Theorems · Theorem · number theory
NumberField.ComplexEmbedding.isConj_ne_one_iff
∀ {K : Type u_1} [inst : Field K] {k : Type u_2} [inst_1 : Field k] [inst_2 : Algebra k K] {φ : K →+* ℂ} {σ : Gal(K/k)},
NumberField.ComplexEmbedding.IsConj φ σ → (σ ≠ 1 ↔ ¬NumberField.ComplexEmbedding.IsReal φ)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- AlgEquivstatement and proof · cited by 1,681
- not_iff_notproof · cited by 159
- NumberField.ComplexEmbedding.IsRealstatement and proof · cited by 38
- NumberField.ComplexEmbedding.IsConjstatement and proof · cited by 24
- NumberField.ComplexEmbedding.isConj_one_iffproof · cited by 4
- NumberField.ComplexEmbedding.IsConj.ext_iffproof · cited by 3
- NumberField.ComplexEmbedding.IsReal.isConjGal_oneproof · cited by 1
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