instSetLike 📖 | CompOp | 1160 mathmath: unitary.spectrum.unitary_conjugate, Unitary.openPartialHomeomorph_source, ValuativeRel.ValueGroupWithZero.mk_one_one, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Matrix.UnitaryGroup.toLin'_one, OreLocalization.OreSet.ore_eq, CStarRing.norm_mul_coe_unitary, mem_map_iff_mem, mem_toSubsemigroup, unitary.star_eq_inv', mem_map_equiv, Unitary.mul_left_inj, RatFunc.mk_def_of_ne, mem_closure_iff_of_fintype, SymplecticGroup.transpose_mem_iff, Unitary.conjStarAlgAut_trans_conjStarAlgAut, RatFunc.mk_coe_def, MonoidHom.coe_mrange, coe_ofClass, subsemiringClosure_toAddSubmonoid, CStarRing.norm_unitary_smul, ValuativeRel.ValueGroupWithZero.mk_eq_one, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, Localization.one_rel, LaurentPolynomial.mk'_one_X_pow, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, Real.hasFDerivAt_fourierChar_neg_bilinear_left, IsOfFinOrder.natCard_powers_le_orderOf, Subgroup.equivSMul_apply_coe, equivOp_symm_apply_coe, Ideal.finite_setOf_absNorm_le₀, le_centralizer_centralizer, NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet_mixedEmbedding, isSMulRegular_iff_mem_nonZeroSMulDivisors, ClassGroup.mk0_integralRep, MonoidHom.eqOn_closureM, reindex_mem_doublyStochastic_iff, LaurentPolynomial.mk'_mul_T, LocalizedModule.r.isEquiv, ClassGroup.mk0_eq_mk0_iff, Valuation.val_mrange_zero, PrimeSpectrum.localization_specComap_range, Matrix.UnitaryGroup.toGL_mul, IsOfFinOrder.mem_powers_iff_mem_zpowers, spinGroup.star_eq_inv, Circle.exp_arg, Fintype.card_coeSort_mrange, Circle.injective_arg, mem_own_rightCoset, coe_invOrderIso_apply, Ideal.IsHomogeneous.iff_exists, coe_pi, Localization.mk_le_mk, IsLocalization.smul_mem_finsetIntegerMultiple_span, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk, val_mem_of_mem_units, smul_mem_pointwise_smul_iff₀, spinGroup.coe_star_mul_self, Unitary.conjStarAlgAut_symm, SymplecticGroup.coe_inv, unitary.map_id, IsLocalizationMap.map_units, mul_leftInvEquiv, pinGroup.coe_star_mul_self, Unitary.mem_pathComponentOne_iff, Unitary.toUnits_injective, Subring.addEquivOp_apply_coe, Real.fderiv_fourierChar_neg_bilinear_right_apply, IsMulIndecomposable.mem_or_inv_mem_closure_baseOf, val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe, OreLocalization.oreDiv_eq_iff, SymplecticGroup.coe_J, leftInvEquiv_symm_mul, top_closure_mul_self_subset, closure_singleton_le_iff_mem, unitary.inv_mul_mem_iff, mem_pi, Matrix.reindex_mem_colStochastic_iff, OreLocalization.oreDiv_one_surjective_of_finite_right, Ring.ordFrac_eq_div, isClosed_topologicalClosure, IsLocalization.map_mk', Unitary.coe_zpow, mem_pos, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, unitsNonZeroDivisorsEquiv_apply, mem_closure, finEquivPowers_apply, selfAdjoint.expUnitaryPathToOne_apply, MonoidWithZeroHom.mrange_nontrivial, Unitary.continuousOn_argSelfAdjoint, fromLeftInv_leftInvEquiv_symm, coe_list_prod, coe_map, selfZPow_pow_sub, Unitary.mapEquiv_symm_apply, IsLocalization.surj, mem_map, selfAdjoint.norm_sq_expUnitary_sub_one, Circle.ofConjDivSelf_coe, HomogeneousLocalization.eq_num_div_den, coe_inf, isScalarTower, spinGroup.star_eq_inv', IsLocalization.mk'_pow, instCanLiftSetCoeAndMemOfNatForallForallForallForallHMul, mem_top, RatFunc.map_apply_ofFractionRing_mk, coe_iSup_of_directed, pinGroup.val_inv_toUnits_apply, Circle.starRingEnd_addChar, IsLocalization.mk'_tmul, mem_doublyStochastic_iff_sum, LaurentPolynomial.mk'_one_X, Localization.localRingHom_mk', val_unitarySubgroupUnitsEquiv_symm_apply_coe, isRightRegular_iff_mem_nonZeroDivisorsRight, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, Valuation.instNontrivialSubtypeUnitsMemSubmonoidValueMonoidOfIsNontrivial, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply, subsemiringClosure_eq_closure, IsLocalization.lift_mem_adjoin_finsetIntegerMultiple, ValuativeRel.zero_srel_coe_posSubmonoid, Matrix.permMatrix_mem_rowStochastic, coe_invOrderIso_symm_apply, LocalizedModule.mk_add_mk, IsLocalizedModule.liftOfLE_mk', Monoid.fg_iff_submonoid_fg, Subgroup.mem_ofUnits_iff_exists_isUnit, Localization.liftOn_zero, IsLocalizedModule.iso_symm_apply, IsLocalization.isUnit_comp, SetLike.GradeZero.coe_submonoid, LocalizedModule.liftOn_mk, pinGroup.star_mul_self, AddCircle.homeomorphCircle'_symm_apply, IsLocalizedModule.iso_apply_mk, mem_inv, OreLocalization.smul_cancel', IsFractionRing.mk'_eq_one_iff_eq, Rat.isFractionRingDen, MvPowerSeries.monomial_mem_nonzeroDivisors, LocalizedModule.divBy_apply, mem_unitarySubgroup_iff, MonoidWithZeroHom.coe_one, Ideal.absNorm_pos_iff_mem_nonZeroDivisors, unitary.coe_star_mul_self