Goal:
    G : t
  ============================
   (forall
      a
       b : sigma
             (fun
                index : sigma (fun _ : VSet.t => sigma (fun _ : V.t => V.t))
              => SPath (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index))),
    NoConfusion_SPath a b -> a = b)


DEBUG:Going to execute:
simpl; intros;
            match goal with
            | H:_ = _ |- _ = _ => try solve_noconf_inv_equiv
            | H:_ = _ |- _ => try solve_noconf_prf
            | |- _ = _ => try solve_noconf_inv
            end