∀ {β : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {f : β → C}
  [inst_1 : CategoryTheory.Limits.HasProduct f] {X : C} {g₁ g₂ : X ⟶ ∏ᶜ f},
  g₁ = g₂ ↔
    ∀ (b : β),
      CategoryTheory.CategoryStruct.comp g₁ (CategoryTheory.Limits.Pi.π f b) =
        CategoryTheory.CategoryStruct.comp g₂ (CategoryTheory.Limits.Pi.π f b)