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Theorems · Theorem · number theory

NumberField.IsTotallyReal.of_algebra

∀ (F : Type u_1) [inst : Field F] (K : Type u_2) [inst_1 : Field K] [NumberField.IsTotallyReal K] [inst_3 : Algebra F K]
  [Algebra.IsAlgebraic F K], NumberField.IsTotallyReal F
Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
Cited by
1 results in Mathlib
Foundations
Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldNumberField.IsTotallyRealAlgebraAlgebra.IsAlgebraic
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Around this declaration

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

NumberField.isTotallyReal_iff_le_maximalRealSubfield · cited by 1NumberField.isTotallyReal…Algebra · cited by 11388AlgebraField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceAlgebra.IsAlgebraic · cited by 322Algebra.IsAlgebraicNumberField.InfinitePlace.comap · cited by 55InfinitePlace.comapNumberField.IsTotallyReal · cited by 21NumberField.IsTotallyRealNumberField.InfinitePlace.comap_surjective · cited by 8InfinitePlace.comap_surje…NumberField.IsTotallyReal.isReal · cited by 7IsTotallyReal.isRealNumberField.InfinitePlace.IsReal.comap · cited by 4IsReal.comapIsTotallyReal.of_algebraCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.