Theorems · Theorem · number theory

NumberField.IsCMField.coe_ringOfIntegersComplexConj

∀ (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.ringOfIntegersComplexConj K) x) = (NumberField.IsCMField.complexConj K) ↑x

Defined in: Mathlib.NumberTheory.NumberField.CMField
Cited by: 1 results in Mathlib
Foundations: Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CharZero NumberField.IsCMField Algebra.IsIntegral

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Fieldstatement and proof · cited by 7,404
AlgEquivstatement · cited by 1,681
CharZerostatement and proof · cited by 932
NumberField.RingOfIntegersstatement and proof · cited by 413
Subfieldstatement · cited by 303
Algebra.IsIntegralstatement and proof · cited by 224
NumberField.RingOfIntegers.valstatement · cited by 74
NumberField.IsCMFieldstatement and proof · cited by 45
NumberField.maximalRealSubfieldstatement · cited by 38
NumberField.IsCMField.complexConjstatement · cited by 14
NumberField.IsCMField.ringOfIntegersComplexConjstatement · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iffproof · cited by 0