∀ {X Y : CategoryTheory.Mon (Type u_1)} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((MonTypeEquivalenceMon.functor.comp (CategoryTheory.forget MonCat)).map f)
      ((fun x => CategoryTheory.Iso.refl ((MonTypeEquivalenceMon.functor.comp (CategoryTheory.forget MonCat)).obj x))
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun x => CategoryTheory.Iso.refl ((MonTypeEquivalenceMon.functor.comp (CategoryTheory.forget MonCat)).obj x))
          X).hom
      ((CategoryTheory.Mon.forget (Type u_1)).map f)