∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasBinaryCoproducts C]
  {A : C} {X Y : CategoryTheory.Over A} (k : X ⟶ Y) (f g : CategoryTheory.Over A) (k_1 : f ⟶ g),
  CategoryTheory.CategoryStruct.comp (X.coprodObj.map k_1)
      (CategoryTheory.Over.homMk
        (CategoryTheory.Limits.coprod.map k.left
          (CategoryTheory.CategoryStruct.id ((CategoryTheory.Functor.id C).obj g.left)))
        ⋯) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.homMk
        (CategoryTheory.Limits.coprod.map k.left
          (CategoryTheory.CategoryStruct.id ((CategoryTheory.Functor.id C).obj f.left)))
        ⋯)
      (Y.coprodObj.map k_1)