∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasProjectiveResolutions C] {X Y : C} (f : X ⟶ Y) (P : CategoryTheory.ProjectiveResolution X)
  (Q : CategoryTheory.ProjectiveResolution Y) (φ : P.complex ⟶ Q.complex),
  CategoryTheory.CategoryStruct.comp (φ.f 0) (Q.π.f 0) = CategoryTheory.CategoryStruct.comp (P.π.f 0) f →
    ∀ {Z : HomotopyCategory C (ComplexShape.down ℕ)} (h : (CategoryTheory.projectiveResolutions C).obj Y ⟶ Z),
      CategoryTheory.CategoryStruct.comp P.iso.inv
          (CategoryTheory.CategoryStruct.comp ((CategoryTheory.projectiveResolutions C).map f) h) =
        CategoryTheory.CategoryStruct.comp ((HomotopyCategory.quotient C (ComplexShape.down ℕ)).map φ)
          (CategoryTheory.CategoryStruct.comp Q.iso.inv h)