Theorems · Theorem · number theory
NumberField.InfinitePlace.isReal_mk_iff
∀ {K : Type u_1} [inst : Field K] {φ : K →+* ℂ},
(NumberField.InfinitePlace.mk φ).IsReal ↔ NumberField.ComplexEmbedding.IsReal φ- Cited by
- 12 results in Mathlib
- Foundations
- Depth 173 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- NumberField.InfinitePlace.IsRealstatement · cited by 301
- NumberField.InfinitePlace.mkstatement · cited by 56
- NumberField.ComplexEmbedding.IsRealstatement and proof · cited by 38
- NumberField.InfinitePlace.isReal_of_mk_isRealproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.comap_embedding_of_isRealproof · cited by 4
- NumberField.InfinitePlace.IsReal.comapproof · cited by 4
- NumberField.IsTotallyComplex.complexEmbedding_not_isRealproof · cited by 3
- NumberField.IsTotallyReal.le_maximalRealSubfieldproof · cited by 3
- NumberField.InfinitePlace.isReal_comap_iffproof · cited by 2
- NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iffproof · cited by 2
- NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConjproof · cited by 1
- NumberField.InfinitePlace.isUnramified_mk_iff_isUnmixedproof · cited by 1
- NumberField.InfinitePlace.isComplex_mk_iffproof · cited by 1
- NumberField.InfinitePlace.IsUnramified.isUnmixedproof · cited by 1
- NumberField.IsCMField.of_forall_isConjproof · cited by 0
- NumberField.IsTotallyReal.complexEmbedding_isRealproof · cited by 0