∀ {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)}
  {G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)} (adj₂ : F ⊣₂ G) {X₁ Y₁ : C₁} {f₁ : X₁ ⟶ Y₁}
  {X₂ Y₂ : C₂} {f₂ : X₂ ⟶ Y₂} {X₃ Y₃ : C₃} {f₃ : X₃ ⟶ Y₃} (sq₁₂ : F.PushoutObjObj f₁ f₂) (sq₁₃ : G.PullbackObjObj f₁ f₃)
  (α : CategoryTheory.Arrow.mk sq₁₂.ι ⟶ CategoryTheory.Arrow.mk f₃) {Z : C₂} (h : (G.obj (Opposite.op X₁)).obj X₃ ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((adj₂.arrowHomEquiv sq₁₂ sq₁₃) α).right
      (CategoryTheory.CategoryStruct.comp sq₁₃.fst h) =
    CategoryTheory.CategoryStruct.comp (adj₂.homEquiv (CategoryTheory.CategoryStruct.comp sq₁₂.inr α.left)) h