Valuation 📖 | CompData | 353 mathmath: Valued.isOpen_closedball, Valuation.IsTrivialOn.valuation_algebraMap_le_one, Irreducible.maximalIdeal_eq_setOf_le_v_coe, ValuationSubring.valuation_lt_one_iff, Valuation.leSubmodule_v_le_of_mem, Valuation.FiniteField.algebraMap_le_one, Valuation.FiniteField.algebraMap_eq_one, Valuation.HasExtension.val_map_le_iff, Valuation.isEquiv_iff_val_sub_one_lt_one, Valuation.one_apply_lt_one_iff, Valuation.mem_maximalIdeal_iff, Valuation.val_mrange_zero, Valuation.mem_leSubmodule_iff, Valuation.mem_supp_iff, Padic.withValUniformEquiv_norm_le_one_iff, Valued.toNormedField.norm_le_one_iff, Rat.padicValuation_cast, Valued.extension_extends, Valued.valuedCompletion_surjective_iff, ValuativeRel.valuation_eq_zero_iff, ValuationSubring.valuation_le_iff, PadicComplex.valuation_extends, Valuation.IsRankOneDiscrete.exists_generator_lt_one', Valuation.IsTrivialOn.eq_one, Valuation.mem_ltIdeal_iff, Valuation.toFun_eq_coe, Valuation.val_le_one_or_val_inv_lt_one, NumberField.FinitePlace.norm_def', IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, FunctionField.inftyValuation.X_inv, Int.padicValuation_lt_one_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, Valuation.IsRankOneDiscrete.generator_mem_valueGroup, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, Valuation.Integers.isPrincipal_iff_exists_isGreatest, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, LaurentSeries.valuation_single_zpow, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, Valuation.instNontrivialSubtypeUnitsMemSubmonoidValueMonoidOfIsNontrivial, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, ValuationSubring.valuation_unit, ArchimedeanClass.FiniteResidueField.mk_eq_zero, Valuation.Compatible.srel_iff_lt, Valuation.isEquiv_iff_val_lt_val, Valuation.isNontrivial_iff_exists_lt_one, Valuation.Integers.valuation_irreducible_lt_one, Int.padicValuation_eq_one_iff, ValuationSubring.mapOfLE_valuation_apply, Valuation.Integers.map_le_one, Valuation.HasExtension.val_map_eq_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, Valuation.ext_iff, Rat.padicValuation_self, Valuation.ltIdeal_v_le_of_mem, Valued.isClopen_ball, Valuation.IsEquiv.pos_iff, Valued.exists_coe_eq_v, ValuativeRel.ValueGroupWithZero.mk_eq_div, Valuation.unit_map_eq, Valuation.Integers.le_of_dvd, Polynomial.valuation_of_mk, Valuation.val_lt_one_iff, Valuation.IsUniformizer.zpowers_eq_valueGroup, Valuation.val_le_one_or_val_inv_le_one, Valuation.map_add_of_distinct_val, Valuation.map_add, Valuation.HasExtension.val_map_lt_iff, Valued.is_topological_valuation, ArchimedeanClass.FiniteElement.val_add, IsValuativeTopology.isOpen_ball, Valuation.map_div, Valuation.one_lt_val_iff, Padic.norm_eq_zpow_log_mulValuation, ValuationSubring.valuation_lt_one_or_eq_one, PowerSeries.intValuation_eq_of_coe, Valuation.one_apply_of_ne_zero, Valued.continuous_valuation, WithVal.apply_symm_equiv, Valuation.val_eq_one_iff, LaurentSeries.val_le_one_iff_eq_coe, AddValuation.toValuation_ofValuation, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_def, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, IsValuativeTopology.isClopen_sphere, FunctionField.valuedFqtInfty.def, Valuation.coe_coe, WithVal.apply_equiv, Valuation.IsEquiv.one_lt_iff_one_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Valuation.mem_unitGroup_iff, Valued.isOpen_sphere, IsDedekindDomain.HeightOneSpectrum.valuation_def, ValuationSubring.valuation_le_one, LaurentSeries.exists_ratFunc_val_lt, ArchimedeanClass.FiniteElement.val_mul, Valued.hasBasis_nhds_zero, Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup, IsValuativeTopology.continuous_valuation, Padic.mulValuation_toFun, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, IsValuativeTopology.mem_nhds_iff', IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, Valuation.toMonoidWithZeroHom_one, Valuation.map_sub_swap, Valuation.isEquiv_iff_val_le_one, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, Valuation.IsUniformizer.val, ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, Valuation.HasExtension.val_map_le_one_iff, Valuation.map_sub, Rat.valuation_le_one_iff_den, Valuation.mem_valuationSubring_iff, Valuation.ofAddValuation_apply, Valuation.Integers.isIntegral_iff_v_le_one, ValuativeExtension.mapValueGroupWithZero_valuation, Valuation.isEquiv_iff_val_eq_one, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, WeierstrassCurve.isGoodReduction_iff, Valuation.Integers.le_iff_dvd, LaurentSeries.exists_Polynomial_intValuation_lt, Valued.continuous_extensionValuation, ValuationSubring.valuation_le_one_iff, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, ValuationSubring.mem_unitGroup_iff, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', ArchimedeanClass.FiniteElement.val_sub, Valuation.toAddValuation_apply, Valued.isClosed_ball, Valuation.zero_iff, Valuation.srel_iff_lt, Valued.isClopen_sphere, PadicAlgCl.valuation_p, PadicComplex.valuation_p, Valued.isClosed_sphere, IsValuativeTopology.isClosed_closedBall, Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator, Valuation.one_apply_eq_zero_iff, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', WithVal.lt_def, IsValuativeTopology.mem_nhds_zero_iff, ModP.preVal_mk, Valuation.apply_posSubmonoid_pos, Valuation.one_srel_iff, RatFunc.valuation_eq_LaurentSeries_valuation, ModP.v_p_lt_preVal, Valuation.IsRankOneDiscrete.generator_zpowers_eq_range, Valuation.mem_leAddSubgroup_iff, Valuation.vle_iff_le, Valued.toNormedField.norm_le_iff, Valuation.map_add', IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, Valuation.Integers.dvdNotUnit_iff_lt, Padic.valuation_p_lt_one, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, Valuation.Integers.valuation_unit, Valuation.IsEquiv.lt_iff_lt, Valuation.map_mul, Valuation.ofAddValuation_toAddValuation, Valued.closure_coe_completion_v_lt, Valued.valuation_isClosedMap, Int.padicValuation_self, Valued.closure_coe_completion_v_mul_v_lt, Valued.valuedCompletion_apply, Valued.cauchy_iff, Valuation.one_apply_le_one, ValuationSubring.valuation_eq_iff, ValuativeRel.one_apply_posSubmonoid, Valuation.instValuationClass, ValuativeRel.trivialRel_eq_ofValuation_one, ArchimedeanClass.FiniteResidueField.mk_eq_mk, Valued.norm_def, Valuation.comap_apply, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, AddValuation.ofValuation_toValuation, NumberField.FinitePlace.norm_def_int, Valuation.leIdeal_v_le_of_mem, Valuation.veq_iff_eq, IsValuativeTopology.hasBasis_nhds_zero', Valuation.extendToLocalization_mk', Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, Valuation.map_one, Valuation.one_vlt_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, Valuation.toAddValuation_symm_eq, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, ArchimedeanClass.FiniteElement.val_zero, Valuation.one_vle_iff, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Valued.toNormedField.one_lt_norm_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, IsValuativeTopology.hasBasis_nhds_zero, Valuation.IsEquiv.eq_zero, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, Valuation.IsNontrivial_iff_exists_one_lt, Valuation.mem_ltAddSubgroup_iff, Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroup, LaurentSeries.valuation_LaurentSeries_equal_extension, Valuation.not_isNontrivial_one, RatFunc.v_def, ArchimedeanClass.FiniteResidueField.mk_ne_zero, Rat.padicValuation_eq_zero_iff, Valuation.map_inv, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Set.unit_valuation_eq_one, IsValuativeTopology.isOpen_closedBall, Valuation.integer.v_irreducible_pos, FunctionField.inftyValuation.X_zpow, ValuativeRel.exists_valuation_div_valuation_eq, Valuation.map_apply, ArchimedeanClass.FiniteElement.val_one, Valuation.IsNontrivial.exists_one_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_def, PadicAlgCl.valuation_def, FunctionField.inftyValuation.X, Valuation.toMonoidWithZeroHom_coe_eq_coe, Valuation.srel_one_iff, PadicAlgCl.valuation_coe, Valuation.IsUniformizer.val_pos, FunctionField.inftyValuedFqt.def, Valuation.vle_one_iff, Valuation.IsEquiv.val_sub_one_lt_one_iff, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, IsValuativeTopology.hasBasis_nhds', Valuation.Integers.valuation_pos_iff_ne_zero, Valued.isOpen_closedBall, Valuation.instNontrivialSubtypeUnitsMemSubgroupValueGroupOfIsNontrivial, Valuation.IsEquiv.one_le_iff_one_le, Valuation.ltSubmodule_v_le_of_mem, