Theorems · Theorem · number theory
NumberField.isTotallyReal_iff_le_maximalRealSubfield
∀ {K : Type u_2} [inst : Field K] [inst_1 : CharZero K] [Algebra.IsAlgebraic ℚ K] {E : Subfield K},
NumberField.IsTotallyReal ↥E ↔ E ≤ NumberField.maximalRealSubfield K- Cited by
- 1 results in Mathlib
- Foundations
- Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebraproof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerproof · cited by 3,896
- CharZerostatement and proof · cited by 932
- RingHom.toAlgebraproof · cited by 337
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Subfieldstatement and proof · cited by 303
- IsScalarTower.of_algebraMap_eq'proof · cited by 101
- NumberField.maximalRealSubfieldstatement and proof · cited by 38
- NumberField.IsTotallyRealstatement and proof · cited by 21
- Subfield.inclusionproof · cited by 4
- NumberField.IsTotallyReal.le_maximalRealSubfieldproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.maximalRealSubfield_eq_top_iff_isTotallyRealproof · cited by 0