Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet_mixedEmbedding

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : NumberField.RingOfIntegers K}
  (hx : (NumberField.mixedEmbedding K) ↑x ∈ NumberField.mixedEmbedding.fundamentalCone.integerSet K),
  ↑(NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet ⟨(NumberField.mixedEmbedding K) ↑x, hx⟩) = x

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 1 results in Mathlib
Foundations: Depth 334 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.

Cites20

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
Setstatement · cited by 53,352
Realstatement · cited by 25,697
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Submonoidstatement · cited by 3,086
nonZeroDivisorsstatement · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.RingOfIntegersstatement and proof · cited by 413
NumberField.InfinitePlace.IsRealstatement · cited by 301

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMapproof · cited by 0