Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.mixedSpace K),
  NumberField.mixedEmbedding.logMap
      (NumberField.mixedEmbedding.mixedSpaceOfRealSpace (NumberField.mixedEmbedding.normAtAllPlaces x)) =
    NumberField.mixedEmbedding.logMap x

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 2 results in Mathlib
Foundations: Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites20

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

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NumberField.InfinitePlace.IsComplexstatement · cited by 272
NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
NumberField.mixedEmbedding.realSpacestatement · cited by 87

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iffproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOneproof · cited by 1