reduced, Submodule.piQuotientLift_mk, AlgHom.IsArithFrobAt.restrict_apply, Ideal.pi_quotient_surjective, IsDedekindDomain.selmerGroup.valuation_ker_eq, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, QuotientAddGroup.completeSpace_left', NumberField.Units.instFreeIntAdditiveQuotientUnitsRingOfIntegersSubgroupTorsion, Submodule.flip_quotDualCoannihilatorToDual_injective, AlgHom.IsArithFrobAt.finite_quotient, CompleteOrthogonalIdempotents.bijective_pi, Subspace.dualPairing_eq, Submodule.mapQ_id, AdicCompletion.eval_comp_of, Ideal.to_quotient_square_comp_toCotangent, Submodule.factor_comp_mk, ringKrullDim_le_ringKrullDim_quotient_add_encard, Group.exponent_quotient_dvd, Module.Basis.sumQuot_repr_inr, AddCircle.gcd_mul_addOrderOf_div_eq, AdicCompletion.val_smul_apply, Action.FintypeCat.toEndHom_trivial_of_mem, QuotientAddGroup.homQuotientZSMulOfHom_id, DoubleQuot.quotQuotEquivComm_symm, QuotientAddGroup.equivIocMod_coe, Subgroup.isQuotientCoveringMap, Ideal.Factors.piQuotientEquiv_map, instIsFractionRingQuotientIdealResidueField, AddAction.isPretransitive_quotient, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, Submodule.unitsQuotEquivRelPic_apply_coe, derivationQuotKerSq_mk, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, QuotientGroup.quotientMulEquivOfEq_mk, QuotientAddGroup.le_comap_mk', HurwitzZeta.hasSum_int_evenKernel₀, QuotientGroup.t1Space_iff, Ideal.Quotient.noZeroDivisors, Submodule.card_eq_card_quotient_mul_card, AddAction.stabilizer_quotient, QuotientGroup.out_conj_pow_minimalPeriod_mem, Submodule.quotientQuotientEquivQuotientAux_mk_mk, LinearIndepOn.quotient_iff_union, DoubleQuot.quotQuotEquivComm_algebraMap, Submodule.factor_surjective, Submodule.Quotient.equiv_apply, Submodule.natAbs_det_basis_change, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, Ideal.Quotient.mk_algebraMap, AddCircle.natCast_div_mul_eq_nsmul, Submodule.cardQuot_apply, Rep.quotientToCoinvariantsFunctor_obj_V, Algebra.FormallyUnramified.iff_comp_injective_of_small, Submodule.range_liftQ, IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure, Polynomial.isIntegral_isLocalization_polynomial_quotient, Ideal.Quotient.algebraMap_mk_of_liesOver, RingQuot.ringQuotToIdealQuotient_apply, IsLocalRing.quotient_artinian_of_mem_minimalPrimes_of_isLocalRing, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, KummerDedekind.quotMapEquivQuotQuotMap_symm_apply, Ideal.mulQuot_injective, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, QuotientAddGroup.map_id_apply
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