Theorems · Theorem · number theory
NumberField.mixedEmbedding.norm_eq_norm
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : K),
NumberField.mixedEmbedding.norm ((NumberField.mixedEmbedding K) x) = ↑|(Algebra.norm ℚ) x|- Cited by
- 7 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.
Cites21
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
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- MonoidHomstatement · cited by 3,629
- Finset.univproof · cited by 3,473
- absstatement and proof · cited by 1,814
- MonoidWithZeroHomstatement · cited by 704
- NumberFieldstatement and proof · cited by 653
- Finset.prod_congrproof · cited by 646
- NumberField.InfinitePlacestatement and proof · cited by 604
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.norm_unitproof · cited by 3
- NumberField.mixedEmbedding.logMap_eq_logEmbeddingproof · cited by 2
- NumberField.mixedEmbedding.norm_eq_zero_iff'proof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.intNorm_coeproof · cited by 1
- NumberField.mixedEmbedding.logMap_torsion_smulproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.exists_unit_smul_memproof · cited by 1