Theorems · Definition · field theory
NormedField.valuation
{K : Type u_1} → [hK : NormedField K] → [IsUltrametricDist K] → Valuation K NNRealThe valuation on a nonarchimedean normed field K defined as nnnorm.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedFieldIsUltrametricDist
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NormedFieldstatement and proof · cited by 1,084
- NNNorm.nnnormproof · cited by 952
- Valuationstatement · cited by 823
- IsUltrametricDiststatement and proof · cited by 177
Cited by7
Results whose statement or proof uses this declaration.
- NormedField.toValuedproof · cited by 14
- Valued.integer.norm_coe_unitproof · cited by 1
- NormedField.valuation_applystatement · cited by 0
- Valued.integer.isUnit_iff_norm_eq_oneproof · cited by 0
- Valued.coe_valuation_eq_rankOne_hom_comp_valuationstatement · cited by 0
- NormedField.valuation.congr_simpstatement and proof · cited by 0
- NormedField.v_eq_valuationstatement · cited by 0