Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  X : All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] []) []
  ============================
   (([] = []) + All2 (λ (x : A) (y : B), All (P x y) []) [] [])%type


DEBUG:Going to execute:
match goal with
           | H:All2 _ ?x ?y
             |- _ =>
                 (first [ is_ctor_list x | is_ctor_list y ]); inversion H;
                  clear H
           | H:All2_fold _ ?x ?y
             |- _ =>
                 (first [ is_ctor_list x | is_ctor_list y ]); inversion H;
                  clear H
           | H:All _ ?x |- _ => is_ctor_list x; inversion H; clear H
           | |- (_ :: _ = []) + _ => right
           | |- (?x = ?x) + _ => left
           end