Theorems · Theorem · number theory
NumberField.IsCMField.exists_isConj
∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [NumberField.IsCMField K] [Algebra.IsAlgebraic ℚ K] (φ : K →+* ℂ), ∃ σ, NumberField.ComplexEmbedding.IsConj φ σ
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Algebra.algebraMapproof · cited by 4,706
- AlgEquivstatement · cited by 1,681
- CharZerostatement and proof · cited by 932
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Subfieldstatement · cited by 303
- NumberField.InfinitePlace.mkproof · cited by 56
- NumberField.InfinitePlace.comapproof · cited by 55
- NumberField.IsCMFieldstatement and proof · cited by 45
- NumberField.maximalRealSubfieldstatement and proof · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.isConj_complexConjproof · cited by 2
- NumberField.IsCMField.complexConj_ne_oneproof · cited by 1