Theorems · Theorem · number theory

NumberField.mixedEmbedding.mem_span_latticeBasis

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] {x : NumberField.mixedEmbedding.mixedSpace K},
  x ∈ Submodule.span ℤ (Set.range ⇑(NumberField.mixedEmbedding.latticeBasis K)) ↔
    x ∈ NumberField.mixedEmbedding.integerLattice K

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 304 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.

Cites30

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
Setproof · cited by 53,352
Realstatement · cited by 25,697
SetLike.coeproof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
Set.imageproof · cited by 5,609
Complexstatement · cited by 5,565
Set.rangestatement and proof · cited by 4,705
Submodule.spanstatement and proof · cited by 1,504
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.span_latticeBasisproof · cited by 1