∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X : C} {f g : CategoryTheory.MonoOver X}
  (h : f.obj.left ≅ g.obj.left) (w : CategoryTheory.CategoryStruct.comp h.hom g.arrow = f.arrow),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoOver.homMk h.hom w) (CategoryTheory.MonoOver.homMk h.inv ⋯) =
    CategoryTheory.CategoryStruct.id f