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Theorems · Theorem · number theory

NumberField.IsTotallyComplex.isComplex

∀ {K : Type u_1} {inst : Field K} [self : NumberField.IsTotallyComplex K] (v : NumberField.InfinitePlace K), v.IsComplex
Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
Cited by
5 results in Mathlib
Foundations
Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NumberField.IsTotallyComplex
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Around this declaration

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

NumberField.IsTotallyComplex.complexEmbedding_not_isReal · cited by 3IsTotallyComplex.complexE…NumberField.IsCMField.exists_isConj · cited by 2IsCMField.exists_isConjNumberField.IsTotallyComplex.mult_eq · cited by 1IsTotallyComplex.mult_eqNumberField.isTotallyComplex_of_algebra · cited by 1NumberField.isTotallyComp…NumberField.CMExtension.eq_maximalRealSubfield · cited by 0CMExtension.eq_maximalRea…Field · cited by 7404FieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.IsTotallyComplex · cited by 19NumberField.IsTotallyComp…IsTotallyComplex.isComplexCITED BYCITES

Cites4

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Cited by5

Results whose statement or proof uses this declaration.