∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] (X : C)
  [inst_1 : CategoryTheory.Limits.HasBinaryProducts C] (f : CategoryTheory.Over X),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.lift f.hom (CategoryTheory.CategoryStruct.id f.left))
      ((CategoryTheory.prodComonad X).δ.app f.left) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.lift f.hom (CategoryTheory.CategoryStruct.id f.left))
      ((CategoryTheory.prodComonad X).map
        (CategoryTheory.Limits.prod.lift f.hom (CategoryTheory.CategoryStruct.id f.left)))