Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.adicCompletion.ext_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K]
[inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] {v : IsDedekindDomain.HeightOneSpectrum R}
{x y : IsDedekindDomain.HeightOneSpectrum.adicCompletion K v}, x = y ↔ x.toCompletion = y.toCompletion- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Multiplicativestatement · cited by 875
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- WithZerostatement · cited by 586
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.valuationstatement · cited by 130
- IsDedekindDomain.HeightOneSpectrum.adicCompletionstatement and proof · cited by 93
- Valuation.Completionstatement · cited by 33
- IsDedekindDomain.HeightOneSpectrum.adicCompletion.toCompletionstatement and proof · cited by 25
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