Theorems · Theorem · number theory
NumberField.nrComplexPlaces_eq_zero_iff
∀ {K : Type u_2} [inst : Field K] [inst_1 : NumberField K],
NumberField.InfinitePlace.nrComplexPlaces K = 0 ↔ NumberField.IsTotallyReal K- Cited by
- 2 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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.
- Fieldstatement and proof · cited by 7,404
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlaceproof · cited by 604
- NumberField.InfinitePlace.IsRealproof · cited by 301
- NumberField.InfinitePlace.IsComplexproof · cited by 272
- NumberField.InfinitePlace.nrComplexPlacesstatement · cited by 52
- NumberField.IsTotallyRealstatement · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.IsTotallyReal.nrComplexPlaces_eq_zeroproof · cited by 1
- NumberField.IsTotallyReal.finrankproof · cited by 1