∀ {G : Type u_1} {k : Type u_2} {V : Type u_3} {W : Type u_4} [inst : Group G] [inst_1 : Field k]
  [inst_2 : AddCommGroup V] [inst_3 : Module k V] [inst_4 : AddCommGroup W] [inst_5 : Module k W]
  [inst_6 : FiniteDimensional k V] (ρ : Representation k G V) (σ : Representation k G W) (a : V →ₗ[k] W),
  (Representation.Equiv.dualTensorHom ρ σ).invFun a = (dualTensorHomEquivOfBasis (Module.Free.chooseBasis k V)).symm a