Theorems · Definition · number theory
NumberField.mixedEmbedding.normAtAllPlaces
{K : Type u_1} → [inst : Field K] → NumberField.mixedEmbedding.mixedSpace K → NumberField.mixedEmbedding.realSpace KThe map from the mixedSpace K to realSpace K that sends each component to its norm.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 174 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- NumberField.InfinitePlaceproof · cited by 604
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- NumberField.mixedEmbedding.realSpacestatement · cited by 87
- NumberField.mixedEmbedding.normAtPlaceproof · cited by 45
Cited by31
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.completeFamilyproof · cited by 5
- NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimagestatement and proof · cited by 4
- NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbeddingstatement · cited by 4
- NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlacesstatement and proof · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_nestatement and proof · cited by 3
- NumberField.mixedEmbedding.continuous_normAtAllPlacesstatement · cited by 3
- NumberField.mixedEmbedding.normAtAllPlaces_applystatement · cited by 3
- NumberField.mixedEmbedding.normAtAllPlaces_nonnegstatement · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlacesstatement and proof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasisstatement · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage_imagestatement and proof · cited by 2
- NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integralstatement and proof · cited by 2