meromorphicNFOn — Mathlib

English

For any divisor d and any subset U, the factorized rational function F = ∏ᶠ u (· − u)^{d(u)} is meromorphic on U.

Русский

Для любого делителя d и произвольной подмножества U функция F = ∏ᶠ u (· − u)^{d(u)} мероморфна на U.

LaTeX

$$$\text{MeromorphicNFOn}\left(\prod^{\mathrm{fin}}_{u} (\cdot - u)^{d(u)}\right) U$$

Lean4

/-- Factorized rational functions are meromorphic in normal form on arbitrary subsets of `𝕜`.
-/
theorem meromorphicNFOn (d : 𝕜 → ℤ) (U : Set 𝕜) : MeromorphicNFOn (∏ᶠ u, (· - u) ^ d u) U := fun _ _ ↦
  meromorphicNFOn_univ d (trivial)

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