∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G),
  (groupHomology.isoShortComplexH1 A).inv =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ShortComplex.homMk (groupHomology.chainsIso₂ A).inv (groupHomology.chainsIso₁ A).inv
        (groupHomology.chainsIso₀ A).inv ⋯ ⋯)
      ((HomologicalComplex.natIsoSc' (ModuleCat k) (ComplexShape.down ℕ) 2 1 0 groupHomology.isoShortComplexH1._proof_1
              groupHomology.isoShortComplexH1._proof_2).inv.app
        (groupHomology.inhomogeneousChains A))