Theorems · Theorem · number theory
NumberField.ComplexEmbedding.isReal_iff
∀ {K : Type u_1} [inst : Field K] {φ : K →+* ℂ},
NumberField.ComplexEmbedding.IsReal φ ↔ NumberField.ComplexEmbedding.conjugate φ = φ- Cited by
- 7 results in Mathlib
- Foundations
- Depth 106 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.
Cites6
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.ComplexEmbedding.conjugatestatement · cited by 40
- NumberField.ComplexEmbedding.IsRealstatement · cited by 38
- isSelfAdjoint_iffproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.embedding_mk_eq_of_isRealproof · cited by 5
- NumberField.IsTotallyReal.le_maximalRealSubfieldproof · cited by 3
- NumberField.InfinitePlace.card_filter_mk_eqproof · cited by 3
- NumberField.InfinitePlace.conjugate_embedding_eq_of_isRealproof · cited by 2
- NumberField.InfinitePlace.LiesOver.isComplex_of_isComplex_underproof · cited by 2
- NumberField.InfinitePlace.IsRamified.comap_embedding_conjugateproof · cited by 2
- NumberField.mixedEmbedding.disjoint_span_commMap_kerproof · cited by 0