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Theorems · Theorem · number theory

NumberField.InfinitePlace.IsComplex.of_comap

∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] (f : k →+* K) {w : NumberField.InfinitePlace K},
  (w.comap f).IsComplex → w.IsComplex
Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by
1 results in Mathlib
Foundations
Depth 175 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.isTotallyComplex_of_algebra · cited by 1NumberField.isTotallyComp…RingHom · cited by 10189RingHomField · cited by 7404FieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.InfinitePlace.comap · cited by 55InfinitePlace.comapFunction.mt · cited by 27Function.mtNumberField.InfinitePlace.not_isReal_iff_isComplex · cited by 25InfinitePlace.not_isReal_…NumberField.InfinitePlace.IsReal.comap · cited by 4IsReal.comapIsComplex.of_comapCITED BYCITES

Cites8

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Cited by1

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