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 : NoConfusion_OnOne2All A B P a b
  ============================
   (a = b)


DEBUG:Going to execute:
match goal with
           | |- ?R ?a ?b =>
                 CoreTactics.destruct_sigma a; CoreTactics.destruct_sigma b;
                  destruct a; DepElim.depelim b; simpl in * |-;
                  CoreTactics.on_last_hyp
                   ltac:(fun id =>
                           hnf in id;
                            CoreTactics.destruct_tele_eq id || destruct id);
                  (solve [ constructor ])
           | |- ?f ?a ?b _ = _ => solve_noconf_inv_eq a b
           end