Documentation Verification Report

AbsoluteValue

📁 Source: Mathlib/Topology/UniformSpace/AbsoluteValue.lean

Statistics

MetricCount
DefinitionsAbsoluteValue, uniformSpace
2
TheoremshasBasis_uniformity
1
Total3

AbsoluteValue

Definitions

NameCategoryTheorems
uniformSpace 📖CompOp
2 mathmath: hasBasis_uniformity, Rat.uniformSpace_eq

Theorems

NameKindAssumesProvesValidatesDepends On
hasBasis_uniformity 📖mathematicalFilter.HasBasis
uniformity
uniformSpace
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
setOf
DFunLike.coe
AbsoluteValue
CommSemiring.toSemiring
CommRing.toCommSemiring
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
funLike
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
UniformSpace.hasBasis_ofFun
NoMaxOrder.exists_gt
instNoMaxOrderOfNontrivial
IsStrictOrderedRing.toIsOrderedRing
DivisionRing.toNontrivial

(root)

Definitions

NameCategoryTheorems
AbsoluteValue 📖CompData
154 mathmath: AbsoluteValue.map_neg, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, NumberField.InfinitePlace.isNontrivial, NumberField.InfinitePlace.eq_iff_isEquiv, Polynomial.cardPowDegree_zero, NumberField.prod_nonarchAbsVal_eq, Height.mulHeight₁_eq, NumberField.isInfinitePlace_iff, Polynomial.exists_partition_polynomial, NumberField.InfinitePlace.isometry_embedding, Padic.complete', AbsoluteValue.map_units_intCast, AbsoluteValue.coe_mk, AbsoluteValue.IsEuclidean.sub_mod_lt, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, AbsoluteValue.eq_zero, NumberField.InfiniteAdeleRing.algebraMap_apply, AbsoluteValue.abs_abv_sub_le_abv_sub, padicNormE.nonarchimedean', Polynomial.exists_partition_polynomial_aux, NumberField.InfinitePlace.Completion.norm_coe, padicNormE.image', AbsoluteValue.eq_on_nat_iff_eq_on_int, NumberField.InfinitePlace.coe_apply, padicNormE.eq_padic_norm', AbsoluteValue.isEquiv_iff_lt_one_iff, AbsoluteValue.map_sub_eq_zero_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, AbsoluteValue.apply_nat_le_self, AbsoluteValue.IsEquiv.le_one_iff, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, Rat.AbsoluteValue.equiv_on_nat_iff_equiv, padicNormE.defn, NumberField.InfinitePlace.Completion.locallyCompactSpace, padicNormE.add_eq_max_of_ne', AbsoluteValue.coe_toMonoidHom, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, Rat.AbsoluteValue.equiv_real_or_padic, AbsoluteValue.abs_apply, Polynomial.gaussNorm_intAdicAbv_le_one, Polynomial.gaussNorm_lt_one_iff_contentIdeal_le, AbsoluteValue.le_sub, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, AbsoluteValue.IsEquiv.lt_iff_lt, NumberField.InfinitePlace.isInfinitePlace, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, NumberField.InfinitePlace.smul_coe_apply, NumberField.place_apply, IsAbsoluteValue.toAbsoluteValue_apply, Padic.padicNormE.is_norm, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, Rat.AbsoluteValue.padic_eq_padicNorm, NumberField.isFinitePlace_iff, AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv, AbsoluteValue.pos, AbsoluteValue.IsEquiv.lt_one_iff, AbsoluteValue.nonneg, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, AbsoluteValue.pos_iff, AbsoluteValue.IsEquiv.le_iff_le, AbsoluteValue.IsEquiv.log_div_log_pos, Height.mulHeight_eq, NumberField.FinitePlace.coe_apply, AbsoluteValue.map_units_int_smul, Height.AdmissibleAbsValues.mulSupport_finite, AbsoluteValue.ext_iff, Polynomial.cardPowDegree_apply, Padic.complete'', MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, Polynomial.exists_approx_polynomial, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, WithAbs.norm_eq_abv, AbsoluteValue.nonnegHomClass, AbsoluteValue.trivial_apply, AbsoluteValue.IsAdmissible.exists_approx, AbsoluteValue.IsEuclidean.map_lt_map_iff', AbsoluteValue.IsEquiv.eq_iff_eq, NumberField.count_multisetInfinitePlace_eq_mult, AbsoluteValue.nonpos_iff, AbsoluteValue.monoidWithZeroHomClass, AbsoluteValue.le_add, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, Padic.exi_rat_seq_conv, AbsoluteValue.coe_toMulHom, AbsoluteValue.IsAdmissible.exists_partition, AbsoluteValue.not_isNontrivial_iff, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, AbsoluteValue.hasBasis_uniformity, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff, NumberField.InfinitePlace.isometry_embedding_of_isReal, AbsoluteValue.exists_one_lt_lt_one_of_not_isEquiv, AbsoluteValue.IsAdmissible.exists_partition', Rat.AbsoluteValue.padic_le_one, AbsoluteValue.sum_le, AbsoluteValue.zeroHomClass, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, AbsoluteValue.map_units_int, AbsoluteValue.IsEquiv.one_lt_iff, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, AbsoluteValue.IsEquiv.eq_one_iff, AbsoluteValue.mulHomClass, AbsoluteValue.map_pow, AbsoluteValue.map_sub, NumberField.AdeleRing.algebraMap_fst_apply, AbsoluteValue.map_prod, Padic.rat_dense', AbsoluteValue.not_isNontrivial_apply, Polynomial.cardPowDegree_nonzero, AbsoluteValue.sub_le, Rat.AbsoluteValue.eq_on_nat_iff_eq, AbsoluteValue.IsAdmissible.exists_approx_aux, Rat.AbsoluteValue.real_eq_abs, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, NumberField.toNNReal_valued_eq_adicAbv, AbsoluteValue.add_le, AbsoluteValue.instMulRingNormClassOfNontrivialOfIsDomain, AbsoluteValue.subadditiveHomClass, AbsoluteValue.IsEquiv.one_le_iff, NumberField.mem_multisetInfinitePlace, AbsoluteValue.IsEuclidean.map_lt_map_iff, AbsoluteValue.IsNontrivial.exists_abv_lt_one, NumberField.FinitePlace.isFinitePlace, AbsoluteValue.apply_natAbs_eq, AbsoluteValue.isEquiv_iff_exists_rpow_eq, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, NumberField.prod_archAbsVal_eq, AbsoluteValue.isAbsoluteValue, AbsoluteValue.listSum_le, AbsoluteValue.map_zero, AbsoluteValue.map_mul, Height.AdmissibleAbsValues.product_formula, AbsoluteValue.coe_toMonoidWithZeroHom, AbsoluteValue.sub_le_add, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, AbsoluteValue.IsNontrivial.exists_abv_gt_one, Rat.AbsoluteValue.apply_le_sum_digits, Polynomial.isPrimitive_iff_forall_gaussNorm_eq_one, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, AbsoluteValue.IsEquiv.log_div_log_eq_log_div_log, NumberField.FinitePlace.norm_def, NumberField.mixedEmbedding.convexBodySum_mem, AbsoluteValue.exists_lt_one_one_le_of_not_isEquiv, ClassGroup.exists_mem_finset_approx', Finset.max_abv_sum_one_le, ClassGroup.exists_mem_finsetApprox, AbsoluteValue.map_one, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk'

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