Theorems · Theorem · number theory

NumberField.mixedEmbedding.latticeBasis_apply

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (i : Module.Free.ChooseBasisIndex ℤ (NumberField.RingOfIntegers K)),
  (NumberField.mixedEmbedding.latticeBasis K) i = (NumberField.mixedEmbedding K) ((NumberField.integralBasis K) i)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites24

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
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Algebra.algebraMapproof · cited by 4,706
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.RingOfIntegersstatement and proof · cited by 413
NumberField.InfinitePlace.IsRealstatement · cited by 301
NumberField.InfinitePlace.IsComplexstatement · cited by 272

Cited by4

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
NumberField.mixedEmbedding.mem_rat_span_latticeBasisproof · cited by 1
NumberField.mixedEmbedding.mem_span_latticeBasisproof · cited by 1
NumberField.mixedEmbedding.latticeBasis_repr_applyproof · cited by 1