Theorems · Theorem · number theory

NumberField.mixedEmbedding.logMap_eq_logEmbedding

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (u : (NumberField.RingOfIntegers K)ˣ),
  NumberField.mixedEmbedding.logMap
      ((NumberField.mixedEmbedding K) ((algebraMap (NumberField.RingOfIntegers K) K) ↑u)) =
    (NumberField.Units.logEmbedding K) (Additive.ofMul u)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
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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Cites33

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement · cited by 25,697
RingHomstatement · cited by 10,189
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Algebra.algebraMapstatement and proof · cited by 4,706
AddMonoidHomstatement · cited by 3,230
Unitsstatement and proof · cited by 2,804
Units.valstatement and proof · cited by 1,966
Module.finrankproof · cited by 1,770
MulZeroClass.zero_mulproof · cited by 1,625

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.logMap_unit_smulproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_neproof · cited by 1