∀ {α β : SemilatSupCat} (e : α.X ≃o β.X),
  CategoryTheory.CategoryStruct.comp { toFun := ⇑e, map_sup' := ⋯, map_bot' := ⋯ }
      { toFun := ⇑e.symm, map_sup' := ⋯, map_bot' := ⋯ } =
    CategoryTheory.CategoryStruct.id α