Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv
∀ (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)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · 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 and proof · cited by 1,032
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.toNNReal_valued_eq_adicAbvproof · cited by 0
- NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbvproof · cited by 0