tendsto_trunc'_atTop — Mathlib

English

As the cut degree grows, trunc' R d f tends to f.

Русский

При росте степени обрезки обрезка' сходится к f.

LaTeX

$$Tendsto (λ d, (trunc' R d f : MvPowerSeries σ R)) atTop (nhds f)$$

Lean4

theorem tendsto_trunc'_atTop [DecidableEq σ] [CommSemiring R] (f : MvPowerSeries σ R) :
    Tendsto (fun d ↦ (trunc' R d f : MvPowerSeries σ R)) atTop (𝓝 f) :=
  by
  rw [tendsto_iff_coeff_tendsto]
  intro d
  exact tendsto_atTop_of_eventually_const fun n (hdn : d ≤ n) ↦ (by simp [coeff_trunc', hdn])

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