Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (i : { w // w ≠ NumberField.Units.dirichletUnitTheorem.w₀ }),
  (NumberField.mixedEmbedding.fundamentalCone.completeBasis K) ↑i =
    ↑NumberField.mixedEmbedding.fundamentalCone.expMap.symm
      (NumberField.mixedEmbedding.normAtAllPlaces
        ((NumberField.mixedEmbedding K)
          ((algebraMap (NumberField.RingOfIntegers K) K)
            ↑(NumberField.Units.fundSystem K (NumberField.mixedEmbedding.fundamentalCone.equivFinRank.symm i)))))

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 3 results in Mathlib
Foundations: Depth 331 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites29

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 and proof · 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
Equiv.symmstatement and proof · cited by 3,681
Units.valstatement and proof · cited by 1,966
Module.Basisstatement and proof · cited by 1,477
OpenPartialHomeomorph.toFun'statement and proof · cited by 745
NumberFieldstatement and proof · cited by 653

Cited by3

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_neproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symmproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasisproof · cited by 0