∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : TopologicalSpace R] [T2Space R] {f : ℕ → ℕ → R} {d : ℕ}
  {s : Finset ℕ},
  0 ∉ s →
    ∀ {g : ℕ →₀ ℕ},
      g ∈ s.finsuppAntidiag d →
        (∀ i ∈ s, (PowerSeries.coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • PowerSeries.X ^ (i * (j + 1))) ≠ 0) →
          ∀ (x : ℕ), x ∣ g x