∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G) (x : ↥(groupCohomology.cocycles₁ A)),
  (CategoryTheory.ConcreteCategory.hom (groupCohomology.iCocycles A 1))
      ((CategoryTheory.ConcreteCategory.hom (groupCohomology.isoCocycles₁ A).inv) x) =
    (CategoryTheory.ConcreteCategory.hom
        (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH1 A).moduleCatLeftHomologyData.i
          (groupCohomology.cochainsIso₁ A).inv))
      x