∀ {X Y Z : BddLat} (f : X ⟶ Y) (g : Y ⟶ Z),
  Lat.ofHom (BddLat.Hom.hom (CategoryTheory.CategoryStruct.comp f g)).toLatticeHom =
    CategoryTheory.CategoryStruct.comp (Lat.ofHom (BddLat.Hom.hom f).toLatticeHom)
      (Lat.ofHom (BddLat.Hom.hom g).toLatticeHom)