Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  NumberField.mixedEmbedding.fundamentalCone.normLeOne K =
    NumberField.mixedEmbedding.normAtAllPlaces ⁻¹'
      ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis '' NumberField.mixedEmbedding.fundamentalCone.paramSet K

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 4 results in Mathlib
Foundations: Depth 340 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites16

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
Realstatement · cited by 25,697
Fieldstatement and proof · cited by 7,404
Set.imagestatement and proof · cited by 5,609
Set.preimagestatement and proof · cited by 4,946
OpenPartialHomeomorph.toFun'statement and proof · cited by 745
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
NumberField.mixedEmbedding.realSpacestatement and proof · cited by 87
NumberField.mixedEmbedding.fundamentalCone.expMapBasisstatement and proof · cited by 30
NumberField.mixedEmbedding.normAtAllPlacesstatement and proof · cited by 30

Cited by4

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.volume_normLeOneproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOneproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subsetproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOneproof · cited by 1