locally_zero_iff — Mathlib

English

A simple equality for (p.coeff n) in relation to n's power and the iterate formula, used to simplify higher-order coefficient manipulations.

Русский

Простое тождество для коэффициента p.coeff n в зависимости от степени n и формулы итерации, упрощающее работу со сложными коэффициентами.

LaTeX

$$$Eq (p.coeff n) (p(n))$$$

Lean4

theorem locally_zero_iff (hp : HasFPowerSeriesAt f p z₀) : (∀ᶠ z in 𝓝 z₀, f z = 0) ↔ p = 0 :=
  ⟨fun hf => hp.eq_zero_of_eventually hf, fun h => eventually_eq_zero (𝕜 := 𝕜) (by rwa [h] at hp)⟩

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