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
  ============================
   (All
      (λ z : B, All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) [] [])
      ls1)


DEBUG:Going to execute:
fun x => lazymatch x with
                    | [] => idtac
                    | _ :: _ => idtac
                    end