Theorems · Theorem · number theory

NumberField.mixedEmbedding.span_latticeBasis

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  Submodule.span ℤ (Set.range ⇑(NumberField.mixedEmbedding.latticeBasis K)) =
    NumberField.mixedEmbedding.integerLattice K

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites19

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
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Complexstatement · cited by 5,565
Set.rangestatement · cited by 4,705
Submodule.spanstatement · cited by 1,504
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.RingOfIntegersstatement · cited by 413
NumberField.InfinitePlace.IsRealstatement · cited by 301

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalDomain_integerLatticeproof · cited by 1