{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (I : CategoryTheory.MorphismProperty C) →
      (κ : Cardinal.{w}) →
        [inst_1 : Fact κ.IsRegular] →
          [inst_2 : OrderBot κ.ord.ToType] →
            [inst_3 : I.IsCardinalForSmallObjectArgument κ] →
              (CategoryTheory.SmallObject.succStruct I κ).prop.TransfiniteCompositionOfShape κ.ord.ToType
                (CategoryTheory.SmallObject.ιIteration I κ)