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
  a0 : A
  ls2 : list A
  b : B
  ls3 : list B
  X1 : All
         (λ z : C, All2 (λ (x : A) (y : B), P x y z) (a0 :: ls2) (b :: ls3))
         ls1
  X : P a0 b a
  X2 : All2 (λ (x : A) (y : B), P x y a) ls2 ls3
  ============================
   (All2 (λ (x : A) (y : B), All (P x y) (a :: ls1)) ls2 ls3)


DEBUG:Going to execute:
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:

No matching clauses for match.
Level 1: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.