Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.torsion_smul_mem_of_mem

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : NumberField.mixedEmbedding.mixedSpace K},
  x ∈ NumberField.mixedEmbedding.fundamentalCone K →
    ∀ {ζ : (NumberField.RingOfIntegers K)ˣ},
      ζ ∈ NumberField.Units.torsion K → ζ • x ∈ NumberField.mixedEmbedding.fundamentalCone K

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 2 results in Mathlib
Foundations: Depth 326 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement · cited by 53,352
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Subgroupstatement · cited by 3,593
one_mulproof · cited by 2,841
Unitsstatement and proof · cited by 2,804
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map_mulproof · cited by 1,137
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.unit_smul_mem_iff_mem_torsionproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.torsion_unitSMul_mem_integerSetproof · cited by 0