Theorems · Theorem · number theory
NumberField.Units.closure_fundSystem_sup_torsion_eq_top
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K], Subgroup.closure (Set.range (NumberField.Units.fundSystem K)) ⊔ NumberField.Units.torsion K = ⊤
The units of the fundamental system and the torsion of K generate the full group of units of K.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 327 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Set.rangestatement and proof · cited by 4,705
- Subgroupstatement and proof · cited by 3,593
- Finset.univproof · cited by 3,473
- Unitsstatement and proof · cited by 2,804
- Finset.prodproof · cited by 2,356
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Set.mem_range_selfproof · cited by 328
- Subgroup.closurestatement and proof · cited by 196
- sup_commproof · cited by 165
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.Units.regOfFamily_div_regulatorproof · cited by 1
- NumberField.IsCMField.closure_realFundSystem_sup_torsionproof · cited by 1