Theorems · Theorem · number theory
NumberField.mixedEmbedding.normAtComplexPlaces_apply_isComplex
∀ {K : Type u_1} [inst : Field K] {x : NumberField.mixedEmbedding.mixedSpace K} (w : { w // w.IsComplex }),
NumberField.mixedEmbedding.normAtComplexPlaces x ↑w = ‖x.2 w‖- Cited by
- 3 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · 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
- Subtype.propproof · cited by 505
- NumberField.InfinitePlace.IsRealstatement · cited by 301
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- NumberField.InfinitePlace.not_isReal_iff_isComplexproof · cited by 25
- NumberField.mixedEmbedding.normAtPlace_apply_of_isComplexproof · cited by 9
- NumberField.mixedEmbedding.normAtComplexPlacesstatement · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symmproof · cited by 1
- NumberField.mixedEmbedding.normAtAllPlaces_eq_of_normAtComplexPlaces_eqproof · cited by 1
- NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpaceproof · cited by 1