Theorems · Theorem · number theory

Set.integer_valuation_le_one

∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (S : Set (IsDedekindDomain.HeightOneSpectrum R))
  (K : Type v) [inst_2 : Field K] [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] (x : ↥(S.integer K))
  {v : IsDedekindDomain.HeightOneSpectrum R}, v ∉ S → (IsDedekindDomain.HeightOneSpectrum.valuation K v) ↑x ≤ 1

Defined in

Mathlib.RingTheory.DedekindDomain.SInteger

Cited by

0 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing