∀ {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],
  autoParam (CategoryTheory.MorphismProperty.IsSmall.{w, v, u} I)
      CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.isSmall._autoParam →
    autoParam (CategoryTheory.LocallySmall.{w, v, u} C)
        CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.locallySmall._autoParam →
      autoParam (CategoryTheory.Limits.HasPushouts C)
          CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.hasPushouts._autoParam →
        autoParam (CategoryTheory.Limits.HasCoproducts C)
            CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.hasCoproducts._autoParam →
          autoParam (CategoryTheory.Limits.HasIterationOfShape κ.ord.ToType C)
              CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.hasIterationOfShape._autoParam →
            (∀ {A B X Y : C} (i : A ⟶ B),
                I i →
                  ∀ (f : X ⟶ Y) (hf : HomotopicalAlgebra.RelativeCellComplex (fun x => I.homFamily) f),
                    CategoryTheory.Limits.PreservesColimit hf.F (CategoryTheory.coyoneda.obj (Opposite.op A))) →
              I.IsCardinalForSmallObjectArgument κ