∀ {F : Type u_1} [inst : NormedField F] [CompleteSpace F] {f : ℕ →* F},
  (∀ {p : ℕ}, Nat.Prime p → ‖f p‖ < 1) →
    ∀ (N : ℕ), (Summable fun m => ‖f ↑m‖) ∧ HasSum (fun m => f ↑m) (∏ p ∈ N.primesBelow, (1 - f p)⁻¹)