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
  H : ∀ (n : nat) (x : A), P n x → f x = x
  ============================
   (f hd :: map f tl = hd :: tl)


DEBUG:Going to execute:
F x2 x1 x0
Level 0: Backtrace:

P is used in hypothesis p.
Level 0: Backtrace:

P is used in hypothesis p.
Level 0: Backtrace:

P is used in hypothesis p.
Level 0: Backtrace:

P is used in hypothesis p.
Level 0: Backtrace:

P is used in hypothesis p.
Level 1: Backtrace:

P is used in hypothesis p.
Level 0: Backtrace:

P is used in hypothesis p.