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


DEBUG:Going to execute:
clear id0