Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  t' : B
  x : A
  l : list A
  l' : list B
  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'
  ============================
   (Some x = Some x × P x t')


DEBUG:Going to execute:
repeat
            match goal with
            | |- ?X1 → ?X2 => intro
            | |- ¬ _ => unfold not at 1; intro
            end