∀ {X Y : BoolAlg} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((BoolAlg.dual.comp BoolAlg.dual).map f)
      ((fun X => BoolAlg.Iso.mk (OrderIso.dualDual ↑X)) Y).hom =
    CategoryTheory.CategoryStruct.comp ((fun X => BoolAlg.Iso.mk (OrderIso.dualDual ↑X)) X).hom
      ((CategoryTheory.Functor.id BoolAlg).map f)