∀ {A : Type u_1} {G : Type u_2} {V : Type u_3} {W : Type u_4} [inst : Semiring A] [inst_1 : Monoid G]
  [inst_2 : AddCommMonoid V] [inst_3 : AddCommMonoid W] [inst_4 : Module A V] [inst_5 : Module A W]
  {ρ : Representation A G V} {σ : Representation A G W} (toIntertwiningMap toIntertwiningMap_1 : ρ.IntertwiningMap σ)
  (e_toIntertwiningMap : toIntertwiningMap = toIntertwiningMap_1) (invFun invFun_1 : W → V)
  (e_invFun : invFun = invFun_1) (left_inv : Function.LeftInverse invFun toIntertwiningMap.toFun)
  (right_inv : Function.RightInverse invFun toIntertwiningMap.toFun),
  { toIntertwiningMap := toIntertwiningMap, invFun := invFun, left_inv := left_inv, right_inv := right_inv } =
    { toIntertwiningMap := toIntertwiningMap_1, invFun := invFun_1, left_inv := ⋯, right_inv := ⋯ }