Theorems · Theorem · number theory
NumberField.Units.norm
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (x : (NumberField.RingOfIntegers K)ˣ), |(Algebra.norm ℚ) ((algebraMap (NumberField.RingOfIntegers K) K) ↑x)| = 1
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 188 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- absstatement and proof · cited by 1,814
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Algebra.normstatement · cited by 155
- Units.isUnitproof · cited by 116
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.norm_unitproof · cited by 3
- NumberField.mixedEmbedding.logMap_eq_logEmbeddingproof · cited by 2
- NumberField.Units.sum_mult_mul_logproof · cited by 2
- NumberField.mixedEmbedding.logMap_torsion_smulproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_powproof · cited by 1
- NumberField.Units.abs_det_eq_abs_detproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.exists_unit_smul_memproof · cited by 1