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Theorems · Theorem · number theory

NumberField.mixedEmbedding.norm_negAt

∀ {K : Type u_1} [inst : Field K] {s : Set { w // w.IsReal }} [inst_1 : NumberField K]
  (x : NumberField.mixedEmbedding.mixedSpace K),
  NumberField.mixedEmbedding.norm ((NumberField.mixedEmbedding.negAt s) x) = NumberField.mixedEmbedding.norm x

negAt preserves the norm.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by
0 results in Mathlib
Foundations
Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
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DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idField · cited by 7404FieldComplex · cited by 5565ComplexContinuousLinearEquiv · cited by 743ContinuousLinearEquivMonoidWithZeroHom · cited by 704MonoidWithZeroHomNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceNumberField.mixedEmbedding.norm · cited by 46mixedEmbedding.normNumberField.mixedEmbedding.negAt · cited by 20mixedEmbedding.negAtmixedEmbedding.norm_negAtCITED BYCITES

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