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
  ls2 : list A
  a1 : A
  ls3 : list A
  X0 : All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1))
         ls2 ls3
  X : P ls2 ls3 a0 a1 a
  X2 : All (P ls2 ls3 a0 a1) ls1
  x : B
  ============================
   (All2_fold (λ (l1 l2 : list A) (x0 y : A), P l1 l2 x0 y x) ls2 ls3)


DEBUG:Going to execute:
fun flags =>
             <Coq.Init.Tauto.not_dep_intros>;
              repeat
               (match reverse goal with
                | id:?X1
                  |- _ =>
                      <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro;
                       clear id
                | id:_ ↔ _ |- _ => elim id; do 2 intro; clear id
                | id:¬ _ |- _ => red in id
                | id:?X1
                  |- _ =>
                      <Coq.Init.Tauto.is_disj> flags X1; elim id; intro;
                       clear id
                | _ =>
                    <Coq.Init.Tauto.find_cut>
                     ltac:(fun id0 id1 X2 =>
                             assert X2; [ exact (id0 id1) | clear id0 ])
                | id:?X1 → ?X2
                  |- _ =>
                      <Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
                       [ intro; clear id
                       | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
                | id:?X1 → ?X2
                  |- _ =>
                      <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2
                       id
                | id:?X1 ↔ ?X2 → ?X3
                  |- _ =>
                      assert ((X1 → X2) → (X2 → X1) → X3) by
                       (do 2 intro; apply id; Ltac.split; Ltac.assumption);
                       clear id
                | id:?X1 → ?X2
                  |- _ =>
                      <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2
                       id
                | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; Ltac.split
                | |- _ ↔ _ => Ltac.split
                | |- ¬ _ => red
                end; <Coq.Init.Tauto.not_dep_intros>)