Theorems · Theorem · number theory

NumberField.mixedEmbedding.mem_rat_span_latticeBasis

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

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Cites29

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
Submodulestatement · cited by 7,192
Complexstatement · 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

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.latticeBasis_repr_applyproof · cited by 1