Goal:
  
  A : Type
  P : nat → A → Type
  f : A → A
  n : nat
  H : ∀ (n : nat) (x : A), P n x → f x = x
  ============================
   ([] = [])


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