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Theorems · Theorem · number theory

NumberField.IsTotallyReal.nrComplexPlaces_eq_zero

∀ (K : Type u_2) [inst : Field K] [inst_1 : NumberField K] [h : NumberField.IsTotallyReal K],
  NumberField.InfinitePlace.nrComplexPlaces K = 0
Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
Cited by
1 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberFieldNumberField.IsTotallyReal
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Around this declaration

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

NumberField.IsCMField.card_infinitePlace_eq_card_infinitePlace · cited by 1IsCMField.card_infinitePl…Field · cited by 7404FieldNumberField · cited by 653NumberFieldNumberField.InfinitePlace.nrComplexPlaces · cited by 52InfinitePlace.nrComplexPl…NumberField.IsTotallyReal · cited by 21NumberField.IsTotallyRealNumberField.nrComplexPlaces_eq_zero_iff · cited by 2NumberField.nrComplexPlac…IsTotallyReal.nrComplexPlaces…CITED BYCITES

Cites5

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Cited by1

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