Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.valueGroupOrderIso_restrict

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (K : Type u_2) [inst_2 : Field K]
  [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R)
  (x : IsDedekindDomain.HeightOneSpectrum.adicCompletion K v),
  (IsDedekindDomain.HeightOneSpectrum.adicCompletion.valueGroupOrderIso K v)
      ((IsDedekindDomain.HeightOneSpectrum.adicCompletion.valuation K v).restrict x) =
    Valued.v.restrict x.toCompletion

Defined in: Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by: 0 results in Mathlib
Foundations: Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Field Algebra IsFractionRing

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DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Subgroupstatement · cited by 3,593
Unitsstatement · cited by 2,804
Multiplicativestatement and proof · cited by 875
Valuationstatement · cited by 823
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
WithZerostatement and proof · cited by 586
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338

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