Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.valuationSubringAtPrime_le_valuation

∀ {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),
  IsDedekindDomain.HeightOneSpectrum.valuationSubringAtPrime K v ≤
    (IsDedekindDomain.HeightOneSpectrum.valuation K v).valuationSubring

Defined in: Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by: 1 results in Mathlib
Foundations: Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Field Algebra IsFractionRing

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Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · 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
Algebra.algebraMapproof · cited by 4,706
Multiplicativestatement · cited by 875
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
WithZerostatement · cited by 586
Ideal.primeComplproof · cited by 462
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
ValuationSubringstatement · cited by 187

Cited by1

Results whose statement or proof uses this declaration.

IsDedekindDomain.HeightOneSpectrum.valuationSubringAtPrime_eq_valuationSubringproof · cited by 0