∀ {α β : BddLat} (e : ↑α.toLat ≃o ↑β.toLat),
  CategoryTheory.CategoryStruct.comp
      (BddLat.ofHom
        (let __src := { toFun := ⇑e.symm, map_sup' := ⋯, map_inf' := ⋯ };
        { toFun := ⇑e.symm, map_sup' := ⋯, map_inf' := ⋯, map_top' := ⋯, map_bot' := ⋯ }))
      (BddLat.ofHom
        (let __src := { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯ };
        { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯, map_top' := ⋯, map_bot' := ⋯ })) =
    CategoryTheory.CategoryStruct.id β