Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max
Deprecated since 2026-03-11Use NumberField.HeightOneSpectrum.adicAbv_add_le_max instead.
∀ (K : Type u_1) [inst : Field K] {R : Type u_2} [inst_1 : CommRing R] [inst_2 : Algebra R K]
[inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R)
[inst_5 : Module.Finite ℤ R] [inst_6 : Module.Free ℤ R] (x y : K),
(NumberField.HeightOneSpectrum.adicAbv K v) (x + y) ≤
max ((NumberField.HeightOneSpectrum.adicAbv K v) x) ((NumberField.HeightOneSpectrum.adicAbv K v) y)Alias of NumberField.HeightOneSpectrum.adicAbv_add_le_max.
The v-adic absolute value satisfies the ultrametric inequality.
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- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement · cited by 17,173
- Algebrastatement · cited by 11,388
- Fieldstatement · cited by 7,404
- Module.Finitestatement · cited by 1,032
- IsFractionRingstatement · cited by 738
- IsDedekindDomainstatement · cited by 668
- Module.Freestatement · cited by 597
- AbsoluteValuestatement · cited by 363
- IsDedekindDomain.HeightOneSpectrumstatement · cited by 338
- NumberField.HeightOneSpectrum.adicAbvstatement · cited by 21
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