Theorems · Definition · number theory
NumberField.maximalRealSubfield
(K : Type u_2) → [inst : Field K] → Subfield K
The maximal real subfield of K. It is totally real,
see NumberField.isTotallyReal_maximalRealSubfield, and contains all the other totally real
subfields of K, see NumberField.IsTotallyReal.le_maximalRealSubfield.
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Complexproof · cited by 5,565
- Star.starproof · cited by 1,082
- Subfieldstatement · cited by 303
Cited by46
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.complexConjstatement · cited by 14
- NumberField.IsCMField.realUnitsproof · cited by 5
- NumberField.IsCMField.equivInfinitePlacestatement and proof · cited by 4
- NumberField.IsCMField.realFundSystemproof · cited by 4
- NumberField.CMExtension.equivMaximalRealSubfieldstatement · cited by 3
- NumberField.IsCMField.ringOfIntegersComplexConjstatement · cited by 3
- NumberField.IsTotallyReal.le_maximalRealSubfieldstatement · cited by 3
- NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iffstatement and proof · cited by 2
- NumberField.IsCMField.complexEmbedding_complexConjstatement · cited by 2
- NumberField.IsCMField.exists_isConjstatement and proof · cited by 2
- NumberField.IsCMField.isConj_complexConjstatement and proof · cited by 2
- NumberField.IsCMField.units_rank_eq_units_rankstatement and proof · cited by 2