Theorems · Theorem · number theory
NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff
∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [inst_2 : NumberField.IsCMField K]
[inst_3 : Algebra.IsIntegral ℚ K] (x : NumberField.RingOfIntegers K),
(NumberField.IsCMField.complexConj K) ↑x = ↑x ↔
∃ y, (algebraMap (NumberField.RingOfIntegers ↥(NumberField.maximalRealSubfield K)) K) y = ↑x- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgEquivstatement · cited by 1,681
- CharZerostatement and proof · cited by 932
- IsIntegralproof · cited by 427
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Subfieldstatement · cited by 303
- Algebra.IsIntegralstatement and proof · cited by 224
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- IsScalarTower.algebraMap_applyproof · cited by 116
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.Units.complexConj_eq_self_iffproof · cited by 0
- NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iffproof · cited by 0