Theorems · Theorem · number theory

NumberField.mixedEmbedding.convexBodyLT_mem

∀ (K : Type u_1) [inst : Field K] (f : NumberField.InfinitePlace K → NNReal) {x : K},
  (NumberField.mixedEmbedding K) x ∈ NumberField.mixedEmbedding.convexBodyLT K f ↔
    ∀ (w : NumberField.InfinitePlace K), w x < ↑(f w)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
Cited by: 1 results in Mathlib
Foundations: Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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Cites22

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
Norm.normproof · cited by 5,413
NNRealstatement and proof · cited by 4,310
NNReal.toRealstatement and proof · cited by 1,260
Metric.ballproof · cited by 735
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.IsRealstatement and proof · cited by 301

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_ltproof · cited by 1