Theorems · Theorem · number theory
RatFunc.valuation_isEquiv_adic_of_not_isEquiv_infty
∀ {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] [inst_4 : DecidableEq (RatFunc K)],
¬v.IsEquiv (RatFunc.inftyValuation K) → ∃! u, v.IsEquiv (IsDedekindDomain.HeightOneSpectrum.valuation (RatFunc K) u)- Defined in
- Mathlib.NumberTheory.RatFunc.Ostrowski
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- ExistsUniquestatement · cited by 268
- IsDedekindDomain.HeightOneSpectrum.valuationstatement · cited by 130
- Valuation.IsEquivstatement and proof · cited by 67
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
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