, IsLocalizedModule.mk'_eq_zero', IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, rotation_apply, toMatrix_rotation, IsFractionRing.mk'_eq_div, Submodule.mem_torsion_iff, Submodule.isTorsion'_powers_iff, mem_smul_pointwise_iff_exists, centralizer_eq_top_iff_subset, Unitary.coe_linearIsometryEquiv_apply, Unitary.inv_mul_mem_iff, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, RatFunc.liftOn_ofFractionRing_mk, IsLocalization.smul_mk'_self, mem_closure_singleton_self, Localization.mk_algebraMap, instMeasurableSMul, topOrderMonoidIso_symm_apply_coe, AddSubmonoid.coe_toSubmonoid_apply, unitary.spectrum.unitary_conjugate', Pell.is_pell_solution_iff_mem_unitary, unitary.mem_iff_self_mul_star, subsemiringClosure_coe, mem_sup, unitary.coe_div, finite_powers, mem_nonZeroDivisors_iff, IsLocalization.mk'_mul_cancel_left, OreLocalization.nonempty_oreSet_iff_of_noZeroDivisors, Unitary.linearIsometryEquiv_coe_apply, Matrix.IsHermitian.eigenvectorUnitary_col_eq, mem_oneLE, MulEquiv.coe_submonoidMap_apply, IsLocalizedModule.exist_integer_multiples, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, val_unitsCentralizerEquiv_apply_coe, LinearIsometryEquiv.trans_smul, Set.IsPWO.submonoid_closure, spinGroup.mem_iff, MvPowerSeries.monomial_mem_nonzeroDivisorsLeft, iSup_eq_closure, num_isRoot_scaleRoots_of_aeval_eq_zero, IsFractionRing.exists_reduced_fraction, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, unitInterval.mem_unitIntervalSubmonoid, FractionalIdeal.isFractional_span_iff, coe_sSup_of_directedOn, unitary.coe_zpow, LocalizedModule.divBy_mul_by, LocalizedModule.mk_mul_mk, Subsemiring.addEquivOp_apply_coe, Complex.UnitDisc.coe_smul_circle, LocalizedModule.mk_eq, mem_inv_pointwise_smul_iff, ValuativeRel.ValueGroupWithZero.mk_eq_div, unitary.map_comp, ValuativeRel.ValueGroupWithZero.exact, OreLocalization.smul_oreDiv_one, ValuativeExtension.mapValueGroupWithZero_mk, NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply, Commute.exists_orderOf_eq_lcm, SymplecticGroup.mem_iff, Subring.mopRingEquivOp_apply_coe, log_mul, coe_bot, mem_nonZeroSMulDivisors_iff, IsLocalizedModule.mk'_add_mk', mem_iSup, OreLocalization.oreDiv_mul_oreDiv, val_unitsCenterToCenterUnits_apply_coe, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, coe_center, spinGroup.coe_mul_star_self, LocalizedModule.mk_cancel, Subgroup.mem_mk, LocalizationMap.subsingleton_iff, pinGroup.val_toUnits_apply, Matrix.IsHermitian.eigenvectorUnitary_mulVec, unitary.mapEquiv_trans, QuadraticAlgebra.norm_eq_one_iff_mem_unitary, LocalizedModule.mem_ker_mkLinearMap_iff, IsIntegral.exists_multiple_integral_of_isLocalization, topEquiv_symm_apply_coe, IsLocalization.surj'', Ideal.absNorm_ne_zero_iff_mem_nonZeroDivisors, lipschitzMul, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, IsLocalization.map_eq_zero_iff, Subgroup.mem_ofUnits_iff, Unitary.spectrum_star_left_conjugate, IsLocalization.integerNormalization_map_to_map, Orientation.rotation_map_complex, Rat.associated_num_den, spinGroup.val_inv_toUnits_apply, RatFunc.mk_eq_localization_mk, coe_pointwise_smul, Unitary.openPartialHomeomorph_symm_apply, Units.mul_inv_mem_unitary, Pell.Solution₁.coe_mk, instIsTopologicalGroupSubtypeMemSubmonoidUnitaryOfContinuousMulOfContinuousStar, IsLocalizedModule.exist_integer_multiples_of_finset, OreLocalization.mul_div_one, unitary.mem_iff, MonoidWithZeroHom.mem_valueMonoid, Unitary.mem_iff_self_mul_star, Matrix.mem_unitaryGroup_iff, IsLocalizedModule.mk'_eq_mk'_iff, RatFunc.mk_eq_mk', OreLocalization.smul_cancel, BoundedContinuousFunction.mem_charPoly, NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst, BoundedContinuousFunction.charAlgHom_apply, ext_iff, inclusion_inj, Circle.arg_eq_arg, Localization.map_isUnit_of_le, unitary.coe_smul, sup_eq_closure_mul, Monoid.IsTorsion.torsionMulEquiv_apply, IsLocalizedModule.finsetIntegerMultiple_image, IsLocalization.mk'_sub, unitarySubgroupUnitsEquiv_apply_coe, centerToMulOpposite_apply_coe, LinearIsometryEquiv.smul_apply, OreLocalization.nonempty_oreSet_iff, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, Localization.mk_intCast, fourier_one, coe_inv_val_mul_coe_val, Unitary.map_coe, LocalizationMap.mk'_one, Module.FinitePresentation.exists_lift_of_isLocalizedModule, Matrix.mem_specialOrthogonalGroup_iff, orderOf_submonoid, Real.Angle.coe_toCircle, unitary.linearIsometryEquiv_coe_symm_apply, mem_sSup_of_directedOn, smul_mem_pointwise_smul_iff, unitary.toUnits_comp_map, nonZeroDivisors_dvd_iff_dvd_coe, OreLocalization.div_eq_one, closure_eq_one_union, Ideal.disjoint_powers_iff_notMem, Matrix.reindex_mem_rowStochastic_iff, le_nonZeroDivisors_iff_isRegular, fourier_neg', MonoidHom.submonoidMap_apply_coe, MvPowerSeries.monomial_mem_nonzeroDivisorsRight, IsOfFinOrder.finite_powers, unitary.norm_sub_eq, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', multiple_mem_adjoin_of_mem_localization_adjoin, Circle.smul_def, IsLocalization.mk'_spec', coe_val_mul_coe_inv_val, Localization.mk_one_eq_monoidOf_mk, IsDedekindDomain.HeightOneSpectrum.valuation_def, val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe, Unitary.coe_symm_linearIsometryEquiv_apply, selfAdjoint.expUnitary_zero, fixedPoints_submonoid_sup, unitary.mem_iff_star_mul_self, IsOfFinOrder.mem_powers_iff_mem_range_orderOf, mem_square, leftInvEquiv_apply, mem_nonZeroDivisors_iff_right, Unitary.instLocPathConnectedSpace, Ideal.disjoint_map_primeCompl_iff_comap_le, mem_comap, OreLocalization.expand', LocalizationMap.mk'_eq_iff_eq, val_inv_unitsTypeEquivIsUnitSubmonoid_symm_apply, Unitary.coe_mul_star_self, Localization.mkHom_surjective, Subsemiring.coe_toSubmonoid, IsLocalizedModule.isRegular_of_smul_left_injective, IsLocalization.finsetIntegerMultiple_image, LocalizedModule.mk_cancel_common_left, IsLocalizationMap.exists_of_eq, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le, Con.mem_coe, OreLocalization.subsingleton_iff, Unitary.mul_star_self, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, IsLocalizedModule.exist_integer_multiples_of_finite, IsLocalization.isUnit_piRingHom_algebraMap_comp_piEvalRingHom, isLocalizedModule_iff, card_bot, Unitary.spectrum_star_right_conjugate, MonoidHom.mem_eqLocusM, mrange_subtype, selfAdjoint.continuous_expUnitary, IsLocalization.algebraMap_mem_map_algebraMap_iff, Unitary.conjStarAlgAut_ext_iff', coe_prod, leftInvEquiv_mul, FractionalIdeal.canonicalEquiv_mk0, QuadraticAlgebra.star_mem_nonZeroDivisors_iff, selfAdjoint.unitarySelfAddISMul_coe, LocalizationMap.eq_iff_exists, Circle.ext_iff, ValuativeRel.ValueGroupWithZero.inv_mk, LaurentPolynomial.mk'_eq, LocalizationMap.mk'_eq_of_same, Matrix.UnitaryGroup.one_apply, ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, IsLocalizedModule.subsingleton_iff, QuadraticAlgebra.mem_unitary, coe_nonZeroDivisorsRight_eq, mem_sInf, unitary.mul_left_inj, Monoid.fg_range, instSubmonoidClass, mem_bot, Polynomial.notMem_nonZeroDivisors_iff, Subgroup.mem_ofUnits_of_isUnit_of_unit_mem, OreLocalization.numeratorRingHom_apply, IsFractionRing.mk'_num_den', Subalgebra.linearEquivOp_apply_coe, IsLocalization.isPrime_iff_isPrime_disjoint, Subring.mem_closure_iff, LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, Circle.coe_inv_eq_conj, MonoidHom.mem_mker, ValuativeRel.ValueGroupWithZero.mk_eq_mk, IsFractionRing.div_surjective, IsLocalization.mk'_algebraMap_eq_mk', Circle.coe_mul, mk_mul_mk_inv_eq_one, Unitary.map_comp, Unitary.mul_right_inj, Subalgebra.mem_saturation_iff, mk_inv_mul_mk_eq_one, unitsTypeEquivIsUnitSubmonoid_apply_coe, Unitary.mapEquiv_apply, HomogeneousLocalization.val_mk, unitInterval.coe_unitIntervalSubmonoid, mul_left_coe_nonZeroDivisors_eq_zero_iff, IsLocalization.localization_localization_surj, IsLocalizedModule.mem_ker_iff, unitary.toUnits_injective, powers_eq_zpowers, Real.Angle.arg_toCircle, Matrix.UnitaryGroup.one_val, OreLocalization.oreDiv_add_oreDiv, isLocalization_iff, Circle.coe_pow, ofMul_image_powers_eq_multiples_ofMul, dvd_cancel_right_coe_nonZeroDivisors, mul_right_coe_nonZeroDivisors_eq_zero_iff, IsLocalization.algebraMap_isUnit_iff, mem_prod, IsLocalization.mk'_self'', Ideal.span_singleton_nonZeroDivisors, instSMulCommClassSubtypeMemCenter_1, mem_closure_singleton, IsArtinianRing.isUnit_iff_mem_nonZeroDivisors, LinearMap.ker_toSpanSingleton_eq_bot_iff, Module.FinitePresentation.exists_free_localizedModule_powers, IsLocalizationMap.surj_pi_of_finite, IsLocalizedModule.fromLocalizedModule_mk, PNat.equivNonZeroDivisorsNat_symm_apply_coe, IsFractionRing.isUnit_map_of_injective, Matrix.convex_colStochastic, Subsemiring.addEquivOp_symm_apply_coe, coe_subtype, ValuativeRel.ValueGroupWithZero.mk_lt_mk, LocalizationMap.mk'_mul_cancel_left, pinGroup.star_eq_inv', OreLocalization.mul_cancel, MulEquiv.ofLeftInverse'_apply, Pell.isPell_iff_mem_unitary, Nat.card_submonoidPowers, Circle.invOn_arg_exp, coe_op, LocalizationMap.mk'_cancel, mem_powers_iff_mem_range_orderOf, val_unitsNonZeroDivisorsEquiv_symm_apply_coe, NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_apply, IsLocalization.smul_bijective, IsLocalization.sec_spec', Unitary.coe_smul, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, MulAction.mem_stabilizerSubmonoid_iff, IsUnit.mem_submonoid_iff, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', IsLocalization.exists_isIntegral_smul_of_isIntegral_map, Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe, IsLocalization.mk'_add_eq_iff_add_mul_eq_mul, IsLocalizedModule.exists_isLocalizedModule_powers_of_finitePresentation, Monoid.IsTorsion.torsionMulEquiv_symm_apply_coe, mul_subset_closure, centerToMulOpposite_symm_apply_coe, LocalizedModule.mk_cancel_common_right, HomogeneousLocalization.den_mem, Valuation.apply_posSubmonoid_pos, Matrix.IsHermitian.cfcAux_apply, Matrix.UnitaryGroup.det_isUnit, Algebra.GrothendieckGroup.inv_mk, LocalizationMap.map_eq_zero_iff, bot_or_exists_ne_one, notMem_nonZeroDivisors_iff, IsLocalization.mk'_mem_map_algebraMap_iff, unitsCenterToCenterUnits_injective, Monoid.exponent_submonoid_dvd, apply_coe_mem_map, Circle.star_addChar, instSMulCommClassSubtypeMemCenter, Subgroup.topEquiv_symm_apply_coe, IsUnit.mem_unitary_of_star_mul_self, Unitary.linearIsometryEquiv_coe_symm_apply, IsLocalization.algEquivOfAlgEquiv_mk', IsLocalizedModule.mk'_cancel', Algebra.adjoin_toSubmodule_le, IsLocalization.map_integerMultiple, mem_inv_pointwise_smul_iff₀, NumberField.Ideal.tendsto_norm_le_div_atTop₀, IsLeftRegular.mem_nonZeroDivisorsLeft, Unitary.star_mul_self, IsLocalizedModule.mk'_one, coe_oneLE, Matrix.UnitaryGroup.inv_val, unitary.spectrum_subset_circle, noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight, LocalizationMap.isUnit_comp, unitary.val_toUnits_apply, ValuativeRel.ValueGroupWithZero.mk_mul_mk, MonoidHom.mrangeRestrict_surjective, Unitary.mul_inv_mem_iff, subtype_injective, Unitary.instIsStarNormal, OreLocalization.ore_eq, MonoidHom.coe_mker, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, Subgroup.coe_set_mk, mem_iSup_prop, Subgroup.mem_ofUnits_iff_toUnits_mem, IsLocalization.localization_localization_map_units, closure_eq, faithfulSMul, Submodule.annihilator_top_inter_nonZeroDivisors, coe_top, Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule, Algebra.GrothendieckGroup.mk_div_mk, Unitary.conjStarAlgAut_apply, IsFractionRing.inv_def, FractionalIdeal.absNorm_eq, Polynomial.Monic.mem_nonZeroDivisors, IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral, centerCongr_symm_apply_coe, IsLocalization.mk'_self', LinearIsometryEquiv.toLinearEquiv_smul, unitary.mapEquiv_symm, ValuativeRel.zero_vlt_coe_posSubmonoid, Unitary.mem_iff_star_mul_self, Polynomial.mem_nonZeroDivisors_iff, Unitary.toAlgEquiv_conjStarAlgAut, le_nonZeroDivisorsLeft_iff_isLeftRegular, pinGroup.units_mem_iff, selfAdjoint.realPart_unitarySelfAddISMul, MonoidHom.submonoidComap_apply_coe, Subgroup.exponent_toSubmonoid, den_dvd_of_is_root, ValuativeRel.one_apply_posSubmonoid, Circle.leftInverse_exp_arg, IsRightRegular.mem_nonZeroDivisorsRight, IsFractionRing.associated_num_den_inv, coe_comap, IsLocalization.mk'_eq_iff_eq, Matrix.transpose_mem_rowStochastic_iff_mem_colStochastic, Monoid.closure_finset_fg, smul_def, OreLocalization.cardinalMk_le_max, coe_inv, mk_mem_nonZeroDivisors_associates, noZeroDivisors_iff_forall_mem_nonZeroDivisors, Matrix.mem_specialUnitaryGroup_iff, LocalizedModule.subsingleton_iff, one_mem, Valuation.extendToLocalization_mk', Unitary.openPartialHomeomorph_target, LocalizationMap.exists_of_sec_mk', IsLocalization.mem_invSubmonoid_iff_exists_mk', Unitary.inv_mem_iff, Ideal.card_norm_le_eq_card_norm_le_add_one, OreLocalization.one_div_mul, spinGroup.mul_star_self, Localization.mk_one_eq_algebraMap, unitary.coe_mul_star_self, mem_pointwise_smul_iff_inv_smul_mem₀, exponent_top, LocalizedModule.smul_def, IsCyclic.exists_monoid_generator, coe_one, card_le_one_iff_eq_bot, coe_unitSphere, fromLeftInv_eq_iff, Circle.norm_coe, val_unitsCentralizerEquiv_symm_apply_coe, IsLocalizedModule.mk'_cancel_right, Matrix.UnitaryGroup.mul_val, fourier_apply, mem_mk, Matrix.IsHermitian.eigenvectorUnitary_apply, Matrix.mem_rowStochastic_iff_sum, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul, IsLocalization.mk'_sec, Unitary.coe_isStarNormal, Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe, IsLocalization.mk'_eq_iff_eq_mul, mem_nonZeroDivisors_iff', OreLocalization.smul_one_oreDiv_one_smul, multiple_mem_span_of_mem_localization_span, fixedPoints_submonoid_iSup, Localization.mk_natCast, pow_right_injective_iff_pow_injective, Matrix.UnitaryGroup.mul_apply, OreLocalization.zero_def, mem_doublyStochastic_iff_mem_rowStochastic_and_mem_colStochastic, IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral', Subsemiring.mopRingEquivOp_apply_coe, IsLocalization.toInvSubmonoid_mul, Unitary.conjStarAlgAut_symm_apply, pow_apply, ClassGroup.mk_mk0, selfAdjoint.star_coe_unitarySelfAddISMul, IsLocalization.scaleRoots_commonDenom_mem_lifts, Orientation.kahler_rotation_left', OreLocalization.mul_cancel', ValuativeRel.left_cancel_posSubmonoid, closure_le_centralizer_centralizer, isLeftRegular_iff_mem_nonZeroDivisorsLeft, MulEquiv.submonoidMap_symm_apply, Unitary.toRingEquiv_conjStarAlgAut, OreLocalization.numeratorHom_apply, SymplecticGroup.mem_iff', Unitary.val_toUnits_apply, mem_pointwise_smul_iff_inv_smul_mem, ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, nontrivial_iff_exists_ne_one, mem_iSup_of_directed, Matrix.UnitaryGroup.ext_iff, Localization.mk_self, Ideal.absNorm_pos_of_nonZeroDivisors, pinGroup.toUnits_injective, MonoidHom.submonoidComap_surjective_of_surjective, pinGroup.mul_star_self, mem_carrier, Localization.r_iff_exists, doublyStochastic_eq_convexHull_permMatrix, unitary.coe_inv, IsLocalizedModule.exists_integer_multiple, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Matrix.IsHermitian.spectral_theorem, Ideal.mem_primeCompl_iff, LocalizationMap.mk'_eq_iff_eq', LocalizationMap.sec_spec', unitary.coe_map, Unitary.coe_div, equivOp_apply_coe, IsLocalizedModule.smul_inj, pinGroup.star_mem_iff, IsLocalization.toInvSubmonoid_surjective, RatFunc.liftAlgHom_apply_ofFractionRing_mk, OreLocalization.mul_inv, rotationOf_coe, IsLocalizedModule.iso_symm_apply_aux, isUnit_iff_mem_nonZeroDivisors_of_finite, IsLocalizedModule.mk'_surjective, LocalizedModule.mk_mul_mk', center.smulCommClass_left, MonoidHom.restrict_mker, Unitary.val_inv_toUnits_apply, IsLocalization.mem_localizationLocalizationSubmodule, Matrix.IsHermitian.eigenvectorUnitary_coe, HomogeneousLocalization.NumDenSameDeg.den_mem, Unitary.norm_map, inv_val_mem_of_mem_units, orderOf_eq_card_powers, Subsemiring.mem_toSubmonoid, IsLocalizedModule.mk'_smul_mk', dense_submonoidClosure_iff_subgroupClosure, closure_submonoidClosure_eq_closure_subgroupClosure, ValuativeRel.exists_valuation_div_valuation_eq, neg_one_mem_torsion, Unitary.toUnits_comp_map, IsLocalizedModule.exists_of_eq, IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, FractionalIdeal.den_mul_self_eq_num, Unitary.coe_map_star, smulCommClass_left, IsLocalization.localization_localization_exists_of_eq, IsLocalization.exists_smul_mem_of_mem_adjoin, unitary.norm_map, Algebra.adjoin_eq_span, isOfFinOrder_coe, Real.hasDerivAt_fourierChar, Matrix.star_eq_inv, IsLocalization.mk'_cancel, coe_sup, LocalizedModule.mul_by_divBy, Orientation.kahler_rotation_left, fromLeftInv_mul, IsLocalization.exist_integer_multiples_of_finset, IsLocalization.smul_mem_iff, IsLocalization.orderIsoOfPrime_symm_apply_coe, mul_cancel_right_coe_nonZeroDivisors, IsLocalization.sec_spec, center.smulCommClass_right, Localization.mk_prod, HomogeneousLocalization.Away.val_mk, eq_top_iff', toIsOrderedMonoid, IsLocalization.map_units_map_submonoid, IsLocalization.exist_integer_multiples_of_finite, Unitary.instSMulCommClassSubtypeMemSubmonoidUnitary, IsLocalization.disjoint_comap_iff, mem_units_iff, Localization.mk_one, Matrix.mem_orthogonalGroup_iff, NumberField.exists_ideal_in_class_of_norm_le, LocalizationMap.eq', mem_centralizer_iff, IsLocalization.toInvSubmonoid_eq_mk', mem_divPairs, scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero, mem_center_iff, Circle.coe_eq_one, unitary.coe_map_star, HomogeneousLocalization.val_awayMap_mk, one_def, RatFunc.liftRingHom_apply_ofFractionRing_mk, extremePoints_doublyStochastic, coe_nonZeroDivisorsLeft_eq, Subring.ringEquivOpMop_symm_apply_coe, mem_own_leftCoset, Real.fourierChar_apply, IsLocalization.tmul_mk', mem_nonZeroDivisorsLeft_iff, FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal, Commute.expUnitary_add, nonZeroDivisors.associated_coe, isLocalizationMap_iff, Subring.coe_toSubmonoid, LocalizationMap.mk'_mul_cancel_right, LocalizationMap.mk'_spec', MonoidWithZeroHom.valueGroup_def, Unitary.isPathConnected_ball, IsArtinianRing.isUnit_iff_mem_nonZeroDivisors_of_mulOpposite, Unitary.map_injective, PNat.equivNonZeroDivisorsNat_apply_coe, Unitary.mapEquiv_symm, HomogeneousLocalization.awayMapAux_mk, Matrix.of_mem_specialOrthogonalGroup_fin_two_iff, fixingSubmonoid_fixedPoints_gc, ValuativeRel.right_cancel_posSubmonoid, IsLocalization.mk'_one, Matrix.mem_colStochastic, instContinuousStarSubtypeMemSubmonoidUnitary, Subsemiring.ringEquivOpMop_symm_apply_coe, mul_def, Subgroup.mem_ofUnits, Matrix.mem_colStochastic_iff_sum, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply, Localization.mk_pow, Subsemiring.coe_closure_eq, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, Unitary.conjStarAlgAut