Mathlib Map

Theorems · Theorem · number theory

NumberField.IsTotallyReal.ofRingEquiv

∀ {F : Type u_1} [inst : Field F] {K : Type u_2} [inst_1 : Field K] [NumberField.IsTotallyReal F] (f : F ≃+* K),
  NumberField.IsTotallyReal K
Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
Cited by
2 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldNumberField.IsTotallyReal
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Around this declaration

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

NumberField.isTotallyReal_iff_ofRingEquiv · cited by 1NumberField.isTotallyReal…NumberField.CMExtension.eq_maximalRealSubfield · cited by 0CMExtension.eq_maximalRea…Field · cited by 7404FieldRingEquiv · cited by 1147RingEquivRingHomClass.toRingHom · cited by 746RingHomClass.toRingHomNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.comap · cited by 55InfinitePlace.comapNumberField.IsTotallyReal · cited by 21NumberField.IsTotallyRealNumberField.IsTotallyReal.isReal · cited by 7IsTotallyReal.isRealNumberField.InfinitePlace.isReal_comap_iff · cited by 2InfinitePlace.isReal_coma…IsTotallyReal.ofRingEquivCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.