Goal:
  
  A : Type
  P : A → A → Type
  a : sigma
        (λ index : sigma (λ _ : list A, list A),
           OnOne2 P (pr1 index) (pr2 index))
  b : sigma
        (λ index : sigma (λ _ : list A, list A),
           OnOne2 P (pr1 index) (pr2 index))
  H : NoConfusion_OnOne2 A P a b
  ============================
   (a = b)


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