∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {I : Type w} {A B : I → C} (f : (i : I) → A i ⟶ B i) {S X : C}
  (πX : X ⟶ S)
  [inst_1 :
    CategoryTheory.Limits.HasColimitsOfShape (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πX))
      C]
  [inst_2 :
    CategoryTheory.Limits.HasPushout (CategoryTheory.SmallObject.functorObjTop f πX)
      (CategoryTheory.SmallObject.functorObjLeft f πX)]
  (x : CategoryTheory.SmallObject.FunctorObjIndex f πX),
  CategoryTheory.CategoryStruct.comp (f x.i)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.Sigma.ι (CategoryTheory.SmallObject.functorObjTgtFamily f πX) x)
        (CategoryTheory.SmallObject.ρFunctorObj f πX)) =
    CategoryTheory.CategoryStruct.comp x.t (CategoryTheory.SmallObject.ιFunctorObj f πX)