∀ (X : Type u_1),
  (BoolAlg.ofHom
        (let __src :=
          { toFun := ⇑(CompleteLatticeHom.setPreimage (CategoryTheory.CategoryStruct.id X)), map_sup' := ⋯,
            map_inf' := ⋯ };
        { toFun := ⇑(CompleteLatticeHom.setPreimage (CategoryTheory.CategoryStruct.id X)), map_sup' := ⋯, map_inf' := ⋯,
          map_top' := ⋯, map_bot' := ⋯ })).op =
    CategoryTheory.CategoryStruct.id (Opposite.op { carrier := Set X, str := Set.instBooleanAlgebra })