Goal:
  
  ============================
   (∀ (A : Type) (P : list A → list A → A → A → Type) 
      (a
       b : sigma
             (λ index : sigma (λ _ : list A, list A),
                All2_fold P (pr1 index) (pr2 index))),
      NoConfusion_All2_fold 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