∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Preadditive C] {D : Type u_2} [inst_3 : CategoryTheory.Category.{u_1, u_2} D]
  [inst_4 : CategoryTheory.Limits.HasZeroObject D] [inst_5 : CategoryTheory.Preadditive D]
  [inst_6 : CategoryTheory.CategoryWithHomology D] (F : CategoryTheory.Functor C D) [inst_7 : F.Additive]
  [F.PreservesHomology] {Z : C} (P : CategoryTheory.ProjectiveResolution Z),
  QuasiIso
    (CategoryTheory.CategoryStruct.comp ((F.mapHomologicalComplex (ComplexShape.down ℕ)).map P.π)
      ((HomologicalComplex.singleMapHomologicalComplex F (ComplexShape.down ℕ) 0).hom.app Z))