∀ {X : Type u_1} {Y : Type u_2} [inst : Preorder X] [inst_1 : Preorder Y] (X_1 : X →o Y),
  CategoryTheory.CategoryStruct.comp
      ({ obj := fun f => f.toFunctor,
            map := fun {X_2 Y_1} f => { app := fun x => CategoryTheory.homOfLE ⋯, naturality := ⋯ }, map_id := ⋯,
            map_comp := ⋯ }.map
        ((CategoryTheory.Iso.refl (CategoryTheory.Functor.id (X →o Y))).hom.app X_1))
      ((CategoryTheory.Iso.refl
              ({ obj := fun F => F.toOrderHom, map := fun {X_2 Y_1} f => CategoryTheory.homOfLE ⋯, map_id := ⋯,
                    map_comp := ⋯ }.comp
                { obj := fun f => f.toFunctor,
                  map := fun {X_2 Y_1} f => { app := fun x => CategoryTheory.homOfLE ⋯, naturality := ⋯ }, map_id := ⋯,
                  map_comp := ⋯ })).hom.app
        ({ obj := fun f => f.toFunctor,
              map := fun {X_2 Y_1} f => { app := fun x => CategoryTheory.homOfLE ⋯, naturality := ⋯ }, map_id := ⋯,
              map_comp := ⋯ }.obj
          X_1)) =
    CategoryTheory.CategoryStruct.id
      ({ obj := fun f => f.toFunctor,
            map := fun {X_2 Y_1} f => { app := fun x => CategoryTheory.homOfLE ⋯, naturality := ⋯ }, map_id := ⋯,
            map_comp := ⋯ }.obj
        X_1)