meromorphicTrailingCoeffAt_of_order_eq_top

English

The set of points where MeromorphicOn f U is analytic in a codiscreteWithin sense forms a membership relation within codiscrete.

Русский

Множество точек, где f аналитична на U в кодискретном смысле, образует отношение принадлежности внутри кодискретности.

LaTeX

$$$\\{x \\in U : AnalyticAt 𝕜 f x\\} \\in \\text{Filter.codiscreteWithin } U$$

Lean4

/-- If `f` is meromorphic of infinite order at `x`, the trailing coefficient is zero by definition.
-/
@[simp]
theorem meromorphicTrailingCoeffAt_of_order_eq_top (h : meromorphicOrderAt f x = ⊤) :
    meromorphicTrailingCoeffAt f x = 0 := by simp_all [meromorphicTrailingCoeffAt]

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