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Theorems · Theorem · number theory

NumberField.isTotallyReal_iff_ofRingEquiv

∀ {F : Type u_1} [inst : Field F] {K : Type u_2} [inst_1 : Field K] (f : F ≃+* K),
  NumberField.IsTotallyReal F ↔ NumberField.IsTotallyReal K
Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
Cited by
1 results in Mathlib
Foundations
Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldField
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Around this declaration

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

NumberField.isTotallyReal_top_iff · cited by 1NumberField.isTotallyReal…Field · cited by 7404FieldRingEquiv · cited by 1147RingEquivRingEquiv.symm · cited by 567RingEquiv.symmNumberField.IsTotallyReal · cited by 21NumberField.IsTotallyRealNumberField.IsTotallyReal.ofRingEquiv · cited by 2IsTotallyReal.ofRingEquivNumberField.isTotallyReal_iff…CITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.