∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃)) [inst_3 : CategoryTheory.Limits.HasPushouts C₃]
  (f₁ : CategoryTheory.Arrow C₁) (f₂ : CategoryTheory.Arrow C₂),
  (F.leibnizPushout.obj f₁).obj f₂ =
    CategoryTheory.Arrow.mk (CategoryTheory.Functor.PushoutObjObj.ofHasPushout F f₁.hom f₂.hom).ι