Theorems · Theorem · number theory

Set.integer.congr_simp

∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (S S_1 : Set (IsDedekindDomain.HeightOneSpectrum R)),
  S = S_1 →
    ∀ (K : Type v) [inst_2 : Field K] [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K], S.integer K = S_1.integer K

Defined in: Mathlib.RingTheory.DedekindDomain.SInteger
Cited by: 0 results in Mathlib
Foundations: Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Field Algebra IsFractionRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Subalgebrastatement · cited by 1,353
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
Set.integerstatement and proof · cited by 8

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.