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:
intros