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


DEBUG:Going to execute:
first
[ All2_All_swap_t_step
| let H1 := fresh in
  let H2 := fresh in
  eapply All_impl;
   [ eapply All_prod
   | intros ? [H1 H2]; constructor; (first [ exact H1 | exact H2 ]) ]; eauto;
   apply IH; clear IH ]
Level 0: Backtrace:

In environment
A : Type
B : Type
P : list A → list A → A → A → B → Type
a : A
ls2 : list A
a0 : A
ls3 : list A
X0 : All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) []) ls2 ls3
Unable to unify "All ?M2992 (?M2993 :: ?M2994)" with
 "All
    (λ z : B,
       All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) 
         (a :: ls2) (a0 :: ls3)) []".
Level 0: Backtrace:

In environment
A : Type
B : Type
P : list A → list A → A → A → B → Type
a : A
ls2 : list A
a0 : A
ls3 : list A
X0 : All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) []) ls2 ls3
Unable to unify "All ?M2992 (?M2993 :: ?M2994)" with
 "All
    (λ z : B,
       All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) 
         (a :: ls2) (a0 :: ls3)) []".