Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  c : C
  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) (c :: ls1)
         → All2 (λ (x : A) (y : B), All (P x y) (c :: ls1)) ls2 ls3
  a0 : A
  ls2 : list A
  b : B
  ls3 : list B
  X : P a0 b c
  X2 : All2 (λ (x : A) (y : B), P x y c) ls2 ls3
  X3 : All
         (λ z : C, All2 (λ (x : A) (y : B), P x y z) (a0 :: ls2) (b :: ls3))
         ls1
  X1 : P a0 b a
  X4 : All2 (λ (x : A) (y : B), P x y a) ls2 ls3
  ============================
   (∀ (n : nat) (x1 : A) (x2 : B),
      n < #|ls2|
      → nth_error ls2 n = Some x1
        → nth_error ls3 n = Some x2 → All (P x1 x2) (c :: a :: ls1))


DEBUG:Going to execute:
done
Level 0: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 1: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.