Theorems · Theorem · number theory
NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace
∀ {K : Type u_1} [inst : Field K] {x : NumberField.mixedEmbedding.realSpace K} {w : NumberField.InfinitePlace K},
0 ≤ x w → (NumberField.mixedEmbedding.normAtPlace w) (NumberField.mixedEmbedding.mixedSpaceOfRealSpace x) = x w- Cited by
- 6 results in Mathlib
- Foundations
- Depth 176 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- Complex.ofRealproof · cited by 1,654
- 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
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlacesproof · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasisproof · cited by 3
- NumberField.mixedEmbedding.normAtAllPlaces_image_preimage_of_nonnegproof · cited by 2
- NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpaceproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlacesproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.logMap_expMapproof · cited by 1