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
  ============================
   (#|ls2| = #|ls3|)


DEBUG:Going to execute:
match goal with
           | H:¬ _ |- _ => solve [ case H; trivial ]
           end
Level 1: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.