Goal:
  
  A : Type
  P : A → A → Type
  t : A
  x : A
  y : A
  l : list A
  l' : list A
  r : P x y
  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
  n : nat
  ============================
   (nth_error l' n = Some t → ∑ t' : A, nth_error l n = Some t' × P t' t)


DEBUG:Going to execute:
congruence
Level 0: Backtrace:

Tactic failure: congruence failed.
Level 0: Backtrace:

Tactic failure: congruence failed.