Theorems · Theorem · number theory
NumberField.InfinitePlace.le_iff_le
∀ {K : Type u_1} [inst : Field K] (x : K) (r : ℝ),
(∀ (w : NumberField.InfinitePlace K), w x ≤ r) ↔ ∀ (φ : K →+* ℂ), ‖φ x‖ ≤ r- Cited by
- 3 results in Mathlib
- Foundations
- Depth 140 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.
Cites10
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 and proof · cited by 25,697
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- NumberField.InfinitePlacestatement and proof · cited by 604
- AbsoluteValueproof · cited by 363
- NumberField.placeproof · cited by 71
- NumberField.InfinitePlace.mkproof · cited by 56
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isRealproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finiteproof · cited by 0