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