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_surjective, Valued.mem_nhds_zero, Valuation.HasExtension.val_map_eq_one_iff, Valued.isOpen_ball, ValuationSubring.mem_principalUnitGroup_iff, NormedField.v_eq_valuation, Valued.mem_nhds, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, Valuation.map_neg, IsNonarchimedeanLocalField.isCompact_closedBall, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, Valued.extensionValuation_apply_coe, ValuativeRel.valuation_surjective, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, Valuation.rel_one_iff, Valuation.IsEquiv.eq_one_iff_eq_one, LaurentSeries.valuation_coe_ratFunc, ValuativeRel.ValueGroupWithZero.embed_mk, AddValuation.toValuation_apply, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, IsValuativeTopology.isClosed_ball, Valuation.Integer.not_isUnit_iff_valuation_lt_one, Valuation.vlt_one_iff, LaurentSeries.valuation_compare, LaurentSeries.tendsto_valuation, Valuation.IsEquiv.le_one_iff_le_one, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, PowerSeries.intValuation_X, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Valuation.IsEquiv.val_eq, Valuation.HasExtension.mk_smul_mk, ValuationSubring.mem_nonunits_iff, Valued.toNormedField.norm_lt_iff, Valuation.map_pow, Valuation.rel_iff_le, Valuation.Integers.valuation_irreducible_pos, NumberField.toNNReal_valued_eq_adicAbv, Valuation.vlt_iff_lt, Valuation.IsUniformizer.iff, Valued.hasBasis_uniformity, Valuation.mem_ltSubmodule_iff, ModP.v_p_lt_val, Valuation.integer.v_irreducible_lt_one, FunctionField.inftyValuation.C, Valuation.IsNontrivial.exists_lt_one, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, Valuation.Integers.isUnit_iff_valuation_eq_one, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, Valuation.extendToLocalization_apply_map_apply, Valuation.mem_leIdeal_iff, Padic.norm_rat_le_one_iff_padicValuation_le_one, Valued.isClosed_closedBall, Set.integer_valuation_le_one, PreTilt.map_eq_zero, Valuation.coe_ltAddSubgroup, Rat.surjective_padicValuation, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, AddValuation.toValuation_symm_eq, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, WithVal.le_def, Valuation.HasExtension.val_map_lt_one_iff, Valuation.toValuation_ofValuation, Valuation.one_le_val_iff, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, ValuationSubring.valuation_eq_one_iff, Valuation.Compatible.vle_iff_le, AddValuation.ofValuation_symm_eq, ValuativeRel.ValueGroupWithZero.lift_valuation, Valuation.coe_mk, Valuation.IsEquiv.lt_one_iff_lt_one, Int.padicValuation_le_one, Valuation.isEquiv_iff_val_lt_one, WithVal.valuation_equiv_symm, NormedField.valuation_apply, Valuation.IsUniformizer.val_lt_one, Valued.loc_const, Valuation.mem_integer_iff, Valuation.one_apply_def, WeierstrassCurve.IsGoodReduction.goodReduction, Valued.isClopen_closedBall, IsValuativeTopology.mem_nhds_iff, ValuationSubring.valuation_surjective, Valuation.pos_iff, Valued.norm_pos_iff_valuation_pos, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, Valuation.map_zero, Valued.toNormedField.norm_lt_one_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Valuation.Integers.one_of_isUnit, Valuation.IsRankOneDiscrete.exists_generator_lt_one, AddValuation.ofValuation_apply, IsValuativeTopology.isOpen_sphere, FunctionField.inftyValuation_apply, ValuationSubring.mapOfLE_comp_valuation, Valuation.val_le_one_iff, LaurentSeries.exists_ratFunc_eq_v, Valued.toNormedField.one_le_norm_iff, Valuation.ofAddValuation_symm_eq, ValuativeRel.ValueGroupWithZero.mk_eq_valuation, Valuation.coeff_zero_minpoly, Valuation.map_add_supp, Valuation.IsRankOneDiscrete.generator_mem_range, IsValuativeTopology.isClopen_closedBall, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, LaurentSeries.valuation_X_pow, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, Int.padicValuation_eq_zero_iff, Valuation.Integers.dvd_iff_le, ArchimedeanClass.FiniteElement.ext_iff, Valuation.one_rel_iff, Valuation.le_one_of_subsingleton, Rat.padicValuation_le_one_iff, Valuation.one_apply_eq_one_iff, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, Polynomial.valuation_X_eq_neg_one
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