∀ (C : Type u_3) (D : Type u_4) [inst : CategoryTheory.Category.{u_1, u_3} C]
  [inst_1 : CategoryTheory.Category.{u_2, u_4} D] (d : D) {X Y : C} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Join.inclLeft C D).map f)
      (CategoryTheory.CostructuredArrow.mk (CategoryTheory.Join.edge Y d)).hom =
    (CategoryTheory.CostructuredArrow.mk (CategoryTheory.Join.edge X d)).hom