Theorems · Theorem · number theory
NumberField.mixedEmbedding.normAtAllPlaces_norm_at_real_places
∀ {K : Type u_1} [inst : Field K] (x : NumberField.mixedEmbedding.mixedSpace K),
NumberField.mixedEmbedding.normAtAllPlaces (fun w => ‖x.1 w‖, x.2) = NumberField.mixedEmbedding.normAtAllPlaces x- Cited by
- 1 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- 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 and proof · cited by 239
- norm_normproof · cited by 113
- NumberField.mixedEmbedding.realSpacestatement · cited by 87
- NumberField.mixedEmbedding.normAtAllPlacesstatement · cited by 30
- NumberField.mixedEmbedding.normAtPlace_apply_of_isComplexproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integralproof · cited by 2