Theorems · Theorem · number theory
NumberField.InfinitePlace.not_isReal_iff_isComplex
∀ {K : Type u_1} [inst : Field K] {w : NumberField.InfinitePlace K}, ¬w.IsReal ↔ w.IsComplex- Cited by
- 25 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 by26
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normAtPlace_apply_of_isComplexproof · cited by 9
- NumberField.InfinitePlace.isReal_or_isComplexproof · cited by 9
- NumberField.InfinitePlace.isUnramified_iffproof · cited by 6
- NumberField.InfinitePlace.not_isUnramified_iffproof · cited by 4
- NumberField.InfinitePlace.prod_eq_prod_mul_prodproof · cited by 3
- NumberField.IsTotallyComplex.complexEmbedding_not_isRealproof · cited by 3
- NumberField.mixedEmbedding.normAtComplexPlaces_apply_isComplexproof · cited by 3
- NumberField.InfinitePlace.IsComplex.mult_eq_twoproof · cited by 2
- NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iffproof · cited by 2
- NumberField.InfiniteAdeleRing.ringEquiv_mixedSpaceproof · cited by 2
- NumberField.InfinitePlace.card_complex_embeddingsproof · cited by 2