∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
  [inst_1 : CategoryTheory.Limits.HasPushout f g] {W : C} {k l : CategoryTheory.Limits.pushout f g ⟶ W},
  k = l ↔
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inl f g) k =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inl f g) l ∧
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inr f g) k =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inr f g) l