Theorems · Definition · field theory
Valuation.norm
{L : Type u_1} →
[inst : Field L] →
{Γ₀ : Type u_2} → [inst_1 : LinearOrderedCommGroupWithZero Γ₀] → (v : Valuation L Γ₀) → [hv : v.RankOne] → L → ℝThe norm function determined by a rank one valuation on a field L.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- NNReal.toRealproof · cited by 1,260
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.restrictproof · cited by 112
- Valuation.RankOnestatement and proof · cited by 32
- Valuation.RankOne.homproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- Valuation.norm_defstatement · cited by 2
- PadicComplex.norm_eq_norm'statement · cited by 1
- Valuation.norm_add_lestatement · cited by 1
- PadicComplex.norm_eq_normstatement and proof · cited by 0
- Valuation.norm_eq_zerostatement and proof · cited by 0
- Valuation.norm_nonnegstatement · cited by 0
- Valuation.norm_pos_iff_valuation_posstatement · cited by 0