∀ {β : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {f g : β → C}
  [inst_1 : CategoryTheory.Limits.HasProduct f] [inst_2 : CategoryTheory.Limits.HasProduct g] (p : (b : β) → f b ⟶ g b)
  (b : β),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Pi.map p) (CategoryTheory.Limits.Pi.π g b) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Pi.π f b) (p b)