∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {A B : C} (e : A ≅ B) (X : CategoryTheory.MonoOver A),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.MonoOver.map e.hom).map
        (((CategoryTheory.MonoOver.mapComp e.hom e.inv).symm ≪≫
                  CategoryTheory.eqToIso ⋯ ≪≫ CategoryTheory.MonoOver.mapId A).symm.hom.app
          X))
      (((CategoryTheory.MonoOver.mapComp e.inv e.hom).symm ≪≫
              CategoryTheory.eqToIso ⋯ ≪≫ CategoryTheory.MonoOver.mapId B).hom.app
        ((CategoryTheory.MonoOver.map e.hom).obj X)) =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.MonoOver.map e.hom).obj X)