∀ {R : Type u_1} [inst : Ring R] (f : ℕ → R) (hf : Invertible (f 1)) (n : ℕ),
  ArithmeticFunction.dirichletInverseFun f hf n =
    if n = 0 then 0
    else
      if n = 1 then ⅟(f 1)
      else
        -⅟(f 1) *
          ∑ d,
            have this := ⋯;
            f (n / ↑d) * ArithmeticFunction.dirichletInverseFun f hf ↑d