Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.adicAbv_intCast_le_one
∀ (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] (n : ℤ), (NumberField.HeightOneSpectrum.adicAbv K v) ↑n ≤ 1The v-adic absolute value of an integer is ≤ 1.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Module.Finitestatement and proof · cited by 1,032
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- AbsoluteValuestatement · cited by 363
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- NumberField.HeightOneSpectrum.adicAbvstatement · cited by 21
Cited by2
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