∀ {α : Type u_1} {K : Type u_4} [inst : CommGroupWithZero K] [inst_1 : TopologicalSpace K] [ContinuousMul K]
  {f g : α → K} {c : K},
  HasProd f c →
    ∀ {s : Finset α}, (∀ a ∈ s, f a ≠ 0) → (∀ a ∉ s, f a = g a) → HasProd g (c * ((∏ i ∈ s, g i) / ∏ i ∈ s, f i))