_mul_apply, continuousSMul, powLogEquiv_apply, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, cfc_unitary_iff, IsLocalizedModule.smul_injective, le_isUnit_iff_zero_notMem, IsLocalization.mk'_mul_mk'_eq_one, Ideal.span_singleton_mem_isPrincipalSubmonoid, AddSubmonoid.coe_toSubmonoid_symm_apply, unitary.toMonoidHom_mapEquiv, isRegular_iff_mem_nonZeroDivisors, ValuativeRel.ValueGroupWithZero.embed_mk, Unitary.map_id, IsUnit.mem_nonZeroDivisors, MonoidWithZeroHom.valueMonoid_eq_valueGroup', Polynomial.X_mem_nonzeroDivisors, coe_pathComponentOne, IsStarProjection.two_mul_sub_one_mem_unitary, Unitary.mapEquiv_trans, biUnion_associatedPrimes_eq_compl_nonZeroDivisors, MulAction.orbit_submonoid_subset, pinGroup.mem_iff, LinearIsometryEquiv.smul_trans, IsLocalization.mk'_eq_zero_iff, MonoidWithZeroHom.val_mrange_zero, continuousMul, Circle.coe_inv, Localization.add_mk, Unitary.inner_map_map, Matrix.specialUnitaryGroup.coe_star, OreLocalization.oreDiv_smul_oreDiv, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, mem_closure_finset, Unitary.norm_sub_eq, unitary_iff_isStarNormal_and_spectrum_subset_unitary, IsFractionRing.num_mul_den_eq_num_iff_eq, pinGroup.star_eq_inv, mem_doublyStochastic, leftInvEquiv_symm_eq_inv, instSubsingletonUnits, MulEquiv.ofLeftInverse'_symm_apply, unitary.coe_star, mem_nonZeroDivisors_of_ne_zero, Matrix.mem_unitaryGroup_iff', IsLocalization.map_units, LocalizedModule.mk'_smul_mk, Subfield.mem_toSubmonoid, Unitary.coe_map, Matrix.convex_rowStochastic, ClassGroup.exists_mk0_eq_mk0, Localization.mk_eq_mk_iff', mem_closure_range_iff, coe_topologicalClosure, mem_powers_iff, unitary.mul_inv_mem_iff, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, FG.finite_irreducible_mem_submonoidClosure, Real.differentiable_fourierChar, nonZeroDivisorsEquivUnits_apply, LocalizationMap.mk'_mul, Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMul, ClassGroup.mk0_surjective, Localization.mkHom_apply, IsLocalization.injective_iff_isRegular, mem_nonZeroDivisors_iff_ne_zero, lipschitzGroup.coe_mem_iff_mem, coe_equivMapOfInjective_apply, Subsemiring.mem_mk, OreLocalization.oreDiv_mul_oreDiv_comm, LocalizationMap.mulEquivOfMulEquiv_mk', Ideal.disjoint_primeCompl_of_liesOver, instMeasurableConstSMul, mem_iInf, Circle.normSq_coe, ValuativeRel.posSubmonoid_def, IsLocalizationMap.surj, IsIdempotentElem.coe_powers, Matrix.permMatrix_mem_colStochastic, mulSingle_mem_pi, MeasureTheory.Measure.instSMulInvariantMeasureSubtypeMemSubmonoidOfIsMulLeftInvariant, Subgroup.val_mem_ofUnits_iff_mem, MonoidHom.coe_mgraph, MvPolynomial.isLocalization_C_mk', Matrix.mem_specialOrthogonalGroup_fin_two_iff, coe_toAddSubmonoid_symm_apply, mem_op, coe_toAddSubmonoid_apply, OreLocalization.numerator_isUnit, Ideal.mem_isPrincipalSubmonoid_iff, fourier_zero', ZMod.toCircle_intCast, IsLocalization.exists_integer_multiple, unitary.mapEquiv_refl, mem_closure_range_iff_of_fintype, ZMod.toCircle_natCast, nonZeroDivisorsEquivUnits_symm_apply_coe, toIsOrderedCancelMonoid, Real.deriv_fourierChar, Monoid.powers_fg, ClassGroup.exists_min, mem_powers_of_prime_card, Subsemiring.coe_set_mk, CategoryTheory.ActionCategory.stabilizerIsoEnd_apply, IsSMulRegular.mem_nonZeroSMulDivisors, LocalizedModule.mk_smul_mk, MonoidHom.coe_mrangeRestrict, coe_square, convex_doublyStochastic, mem_biSup_of_directedOn, NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMap, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, Module.End.mem_submonoidCenter_iff, LinearIsometryEquiv.symm_units_smul, OreLocalization.one_def, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, IsLocalizedModule.fromLocalizedModule'_mk, Unitary.mem_iff, IsLocalization.AtPrime.isUnit_mk'_iff, Real.differentiable_fourierChar_neg_bilinear_right, Unitary.instIsScalarTowerSubtypeMemSubmonoidUnitary, Subalgebra.linearEquivOp_symm_apply_coe, QuadraticAlgebra.coe_mem_nonZeroDivisors_iff, Localization.mk_mul, Circle.coeHom_apply, Localization.mk_lt_mk, rootsOfUnityCircleEquiv_apply, FractionalIdeal.map_canonicalEquiv_mk0, OreLocalization.oreDiv_one_surjective_of_finite_left, IsOfFinOrder.powers_eq_image_range_orderOf, mem_closure_inv, LinearIsometryEquiv.symm_smul_apply, mem_unop, Circle.coe_inj, IsLocalization.mk'_mul_cancel_right, IsLocalization.exists_integer_multiple', IsRegular.mem_nonZeroDivisors, IsLocalizedModule.mk'_mul_mk', IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, LocalizationMap.mk'_eq_zero_iff, StarAlgebra.adjoin_eq_span, Orientation.kahler_rotation_right, mul_cancel_left_coe_nonZeroDivisors, Unitary.coe_neg, SymplecticGroup.coe_inv', Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