Theorems · Theorem · number theory
NumberField.mixedEmbedding.normAtPlace_nonneg
∀ {K : Type u_1} [inst : Field K] (w : NumberField.InfinitePlace K) (x : NumberField.mixedEmbedding.mixedSpace K),
0 ≤ (NumberField.mixedEmbedding.normAtPlace w) x- Cited by
- 11 results in Mathlib
- Foundations
- Depth 175 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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Norm.normproof · cited by 5,413
- norm_nonnegproof · cited by 725
- MonoidWithZeroHomstatement and proof · cited by 704
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.IsComplexstatement · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- NumberField.mixedEmbedding.normAtPlacestatement · cited by 45
Cited by11
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normAtAllPlaces_nonnegproof · cited by 3
- NumberField.mixedEmbedding.norm_eq_sup'_normAtPlaceproof · cited by 2
- NumberField.mixedEmbedding.norm_nonnegproof · cited by 2
- NumberField.mixedEmbedding.convexBodySumFun_eq_zero_iffproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlacesproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOneproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_memproof · cited by 1
- NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlacestatement and proof · cited by 1
- NumberField.mixedEmbedding.norm_le_convexBodySumFunproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOneproof · cited by 1
- NumberField.mixedEmbedding.convexBodySumFun_nonnegproof · cited by 1