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


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