∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Abelian C] {X Y Z : C}
  (f : X ⟶ Y) (g : Y ⟶ Z) (P : CategoryTheory.ProjectiveResolution X) (R : CategoryTheory.ProjectiveResolution Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ProjectiveResolution.lift (CategoryTheory.CategoryStruct.comp f g) P R) R.π =
    CategoryTheory.CategoryStruct.comp P.π ((ChainComplex.single₀ C).map (CategoryTheory.CategoryStruct.comp f g))