Theorems · Theorem · number theory

NumberField.canonicalEmbedding.mem_rat_span_latticeBasis

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (x : K),
  (NumberField.canonicalEmbedding K) x ∈ Submodule.span ℚ (Set.range ⇑(NumberField.canonicalEmbedding.latticeBasis K))

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 300 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
RingHomstatement and proof · cited by 10,189
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Complexstatement and proof · cited by 5,565
Set.rangestatement and proof · cited by 4,705
Finset.univproof · cited by 3,473
Finset.sum_congrproof · cited by 2,323
Submodule.spanstatement and proof · cited by 1,504
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
Module.Basis.reprproof · cited by 498

Cited by1

Results whose statement or proof uses this declaration.

NumberField.canonicalEmbedding.integralBasis_repr_applyproof · cited by 1