Goal:
  
  A : Type
  B : Type
  P : list A → list A → A → A → B → Type
  a : B
  ls1 : list B
  IH : ∀ ls2 ls3 : list A,
         All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) ls1) ls2
           ls3
         → All
             (λ z : B,
                All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) ls2
                  ls3) ls1
  a0 : A
  ls3 : list A
  X : All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1))
        [] (a0 :: ls3)
  ============================
   (All
      (λ z : B,
         All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) []
           (a0 :: ls3)) (a :: ls1))


DEBUG:Going to execute:
first
[ progress intros
| progress subst
| let is_ctor_list x := lazymatch x with
                        | [] => idtac
                        | _ :: _ => idtac
                        end in
  match goal with
  | H:All2 _ ?x ?y
    |- _ => (first [ is_ctor_list x | is_ctor_list y ]); inversion H; clear H
  | H:All2_fold _ ?x ?y
    |- _ => (first [ is_ctor_list x | is_ctor_list y ]); inversion H; clear H
  | H:All _ ?x |- _ => is_ctor_list x; inversion H; clear H
  | |- (_ :: _ = []) + _ => right
  | |- (?x = ?x) + _ => left
  end
| exactly_once constructor
| solve
[ eauto
| (first [ eapply All2_impl | eapply All2_fold_impl | eapply All_impl ]); tea;
   cbn; intros *; inversion 1 + constructor; subst; eauto ]
| congruence
| now
apply All_refl; constructor
| apply All2_from_nth_error => //; lia
| progress cbn in *
| match goal with
  | H:?x ≠ ?x ∨ ?A |- _ => assert A by now destruct H; clear H
  end ]