∀ {X Y Z : SemilatInfCat} (f : X ⟶ Y) (g : Y ⟶ Z),
  PartOrd.ofHom { toFun := ⇑(CategoryTheory.CategoryStruct.comp f g).toInfHom, monotone' := ⋯ } =
    CategoryTheory.CategoryStruct.comp (PartOrd.ofHom { toFun := ⇑f.toInfHom, monotone' := ⋯ })
      (PartOrd.ofHom { toFun := ⇑g.toInfHom, monotone' := ⋯ })