∀ {k : Type u_3} {G : Type u_4} {V : Type u_1} {W : Type u_2} [inst : CommSemiring k] [inst_1 : Group G]
  [inst_2 : AddCommMonoid V] [inst_3 : Module k V] [inst_4 : AddCommMonoid W] [inst_5 : Module k W]
  (ρV : Representation k G V) (ρW : Representation k G W) (g h : G),
  { toFun := fun f => ρW (g * h) ∘ₗ f ∘ₗ ρV (g * h)⁻¹, map_add' := ⋯, map_smul' := ⋯ } =
    { toFun := fun f => ρW g ∘ₗ f ∘ₗ ρV g⁻¹, map_add' := ⋯, map_smul' := ⋯ } *
      { toFun := fun f => ρW h ∘ₗ f ∘ₗ ρV h⁻¹, map_add' := ⋯, map_smul' := ⋯ }