∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V),
  (Representation.Coinvariants.mk (ρ.tprod (Representation.leftRegular k G)) ∘ₗ
        (TensorProduct.mk k V (G →₀ k)).flip fun₀ | 1 => 1) ∘ₗ
      ρ.ofCoinvariantsTprodLeftRegular =
    LinearMap.id