Mathlib Map

Theorems · Theorem · number theory

NumberField.mixedEmbedding.normAtPlace_apply

∀ {K : Type u_1} [inst : Field K] (w : NumberField.InfinitePlace K) (x : K),
  (NumberField.mixedEmbedding.normAtPlace w) ((NumberField.mixedEmbedding K) x) = w x
Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by
8 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field

Around this declaration

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

NumberField.mixedEmbedding.norm_eq_norm · cited by 7mixedEmbedding.norm_eq_no…NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding · cited by 4mixedEmbedding.normAtAllP…NumberField.mixedEmbedding.logMap_eq_logEmbedding · cited by 2mixedEmbedding.logMap_eq_…NumberField.mixedEmbedding.convexBodySum_mem · cited by 1mixedEmbedding.convexBody…NumberField.mixedEmbedding.logMap_torsion_smul · cited by 1mixedEmbedding.logMap_tor…NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne · cited by 1fundamentalCone.expMap_ba…NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm · cited by 1fundamentalCone.realSpace…NumberField.mixedEmbedding.unit_smul_eq_zero · cited by 0mixedEmbedding.unit_smul_…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom · cited by 10189RingHomField · cited by 7404FieldComplex · cited by 5565ComplexNorm.norm · cited by 5413Norm.normMonoidWithZeroHom · cited by 704MonoidWithZeroHomNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceNumberField.InfinitePlace.embedding · cited by 78InfinitePlace.embeddingNumberField.mixedEmbedding · cited by 52NumberField.mixedEmbeddingNumberField.mixedEmbedding.normAtPlace · cited by 45mixedEmbedding.normAtPlaceRingHom.pi · cited by 26RingHom.pimixedEmbedding.normAtPlace_ap…CITED BYCITES

Cites19

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

Cited by8

Results whose statement or proof uses this declaration.