∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G) (x : ↥(groupCohomology.cocycles₂ A)),
  (CategoryTheory.ConcreteCategory.hom (groupCohomology.iCocycles A 2))
      ((CategoryTheory.ConcreteCategory.hom (groupCohomology.isoCocycles₂ A).inv) x) =
    (CategoryTheory.ConcreteCategory.hom (groupCohomology.cochainsIso₂ A).inv)
      ((ModuleCat.Hom.hom (groupCohomology.shortComplexH2 A).g).ker.subtype x)