Theorems · Definition · number theory
NumberField.Units.fundSystem
(K : Type u_1) → [inst : Field K] → [inst_1 : NumberField K] → Fin (NumberField.Units.rank K) → (NumberField.RingOfIntegers K)ˣ
A fundamental system of units of K. The units of fundSystem are arbitrary lifts of the
units in basisModTorsion.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 324 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Unitsstatement · cited by 2,804
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement · cited by 413
- Quotient.outproof · cited by 141
- Additive.toMulproof · cited by 109
- NumberField.Units.rankstatement and proof · cited by 46
- NumberField.Units.basisModTorsionproof · cited by 4
Cited by25
Results whose statement or proof uses this declaration.
- NumberField.Units.regulator_eq_regOfFamily_fundSystemstatement · cited by 7
- NumberField.mixedEmbedding.fundamentalCone.completeFamilyproof · cited by 5
- NumberField.Units.isMaxRank_fundSystemstatement and proof · cited by 4
- NumberField.Units.logEmbedding_fundSystemstatement and proof · cited by 4
- NumberField.IsCMField.realFundSystemproof · cited by 4
- NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_nestatement and proof · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply''proof · cited by 3
- NumberField.Units.closure_fundSystem_sup_torsion_eq_topstatement and proof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'statement and proof · cited by 2
- NumberField.Units.exist_unique_eq_mul_prodstatement and proof · cited by 2
- NumberField.IsCMField.closure_realFundSystem_sup_torsionproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_powproof · cited by 1