Goal:
  
  A : Type
  P : A → A → Type
  l : list A
  l' : list A
  t : A
  Hall : All2 P l l'
  ============================
   (∀ n : nat,
      nth_error l' n = Some t → ∑ t' : A, nth_error l n = Some t' × P t' t)


DEBUG:Going to execute:
induction Hall; destruct n; simpl