Theorems · Theorem · number theory

NumberField.FinitePlace.equivHeightOneSpectrum_symm_apply

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
  (v : IsDedekindDomain.HeightOneSpectrum (NumberField.RingOfIntegers K)) (x : K),
  (NumberField.FinitePlace.equivHeightOneSpectrum.symm v) x = ‖(NumberField.FinitePlace.embedding v) x‖

Defined in: Mathlib.NumberTheory.NumberField.Completion.FinitePlace
Cited by: 1 results in Mathlib
Foundations: Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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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
RingHomstatement · cited by 10,189
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Norm.normstatement · cited by 5,413
Equiv.symmstatement · cited by 3,681
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
IsDedekindDomain.HeightOneSpectrum.adicCompletionstatement · cited by 93
NumberField.FinitePlacestatement · cited by 35

Cited by1

Results whose statement or proof uses this declaration.

NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_applyproof · cited by 0