∀ {β : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (G : CategoryTheory.Functor C D) (f : β → C)
  [inst_2 : CategoryTheory.Limits.HasProduct f] [inst_3 : CategoryTheory.Limits.HasProduct fun b => G.obj (f b)]
  (b : β),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.piComparison G f)
      (CategoryTheory.Limits.Pi.π (fun b => G.obj (f b)) b) =
    G.map (CategoryTheory.Limits.Pi.π f b)