∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z W : C} (f : X ⟶ Y) (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct W X] [inst_2 : CategoryTheory.Limits.HasBinaryProduct W Y]
  [inst_3 : CategoryTheory.Limits.HasBinaryProduct W Z] {Z_1 : C} (h : W ⨯ Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.prod.map (CategoryTheory.CategoryStruct.id W) (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.map (CategoryTheory.CategoryStruct.id W) f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.map (CategoryTheory.CategoryStruct.id W) g) h)