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


DEBUG:Going to execute:
first
[ All2_All_swap_t_step
| let H1 := fresh in
  let H2 := fresh in
  eapply All2_fold_impl;
   [ eapply All2_fold_prod
   | intros * [H1 H2]; constructor; (first [ exact H1 | exact H2 ]) ];
   (let IH' := fresh in
    eauto; edestruct IH as [IH'| IH']; try (apply IH'; clear IH'); clear IH) ]
Level 0: Backtrace:

In environment
A : Type
B : Type
P : list A → list A → A → A → B → Type
a : B
ls1 : list B
IH : ∀ ls2 ls3 : list A,
       All
         (λ z : B,
            All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) ls2 ls3)
         ls1
       → (ls1 = []) +
         All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) ls1) ls2
           ls3
X1 : All
       (λ z : B,
          All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) [] []) ls1
Unable to unify "All2_fold ?M2982 (?M2983 :: ?M2985) (?M2984 :: ?M2986)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1)) []
    []".
Level 0: Backtrace:

In environment
A : Type
B : Type
P : list A → list A → A → A → B → Type
a : B
ls1 : list B
IH : ∀ ls2 ls3 : list A,
       All
         (λ z : B,
            All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) ls2 ls3)
         ls1
       → (ls1 = []) +
         All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) ls1) ls2
           ls3
X1 : All
       (λ z : B,
          All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) [] []) ls1
Unable to unify "All2_fold ?M2982 (?M2983 :: ?M2985) (?M2984 :: ?M2986)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1)) []
    []".