∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{u_1, u_2} D] {W X Y : C} {f : W ⟶ X} {g : W ⟶ Y}
  (c : CategoryTheory.Limits.PushoutCocone f g) (G : CategoryTheory.Functor C D),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.PushoutCocone.inl
        ((CategoryTheory.Limits.Cocone.precompose
              (CategoryTheory.Limits.diagramIsoSpan ((CategoryTheory.Limits.span f g).comp G)).symm.hom).obj
          (G.mapCocone c)))
      (CategoryTheory.Iso.refl
          ((CategoryTheory.Limits.Cocone.precompose
                  (CategoryTheory.Limits.diagramIsoSpan ((CategoryTheory.Limits.span f g).comp G)).symm.hom).obj
              (G.mapCocone c)).pt).hom =
    (c.map G).inl