Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.realSpace K),
  ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis x =
    ↑NumberField.mixedEmbedding.fundamentalCone.expMap
      ((NumberField.mixedEmbedding.fundamentalCone.completeBasis K).equivFun.symm x)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 1 results in Mathlib
Foundations: Depth 331 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
RingHom.idstatement · cited by 18,349
Fieldstatement and proof · cited by 7,404
LinearEquivstatement · cited by 3,317
LinearEquiv.symmstatement · cited by 1,461
OpenPartialHomeomorph.toFun'statement · cited by 745
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
Module.Basis.equivFunstatement · cited by 88
NumberField.mixedEmbedding.realSpacestatement and proof · cited by 87
NumberField.mixedEmbedding.fundamentalCone.expMapBasisstatement · cited by 30

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasisproof · cited by 0