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- 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Norm.normproof · cited by 5,413
- MonoidWithZeroHomstatement · cited by 704
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement · cited by 239
- NumberField.InfinitePlace.embeddingproof · cited by 78
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.norm_eq_normproof · cited by 7
- NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbeddingproof · cited by 4
- NumberField.mixedEmbedding.logMap_eq_logEmbeddingproof · cited by 2
- NumberField.mixedEmbedding.convexBodySum_memproof · cited by 1
- NumberField.mixedEmbedding.logMap_torsion_smulproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_neproof · cited by 1
- NumberField.mixedEmbedding.unit_smul_eq_zeroproof · cited by 0