∀ {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]
  {G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)} {f₁ : CategoryTheory.Arrow C₁}
  {f₃ : CategoryTheory.Arrow C₃} (sq₁₃ : G.PullbackObjObj f₁.hom f₃.hom),
  sq₁₃.mapArrowLeft sq₁₃ (CategoryTheory.CategoryStruct.id f₁) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Arrow.mk sq₁₃.π)