Theorems · Theorem · number theory
NumberField.IsTotallyComplex.complexEmbedding_not_isReal
∀ {K : Type u_2} [inst : Field K] [NumberField.IsTotallyComplex K] (φ : K →+* ℂ), ¬NumberField.ComplexEmbedding.IsReal φ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Iff.notproof · cited by 489
- NumberField.InfinitePlace.mkproof · cited by 56
- NumberField.ComplexEmbedding.IsRealstatement · cited by 38
- NumberField.InfinitePlace.not_isReal_iff_isComplexproof · cited by 25
- NumberField.IsTotallyComplexstatement and proof · cited by 19
- NumberField.InfinitePlace.isReal_mk_iffproof · cited by 12
- NumberField.IsTotallyComplex.isComplexproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.isConj_eq_isConjproof · cited by 1
- NumberField.IsCMField.complexConj_ne_oneproof · cited by 1
- NumberField.IsCMField.of_forall_isConjproof · cited by 0