Theorems · Theorem · number theory
NumberField.IsCMField.orderOf_complexConj
∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [inst_2 : NumberField.IsCMField K] [inst_3 : Algebra.IsIntegral ℚ K], orderOf (NumberField.IsCMField.complexConj K) = 2
The complex conjugation is an automorphism of degree 2.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement · cited by 1,681
- CharZerostatement and proof · cited by 932
- orderOfstatement · cited by 324
- Subfieldstatement · cited by 303
- Algebra.IsIntegralstatement and proof · cited by 224
- AlgEquiv.extproof · cited by 60
- NumberField.IsCMFieldstatement and proof · cited by 45
- NumberField.maximalRealSubfieldstatement · cited by 38
- Function.iterate_oneproof · cited by 34
- NumberField.IsCMField.complexConjstatement and proof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.zpowers_complexConj_eq_topproof · cited by 1