∀ {k G : Type u} [inst : CommRing k] [inst_1 : CommGroup G] [inst_2 : Fintype G] (A : Rep k G) (g : G)
  (hg : ∀ (x : G), x ∈ Subgroup.zpowers g) (i : ℕ)
  (a :
    TensorProduct k (↑A.V) (G →₀ k) ⧸
      (Representation.Coinvariants.ker (A.ρ.tprod (Representation.leftRegular k G))).toAddSubgroup),
  (ModuleCat.Hom.hom ((Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso A g hg).hom.f i)) a =
    (QuotientAddGroup.lift (Representation.Coinvariants.ker (A.ρ.tprod (Representation.leftRegular k G))).toAddSubgroup
        (TensorProduct.lift (Finsupp.linearCombination k fun g => A.ρ g⁻¹) ∘ₗ
            ↑(TensorProduct.comm k (↑A.V) (G →₀ k))).toAddMonoidHom
        ⋯)
      a