Theorems · Theorem · number theory
RatFunc.valuation_isEquiv_adic_of_valuation_X_le_one
∀ {K : Type u_1} {Γ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ]
{v : Valuation (RatFunc K) Γ} [v.IsRankOneDiscrete] [Valuation.IsTrivialOn K v],
v RatFunc.X ≤ 1 → ∃ u, v.IsEquiv (IsDedekindDomain.HeightOneSpectrum.valuation (RatFunc K) u)- Defined in
- Mathlib.NumberTheory.RatFunc.Ostrowski
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Multiplicativestatement · cited by 875
- Valuationstatement and proof · cited by 823
- WithZerostatement · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsDedekindDomain.HeightOneSpectrumstatement · cited by 338
- RatFuncstatement and proof · cited by 301
- IsDedekindDomain.HeightOneSpectrum.valuationstatement · cited by 130
- Valuation.IsEquivstatement · cited by 67
- RatFunc.Xstatement and proof · cited by 58
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.valuation_isEquiv_infty_or_adicproof · cited by 1