Goal:
  
  A : Type
  B : Type
  P : list A → list A → A → A → B → Type
  b : B
  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)
           (b :: ls1)
         → All2_fold
             (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: 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)) (b :: a :: ls1)
    → All2_fold
        (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: 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 H1 := fresh in
  let H2 := fresh in
  eapply All2_fold_impl; [ eapply IH |  ]; clear IH ]
Level 0: Backtrace:

In environment
A : Type
B : Type
P : list A → list A → A → A → B → Type
b, 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)
         (b :: ls1)
       → All2_fold
           (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: ls1)) ls2
           ls3
X0 : 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 ?M3206 (?M3207 :: ?M3209) (?M3208 :: ?M3210)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: a :: ls1))
    [] []".
Level 0: Backtrace:

In environment
A : Type
B : Type
P : list A → list A → A → A → B → Type
b, 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)
         (b :: ls1)
       → All2_fold
           (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: ls1)) ls2
           ls3
X0 : 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 ?M3206 (?M3207 :: ?M3209) (?M3208 :: ?M3210)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: a :: ls1))
    [] []".