Theorems · Theorem · number theory
NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.mixedSpace K),
‖x‖₊ = Finset.univ.sup fun w => NNReal.mk ((NumberField.mixedEmbedding.normAtPlace w) x) ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- Finsetproof · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Norm.normproof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- Finset.univstatement and proof · cited by 3,473
- absproof · cited by 1,814
- NNReal.toRealproof · cited by 1,260
- OrderBotproof · cited by 1,055
- NNNorm.nnnormstatement and proof · cited by 952
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.norm_eq_sup'_normAtPlaceproof · cited by 2