Goal:
  
  A : Type
  P : nat → A → Type
  f : A → A
  n : nat
  hd : A
  tl : list A
  p : P n hd
  X : Alli P (S n) tl
  IHX : (∀ (n : nat) (x : A), P n x → f x = x) → map f tl = tl
  ============================
   ((∀ (n : nat) (x : A), P n x → f x = x) → f hd :: map f tl = hd :: tl)


DEBUG:Going to execute:
match goal with
           | |- ?X1 → ?X2 => intro
           | |- ¬ _ => unfold not at 1; intro
           end
Level 0: Backtrace:

No matching clauses for match.