Theorems · Theorem · number theory

NumberField.canonicalEmbedding.latticeBasis_apply

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

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 7 results in Mathlib
Foundations: Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites22

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
RingHomstatement and proof · cited by 10,189
Fieldstatement and proof · cited by 7,404
Complexstatement and proof · cited by 5,565
Algebra.algebraMapproof · cited by 4,706
Equiv.symmproof · cited by 3,681
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
Equiv.apply_symm_applyproof · cited by 346
Module.Free.ChooseBasisIndexstatement and proof · cited by 133
Module.Basis.reindexproof · cited by 57

Cited by7

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.latticeBasis_applyproof · cited by 4
NumberField.basisMatrix_eq_embeddingsMatrixReindexproof · cited by 2
NumberField.conj_basisMatrixproof · cited by 1
NumberField.canonicalEmbedding.integralBasis_repr_applyproof · cited by 1
NumberField.canonicalEmbedding.mem_rat_span_latticeBasisproof · cited by 1
NumberField.mixedEmbedding.disjoint_span_commMap_kerproof · cited by 0
NumberField.canonicalEmbedding.mem_span_latticeBasisproof · cited by 0