Theorems · Theorem · number theory

NumberField.mixedEmbedding.pos_of_notMem_negAt_plusPart

∀ {K : Type u_1} [inst : Field K] {s : Set { w // w.IsReal }} (A : Set (NumberField.mixedEmbedding.mixedSpace K))
  {x : NumberField.mixedEmbedding.mixedSpace K},
  x ∈ ⇑(NumberField.mixedEmbedding.negAt s) '' NumberField.mixedEmbedding.plusPart A →
    ∀ {w : { w // w.IsReal }}, w ∉ s → 0 < x.1 w

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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Cites15

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 and proof · cited by 53,352
Realstatement and proof · cited by 25,697
RingHom.idstatement · cited by 18,349
Fieldstatement and proof · cited by 7,404
Set.imagestatement and proof · cited by 5,609
Complexstatement · cited by 5,565
ContinuousLinearEquivstatement · cited by 743
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
NumberField.InfinitePlace.IsComplexstatement · cited by 272
NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.disjoint_negAt_plusPartproof · cited by 1
NumberField.mixedEmbedding.mem_negAt_plusPart_of_memproof · cited by 1