Theorems · Theorem · number theory
NumberField.InfinitePlace.isComplex_iff
∀ {K : Type u_1} [inst : Field K] {w : NumberField.InfinitePlace K},
w.IsComplex ↔ ¬NumberField.ComplexEmbedding.IsReal w.embedding- Cited by
- 7 results in Mathlib
- Foundations
- Depth 168 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- NumberField.InfinitePlace.embeddingstatement and proof · cited by 78
- NumberField.InfinitePlace.mkproof · cited by 56
- NumberField.ComplexEmbedding.conjugateproof · cited by 40
- NumberField.ComplexEmbedding.IsRealstatement and proof · cited by 38
- NumberField.InfinitePlace.mk_embeddingproof · cited by 25
- NumberField.InfinitePlace.mk_eq_iffproof · cited by 5
- NumberField.ComplexEmbedding.isReal_conjugate_iffproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.not_isReal_iff_isComplexproof · cited by 25
- NumberField.InfinitePlace.not_isComplex_iff_isRealproof · cited by 5
- NumberField.InfinitePlace.IsRamified.isMixed_conjugate_embeddingproof · cited by 2
- NumberField.InfinitePlace.IsRamified.isMixed_embeddingproof · cited by 2
- NumberField.InfinitePlace.LiesOver.isComplex_of_isComplex_underproof · cited by 2
- NumberField.InfinitePlace.isRamified_mk_iff_isMixedproof · cited by 1
- NumberField.InfinitePlace.IsRamified.ne_conjugateproof · cited by 1