NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv

Deprecated since 2026-03-11Use NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv instead.

∀ (K : Type u_1) [inst : Field K] {R : Type u_2} [inst_1 : CommRing R] [inst_2 : Algebra R K]
  [inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R)
  [inst_5 : Module.Finite ℤ R] [inst_6 : Module.Free ℤ R]
  (x : WithVal (IsDedekindDomain.HeightOneSpectrum.valuation K v)),
  ↑((WithZeroMulInt.toNNReal ⋯) (Valued.v x)) =
    (NumberField.HeightOneSpectrum.adicAbv K v) ((WithVal.equiv (IsDedekindDomain.HeightOneSpectrum.valuation K v)) x)

Alias of NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv.

Defined in: Mathlib.NumberTheory.NumberField.Completion.FinitePlace
Cited by: 0 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CommRing Algebra IsDedekindDomain IsFractionRing Module.Finite Module.Free

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DFunLike.coestatement · cited by 62,936
Realstatement · cited by 25,697
CommRingstatement · cited by 17,173
Algebrastatement · cited by 11,388
Fieldstatement · cited by 7,404
Idealstatement · cited by 4,748
NNRealstatement · cited by 4,310
NNReal.toRealstatement · cited by 1,260
RingEquivstatement · cited by 1,147
Module.Finitestatement · cited by 1,032
Multiplicativestatement · cited by 875
Valuationstatement · cited by 823

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