Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  a : C
  ls1 : list C
  IH : ∀ (ls2 : list A) (ls3 : list B),
         All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
         → All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
  ============================
   (All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] []) 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
C : Type
P : A → B → C → Type
a : C
ls1 : list C
IH : ∀ (ls2 : list A) (ls3 : list B),
       All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
       → All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
Unable to unify "All2 ?M3013 (?M3014 :: ?M3016) (?M3015 :: ?M3017)" with
 "All2 (λ (x : A) (y : B), P x y a) [] []".
Level 0: Backtrace:

In environment
A : Type
B : Type
C : Type
P : A → B → C → Type
a : C
ls1 : list C
IH : ∀ (ls2 : list A) (ls3 : list B),
       All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
       → All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
Unable to unify "All2 ?M3013 (?M3014 :: ?M3016) (?M3015 :: ?M3017)" with
 "All2 (λ (x : A) (y : B), P x y a) [] []".