Theorems · Theorem · number theory
NumberField.mixedEmbedding.norm_nonneg
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.mixedSpace K),
0 ≤ NumberField.mixedEmbedding.norm x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 298 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Finset.univproof · cited by 3,473
- MonoidWithZeroHomstatement · cited by 704
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement · cited by 301
- NumberField.InfinitePlace.IsComplexstatement · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- pow_nonnegproof · cited by 141
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_memproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_leproof · cited by 0