Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  a : sigma
        (λ index : sigma (λ _ : list B, sigma (λ _ : list A, list A)),
           OnOne2All P (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  b : sigma
        (λ index : sigma (λ _ : list B, sigma (λ _ : list A, list A)),
           OnOne2All P (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  H : a = b
  ============================
   (NoConfusion_OnOne2All A B P 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