adicAbvDef — Mathlib

English

The v-adic absolute value on K is defined by a fixed base b > 1 via the v-valuation; explicitly, |x|_v = toNNReal(ne_zero_of_lt hb)(v.valuation K x).

Русский

Адическая абсолютная величина по v задаётся через v-валидировку с основанием b>1: |x|_v = toNNReal(ne_zero_of_lt hb)(v.valuation K x).

LaTeX

$$def adicAbvDef (v) {b : NNReal} (hb : 1 < b) (x) := toNNReal (ne_zero_of_lt hb) (v.valuation K x)$$

Lean4

/-- The `v`-adic absolute value function on `K` defined as `b` raised to negative `v`-adic
valuation, for some `b` in `ℝ≥0` -/
def adicAbvDef (v : HeightOneSpectrum R) {b : NNReal} (hb : 1 < b) := fun x ↦
  toNNReal (ne_zero_of_lt hb) (v.valuation K x)

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