, ValuativeExtension.mapPosSubmonoid_apply_coe, fourier_coe_apply', Unitary.star_eq_inv, Subsemiring.closure_submonoid_closure, IsLocalizedModule.map_units, OreLocalization.smul_div_one, subtype_comp_inclusion, CStarRing.norm_coe_unitary_mul, mem_powers, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, RatFunc.liftOn_def, instContinuousInvSubtypeMemSubmonoidUnitaryOfContinuousStar, mem_closure_finset', Matrix.UnitaryGroup.toLin'_mul, MonoidWithZeroHom.one_mem_valueMonoid, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Subgroup.mem_toSubmonoid, AlgebraicGeometry.StructureSheaf.comap_basicOpen, zero_notMem_nonZeroDivisorsRight, IsLocalization.AtPrime.isUnit_to_map_iff, Monoid.closure_finite_fg, leftInvEquiv_symm_fromLeftInv, coe_iInf, ValuativeRel.ValueGroupWithZero.mk_le_mk, ZMod.toCircle_apply, IsLocalization.mul_toInvSubmonoid, IsLocalization.algebraMap_mk', exists_bijective_map_powers, LocalizationMap.eq_mk'_iff_mul_eq, Subgroup.coe_toSubmonoid, Circle.arg_exp, IsLocalization.mk'_eq_iff_eq', IsLocalization.span_invSubmonoid, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, LocalizationMap.map_units, pinGroup.coe_star, irreducible_mem_submonoidClosure_subset, Matrix.mem_orthogonalGroup_iff', smulCommClass_right, ValuativeRel.ValueGroupWithZero.lift_zero, CommMonoid.primaryComponent.exists_orderOf_eq_prime_pow, Real.differentiable_fourierChar_neg_bilinear_left, OreLocalization.one_div_smul, fromLeftInv_one, IsLocalizedModule.eq_iff_exists, transpose_mem_doublyStochastic_iff, FractionalIdeal.equivNum_apply, MvPowerSeries.X_mem_nonzeroDivisors, IsLocalization.invertible_mk'_one_invOf, ClassGroup.equiv_mk0, unitary.isPathConnected_ball, ValuativeRel.ValueGroupWithZero.mk_self, subsemiringClosure_mem, IsLocalizedModule.smul_mem_finsetIntegerMultiple_span, Matrix.UnitaryGroup.toGL_one, MonoidWithZeroHom.mem_valueMonoid_iff, dvd_cancel_left_coe_nonZeroDivisors, Circle.coe_exp, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, top_closure_mul_self_eq, IsLocalization.integerNormalization_spec, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, mem_closure_of_mem, fromCommLeftInv_apply, IsLocalization.eq_mk'_iff_mul_eq, NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_surjective, fourier_add', NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply, BoundedContinuousFunction.charMonoidHom_apply, FractionalIdeal.den_mul_self_eq_num', IsFractionRing.num_den_reduced, QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff, pinGroup.coe_mul_star_self, Subgroup.equivSMul_symm_apply_coe, Localization.r_iff_oreEqv_r, Matrix.mem_rowStochastic, coe_multiset_prod, Zsqrtd.norm_eq_one_iff_mem_unitary, IsFractionRing.associated_den_num_inv, ValuativeRel.ValueGroupWithZero.lift_valuation, MonoidHom.subgroupComap_apply_coe, coe_centralizer, coe_set_mk, IsUnit.mem_unitary_of_mul_star_self, Ideal.exists_disjoint_powers_of_span_eq_top, IsLocalization.mk'_add, mem_inf, closure_closure_coe_preimage, Subring.mem_toSubmonoid, ClassGroup.mk0_eq_mk0_inv_iff, noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one, IsLocalizedModule.map_integerMultiple, Algebra.GrothendieckGroup.lift_apply, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe, topEquiv_toMonoidHom, MonoidHom.restrict_mrange, LocalizationMap.mk'_self', Circle.toUnits_apply, Matrix.transpose_mem_colStochastic_iff_mem_rowStochastic, fromLeftInv_eq_inv, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, IsLocalization.mem_map_algebraMap_iff, PrimeSpectrum.localization_comap_range, IsLocalization.orderIsoOfPrime_apply_coe, Unitary.coe_star_mul_self, ValuativeRel.ValueGroupWithZero.lift_one, unitary.map_injective, Unitary.instStarModuleSubtypeMemSubmonoidUnitary, LocalizationMap.surj, permMatrix_mem_doublyStochastic, val_unitsTypeEquivIsUnitSubmonoid_symm_apply, IsLocalization.exist_integer_multiples, Unitary.toMonoidHom_mapEquiv, IsUnit.mem_unitary_iff_mul_star_self, Unitary.star_mem_iff, sup_eq_range, LocalizationMap.mk'_sec, topOrderMonoidIso_apply, IsUnit.Submonoid.coe_inv, mem_powers_iff_mem_zpowers, Unitary.openPartialHomeomorph_apply, Real.probChar_apply, powersEquivPowers_apply, fixedPoints_antitone, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, Unitary.argSelfAdjoint_coe, subset_closure, surjOn_iff_le_map, Circle.coe_injective, unitary.mul_star_self, centerCongr_apply_coe, spinGroup.coe_star, CommMonoid.torsion.isTorsion, coe_sInf, inclusion_injective, Circle.coe_zpow, MonoidHom.mrangeRestrict_mker, unitary.star_mem_iff, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, QuadraticAlgebra.norm_mem_nonZeroDivisors_iff, OreLocalization.nontrivial_iff, FixedPoints.mem_submonoid, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, coe_unop, zero_notMem_nonZeroDivisorsLeft, coe_inclusion, IsFractionRing.num_mul_den_eq_num_iff_eq', LocalizationMap.mk'_eq_iff_eq_mul, coe_pos, CStarAlgebra.exists_sum_four_unitary, Localization.awayLift_mk, powLogEquiv_symm_apply, Subalgebra.mopAlgEquivOp_apply_coe, Unitary.coe_star, MonoidHom.subgroupMap_apply_coe, IsLocalization.eq, zero_notMem_nonZeroDivisors, subsemiringClosure_toNonUnitalSubsemiring, IsLocalizedModule.mk'_cancel, Matrix.UnitaryGroup.star_mul_self, NormedSpace.exp_mem_unitary_of_mem_skewAdjoint, Subalgebra.algEquivOpMop_symm_apply_coe, IsLocalization.map_algebraMap_ne_top_iff_disjoint, LocalizedModule.liftOn₂_mk, Unitary.conjStarAlgAut_star_apply, ClassGroup.integralRep_mem_nonZeroDivisors, Circle.coe_div, notMem_nonZeroDivisorsLeft_iff, LocalizationMap.exists_of_eq, Circle.coe_one, notMem_nonZeroDivisors_iff_right, IsMulIndecomposable.apply_ne_one_iff_mem_closure, mul_mem_nonZeroDivisors, bot_or_nontrivial, unitary.coe_neg, le_nonZeroDivisorsRight_iff_isRightRegular, LinearIsometryEquiv.toContinuousLinearEquiv_smul, FractionalIdeal.den_mem_inv, unitary.star_eq_inv, unitary.mem_pathComponentOne_iff, Subgroup.topEquiv_apply, LocalizationMap.sec_spec, isNilpotent_iff_zero_mem_powers, Real.fderiv_fourierChar_neg_bilinear_left_apply, coe_mul_self_eq, RatFunc.laurentAux_ofFractionRing_mk, Unitary.mapEquiv_refl, LocalizationMap.mk'_spec, FractionalIdeal.coe_mk0, CStarRing.norm_coe_unitary, Algebra.mem_algebraMapSubmonoid_of_mem, mem_fixingSubmonoid_iff, Unitary.star_eq_inv', finEquivPowers_symm_apply, Subsemiring.mem_closure_iff, FractionRing.mk_eq_div, sup_eq_closure, closure_le, IsLocalization.surj₂, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, mem_closure_pair, LocalizedModule.mkLinearMap_apply, Localization.sub_mk, ofAdd_image_multiples_eq_powers_ofAdd, IsLocalizedModule.mk'_cancel_left, Circle.argEquiv_apply_coe, ValuativeRel.ValueGroupWithZero.mk_eq_valuation, IsLocalization.exists_of_eq, CStarAlgebra.span_unitary, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, SymplecticGroup.J_mem, mem_closure_iff_exists_finset_subset, coe_mul, exists_mem_sup, IsFractionRing.isUnit_den_zero, IsUnit.mem_unitary_iff_star_mul_self, powers_le, topEquiv_apply, CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply, pow_coe, IsLocalization.eq_iff_exists, OreLocalization.oreDiv_one_smul, notMem_nonZeroDivisorsRight_iff, Unitary.conjStarAlgAut_ext_iff, IsOfFinOrder.powers_eq_zpowers, Unitary.spectrum_subset_circle, IsLocalizedModule.mk'_eq_iff, spinGroup.toUnits_injective, eq_bot_iff_card, mem_closure_image_one_lt_iff, coe_finset_prod, Subfield.coe_toSubmonoid, Module.FinitePresentation.exists_basis_localizedModule_powers, infinite_powers, Unitary.isUnit_coe, Complex.UnitDisc.coe_circle_smul, ZMod.stdAddChar_apply, coe_powers, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, unitary.mul_right_inj, IsFractionRing.lift_mk', LocalizationMap.sec_zero_fst, IsLocalization.smul_toInvSubmonoid, IsLocalization.subsingleton_iff, Commute.expUnitary, exists_mem_doublyStochastic_eq_smul_iff, IsLocalization.mk'_spec, Circle.argPartialEquiv_apply, MeasureTheory.charFun_eq_integral_probChar, LocalizedModule.oreEqv_eq_r, unitary.star_mul_self, subtype_apply, Units.inv_mul_mem_unitary, Unitary.coe_inv, MonoidHom.mem_mrange, Subring.addEquivOp_symm_apply_coe, selfAdjoint.expUnitary_coe, MonoidHom.mem_mgraph, IsFractionRing.isUnit_den_iff, Localization.mem_range_mapToFractionRing_iff, Complex.rotation, isClosed_unitary, Matrix.UnitaryGroup.inv_apply, closure_eq_image_prod, IsLocalizedModule.eq_zero_iff, spinGroup.star_mul_self, IsLocalizedModule.surj', spinGroup.val_toUnits_apply, spinGroup.star_mem_iff, IsLocalizedModule.mk'_mul_mk'_of_map_mul, MonoidHom.submonoidMap_surjective, IsLocalizedModule.surj, unitary.inner_map_map, BoundedContinuousFunction.char_apply, IsLocalizedModule.iso_mk_one, mul_fromLeftInv, selfAdjoint.joined_one_expUnitary, LocalizationMap.surj₂, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, mul_leftInvEquiv_symm, IsLocalization.mk'_mul, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', IsLocalization.ringEquivOfRingEquiv_mk', unitary.continuousOn_argSelfAdjoint, Localization.mk_eq_mk_iff, CommMonoid.coe_primaryComponent, IsLocalizedModule.mk'_sub_mk', mem_nonZeroDivisorsRight_iff, IsLocalizedModule.injective_iff_isRegular, OreLocalization.inv_def, unitary.linearIsometryEquiv_coe_apply, LocalizationMap.eq
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