Theorems · Theorem · number theory
NumberField.Units.pos_at_place
∀ {K : Type u_1} [inst : Field K] (x : (NumberField.RingOfIntegers K)ˣ) (w : NumberField.InfinitePlace K),
0 < w ((algebraMap (NumberField.RingOfIntegers K) K) ↑x)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.RingOfIntegersstatement and proof · cited by 413
- NumberField.InfinitePlace.pos_iffproof · cited by 6
- NumberField.Units.coe_ne_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zeroproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.exists_unitproof · cited by 1