Theorems · Theorem · number theory
NumberField.maximalRealSubfield_eq_top_iff_isTotallyReal
∀ {K : Type u_2} [inst : Field K] [inst_1 : CharZero K] [Algebra.IsAlgebraic ℚ K],
NumberField.maximalRealSubfield K = ⊤ ↔ NumberField.IsTotallyReal K- Cited by
- 0 results in Mathlib
- Foundations
- Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- le_reflproof · cited by 2,061
- CharZerostatement and proof · cited by 932
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Subfieldstatement and proof · cited by 303
- Algebra.IsIntegralproof · cited by 224
- NumberField.maximalRealSubfieldstatement and proof · cited by 38
- NumberField.IsTotallyRealstatement and proof · cited by 21
- Algebra.IsIntegral.tower_topproof · cited by 3
- NumberField.isTotallyReal_iff_le_maximalRealSubfieldproof · cited by 1
- NumberField.IsTotallyReal.maximalRealSubfield_eq_topproof · cited by 1
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