limit_zero_of_norm_tendsto_zero — Mathlib

English

The p-adic integers 𝓞_{ℂ_p} form the valuation subring of ℂ_p consisting of elements with valuation ≤ 1.

Русский

p-адические целые числа 𝓞_{ℂ_p} образуют подколлекцию по valuation(≤ 1) внутри ℂ_p.

LaTeX

$$$\mathcal{O}_{\mathbb{C}_p} = \{ x ∈ \mathbb{C}_p : v(x) \le 1\}.$$$

Lean4

theorem limit_zero_of_norm_tendsto_zero : F.aeval ncs.lim = 0 :=
  by
  refine tendsto_nhds_unique ?_ (tendsto_zero_of_norm_tendsto_zero hnorm)
  rw [← Polynomial.eval_map_algebraMap]
  refine (comp_tendsto_lim ncs).congr ?_
  simp

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