∀ {k : Type u_1} {G : Type u_4} {H : Type u_2} [inst : CommRing k] [inst_1 : Group G] [inst_2 : Group H] (φ : G →* H)
  {A : Type u_3} [inst_3 : AddCommGroup A] [inst_4 : Module k A] (ρ : Representation k G A) (h : H) (x : G),
  LinearMap.rTensor A (Finsupp.lmapDomain k k fun x => x * h⁻¹) ∘ₗ
      (Representation.tprod (MonoidHom.comp (Representation.leftRegular k H) φ) ρ) x =
    (Representation.tprod (MonoidHom.comp (Representation.leftRegular k H) φ) ρ) x ∘ₗ
      LinearMap.rTensor A (Finsupp.lmapDomain k k fun x => x * h⁻¹)