{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] →
            {motive : I.IsCardinalForSmallObjectArgument κ → Sort u_1} →
              (t : I.IsCardinalForSmallObjectArgument κ) →
                ((isSmall : CategoryTheory.MorphismProperty.IsSmall.{w, v, u} I) →
                    (locallySmall : CategoryTheory.LocallySmall.{w, v, u} C) →
                      (hasPushouts : CategoryTheory.Limits.HasPushouts C) →
                        (hasCoproducts : CategoryTheory.Limits.HasCoproducts C) →
                          (hasIterationOfShape : CategoryTheory.Limits.HasIterationOfShape κ.ord.ToType C) →
                            (preservesColimit :
                                ∀ {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))) →
                              motive ⋯) →
                  motive t