Theorems · Theorem · number theory
NumberField.InfinitePlace.not_isComplex_iff_isReal
∀ {K : Type u_1} [inst : Field K] {w : NumberField.InfinitePlace K}, ¬w.IsComplex ↔ w.IsReal- Cited by
- 5 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.IsComplexstatement · cited by 272
- NumberField.InfinitePlace.embeddingproof · cited by 78
- NumberField.ComplexEmbedding.IsRealproof · cited by 38
- NumberField.InfinitePlace.isReal_iffproof · cited by 13
- NumberField.InfinitePlace.isComplex_iffproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.isUnramified_iffproof · cited by 6
- NumberField.InfinitePlace.IsUnramified.isUnmixedproof · cited by 1
- NumberField.InfinitePlace.IsUnramified.isUnmixed_conjugateproof · cited by 1
- NumberField.InfinitePlace.IsUnramified.liesOver_isReal_overproof · cited by 1
- NumberField.InfinitePlace.LiesOver.isReal_of_isReal_overproof · cited by 0