Theorems · Theorem · number theory

NumberField.CMExtension.equivMaximalRealSubfield_apply

∀ (F : Type u_1) (K : Type u_2) [inst : Field F] [inst_1 : NumberField.IsTotallyReal F] [inst_2 : Field K]
  [inst_3 : CharZero K] [inst_4 : Algebra.IsIntegral ℚ K] [inst_5 : NumberField.IsTotallyComplex K]
  [inst_6 : Algebra F K] [inst_7 : Algebra.IsQuadraticExtension F K] (x : F),
  ↑((NumberField.CMExtension.equivMaximalRealSubfield F K) x) = (algebraMap F K) x

Defined in: Mathlib.NumberTheory.NumberField.CMField
Cited by: 1 results in Mathlib
Foundations: Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField.IsTotallyReal Field CharZero Algebra.IsIntegral NumberField.IsTotallyComplex Algebra Algebra.IsQuadraticExtension

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Cites14

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

DFunLike.coestatement · cited by 62,936
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement · cited by 4,706
RingEquivstatement · cited by 1,147
CharZerostatement and proof · cited by 932
Subfieldstatement · cited by 303
Algebra.IsIntegralstatement and proof · cited by 224
NumberField.maximalRealSubfieldstatement · cited by 38
NumberField.IsTotallyRealstatement and proof · cited by 21
NumberField.IsTotallyComplexstatement and proof · cited by 19

Cited by1

Results whose statement or proof uses this declaration.

NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_applyproof · cited by 0