∀ (X : BoolAlg),
  HeytAlg.ofHom
      { toFun := ⇑(BoolAlg.Hom.hom (CategoryTheory.CategoryStruct.id X)), map_sup' := ⋯, map_inf' := ⋯, map_bot' := ⋯,
        map_himp' := ⋯ } =
    CategoryTheory.CategoryStruct.id (HeytAlg.of ↑X)