Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  a : C
  ls1 : list C
  IH : ∀ (ls2 : list A) (ls3 : list B),
         All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
         → (ls1 = []) + All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
  b : B
  ls3 : list B
  ============================
   (All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] (b :: ls3)) (a :: ls1)
    → (a :: ls1 = []) +
      All2 (λ (x : A) (y : B), All (P x y) (a :: ls1)) [] (b :: ls3))


DEBUG:Going to execute:
first
[ All2_All_swap_t_step
| let H1 := fresh in
  let H2 := fresh in
  eapply All2_impl;
   [ eapply All2_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
C : Type
P : A → B → C → Type
a : C
ls1 : list C
IH : ∀ (ls2 : list A) (ls3 : list B),
       All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
       → (ls1 = []) + All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
X1 : All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] []) ls1
Unable to unify "All2 ?M2984 (?M2985 :: ?M2987) (?M2986 :: ?M2988)" with
 "All2 (λ (x : A) (y : B), All (P x y) (a :: ls1)) [] []".
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),
       All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
       → (ls1 = []) + All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
X1 : All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] []) ls1
Unable to unify "All2 ?M2984 (?M2985 :: ?M2987) (?M2986 :: ?M2988)" with
 "All2 (λ (x : A) (y : B), All (P x y) (a :: ls1)) [] []".