Goal:
  
  ============================
   (∀ (A : Type) (P : A → A → Type) (a
                                     b : sigma
                                           (λ index : 
                                               sigma 
                                                 (λ _ : list A, list A),
                                              OnOne2 P 
                                                (pr1 index) 
                                                (pr2 index))) 
      (e : a = b),
      (λ (A0 : Type) (P0 : A0 → A0 → Type) (a0
                                            b0 : sigma
                                                 (λ index : 
                                                 sigma
                                                 (λ _ : list A0, list A0),
                                                 OnOne2 P0 
                                                 (pr1 index) 
                                                 (pr2 index))) 
         (H : NoConfusion_OnOne2 A0 P0 a0 b0),
         noConfusion_OnOne2_obligation_1 A0 P0 a0 b0 H) A P a b
        ((λ (A0 : Type) (P0 : A0 → A0 → Type) (a0
                                               b0 : 
                                               sigma
                                                 (λ index : 
                                                 sigma
                                                 (λ _ : list A0, list A0),
                                                 OnOne2 P0 
                                                 (pr1 index) 
                                                 (pr2 index))) 
            (H : a0 = b0), noConfusion_OnOne2_obligation_2 A0 P0 a0 b0 H) A P
           a b e) = e)


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