Theorems · Theorem · number theory

Rat.HeightOneSpectrum.valuation_equiv_padicValuation

∀ {R : Type u_2} [inst : CommRing R] [inst_1 : Algebra R ℚ] [inst_2 : IsIntegralClosure R ℤ ℚ]
  [inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R ℚ] (v : IsDedekindDomain.HeightOneSpectrum R),
  (IsDedekindDomain.HeightOneSpectrum.valuation ℚ v).IsEquiv (Rat.padicValuation ↑(Rat.HeightOneSpectrum.primesEquiv v))

Defined in: Mathlib.NumberTheory.Padics.HeightOneSpectrum
Cited by: 0 results in Mathlib
Foundations: Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Algebra IsIntegralClosure IsDedekindDomain IsFractionRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites32

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

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Equivstatement · cited by 8,337
Idealproof · cited by 4,748
Nat.Primestatement · cited by 2,059
Ideal.spanproof · cited by 948
Multiplicativestatement · cited by 875
IsFractionRingstatement and proof · cited by 738
Ideal.mapproof · cited by 692
IsDedekindDomainstatement and proof · cited by 668
WithZerostatement · cited by 586

Cited by1

Results whose statement or proof uses this declaration.

Rat.HeightOneSpectrum.withValEquivproof · cited by 0