∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ S₂ : CategoryTheory.ShortComplex C} (φ : S₁ ⟶ S₂) [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology] {Z : C}
  (h : S₂.homology ⟶ Z),
  CategoryTheory.CategoryStruct.comp S₁.homologyπ
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.homologyMap φ) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.cyclesMap φ)
      (CategoryTheory.CategoryStruct.comp S₂.homologyπ h)