Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage_image

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

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 2 results in Mathlib
Foundations: Depth 328 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites19

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

DFunLike.coeproof · cited by 62,936
Setstatement · cited by 53,352
Realproof · 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
NumberFieldstatement and proof · cited by 653
NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
subset_antisymmproof · cited by 150
NumberField.mixedEmbedding.realSpacestatement and proof · cited by 87
NumberField.mixedEmbedding.normproof · cited by 46
Set.subset_preimage_imageproof · cited by 44

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimageproof · cited by 4
NumberField.mixedEmbedding.fundamentalCone.volume_normLeOneproof · cited by 2