Theorems · Theorem · number theory

NumberField.IsCMField.ofCMExtension

∀ (F : Type u_1) (K : Type u_2) [inst : Field F] [NumberField.IsTotallyReal F] [inst_2 : Field K] [inst_3 : CharZero K]
  [Algebra.IsIntegral ℚ K] [NumberField.IsTotallyComplex K] [inst_6 : Algebra F K] [Algebra.IsQuadraticExtension F K],
  NumberField.IsCMField K

If K/F is a CM-extension then K is a CM-field.

Defined in: Mathlib.NumberTheory.NumberField.CMField
Cited by: 1 results in Mathlib
Foundations: Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField.IsTotallyReal Field CharZero Algebra.IsIntegral NumberField.IsTotallyComplex Algebra Algebra.IsQuadraticExtension

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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
Fieldstatement and proof · cited by 7,404
CharZerostatement and proof · cited by 932
Algebra.IsIntegralstatement and proof · cited by 224
NumberField.IsCMFieldstatement · cited by 45
NumberField.IsTotallyRealstatement and proof · cited by 21
NumberField.IsTotallyComplexstatement and proof · cited by 19
Algebra.IsQuadraticExtensionstatement and proof · cited by 11

Cited by1

Results whose statement or proof uses this declaration.

NumberField.IsCMField.of_forall_isConjproof · cited by 0