Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (s : Set (NumberField.mixedEmbedding.realSpace K)),
  NumberField.mixedEmbedding.normAtAllPlaces ''
      NumberField.mixedEmbedding.normAtAllPlaces ⁻¹' ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis '' s =
    ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis '' s

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 2 results in Mathlib
Foundations: Depth 332 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites15

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 · cited by 4,946
LT.lt.leproof · cited by 2,189
OpenPartialHomeomorph.toFun'statement and proof · cited by 745
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.mixedEmbedding.mixedSpacestatement · cited by 239
NumberField.mixedEmbedding.realSpacestatement and proof · cited by 87
NumberField.mixedEmbedding.fundamentalCone.expMapBasisstatement and proof · cited by 30

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.volume_normLeOneproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closureproof · cited by 1