∀ {C : Type u_2} {D : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} D] {F : C → D}
  {X Y : CategoryTheory.InducedCategory D F} (f : F X ≅ F Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.InducedCategory.homMk f.inv)
      (CategoryTheory.InducedCategory.homMk f.hom) =
    CategoryTheory.CategoryStruct.id Y