isNonarchimedean_adicAbv — Mathlib

English

The v-adic absolute value is defined by evaluating the valuation via NNReal(absNorm).

Русский

V-подобная абсолютная величина задаётся через NNReal(absNorm) и валюацию.

LaTeX

$$$\text{adicAbv}(v,x)= \mathrm{toNNReal}(\operatorname{absNorm}(v),\operatorname{valuation}(v,x))$$$

Lean4

/-- The `v`-adic absolute value is nonarchimedean -/
theorem isNonarchimedean_adicAbv : IsNonarchimedean (adicAbv v) :=
  v.isNonarchimedean_adicAbv <| one_lt_absNorm_nnreal v

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